Abductive Cognition: The Epistemological and Eco

Abductive Cognition: The Epistemological and Eco
Cognitive Systems Monographs
Volume 3
Editors: Rüdiger Dillmann · Yoshihiko Nakamura · Stefan Schaal · David Vernon
Lorenzo Magnani
Abductive Cognition
The Epistemological and Eco-Cognitive
Dimensions of Hypothetical Reasoning
ABC
Rüdiger Dillmann, University of Karlsruhe, Faculty of Informatics, Institute of Anthropomatics,
Robotics Lab., Kaiserstr. 12, 76128 Karlsruhe, Germany
Yoshihiko Nakamura, Tokyo University Fac. Engineering, Dept. Mechano-Informatics, 7-3-1 Hongo,
Bukyo-ku Tokyo, 113-8656, Japan
Stefan Schaal, University of Southern California, Department Computer Science, Computational Learning & Motor Control Lab., Los Angeles, CA 90089-2905, USA
David Vernon, Khalifa University Department of Computer Engineering, PO Box 573, Sharjah, United
Arab Emirates
Authors
Lorenzo Magnani
Dipartimento di Filosofia
Universitá di Pavia
Piazza Botta 6
27100 Pavia Italy
E-mail: [email protected]
ISBN 978-3-642-03630-9
e-ISBN 978-3-642-03631-6
DOI 10.1007/978-3-642-03631-6
Cognitive Systems Monographs
ISSN 1867-4925
Library of Congress Control Number: 2008942040
c 2009
Springer-Verlag Berlin Heidelberg
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To my daughter Giovanna
How was it that man was ever led to entertain that true theory?
You cannot say that it happened by chance, because the possible
theories, if not strictly innumerable, at any rate exceed a trillion
– or the third power of a million; and therefore the chances are
too overwhelmingly against the single true theory in the twenty
or thirty thousand years during which man has been a thinking
animal, ever having come into any man’s head. Besides, you cannot
seriously think that every little chicken, that is hatched, has to
rummage through all possible theories until it lights upon the good
idea of picking up something and eating it. On the contrary, you
think the chicken has an innate idea of doing this; that is to say,
that it can think of this, but has no faculty of thinking anything
else. The chicken you say pecks by instinct. But if you are going to
think every poor chicken endowed with an innate tendency toward
a positive truth, why should you think that to man alone this gift
is denied?
Charles Sanders Peirce
Preface
This volume explores abductive cognition, an important but, at least until the
third quarter of the last century, neglected topic in cognition. It integrates
and further develops ideas already introduced in a previous book, which I
published in 2001 (Abduction, Reason, and Science. Processes of Discovery
and Explanation, Kluwer Academic/Plenum Publishers, New York).
The status of abduction is very controversial. When dealing with abductive
reasoning misinterpretations and equivocations are common. What are the
differences between abduction and induction? What are the differences between abduction and the well-known hypothetico-deductive method? What
did Peirce mean when he considered abduction both a kind of inference and a
kind of instinct or when he considered perception a kind of abduction? Does
abduction involve only the generation of hypotheses or their evaluation too?
Are the criteria for the best explanation in abductive reasoning epistemic, or
pragmatic, or both? Does abduction preserve ignorance or extend truth or
both? How many kinds of abduction are there? Is abduction merely a kind
of “explanatory” inference or does it involve other non-explanatory ways of
guessing hypotheses?
The book aims at increasing knowledge about creative and expert inferences. The study of these high-level methods of abductive reasoning is situated at the crossroads of philosophy, logic, epistemology, artificial intelligence, neuroscience, cognitive psychology, animal cognition and evolutionary
theories; that is, at the heart of cognitive science. Philosophers of science in
the twentieth century have traditionally distinguished between the inferential
processes active in the logic of discovery and the ones active in the logic of justification. Most have concluded that no logic of creative processes exists and,
moreover, that a rational model of discovery is impossible. In short, scientific
creative inferences are irrational and there is no “reasoning” to hypotheses.
On the other hand, some research in the area of artificial intelligence has
shown that methods for discovery could be found that are computationally
adequate for rediscovering – or discovering for the first time – empirical or
theoretical laws and theorems.
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Moreover, the study of diagnostic, visual, spatial, analogical, and temporal
reasoning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with only the help of
classical logic. Abduction is also useful in describing the different roles played
by the various kinds of medical reasoning, from the point of view both of human agents and of computational programs that perform medical tasks such
as diagnosis. However, non-standard logic has shown how we can provide rigorous formal models of many kinds of abductive reasoning such as the ones
involved in defeasible and uncertain inferences. Contradictions and inconsistencies are fundamental in abductive reasoning, and abductive reasoning
is appropriate for “governing” inconsistencies. In chapter two many ways of
governing inconsistencies will be considered, ranging from the methods activated in diagnostic settings and consistency-based models to the typical ones
embedded in some form of creative reasoning, the interpretations in terms of
conflicts and competitions to the actions performed on empirical and conceptual anomalies and from the question of generating inconsistencies by radical
innovation to the connectionist treatment of coherence.
In 1998 Jaakko Hintikka had already contended that abduction is the
“fundamental problem of contemporary epistemology”. My aim is to combine philosophical, logical, cognitive, eco-cognitive, neurological, and computational issues, while also discussing some cases of reasoning in everyday
settings, in expert inferences, and in science. The main thesis is that abduction is a basic kind of human cognition, not only helpful in delineating the
first principles of a new theory of science, but also extremely useful in the
unification of interdisciplinary perspectives, which would otherwise remain
fragmented and dispersed, and thus devoid of the necessary philosophical
analysis. In sum, the present book aims at having a strong interdisciplinary
nature, encompassing mathematical and logical cases, biological and neurological aspects and analysis of the epistemological impact of the problems
caused by the “mathematical physics” of abduction.
The interdisciplinary character of abduction is central and its fertility in
various areas of research is evident. The book also addresses the central epistemological question of hypothesis withdrawal in science by discussing historical
cases (chapter two), where abductive inferences exhibit their most appealing
cognitive virtues. Finally, an interesting and neglected point of contention
about human reasoning is whether or not concrete manipulations of external
objects influence the generation of hypotheses, for example in science. The
book provides an indepth study of what I have called manipulative abduction,
showing how we can find methods of constructivity in scientific and everyday
reasoning based on external models and cognitive and epistemic mediators.
The book also illustrates the problem of “multimodal abduction”, recently
pointed out by Paul Thagard, which refers to the various aspects of abductive reasoning, neurological, verbal-propositional, sentential, emotional and
manipulative. Multimodal abduction is also appropriate when taking into
account the dynamics of the hybrid interplay of the aspects above and the
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XI
semiotic role played by what I call “semiotic anchors”. These anchors constitute ways of favoring hybrid reasoning in various cognitive and epistemic
tasks and they play an important role in that event of “externalization of the
mind” that researchers such as Andy Clark, Edwin Hutchins, Steven Mithen
and others have labelled in various ways, ultimately resorting to the idea of
the importance of the external cognitive tools and mediators in cognition.
The book provides some case studies derived from the history of discoveries
in science, logic, and mathematics, also taking advantage of the agent based
perspective” proposed by Dov Gabbay and John Woods.
A central target has been to further study the concept of non-explanatory
and instrumental abduction, introduced by Gabbay and Woods in their GW model of abduction (a model they contrast with the AKM -model, previously
proposed by myself, Atocha Aliseda, Theo Kuipers, Ant Kakas and Peter
Flach, and Joke Meheus). Non-explanatory and instrumental aspects of abduction (together with the distinction between propositional and strategic
plausibility in hypothetical reasoning) have to be discussed and further clarified, especially because they play a crucial role in scientific, mathematical,
and logical abduction.
The first chapter, Theoretical and Manipulative Abduction. Conjectures
and Manipulations: the Extra-Theoretical Dimension of Scientific Discovery,
provides an illustration of the main distinctions concerning abductive reasoning concerning creative and selective, theoretical and manipulative abduction,
and its primal explanatory character. The significance of the original syllogistic framework proposed by Peirce is also explained together with the status
of some recent logical models of abduction. Moreover, some sections introduce the extra-theoretical dimension of scientific reasoning, with the help of
the concept of model-based and manipulative abduction. Creativity and discovery are no longer seen as mysterious irrational processes, but, thanks to
constructive accounts, they appear as a complex relationship among different
inferential steps that can be clearly analyzed and identified. The last part of
the chapter is devoted to illustrating the problem of the extra-theoretical
explanatory dimension of reasoning and discovery from the perspective of
some mathematical cases derived from calculus, where internal and external
aspects (optical diagrams) of cognition are at play.
The second chapter, Non-Explanatory and Instrumental Abduction. Plausibility, Implausibility, Ignorance Preservation, analyzes and criticizes the difference between GW -model and AKM -model by providing a strict examination of the contrast between explanatory, non-explanatory, and instrumental
abduction. Case studies derived from the field of the epistemology of physics,
from logic and from mathematics are studied because they are particularly
useful to further illustrate the non-explanatory and instrumental aspects of
abductive cognition. The issue of instrumental abduction is especially important when intertwined with the exquisite epistemological problem of the role
of unfalsifiable hypotheses in scientific reasoning. The role of contradictions,
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inconsistencies and preinventive forms, and of the computational “automatic
abductive scientists” in abductive cognition is also addressed.
The last part of the chapter is devoted to illustrating the problem of the
extra-theoretical dimension of cognition from the perspective of the famous
discovery of non-Euclidean geometries. This case study is particularly appropriate to the present chapter because it shows relevant aspects of diagrammatic abduction, which involve intertwined processes of both explanatory
and non-explanatory abduction acting at the model-based level in what I
call mirror and unveiling diagrams. Finally, the last section also deals with
the epistemologically some very interesting computational AI applications
expressly devoted to the simulation of geometrical reasoning.
The main concern of the third chapter, Semiotic Brains and Artificial
Minds. How Brains Make Up Material Cognitive Systems, is to furnish an integrated analysis of the abductive processes from an updated epistemological
and cognitive/semiotic point of view. Creative abductive reasoning is a risky
sort of inference that constitutes a central process in conceptual change in
science, mathematics, and logic. Its embodied and distributed aspects and its
role in what I call epistemic mediators constitute a central issue of this chapter. Part of the chapter is devoted to the analysis, at a cognitive, neurological,
semiotic and epistemological level, of the “externalization of the mind” also
considering some classical insights furnished by Turing in the article ”Intelligent Machinery”(1948) and some conclusions derived from the paleoanthropological research on what Steven Mithen has called “disembodiment of
the mind”. The related concepts of mimetic and creative representations and
of “mimetic mind” are introduced and explained; a further examination of
the problem of on-line and off-line intelligence, in the framework of the relationship between language and inner rehearsal, is provided. The chapter also
illustrates abduction from a dynamic perspective and the abductive process
of external diagrammatization and iconic brain coevolution, with the help of
some mathematical examples. A final scrutiny of the epistemological status
of the psychoanalytic concepts of projection and introjection and of psychic
externalized “symbols” is accomplished, aided by the concept of manipulative
abduction.
In the fourth chapter, Neuro-Multimodal Abduction. Pre-Wired Brains,
Embodiment, Neurospaces, starting from the results illustrated in the previous chapters regarding the fact that abductive cognition is occurring in a
“distributed” framework and in a hybrid way, that is in the interplay between internal and external signs, I contend that we can reconceptualize abduction neurologically. From this perspective abduction is a process in which
one neural structure representing the explanatory target generates another
neural structure that constitutes a hypothesis. A whole neuro-multimodal
framework is depicted, aiming at increasing knowledge about the fact that
the classical perspective on abduction, based on logic only, captures limited
properties of this cognitive process and considerably disregards model-based
aspects. The neuro-multimodal perspective also aims at: i) clarifying the
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XIII
distinction between the hardwired and pre-wired/plastic aspects of abduction; ii) a new understanding of some features of the problem of action and
decision in formal reasoning, where a new integrated perspective on action
can be worked out, taking advantage of the distinction between thought and
motor action, which are both seen as the fruit of brain activity; ii) analyzing the role of abduction in the fundamental mammalian model-based
cognitive activities, which relate to representation of object locations within
the spatial/pseudo-geometrical framework. A final section is devoted to some
philosophical issues arising from the traditions of phenomenology and psychology that are of special interest in elucidating some features of visual and
spatial abduction.
Chapter five, Animal Abduction. From Mindless Organisms to Artifactual
Mediators, is mainly dedicated to clarifying the Peircean originary conflict
between the view of abduction as inferential as opposed to instinctual. The
first two sections address this puzzling Peircean problem trying to show how
his research was anticipatory of central problems and topics of present cognitive science research. Some speculations concerning abduction in terms of
the dichotomies between perception and inference, iconicity and logicality,
instinct and strategies, should just be admired and closely studied. These
basic insights naturally led me to analyze the problem of animal abduction,
which represents the other main theme of the chapter. Many animals – traditionally considered “mindless” organisms – make up a series of signs and are
engaged in making, manifesting or reacting to a series of signs. Through this
semiotic activity – which is fundamentally model-based – they are engaged
in “being cognitive agents” and therefore in thinking “intelligently”. An important effect of this semiotic activity is a continuous process of “hypothesis
generation” that can be seen at the level of both instinctual behavior, as a
kind of “hard-wired” cognition, and representation-oriented behavior, where
nonlinguistic pseudothoughts drive a plastic model-based cognitive role. This
activity is at the root of a variety of abductive performances, which are also
analyzed in the light of the concept of affordance, further explored in chapter
six. Another important character of the model-based cognitive activity above
is the externalization of artifacts that play the role of mediators in animal,
languageless, reflexive thinking. The interplay between internal and external
representations exhibits a new cognitive perspective on the mechanisms underlying the semiotic emergence of abductive processes in important areas of
model-based thinking of mindless organisms. To illustrate this process I also
take advantage of the case of affect attunement, which exhibits an impressive case of model-based communication, of the problems of pseudological
and reflexive thinking and of the role of pseudoexplanatory guesses in animal
plastic cognition.
The title of chapter six is Abduction, Affordances, and Cognitive Niches.
Sharing Representations and Creating Chances through Cognitive Niche Construction. As a matter of fact, humans continuously delegate and distribute
cognitive functions to the environment to lessen their limits. They build
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models, representations, and other various mediating structures, that are
considered to aid thought. In doing these, humans are engaged in a process
of cognitive niche construction. In this sense, I argue that a cognitive niche
emerges from a network of continuous interplays of hypothetical cognition
between individuals and the environment, in which people alter and modify the environment by mimetically externalizing fleeting thoughts, private
ideas, etc., into external supports. Hence, cognitive niche construction may
also contribute to making a great portion of knowledge available that would
otherwise remain simply unexpressed or unreachable. Abductive cognition is
a central driver of those designing activities that are closely related to the
process of so-called “niche construction”. The exploitation of this basically
biological concept seems useful to study all those situations that require the
transmission and sharing of knowledge, information and, more generally, cognitive resources. Further, some issues concerning the process of transmission
and selection of the extragenetic information that is embedded in cognitive
niche transformations are considered and their supposed loosely Darwinian
character is stressed.
In dealing with the exploitation of cognitive resources embedded in the
environment, the notion of affordance, originally proposed by James J. Gibson to illustrate the hybrid character of visual perception, together with the
proximal/distal distinction described by Egon Brunswik, are relevant. In order to solve various controversies on the concept of affordance and on the
status of the proximal/distal dichotomy, I will take advantage of some useful
insights that come from the study on abduction. Abduction may also fruitfully describe all those human and animal hypothetical inferences that are
operated through actions made up of smart manipulations to both detect
new affordances and to create manufactured external objects that offer new
affordances/cues.
Chapter seven, Abduction in Human and Logical Agents. Hasty Generalizers, Hybrid Abducers, Fallacies, addresses the problem of logical models of
abduction, already introduced in the first chapter. This chapter presents the
problem in an agent-based perspective. It is acknowledged that intellectual
artifacts like “logical agents” are “ideal” tools for thoughts as is language.
These are tools for exploring, expanding, and manipulating our own minds
so that creative abductive “new ways of inferring”, performed by the “biological” human agents, arise in an unexpected and distributed interplay
between brains (and their internal representations) and external representations. The analysis of this issue demonstrates further results regarding the
following problems: i) deductive reasoning involves the employment of logical
rules in a heuristic manner, even maintaining the truth preserving character:
the application of the rules is organized in a way that is able to recommend
a particular course of actions instead of another one. Moreover, very often
the heuristic procedures of deductive reasoning are performed by means of an
“in-formal” (often model-based) abduction; ii) in an agent-based framework
fallacies can be redefined and considered as good ways of reasoning; we can
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hypothesize that what I call manipulative abduction can be re-interpreted
as a form of practical reasoning a better understanding of which can furnish
a description of human beings as hybrid thinkers in so far they are users
of ideal (logical/mathematical) and computational agents; iii) abduction can
be seen in an extended eco-logical perspective in so far as it is involved in
dialectic processes, where, as a fallacy – from the classical logical perspective,
it is exploited in a “distributed” cognitive framework, where epistemic (but
also moral) conflicts and negotiations are normally at play.
The last chapter, Morphodynamical Abduction. Causation of Hypotheses
by Attractors Dynamics, presents some central epistemological, semiotic, and
cognitive aspects of what can be called morphodynamical abduction in the
perspective of dynamical systems in physics and catastrophe theory in mathematics. Indeed, an integration of the traditional computational view with
some ideas developed inside the so-called dynamical approach can suggest
some important insights. What is the role of abduction in the dynamical
system approach? What is the role of the dichotomy salient/pregnant mathematically depicted by the catastrophe theory with respect to abduction?
What is embodied cognition from the point of view – so to say – of its
“mathematical physics”? To grasp the role of abduction in these scientific
traditions I provide an analysis of the concepts of anticipation, adumbration,
attractor, and of the dichotomy salient/pregnant: the result is the description of the abductive generation of new hypotheses in terms of a catastrophic
rearrangement of the parameters responsible for the behavior of the system.
The main concern of the part of the chapter devoted to the catastrophe theory is to demonstrate that pregnances and saliences provide a further help in
increasing knowledge about abductive “hypothesis generation” at the level of
both instinctual behavior and representation-oriented behavior, where nonlinguistic features drive a “plastic” model-based cognitive role. Furthermore,
in terms of dynamic systems and of Thom’s mathematical modeling we reach
a first sketch of a “physics of abduction”, where its cognitive essence is seen
in a whole unified naturalistic framework where all phenomena, and so cognition, gain a fundamental eco-physical significance, which also nicely includes
some aspects related to a kind of “social epistemology”.
A related problem is treated in section 8.6, which illustrates the so-called
coalition enforcement hypothesis, which sees humans as self-domesticated
animals engaged in a continuous hypothetical activity of building morality,
incorporating punishing policies at the same time. Abduction is still at stake,
the direct consequence of coalition enforcement being development and the
central role of cultural heritage (morality and sense of guilt included). The
long-lived and abstract human sense of guilt represents a psychological adaptation which abductively anticipates the appraisal of a moral situation in
order to avoid becoming a target of coalitional enforcement.
I started to think upon the research to be exposed in this second book on
abduction in 2001 while I was a visiting professor at Georgia Institute of Technology in Atlanta. In addition to my work here in Italy, I further reshaped the
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manuscript in 2003 as a Weissman Distinguished Visiting Professor at The
City University of New York, which provided an excellent work environment,
and during visits to the Department of Philosophy of Sun Yat-sen University, in Guangzhou (Canton), P.R. China, where I was visiting professor from
2005 to 2008. These visits added an excellent source of further research and
forged strong academic relationships with Asian colleagues, adding to those
in the EU and USA. I am grateful to all my colleagues there and in other
Universities worldwide for their helpful suggestions and much more. For valuable comments and discussions on a previous draft and about abduction I
am particularly grateful to the two anonymous referees and to John Woods,
Paul Thagard, Michael Leyton, Dov Gabbay, Claudio Pizzi, Emanuele Bardone, David Gooding, Atocha Aliseda, John Josephson, Walter Carnielli,
B. Chandrasekaran, Jon Williamson, Eliano Pessa, Gianluca Introzzi, Douglas Walton, Cameron Shelley, Sami Paavola, Woosuk Park, Giuseppe Longo,
Thomas Addis, Diderik Batens, Joke Meheus, Simon Colton, Gerhard Schurz,
Ilkka Niniluoto, Theo A. F. Kuipers, Ryan D. Tweney, Peter Flach, Antony
Kakas, Oliver Ray, Akinori Abe, Luis A. Pineda, A. Shimojima, P. Langley, Demetris P. Portides, Tommaso Bertolotti. Some sections of chapters
one, six, seven, and eight have been written in collaboration with my former
Ph.D. students: section 1.7 with Riccardo Dossena, sections 6.1.1, 6.1.2 and
6.2-6.6 with Emanuele Bardone, sections 7.4.2 with Elia Belli, and section
8.1 with Matteo Piazza. The research related to this volume was supported
by grants from the Italian Ministry of University, University of Pavia, and
the CARIPLO Foundation (Cassa di Risparmio delle Provincie Lombarde).
The preparation of the volume would not have been possible without the
contribution of resources and facilities of the Computational Philosophy Laboratory (Department of Philosophy, University of Pavia, Italy). This project
was conceived as a whole, but as it developed various parts have become
articles, which have now been excerpted, revised, and integrated into the
current text. I am grateful to Springer for permission to include portions of
previously published articles.
Pavia, Italy
June 2009
Lorenzo Magnani
Contents
1
2
Theoretical and Manipulative Abduction Conjectures
and Manipulations: The Extra-Theoretical Dimension
of Scientific Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Computational Modeling as a Pragmatic Rule for Clarity . . .
1.2 Computational Modeling and the Problem of Scientific
Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Abduction and Retroduction . . . . . . . . . . . . . . . . . . . . . .
1.3 What Is Abduction? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 The Syllogistic Framework and the ST-Model . . . . . . .
1.3.2 Abduction as Hypothesis Generation, Abduction as
Hypothesis Generation and Evaluation . . . . . . . . . . . . .
1.4 Sentential Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Abduction and Induction in Logic Programming . . . .
1.5 Model-Based Creative Abduction . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Conceptual Change and Creative Reasoning in
Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2 Model-Based Abduction and Its External
Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Manipulative Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1 Unexpressed Knowledge, Knowledge Creation, and
External Mediators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 External Representations and Epistemic Mediators . .
1.6.3 Segregated Knowledge and the “World of Paper” . . . .
1.7 Mirroring Hidden Properties through Optical Diagrams . . . .
41
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Non-explanatory and Instrumental Abduction
Plausibility, Implausibility, Ignorance Preservation . . . . . . .
2.1 Is Abduction an Ignorance-Preserving Cognition? . . . . . . . . . .
2.1.1 The Ignorance Preserving Character of Abduction . . .
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1
2
3
4
7
9
18
23
29
31
31
34
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2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
Contents
2.1.2 Truth Preserving and Ignorance Preserving
Inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 AKM and GW Schemas of Abduction . . . . . . . . . . . . .
Non-explanatory Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Gödel and Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Instrumental Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 On Propositional and Strategic Plausibility and
Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Governing Inconsistencies in Science through Explanatory,
Non-explanatory, and Instrumental Abduction . . . . . . . . . . . .
2.4.1 Empirical Anomalies and Explanatory Abduction . . .
2.4.2 Conceptual Anomalies, Explanatory, and
Non-explanatory Abduction . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Generating Inconsistencies by Radical Innovation . . . .
2.4.4 Maintaining Inconsistencies: Static and Dynamic
Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.5 Contradicting, Conflicting, Failing, and
Instrumental Abduction . . . . . . . . . . . . . . . . . . . . . . . . . .
A Note on Preinventive Forms, Disconfirming Evidence,
Unexpected Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Withdrawing Unfalsifiable Hypotheses Found through
Explanatory and Instrumental Abduction . . . . . . . . . . . . . . . . .
2.6.1 Negation as Failure in Query Evaluation . . . . . . . . . . .
2.6.2 Withdrawing Conventions and Instrumental
Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.3 Withdrawing Constructions and Explanatory and
Instrumental Abduction . . . . . . . . . . . . . . . . . . . . . . . . . .
Automatic Abductive Scientists . . . . . . . . . . . . . . . . . . . . . . . . .
Geometrical Construction Is a Kind of Manipulative
Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mirror Diagrams: Externalizing Mental Models to
Represent Imaginary Entities . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.1 Internal and External Representations . . . . . . . . . . . . .
Mirror Diagrams and the Infinite . . . . . . . . . . . . . . . . . . . . . . . .
2.10.1 Abducing First Principles through Bodily Contact . . .
2.10.2 Expansion of Scope Strategy . . . . . . . . . . . . . . . . . . . . . .
2.10.3 Infinite/Finite Interplay . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.4 Non-euclidean Parallelism: Coordination and
Inconsistency Detection . . . . . . . . . . . . . . . . . . . . . . . . . .
Unveiling Diagrams in Lobachevsky’s Discovery as
Gateways to Imaginary Entities . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.1 Euclidean/Non-euclidean Model Matching
Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.2 Consistency-Searching Strategy . . . . . . . . . . . . . . . . . . .
2.11.3 Loosing Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.12 Mechanizing Manipulative Abduction . . . . . . . . . . . . . . . . . . . . 139
2.12.1 Automatic Geometrical Constructions as
Extra-Theoretical Epistemic Mediators . . . . . . . . . . . . . 139
2.12.2 Automatic “Thinking through Doing” . . . . . . . . . . . . . . 141
3
Semiotic Brains and Artificial Minds
How Brains Make Up Material Cognitive Systems . . . . . . .
3.1 Turing Unorganized Machines . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Logical, Practical, Unorganized, and Paper
Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Continuous, Discrete, and Active Machines . . . . . . . . .
3.1.3 Mimicking Human Education . . . . . . . . . . . . . . . . . . . .
3.2 Brains as Unorganized Machines . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The Infant Cortex as an Unorganized Machine . . . . . .
3.3 From the Prehistoric Brains to the Universal Machines . . . . .
3.3.1 Private Speech and Fleeting Consciousness . . . . . . . . .
3.3.2 Material Culture as Distributed Cognition and
Semiosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Semiotic Delegations through the Disembodiment
of Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Mimetic and Creative Representations . . . . . . . . . . . . . . . . . . .
3.4.1 External and Internal Representations . . . . . . . . . . . . .
3.4.2 Language as the Ultimate Artifact . . . . . . . . . . . . . . . . .
3.5 Model-Based Abduction and Semiosis beyond Peirce . . . . . . .
3.5.1 Man Is an External Sign . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Cultured Unconscious and External/Internal
Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 Duties, Abductions, and Habits . . . . . . . . . . . . . . . . . . .
3.6 Constructing Meaning through Mimetic and Creative
External Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Constructing Meaning through Manipulative
Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Manipulating Meanings through External Semiotic
Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Geometrical Construction Is a Kind of
Manipulatxive Abduction . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 The Semiosis of Re-embodiment and Its
Sensorimotor Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.5 On-line and Off-line Intelligence Intertwined: The
Problem of Language and of Inner Rehearsal . . . . . . . .
3.6.6 External Diagrammatization and Iconic Brain
Coevolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.7 Delegated and Intrinsic Constraints in External
Agents and the Role of Anchors in Conceptual
Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.7 Mimetic Minds as Semiotic Minds . . . . . . . . . . . . . . . . . . . . . . .
3.8 “Symbols” as Memory Mediators. Maximizing
Abducibility through Psychic Energy Mediators . . . . . . . . . . .
3.8.1 Mythologization of External “Observations” . . . . . . . .
3.8.2 Cognitive/Affective Delegations to Artifacts . . . . . . . .
3.8.3 Artifacts as Memory Mediators . . . . . . . . . . . . . . . . . . .
3.8.4 Artifacts as Symbols That Maximize Abducibility . . .
4
5
Neuro-multimodal Abduction
Pre-wired Brains, Embodiment, Neurospaces . . . . . . . . . . .
4.1 Multimodal Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Neuroabduction: Internal and External Semiotic Carriers . . .
4.3 Pre-wired Brains and Embodiment . . . . . . . . . . . . . . . . . . . . . .
4.3.1 The Pre-wired Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Embodiment and Intentionality . . . . . . . . . . . . . . . . . . .
4.4 Actions vs. Thoughts? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Decision Making and Action . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Decision and Emotion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 The Agent-Based and Abductive Structure of Reasons in
Moral Deliberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 The Ontology of Reasons . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Abduction in Practical Agent-Based Reasoning . . . . .
4.6 Picking Up Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Spatial Frameworks, Anticipation, and Geometry . . . . . . . . . .
4.7.1 Abduction and Neurospaces . . . . . . . . . . . . . . . . . . . . . .
4.7.2 Adumbrations: Perceptions and Kinesthetic
Sensations Intertwined . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.3 The Genesis of Space . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.4 Anticipations as Abductions . . . . . . . . . . . . . . . . . . . . . .
4.7.5 The Genesis of Geometrical Idealities . . . . . . . . . . . . .
4.8 Non-conceptual and Spatial Abilities . . . . . . . . . . . . . . . . . . . . .
Animal Abduction
From Mindless Organisms to Artifactual Mediators . . . . . .
5.1 Iconicity and Logicality in Reasoning . . . . . . . . . . . . . . . . . . . .
5.1.1 Perception vs. Inference . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Iconicity Hybridates Logicality . . . . . . . . . . . . . . . . . . . .
5.2 Instinct vs. Heuristic Strategies . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 The Peircean Abductive Chicken and Animal
Hypothetical Cognition . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Instinct-Based Abduction . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Mind and Matter Intertwined . . . . . . . . . . . . . . . . . . . . .
5.2.4 Peircean Chickens, Human Agents, Logical Agents . . .
5.3 Mindless Organisms and Cognition . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Worm Intelligence, Abductive Chickens, Instincts . . . .
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5.3.2 Nonlinguistic Representational States . . . . . . . . . . . . . .
5.4 Animal Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 “Wired Cognition” and Pseudothoughts . . . . . . . . . . . .
5.4.2 Plastic Cognition in Organisms’ Pseudoexplanatory
Guesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Artifacts and Classical and Instrumental
Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Affordances and Abduction . . . . . . . . . . . . . . . . . . . . . . .
5.5 Perception as Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Reifications and Beliefs . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Perception as Abduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Is Instinct Rational? Are Animals Intelligent? . . . . . . . . . . . .
5.6.1 Rationality of Instincts . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Levels of Rationality in Animals . . . . . . . . . . . . . . . . . . .
5.7 Artifactual Mediators and Languageless Reflexive
Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1 Animal Artifactual Mediators . . . . . . . . . . . . . . . . . . . . .
5.7.2 Pseudological and Reflexive Thinking . . . . . . . . . . . . . .
5.7.3 Affect Attunement and Model-Based
Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Abduction, Affordances, and Cognitive Niches
Sharing Representations and Creating Chances through
Cognitive Niche Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Cognitive Niches: Humans as Chance Seekers . . . . . . . . . . . . .
6.1.1 Incomplete Information and Human Cognition . . . . . .
6.1.2 Cognitive Niche Construction and Human
Cognition as a Chance-Seeker System . . . . . . . . . . . . . .
6.1.3 What Are the Cognitive Niches? . . . . . . . . . . . . . . . . . .
6.1.4 Extragenetic Information, Loosely Darwinian
Effects, Baldwin Effect . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.5 Niche Construction and Distributed Human
Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Affordances and Cognition: The Received View . . . . . . . . . . . .
6.2.1 The Notion of Affordance and Its Inferential
Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Affordances Are Opportunities for Action . . . . . . . . . .
6.2.3 Affordances Are Ecological Facts . . . . . . . . . . . . . . . . . .
6.2.4 Affordances Imply the Mutuality of Perceiver and
Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Affordances as Eco-Cognitive Interactional Structures . . . . . .
6.3.1 Pseudothoughts and Model-Based Thinking in
Humans and Animals: Affordances as Chances . . . . . .
6.4 Direct and Mediated Perception, Proximal and Distal
Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.4.1 Direct and Mediated Affordances . . . . . . . . . . . . . . . . . .
6.4.2 Proximal and Distal Environment . . . . . . . . . . . . . . . . .
6.4.3 Reconciling Direct and Mediated Perception:
Ecological and Constructivist Approaches
Intertwined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4 Attunement, Affordances, and Cognitive Artifacts:
Extracting and Creating Affordances . . . . . . . . . . . . . . .
6.5 Affordances and Abduction: The Plasticity of
Environmental Situatedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Innovating through Affordance Creation . . . . . . . . . . . . . . . . . .
6.6.1 Latent Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 Creating Chances through Manipulating Artifacts
and External Representations . . . . . . . . . . . . . . . . . . . . .
7
Abduction in Human and Logical Agents
Hasty Generalizers, Hybrid Abducers, Fallacies . . . . . . . . . .
7.1 Beyond Peirce: Human Agents, Logical Agents . . . . . . . . . . . .
7.2 Logical Agents as Mimetic and Creative Representations
and Mediators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Externalization in Demonstrative Environments . . . . . . . . . . .
7.3.1 Model-Based Abduction in Demonstrative
Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Model-Based Heuristic and Deductive Reasoning . . . .
7.3.3 Ideal Logical Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Hasty Generalizers and Hybrid Abducers in Agent-Based
Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1 Agent-Based Reasoning, Agent-Based Logic,
Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.2 Beings-Like-Us as Hasty Generalizers: Induction as
a Fallacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 External and Internal Representations in Hybrid Abducers
and Inducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.1 Logic Programs as Agents: External Observations
and Internal Knowledge Assimilation . . . . . . . . . . . . . .
7.5.2 Hybrid Inducers and Abducers . . . . . . . . . . . . . . . . . . . .
7.6 Manipulative Abduction, Hybrid Reasoning, Fallacies . . . . . .
7.6.1 Merely Successful and Successful Abductive and
Inductive Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.2 Abduction, Fallacies, Rhetoric, and Dialectics . . . . . . .
7.7 Intelligence as Smart Heuristic: Ecological Thinking vs.
Logical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7.1 Reducing Information . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8 Fallacies as Distributed “Military” Intelligence . . . . . . . . . . . .
7.8.1 Distributing Fallacies . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8.2 Military Intelligence through Fallacies . . . . . . . . . . . . . .
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7.8.3 Abduction in Argument Evaluation and
Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
7.8.4 Narrative Abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
8
Morphodynamical Abduction
Causation of Hypotheses by Attractors Dynamics . . . . . . .
8.1 Abduction as Embodied Cognition . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Discreteness and Cognition: Imitation vs.
Intelligibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.2 Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.3 Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.4 Cognitive Processes as Super-Representational . . . . . .
8.1.5 Embodied Cognition and Qualitative Modeling . . . . . .
8.2 Morphodynamical Abduction and Adumbrations . . . . . . . . . .
8.2.1 Hypotheses Anticipation and Abduction . . . . . . . . . . . .
8.3 Abduction, Pregnances, Affordances . . . . . . . . . . . . . . . . . . . . .
8.3.1 Saliences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Pregnances as Eco-Cognitive Forms . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Pregnances and Human Language . . . . . . . . . . . . . . . . .
8.5 Semiotic Brains Make Up Signs: Mental and Mindless
Semiosis through Abductive Anticipation . . . . . . . . . . . . . . . . .
8.5.1 Language Acquisition through Attunement and
Parental Deixis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.2 “Discreteness” and Cognition . . . . . . . . . . . . . . . . . . . . .
8.6 Hypothetical Cognition and Coalition Enforcement:
Language, Morality, and Violence . . . . . . . . . . . . . . . . . . . . . . . .
8.6.1 Coalition Enforcement . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.2 The Role of Abduction in the Moral/Violent
Nature of Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
Chapter 1
Theoretical and Manipulative Abduction
Conjectures and Manipulations: The Extra-Theoretical
Dimension of Scientific Discovery
More than a hundred years ago, the American philosopher Charles Sanders Peirce,
when working on logical and philosophical problems, suggested the concept of
pragmatism (“pragmaticism”, in his own words) as a logical criterion to analyze
what words and concepts express through their practical meaning. Many authors
have illustrated creative processes and reasoning, especially in the case of scientific practices. In fact, many philosophers have usually offered a number of ways of
construing hypotheses generation, but they aim at demonstrating that the activity of
generating hypotheses is paradoxical, obscure, and thus not analyzable.
Those descriptions are often so far from Peircean pragmatic prescription and so
abstract to result completely unknowable and obscure. To dismiss this tendency and
gain interesting insight about cognitive creativity and the so-called “logic of scientific discovery” we need to build constructive procedures, which could play a role
in moving the problem solving process forward by implementing them in some actual models. The “computational turn” gave us a new way to understand creative
processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence,
logical, and cognitive science tools, philosophy allows us to test concepts and ideas
previously conceived only in abstract terms. It is in the perspective of these actual computational models that I have founded the central role of abduction in the
explanation of creative reasoning in science.
This chapter aims at introducing the distinction between two kinds of abduction, theoretical and manipulative, in order to provide an integrated framework to
explain some of the main aspects of both creative and model-based reasoning effects engendered by the practice of science and everyday reasoning. The distinction
appears to be extremely convenient, after having illustrated the sentential models
together with their limitations (section 1.4), creativity will be viewed as the result
of the highest cases of theoretical abduction demonstrating the role of so-called
model-based abduction (section 1.5). Moreover, I will delineate what I call manipulative abduction (section 1.6) by showing how we can find methods of manipulative
constructivity.
From this perspective, creativity and discovery are no longer seen as mysterious irrational processes, but, thanks to constructive accounts, they are viewed as
L. Magnani: Abductive Cognition, COSMOS 3, pp. 1–61.
c Springer-Verlag Berlin Heidelberg 2009
springerlink.com 2
1 Theoretical and Manipulative Abduction
complex relationships among different inferential steps that can be clearly analyzed
and identified. I maintain that the analysis of sentential, model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development
of programs computationally adequate in rediscovering, or discovering for the first
time, for example, scientific hypotheses or mathematical theorems. In this chapter
attention will be focused on those particular kinds of abductive cognition that resort
to the existence of extra-theoretical ways of thinking – thinking through doing. Indeed many cognitive processes are centered on external representations, as a means
to create communicable accounts of new experiences ready to be integrated into previously existing systems of experimental and theoretical practices. The last part of
the chapter is devoted to illustrating the problem of the extra-theoretical explanatory
dimension of reasoning and discovery from the perspective of some mathematical
cases derived from calculus, where internal and external aspects (optical diagrams)
of cognition are at play.
1.1
Computational Modeling as a Pragmatic Rule for Clarity
What I call “computational philosophy”,1 aims at investigating many important concepts and problems of the philosophical and epistemological tradition in a new way
by taking advantage epistemological, cognitive, and artificial intelligence (AI) computational methodologies. I maintain that the results of computational philosophy
meet the classical requirements of Peircean “pragmatic” ambitions and nicely tie
together both issues related to the dynamics of information and its systematic embodiment in segments of “knowledge”. In the second half of the nineteenth century
the great American philosopher Charles Sanders Peirce suggested the idea of pragmatism as a logical criterion to analyze what words and concepts express through
their practical meaning. In “The fixation of belief” [1877] Peirce enumerates four
main methods by means of which it is possible to fix belief: the method of tenacity,
the method of authority, the a priori method and, finally, the method of science, by
means of which, thanks to rigorous research, “[. . . ] we can ascertain by reasoning
how things really and truly are; and any man, if he has sufficient experience and he
reasons enough about it, will be led to the one True conclusion” [Peirce, 1987, p.
255]. Only the scientific method leads to identify what is “real”, that is “true”.
Peirce will more clearly explain the public notion of truth here exposed, and the
interpretation of reality as the final purpose of the human inquiry, in his subsequent
paper “How to make our ideas clear” [1878]. Here Peirce addresses attention on the
notions of “clear idea” and “belief”. “Whoever has looked into a modern treatise on
logic of the common sort, will doubtlessly remember the two distinctions between
clear and obscure conceptions, and between distinct and confused conceptions” he
writes [Peirce, 1987, p. 257]. A clear idea is defined as one which is apprehended
so that it will be recognized wherever it is met, and so that no other will be mistaken
for it. If it fails to be clear, it is said to be obscure. On the other hand, a distinct idea
1
Topics and aims of computational philosophy are illustrated in [Magnani, 1997].
1.2 Computational Modeling and the Problem of Scientific Discovery
3
is defined as one which contains nothing which is not clear. In this paper Peirce is
clearly opposing traditional philosophical positions, such as those by Descartes and
Leibniz, who consider clarity and distinction of ideas only from a merely psychological and analytical perspective:
It is easy to show that the doctrine that familiar use and abstract distinctness make
the perfection of apprehension has its only true place in philosophies which have long
been extinct; and it is now time to formulate the method of attaining to a more perfect
clearness of thought, such as we see and admire in the thinkers of our own time [Peirce,
1987, p. 258].
Where do we have, then, to look for a criterion of clarity, if philosophy has become
too obscure, irrational and confusing, if “[. . . ] for an individual, however, there can
be no question that a few clear ideas are worth more than many confused ones?”
[Peirce, 1987, p. 260]. “The action of thought is excited by the irritation of doubt,
and ceases when belief is attained; so that the production of belief is the sole function
of thought” [Peirce, 1987, p. 261]. And belief “[. . . ] is something that we are aware
of [. . . ] it appeases the irritation of doubt; and, third, it involves the establishment in
our nature of a rule of action, or, say for short, a habit” [Peirce, 1987, p. 263]. Hence,
the whole function of thought is to produce habits of action. This leads directly to the
methodological pragmatic theory of meaning, a procedure to determine the meaning
of a proposition:
To develop its meaning, we have, therefore, simply to determine what habits it produces, for what a thing means is simply what habits it involves. Now, the identity of a
habit depends on how it might lead us to act, not merely under such circumstances as
are likely to arise, but under such as might possibly occur, no matter how improbable
they may be. Thus, we come down to what is tangible and conceivably practical, as the
root of every real distinction of thought, no matter how subtile it may be; and there is
no distinction of meaning so fine as to consist in anything but a possible difference of
practice [Peirce, 1987, pp. 265-266].
In this way Peirce creates the equivalence among idea, belief and habit, and can
define the rule by which we can reach the highest grade of intellectual clearness,
pointing out that is impossible to have an idea in our minds which relates to anything but conceived sensible effects of things. Our idea of something is our idea of
its sensible effects: “Consider what effects, that might conceivably have practical
bearings, we conceive the object of our conception to have. Then, our conception
of these effects is the whole of our conception of the object” [Peirce, 1987, p. 266].
This rule founds the pragmatic procedure thanks to which it is possible to fix our
ideas.
1.2
Computational Modeling and the Problem of Scientific
Discovery
Peirce’s conception of clarity contains the idea that to define the meaning of words
and concepts we have to “test” them: the whole conception of some quality lies in
4
1 Theoretical and Manipulative Abduction
its conceivable effects. As he reminds us by the example of the concept of hardness
“[. . . ] there is absolutely no difference between a hard thing and a soft thing so long
as they are not brought to the test” [Peirce, 1987, p. 266]. Hence, we can define the
“hardness” by looking at those predictable events that occur every time we think of
testing some thing.
This methodological criterion can be useful to solve the problem of creative reasoning, and to describe, in rational terms, some aspects of the delicate question of
a “logic of discovery”: what do we mean by “creative”, and how can a “creative
process” be described? Much has been said on the problem of creativity and hypotheses generation. In the history of philosophy there are at least three important
ways for designing the role of hypothesis generation, considered in the perspective
of problem solving performances. But all aim at demonstrating that the activity of
generating hypotheses is paradoxical, illusory, obscure, implicit, and not analyzable.
Plato’s doctrine of reminiscence can be looked at from the point of view of an epistemological argument about the paradoxical concept of “problem-solving”: in order
to solve a problem one must in some sense already know the answer, there is no real
generation of hypotheses, there is only recollection. The activity of Kantian schematism is also implicit, resulting from imagination and completely unknowable, empty,
and devoid of any possibility of being rationally analyzed. It is an activity of tacit
knowledge, “an art concealed in the depths of the human soul, whose real modes of
activity nature is hardly likely ever to allow us to discover, and to have open to our
gaze” [Kant, 1929, A141-B181, p. 183]. In turn Polanyi thinks that if all knowledge
is explicit and capable of being clearly stated, then we cannot know of the existence
of a problem or look for its solution; if problems nevertheless exist, and discoveries
can be made by solving them, we can know things that we cannot express: consequently, the role of so-called tacit knowledge “the intimation of something hidden,
which we may yet discover” is central [Polanyi, 1966].
In all these descriptions, the problem is that the definition of concepts like “creativity” and “discovery” is a priori. Following Peirce, the definitions of concepts
of this sort are not usually based upon any observed facts, at least not in any great
degree; even if sometimes these beliefs are in harmony with natural causes. They
have been chiefly adopted because their fundamental propositions seemed “agreeable to reason”. That is, we find ourselves inclined to believe them. Usually this
frame leads to a proliferating verbosity, in which theories are often incomprehensible and lead to some foresight just by intuition. But a theory which needs intuition
to determine what it predicts has poor explanatory power. It just “[. . . ] makes of
inquiry something similar to the development of taste” [Peirce, 1987, p. 254].
1.2.1
Abduction and Retroduction
Many philosophical efforts in the last century have been spent in studying the conceptual change in science. In the mid-1960s many critics challenged the comforting
picture of conceptual change in terms of continuous and cumulative steps. Contrary
to this picture Kuhn claimed that conceptual change in science is analyzable as a
1.2 Computational Modeling and the Problem of Scientific Discovery
5
kind of irrational and obscure Gestalt-switch, that accounts for the inventive processes and the achievement of new scientific theories and paradigms [Kuhn, 1962].
Kuhn argued that major changes in science are best characterized as revolutions,
involving the over-throw and the replacement of the reigning conceptual systems
and world views by means of new ones incommensurable with them. Kuhn brought
philosophers of science to distinguish between the logic of discovery and the logic
of justification (i.e. the distinction between the psychological side of creation and
the logic argument of proving new discovered ideas by facts).2 Most have concluded
that no logic of discovery exists and, moreover, that a “rational” model of discovery is impossible. In short, scientific creative reasoning should be non-rational or
irrational and there is no reasoning towards hypotheses.
In the last decades philosophers of science have abandoned this attitude. The researchers who work on scientific change tend now to focus attention on the problem
of rational choice between competing theories and hypotheses and on the discovery
processes. This also leads to the problem of understanding how scientists combine
their individual human cognitive abilities with the conceptual resources available
to them as members of a scientific community and of a wider natural and social
context. It is by means of this synthesis that the creation, elaboration, and communication of a new emerging representation of a scientific domain is made possible.
This chapter aims at introducing and further deepening the distinction, I have already illustrated in my previous book on abduction [Magnani, 2001b], between two
kinds of abduction, theoretical and manipulative, in order to provide an integrated
framework to explain some of the main aspects of both creative and model-based
reasoning effects engendered by the practice of science and in everyday reasoning.
The distinction appears to be extremely convenient: after having illustrated the sentential models together with their limitations (section 1.4), creativity will be viewed
as the result of the highest cases of theoretical abduction showing the role of the
so-called model-based abduction (section 1.5). Moreover, I will delineate what I
call manipulative abduction (section 1.6) by showing how we can find methods
of manipulative constructivity, where the XX century epistemological tradition has
settled the most negative effects of theory-ladenness.
Abduction is a popular term in many fields of AI, such as diagnosis, planning, natural language processing, motivation analysis, logic programming, and
probability theory. Moreover, abduction is important in the interplay between AI
and philosophy, cognitive science, historical, temporal, and narrative reasoning,
decision-making, legal reasoning, and emotional cognition.3 Six volumes (monographs and collections) are currently available [Josephson and Josephson, 1994;
Flach and Kakas, 2000b; Kuipers, 2000; Magnani, 2001b; Gabbay and Woods,
2005; Aliseda, 2006; Walton, 2004] and three special issues of international journals (Philosophica, 1998 61(1); Foundations of Science, 2004, 9; 2008, 13(1); Logic
Journal of the IGPL, 2006 14(1)). Of course many articles from various disciplinary
2
3
A perspective originally established by [Reichenbach, 1938] and [Popper, 1959].
A list of the classical bibliography on abduction is given in [Magnani, 2001b].
6
1 Theoretical and Manipulative Abduction
fields of research are continually published on this topic.4 Let us consider the following interesting passage, from an article by [Simon, 1965], dealing with the logic
of normative theories:
The problem-solving process is not a process of “deducing” one set of imperatives
(the performance programme) from another set (the goals). Instead, it is a process
of selective trial and error, using heuristic rules derived from previous experience,
that is sometimes successful in discovering means that are more or less efficacious in
attaining some end. If we want a name for it, we can appropriately use the name coined
by Peirce and revived recently by Norwood Hanson [1958]: it is a retroductive process.
The nature of this process – which has been sketched roughly here – is the main subject
of the theory of problem-solving in both its positive and normative versions [Simon,
1977, p. 151].
Simon states that discovering means that are more or less efficacious in attaining
some end are performed by a retroductive process. He goes on to show that it is
easy to obtain one set of imperatives from another set by processes of discovery
or retroduction, and that the relation between the initial set and the derived set is
not a relation of logical implication. I completely agree with Simon: retroduction
(that is abduction, cf. below) is the main subject of the theory of problem-solving
and developments in the fields of cognitive science and artificial intelligence have
strengthened this conviction.
[Hanson, 1958, p. 54] is perfectly aware of the fact that an enormous range of
explanations (and causes) exists for any event:
There are as many causes of x as there are explanations of x. Consider how the cause
of death might have been set out by a physician as “multiple hemorrhage”, by the
barrister as “negligence on the part of the driver”, by a carriage-builder as “a defect in
the brakeblock construction”, by a civic planner as “the presence of tall shrubbery at
that turning”.
The word “retroduction” used by Simon is the Hansonian neopositivistic one replacing the Peircean classical word abduction. Following Hanson’s point of view Peirce
“[. . . ] regards an abductive inference (such as ‘The observed position of Mars falls
between a circle and an oval, so the orbit must be an ellipse’) and a perceptual judgment (such as ‘It is laevorotatory’) as being opposite sides of the same coin”. It is
also well-known that Hanson relates abduction to the role of patterns in reasoning
and to the Wittgensteinian “Seeing that” [Hanson, 1958, p. 86].
As Fetzer has stressed, from a philosophical point of view the main modes of
argumentation for reasoning from premises to conclusions are expressed by these
three general kinds of reasoning: deductive (demonstrative, non ampliative, additive), inductive (non-demonstrative, ampliative, non additive), fallacious (neither,
irrelevant, ambiguous). Abduction, which expresses likelihood in reasoning, is a
typical form of fallacious inference: “[. . . ] it is a matter of utilizing the principle
4
General classical considerations on abduction in science and AI can also be found in [Gooding,
1996; Josephson and Josephson, 1994; Kuipers, 1999; Thagard, 1988; Shrager and Langley,
1990].
1.3 What Is Abduction?
7
of maximum likelihood in order to formalize a pattern of reasoning known as ‘inference to the best explanation”’ [Fetzer, 1990, p. 103].5 These different kinds of
reasoning will be illustrated in the following section.
Many researchers in the area of cognitive science consider scientific thinking (and
thinking activity in general), as related to a kind of “representational” system that
we can implement in a computational model: thinking is a form of computation.
Following the idea that a full understanding of mental processes is possible only
from a computational perspective [Johnson-Laird, 1983], these models have been
implemented in AI programs where data structures and procedures correspond to
assumed mental structures and processes [Thagard, 1992].6 In the last decades, also
to better understand the complex problem of conceptual change in science, besides
the ideas elaborated in the AI areas of knowledge representation, problem solving,
and machine learning, we needed the important concept of abduction.7 Scientific
theories contain many theoretical hypotheses that cannot be built by simple generalization of observations. Indeed, Peirce presented abduction as a mechanism by
which it is possible to account for the generation of new explanatory hypotheses in
science.
As I have illustrated in the first section of this chapter, a suggestion that can help
to solve the enigma of discovery and creativity comes from the “computational turn”
developed in the last years. Recent computational philosophy research in the field
of cognitive science make use of tools able to overcome those puzzling speculative
problems, or, at least, to redefine them in a strict pragmatical sense. In fact, taking
advantage of modern tools of logic, artificial intelligence, and of other cognitive
science disciplines, computational philosophy is able to construct actual models of
studied processes. It is an interesting constructive rational alternative that, disregarding the most abstract level of philosophical analysis can offer clear and testable
architectures of creative processes.
1.3
What Is Abduction?
The development of human society has now reached a technological level in which
issues concerning the creation and dynamics of information – especially in science
– are absolutely crucial. As I have already said, inside the computational philosophy framework, a new paradigm, aimed at unifying the different perspectives and
providing some new design insights, arose by emphasizing the significance of the
5
6
7
On the inference to the best explanation see also [Harman, 1965; Harman, 1968; Thagard, 1987;
Lipton, 2004].
It is the so-called “computational-representational understanding of the mind” (CRUM)
[Thagard, 1996].
In my previous book on abduction [Magnani, 2001b] I have already illustrated some basic philosophical, logical, cognitive, and computational aspects of the concept of abduction. This book
aims at further increasing knowledge taking advantage of other intellectual achievements, not
only related to philosophy, logic, and artificial intelligence, but also concerning biology, neurology, anthropology, ecological psychology, dynamical system theory.
8
1 Theoretical and Manipulative Abduction
concept of abduction, in order to illustrate the problem-solving process and to propose a unified and rational epistemological model of scientific discovery, diagnostic
reasoning, and other kinds of creative and hypothetical reasoning.
A hundred years ago, Charles Sanders Peirce [1931-1958] coined the concept of
abduction in order to illustrate that the process of scientific discovery is not irrational and that a methodology of discovery is possible. Peirce interpreted abduction
essentially as an “inferential” creative process of generating a new “explanatory”
hypothesis. Abduction has a logical form (fallacious, if we model abduction by using classical syllogistic logic)8 distinct from deduction and induction. Many reasoning conclusions that are not derived in a deductive manner are abductive. For
instance, if we see a broken horizontal glass on the floor we might explain this fact
by postulating the effect of wind blowing shortly before: this is not certainly a deductive consequence of the glass being broken (a cat may well have been responsible
for it).9 Abduction is the process of inferring10 certain facts and/or laws and hypotheses that render some sentences plausible,11 that explain (and also sometimes
discover) some (eventually new) phenomenon or observation; it is the process of
reasoning in which explanatory hypotheses are formed and evaluated.
It is important to note that I adopt in this chapter the view of abduction that it is
immediately a generation of plausible hypotheses. Although this claim may be true
in various contexts, it is not so generally. I am thinking particularly of Descartes’s
implausible arguments in the Meditations, in which he suggests, for example, that
our experiences are caused not by the world stimulating our sensory organs but by
the machinations of an evil demon. Such a claim is highly implausible, but that does
not deter Descartes given his project of finding any kind of doubt against a belief.
Of course, Peirce famously castigated Descartes by remarking that we cannot begin
with complete doubt and argued that Descartes’s project was a fool’s errand. Is
implausible abduction really abduction? I will treat this problem in the following
chapter when dealing with the so-called “instrumental abduction”.
Moreover, we have to remember that although explanatory hypotheses can be
elementary, there are also cases of composite, multipart hypotheses. Anyway, some
hypotheses are empty from the explanatory point of view: for example the generalization “every object in the population is female or male” does not explain that
Maria is female, since it requires the additional knowledge that Maria is not male.
8
9
10
11
The abductive inference rule corresponds to the well-known fallacy called affirming the
consequent.
This event constitutes in its turn an anomaly that needs to be solved/explained but I have to
anticipate that surprise or anomalies do not constitute an intrinsic requirement for abduction.
“It must be remembered that abduction, although it is little hampered by logical rules, nevertheless is logical inference, asserting its conclusion only problematically or conjecturally, it is true,
but nevertheless having a perfect logical form” [Peirce, 1931-1958, 5.188].
Peirce thinks that humans’s capacity to make abductive plausible hypotheses is ultimately based
on the instinct. His idea is in itself abductive “It is a primary hypothesis underlying all abduction
that the human mind is akin to the truth in the sense that in a finite number of guesses it will
light upon the correct hypothesis” [Peirce, 1931-1958, 7.220]. I will illustrate the role of instinct
in abduction the first two sections 5.1 and 5.2 of chapter five.
1.3 What Is Abduction?
9
The process of finding such generalizations has been called confirmatory (or descriptive) induction :
A typical form of explanatory induction is concept learning, where we want to learn
a definition of a given concept C in terms of other concepts. This means that our inductive hypotheses are required to explain (logically entail) why particular individuals
are Cs, in terms of the properties they have. However, in the more general case of
confirmatory induction we are not given a fixed concept to be learned. The aim is to
learn relationships between any of the concepts, with no particular concept singled
out. The formalization of confirmatory hypothesis formation cannot be based on logical entailment, as in Peirce’s abduction. Rather, it is a quantitative form of degree of
confirmation, which explains its name [Flach and Kakas, 2000a].
Theoretical and manipulative abduction are treated in this chapter in the perspective of the orthodox Peircean explanatory view: non-explanatory and instrumental abduction, not clearly considered by Peirce, will be illustrated in detail in the
following chapter.
1.3.1
The Syllogistic Framework and the ST-Model
First, it is necessary to show the connections between abduction, induction, and deduction and to stress the significance of abduction to illustrate the problem-solving
process. I think the example of diagnostic reasoning is an excellent way to introduce abduction. Some years ago I have developed with others [Lanzola et al., 1990;
Ramoni et al., 1992] an epistemological model of medical reasoning, called the
Select and Test Model (ST-model) [Magnani, 1992; Stefanelli and Ramoni, 1992]
which can be described in terms of the classical notions of abduction, deduction and
induction; it describes the different roles played by such basic inference types in
developing various kinds of medical reasoning (diagnosis, therapy planning, monitoring) but can be extended and regarded also as an illustration of scientific theory
change. The model is consistent with the Peircean view about the various stages of
scientific inquiry in terms of “hypothesis” generation, deduction (prediction), and
induction.
The type of inference called abduction was also studied by Aristotelian syllo, and later on by medieval reworkers of syllogism.
gistics, as a form of
As I have already noted, Peirce,12 interpreted abduction essentially as an “inferential” creative process of generating a new hypothesis: it is extremely important
to note the special meaning attributed to the adjective “inferential” by Peirce in its
broad philosophical and semiotic perspective, that I will better illustrate below in
section 1.5.
Abduction and induction, viewed together as processes of production and gen.13 As
eration of new hypotheses, are sometimes called reduction, that is
12
13
Cf. [Frankfurt, 1958; Reilly, 1970; Fann, 1970; Davis, 1972; Ayim, 1974; Anderson, 1986;
Anderson, 1987; Kapitan, 1990; Hookway, 1992; Debrok, 1997; Roesler, 1997; Wirth, 1997].
Sometimes
is translated with retroduction, so it is simply referred to abduction (see
above in this section).
10
1 Theoretical and Manipulative Abduction
Fig. 1.1 Creative and selective abduction
[Lukasiewicz, 1970] makes clear, “Reasoning which starts from reasons and looks
for consequences is called deduction; that which starts from consequences and looks
for reasons is called reduction”. The celebrated example given by Peirce is Kepler’s
conclusion that the orbit of Mars must be an ellipse.14
There are two main epistemological meanings of the word abduction [Magnani,
1988; Magnani, 1991; Magnani, 2001b]: 1) abduction that only generates “plausible”15 hypotheses (“selective” or “creative”) and 2) abduction considered as inference “to the best explanation”, which also evaluates hypotheses (cf. Figure 1.1)
[Harman, 1973; Thagard, 1988; Lipton, 2004].16 An illustration from the field of
medical knowledge is represented by the discovery of a new disease and the manifestations it causes which can be considered as the result of a creative abductive
inference. Therefore, “creative” abduction deals with the whole field of the growth
of scientific knowledge. This is irrelevant in medical diagnosis where instead the
task is to “select” from an encyclopedia of pre-stored diagnostic entities. We can
call both inferences ampliative, selective and creative, because in both cases the
reasoning involved amplifies, or goes beyond, the information incorporated in the
premises [Magnani, 1992].
All we can expect of our “selective” abduction, is that it tends to produce hypotheses for further examination that have some chance of turning out to be the best
explanation. Selective abduction will always produce hypotheses that give at least a
partial explanation and therefore have a small amount of initial plausibility. In the
syllogistic view (see below) concerning abduction as inference to the best explanation advocated by Peirce one might require that the final chosen explanation be the
most plausible.
When we speak of abduction as inference to the best explanation, we have to note
that the adjective “best” has to be taken in a Pickwickian sense: actually abduction
14
15
16
A clear reconstruction of Kepler’s discovery is given in [Gorman, 1998].
A further analysis of this important concept is illustrated in subsection 2.3.1, chapter two of this
book.
Further explanations of this bipolar distinction (and about the use herein of the concept of
plausibility) are given below in this chapter.
1.3 What Is Abduction?
11
never reaches the status of best hypothesis, we have to intend the word “best” in a
contextual and provisional way. As I will explain in detail in the following chapter
(section 2.1), the agent’s abduction must be considered as preserving the ignorance
that already gave rise to her ignorance-problem. In this perspective, recently suggested and illustrated by [Gabbay and Woods, 2005], abduction does not have to
be considered a “solution” of an ignorance problem, but rather a response to it, in
which the agent reaches presumptive attainment rather than actual attainment. It is
clear that in this framework the inference to the best explanation – if considered as
a truth conferring achievement – cannot be a case of abduction, because abductive
inference is essentially ignorance preserving. It is also important to note that the
emphasis given along this chapter to the “explanatory” character of abductive reasoning is strictly related to the Peircean point of view: Gabbay and Woods have
particularly stressed that abduction is not intrinsically explanatory, not only, abduction can be merely radically instrumental. I will extensively explain these aspects
of abductive cognition in the following chapter (sections 2.2 and 2.3).
What I call theoretical abduction certainly illustrates much of what is important
in creative abductive reasoning, in humans and in computational programs, especially the objective of selecting and creating a set of hypotheses (diagnoses, causes,
hypotheses) that are able to dispense good (preferred) explanations of data (observations), but fails to account for many cases of explanations occurring in science and
in everyday reasoning when the exploitation of environment is crucial. It fails to account for those cases in which there is a kind of “discovering through doing”, cases
in which new and still unexpressed information is codified by means of manipulations of some external objects (epistemic mediators). I maintain that there are two
kinds of theoretical abduction, “sentential”, related to logic and to verbal/symbolic
inferences, and “model-based”, related to the exploitation of internalized models of
diagrams, pictures, etc., cf. below in this chapter (cf. Figure 1.2).
Fig. 1.2 Theoretical abduction
12
1 Theoretical and Manipulative Abduction
The concept of manipulative abduction17 captures a large part of scientific thinking where the role of action is central, and where the features of this action are implicit and hard to be elicited: action can provide otherwise unavailable information
that enables the agent to solve problems by starting and by performing a suitable
abductive process of generation or selection of hypotheses.18
The epistemological distinction – which I will illustrate and elaborate upon in
the following pages – between theoretical and manipulative abduction is certainly
based on the possibility of separating the two aspects in real cognitive processes,
resorting to the differentiation between off-line (theoretical, when only inner aspects
are at stake) and on-line (manipulative, where the interplay between internal and
external aspects is fundamental.19 Some authors have raised doubts about the online/off-line distinction on the grounds that no thinking agent is ever wholly on-line
or wholly off-line. I think this distinction is at least useful from an epistemological
perspective as a way of theoretically illustrating different cognitive levels, which
in the following chapters will be further analyzed and seen at work, in human and
animal cognition.
We know that throughout his career Peirce defended the thesis that, besides
deduction and induction,20 there is a third mode of inference that constitutes the
only method for really improving scientific knowledge, which he called abduction.
Science improves and grows continuously, but this continuous enrichment cannot
be due to deduction, nor to induction: deduction does not produce any new idea,
whereas induction produces very simple ideas. New ideas in science are due to abduction, a particular kind of non-deductive21 inference that involves the generation
and evaluation of explanatory hypotheses.
I and others [Ramoni et al., 1992] have developed an epistemological model of
medical reasoning, called the Select and Test Model (ST-model) which can be described in terms of the classical notions of abduction, deduction and induction. It
17
18
19
20
21
The concepts of theoretical and manipulative abduction and of epistemic mediators are introduced in [Magnani, 2001b].
I have collected in a recent special issue of the Logic Journal of the IGPL [Magnani, 2006a]
various contributions regarding research on abduction in the areas of epistemology, artificial
intelligence, and of the logic of “so–called practical reasoning”. [Patokorpi, 2007] adopts and
enriches my distinction between selective, creative, non-sentential and manipulative abduction
and applies abduction to the pedagogical problem of analyzing how learners learn in an information society technology (IST): abduction highlights the main features of IST enhanced
learning. In a recent paper [Schurz, 2008] further extends my characterization of abductive reasoning proposing a classification of different patterns particularly related to what I call creative
abduction. The article illustrates the features of several kinds of creative abductions, such as
theoretical model abduction, common cause abduction and statistical factor analysis, and illustrates them by various real case examples. It is also suggested to demarcate scientifically fruitful
abductions from purely speculative abductions by using the criterion of causal unification.
The distinction between off-line and on-line thinking is analyzed in detail in chapter three of
this book, subsection 3.6.5.
Peirce clearly contrasted abduction with induction and deduction, by using the famous syllogistic model I will describe below in this section. More details on the differences between abductive
and inductive/deductive inferences can be found in [Flach and Kakas, 2000b] and [Magnani,
2001b]; cf. also below, subsection 1.4.1.
Non-deductive if we use the attribute “deductive” as designated by classical logic.
1.3 What Is Abduction?
13
describes the different roles played by such basic inference types in developing various kinds of medical reasoning (diagnosis, therapy planning, monitoring) but can
be extended and regarded also as an illustration of scientific theory change.22 The
model is consistent with the Peircean view regarding the various stages of scientific
inquiry in terms of “hypothesis” generation, deduction (prediction), and induction.
As previously illustrated, I have introduced a distinction between “creative” and
“selective” abduction. Selective abduction will always produce hypotheses that give
at least a partial explanation and therefore have a small amount of initial plausibility.
In the syllogistic view advocated by Peirce (see below) concerning abduction as
inference to the best explanation one might require that the final chosen explanation
be the most plausible. Since the time of John Stuart Mill, the name given to all kinds
of non deductive reasoning has been induction, considered as an aggregate of many
methods for discovering causal relationships. Consequently induction in its widest
sense is an ampliative process of the generalization of knowledge. Peirce [1955a]
distinguished various types of induction: a common feature of all kinds of induction
is the ability to compare individual statements: by using induction it is possible 1)
to synthesize individual statements into general laws – inductive generalizations –
in a defeasible way, but 2) it is also possible to confirm or discount hypotheses.
Following Peirce, I am clearly referring here to the latter type of induction, that
in the ST-model is used as the process of reducing the uncertainty of established
hypotheses by comparing their consequences with observed facts.23 Some authors
stress that abduction and induction derive from a common source, the hypothetical
or non-deductive reasoning, others emphasize the various aspects that distinguish
them, that is how specifically abduction and induction extend our knowledge. In
other cases it is affirmed that all non-deductive reasoning is of the same type, which
is called induction [Flach and Kakas, 2000a].
Further classifications of inductive arguments have been proposed, such as arguments based on samples, (that is inductive generalizations), arguments from analogy, and statistical syllogisms [Salmon, 1990]. Finally, we have to remember that
in the case of the so-called inductive logic [Carnap, 1950] the aim is to solve the
problem of knowing the degree of belief we should attribute to the hypothetical
conclusion H, given evidence E collected in the premises of an inductive argument,
that is identified with the conditional probability P(H|E). This formalization of the
inductive support is also called confirmation theory: it does not deal with the problem of individuating the ways of “generating” inductive hypotheses but refers to
a logic of hypothesis “evaluation”. Abduction creates or selects hypotheses; from
these hypotheses consequences are derived by deduction that are compared with the
available data by induction. This perspective on hypothesis testing in terms of induction is also known in philosophy of science as the “hypothetico-deductive method”
[Hempel, 1966] and is related to the idea of confirmation of scientific hypotheses,
22
23
I have illustrated the problem of diagnosis, therapy, and monitoring and the related AI computational programs in [Magnani, 2001b, chapter four].
It is possible to treat every good inductive generalization as an instance of abduction [Josephson,
2000].
14
1 Theoretical and Manipulative Abduction
predominant in neopositivistic philosophy but also present in the anti-inductivist
tradition of falsificationism [Popper, 1959].
In summary, it is important to note that if in diagnostic settings and in the classical
syllogistic framework I am illustrating in this chapter we basically refer to induction simply as a way of confirming or discounting hypotheses, in various cases of
mathematical reasoning, where model-based and manipulative abduction is at play,
induction “also” plays the usual generalizing role. In these cases the reasoners have
to produce new hypothetical knowledge, H, which extends their own preexistent
theories such that the observations on which they work can be first of all deduced
by the new abductively enriched theories. They abductively provide new individual
and situated “samples”, which offer chances for further knowledge. Each of these
abductive situated results can in turn generate further universal inductive generalizations possibly to be withdrawn because of disconfirmation; in this last case a
further cyclic abductive-inductive process can restart. The “specificity” of the generated abductive hypotheses is related to their ignorance-preserving character (cf the
following chapter, section 2.1); the “generality” of inductive hypotheses is related
to their truth-conferring/probability-enhancing character, at the same time occasionally endowed with an evaluative function. Abductively building new situated results
is in these cases central to make possible an induction able to generate new general knowledge, in these cases not reachable through abduction (further details on
the relationship between abduction and induction are illustrated below in subsection
1.4.1).24 This kind of interplay between abduction and induction is also occurring
in the mathematical case I will exploit in chapter three, subsection 3.6.2, to illustrate
important aspects of “manipulative” abduction.
Deduction is an inference that refers to a logical implication. Deduction may
be distinguished from abduction and induction on the grounds that the truth of the
conclusion of the inference is guaranteed by the truth of the premises on which it
is based only in deduction. Deduction refers to the so-called non-defeasible arguments. It should be clear that, on the contrary, when we say that the premises of an
argument provide partial support for the conclusion, we mean that if the premises
were true, they would give us good reasons – but not conclusive reasons – to accept
the conclusion. That is to say, although the premises, if true, provide some evidence
to support the conclusion, the conclusion may still be false (arguments of this type
are called inductive, or abductive, arguments).
24
I have described this specific kind of abductive/inductive process in [Magnani, 2009b], also
illustrating the research provided by [Rivera and Rossi Becker, 2007]. Taking advantage of my
concept of manipulative abduction the authors study a pedagogical framework concerning the
need of increasing knowledge on the ways in which learners (abducers) in the area of school
algebra develop their abilities. They illustrate the case of different subjects [elementary majors]
who are given sequences of figural and numerical cues which taken together comprise classes
of abstract objects such as even and odd numbers and related diagrams. These sequences are the
basis of subjects’ subsequent – multimodal (cf. this book, chapter four, section 4.1) – abductions
and inductive generalizations and/or evaluations.
1.3 What Is Abduction?
15
All these distinctions need to be exemplified. To describe how the three inferences operate, it is useful to start with a very simple example dealing with diagnostic
reasoning and illustrated (as Peirce initially did),25 in syllogistic terms:
1. If a patient is affected by a pneumonia, his/her level of white blood cells is
increased.
2. John is affected by a pneumonia.
3. John’s level of white blood cells is increased.
(This syllogism is known as Barbara).
By deduction we can infer (3) from (1) and (2). Two other syllogisms can be
obtained from Barbara if we exchange the conclusion (or Result, in Peircean terms)
with either the major premise (the Rule) or the minor premise (the Case): by induction we can go from a finite set of facts, like (2) and (3), to a universally quantified
generalization – also called categorical inductive generalization, like the piece of
hematologic knowledge represented by (1) (in this case we meet induction as the
ability to generate simple laws, contrasted with induction as a way to confirm or
discard hypotheses, cf. above).26 Starting from knowing – selecting – (1) and “observing” (3) we can infer (2) by performing a selective abduction.27 The abductive
inference rule corresponds to the well-known fallacy called affirming the consequent
(simplified to the propositional case)
ϕ →ψ
ψ
ϕ
It is useful to give another example, describing an inference very similar to the
previous one:
1. If a patient is affected by a beta-thalassemia, his/her level of hemoglobin A2 is
increased.
2. John is affected by a beta-thalassemia.
3. John’s level of hemoglobin A2 is increased.
Such an inference is valid, that is not affected by uncertainty, since the manifestation (3) is pathognomonic for beta-thalassemia (as expressed by the biconditional
in ϕ ↔ ψ ). This is a special case, where there is no abduction because there is
no “selection”, in general clinicians very often have to deal with manifestations
25
26
27
Some authors [Flach and Kakas, 2000a; Aliseda, 2000] distinguish between Peircean early syllogistic theory and his later “inferential” one, in which abduction refers to the whole hypothesis
formation component of explanatory reasoning (cf. below section 1.5).
We can consider this inference a sort of generalization from a sample of patients [or of beans]
to the whole population of them [or of beans in the bag].
We have to remark that at the level of the syllogistic treatment of the subject Peirce calls this kind
of argumentation “hypothesis”; he will introduce the term abduction only in his later theory.
16
1 Theoretical and Manipulative Abduction
which can be explained by different diagnostic hypotheses: in this case the inference
rule corresponds to
ϕ ↔ψ
ψ
ϕ
Thus, selective abduction is the making of a preliminary guess that introduces a set
of plausible diagnostic hypotheses, followed by deduction to explore their consequences, and by induction to test them with available patient data, (1) to increase
the likelihood of a hypothesis by noting evidence explained by that one, rather than
by competing hypotheses, or (2) to refute all but one (cf. Figure 1.3.)
Structuring
Diagnostic
Space
Diagnostic
Hypotheses
Abduction
Clinical
Evidences
to be explained
Induction
Deduction
Abstraction
Observed
Data
Expected
Data
Request
new Data
Fig. 1.3 ST-Model. The epistemological model of diagnostic reasoning.
If during this first cycle new information emerges, hypotheses not previously considered can be suggested and a new cycle takes place. In this case the nonmonotonic
character of abductive reasoning is clear and arises from the logical unsoundness of
1.3 What Is Abduction?
17
the inference rule: it draws defeasible conclusions from incomplete information.28
All recent logical accounts (“deductive”) concerning abduction have pointed out
that it is a form of nonmonotonic reasoning. It is important to allow the guessing
of explanations for a situation, in order to discount and abandon old hypotheses, so
as to enable the tentative adoption of new ones, when new information about the
situation makes them no longer the best.29
As [Stephanou and Sage, 1987] pointed out, uncertainty and imperfect information are fundamental characteristics of the knowledge relative to hypothetical reasoning. The nonmonotonic character of the ST-model arises not only from the above
mentioned nonmonotonic character of deductive inference type involved in it, but
also from the logical unsoundness of the ascending part of the cycle guessing hypotheses to be tested. [Doyle, 1988] pointed out that, since their unsoundness, these
guesses do not exhibit the truth-preservative behavior of ideal rationality characterizing the incremental deduction of classical logic, but the nonmonotonic behavior
of limited rationality of commonsense reasoning [Simon, 1969], that allows to discharge and abandon old hypotheses to make possible the tentative adoption of new
ones. Notice that this adoption is not merely tentative but rationally tentative, in
the sense that, just as abduction, it is based on a reasoned selection of knowledge
[Truesdell, 1984] and on some preference criteria which avoid the combinatorial
explosion of hypotheses generation.
One of the principal means of limiting rationality is indeed to limit efforts by directing attention to some areas and ignoring others. This character matches exactly
with the ability of an expert in generating a small set of hypotheses to be carefully
tested. But in such a case, the expert has to be ready to withdraw paths of reasoning when they diverge from the correct path, that is from the path that would have
taken the expert had considering the ignored knowledge portions. In such a way,
the nonmonotonic character turns out as a foundational epistemological feature of
the ST-model of medical reasoning, since this nonmonotonic character is the result
not of a mere lack of information but of a reasoned limiting of information imposed
by its own logical unsoundness. Finally, we have to remember that in the ST-model
the first meaning (see above) of the word abduction is adopted: abduction that only
generates “plausible” hypotheses (of course in this case selective).
Modern logic allows us to account for this dynamic behavior of abduction also
by the concept of belief revision. Belief revision [Alchourrón et al., 1985] is a
28
29
A logical system is monotonic if the function Theo that relates every set of wffs to the set of
their theorems holds the following property: for every set of premises S and for every set of
premises S , S ⊆ S implies Theo(S) ⊆ Theo(S ). Traditional deductive logics are always monotonic: intuitively, adding new premises (axioms) will never invalidate old conclusions. In a nonmonotonic system, when axioms, or premises, increase, their theorems do not [Ginsberg, 1987;
Lukaszewicz, 1970; Magnani and Gennari, 1997]. Following this deductive nonmonotonic view
of abduction, we can stress the fact that in actual abductive medical reasoning, when we increase
symptoms and patients’ data [premises], we are compelled to abandon previously derived plausible diagnostic hypotheses [theorems], as already – epistemologically – illustrated by the STmodel.
The relationship in practical reasoning between nonmonotonicity and scant resources of effort
and time is treated in the recent [Gabbay and Woods, 2008].
18
1 Theoretical and Manipulative Abduction
dynamic notion dealing with the current stage of reasoning. At each stage of reasoning, if it is correct, a belief is held on the basis that that reasoning is justified, even
if subsequent stages dictate its retraction. A logic of belief for abduction has been
proposed by [Levesque, 1989], and the role of belief revision functions in abduction
has already been studied by [Jackson, 1989] (cf. below section 1.4). Clearly abduction in medical diagnostic reasoning can be seen as an example of nonmonotonic
deduction.30
1.3.2
Abduction as Hypothesis Generation, Abduction as
Hypothesis Generation and Evaluation
As stated above, there are two main epistemologico/cognitive meanings of the word
abduction: (1) abduction that only generates plausible hypotheses (selective or creative) – this is the meaning of abduction accepted in my epistemological model –
and (2) abduction considered as inference to the best explanation, that also evaluates hypotheses by induction. In the latter sense the classical meaning of selective
abduction as inference to the best explanation (for instance in medicine, to the best
diagnosis) is described by the complete abduction–deduction–induction cycle. This
distinction needs further clarification.
It is clear that the two meanings are related to the distinction between hypothesis generation and hypothesis evaluation, so abduction is the process of generating
explanatory hypotheses, and induction matches the hypothetico-deductive method
of hypothesis testing (1st meaning). However, we have to remember (as we have already stressed) that sometimes in the literature (and also in Peirce’s texts) the word
abduction is also referred to the whole cycle, that is as an inference to the best explanation (2nd meaning).
As Thagard has pointed out [1988, p. 53] the question was controversial in Peirce’s
writings too. Before the 1890s, Peirce discussed the hypothesis as follows: “Hypothesis is where we find some very curious circumstance which would be explained by the
supposition that it was the case of a certain general rule, and thereupon adopt that supposition” [Peirce, 1931-1958, 2.624]. When Peirce replaced hypothesis with abduction he said that it “furnishes the reasoner with the problematic theory which induction
verifies” [Peirce, 1931-1958, 2.776]. Thagard ascribes to the editors of Peirce’s work
the responsibility for having clouded this change in his thinking by including discussions of hypothesis under the heading of “Abduction”, “[. . . ] obscuring his shift from
the belief that inference to an explanatory hypothesis can be a kind of justification to
the weaker view that it is only a form of discovery”. The need for a methodological
criterion of justification is caused by the fact that – at least in the Peircean framework
– an abduced hypothesis that explains a certain puzzling fact should not be accepted
30
A more detailed description of abductive reasoning in diagnosis (and in “medical” diagnosis) is
provided in my book [Magnani, 2001b, chapter four] and in [Gabbay and Woods, 2005, chapter six]. An interesting recent exploitation of genetic algorithms and computational paradigms
inspired by the natural evolution to model abduction in medical diagnosis is illustrated in
[Romdhane and Ayeb, 2009].
1.3 What Is Abduction?
19
because of the possibility of other explanations. Having a hypothesis that explains a
certain number of facts is far from a guarantee of being true.
In the previous section I have noted that when we speak of abduction as inference
to the best explanation, we have to add that the adjective “best” has to be taken in a
Pickwickian sense: the idea that the concept of abduction would always also strictly
involve its empirical evaluation by induction contrasts with its primitive character
of ignorance preserving cognition. In this perspective abduction does not have to
be considered a “solution” of a problem, because it only calls for a response to it,
with the aim of mitigating ignorance. I think that it is on this basis that Gabbay
and Woods contend, in their book on abduction that “A decision to send a proposition (etc.) to experimental trial is neither necessary nor sufficient for its abduction”
[Gabbay and Woods, 2005, p. 86]. All the more reason to unlink the idea of abduction as inference to best explanation from the processes of experimental evaluation.
Abduced hypotheses are adopted as a positive basis for action in various ways and
for various reasons (only subclasses of abductive hypotheses are adopted only after
a Peircean process of inductive empirical evaluation).
It is important to note that already at the generation phase of genuine abduction
many processes – so to say – of a kind of confrontation (if not exactly of evaluation) with something external to the individual brain, even if not due to experimental
tests, can be present, so that we can say (as I noted above in the previous section)
that abduction considered as a way of generating hypotheses is often of course immediately a generation of “plausible” hypotheses; that is hypotheses which can be
“adopted” in so far as they are considered sufficiently plausible. The presence of
these continuous stages of confrontation/coordination with external constrained and
fruitful cognitive offerings will be better grasped thanks to the concept of manipulative abduction, which takes into account the external dimension of abductive
reasoning (see below in this chapter, subsection 1.5.2 and section 1.6), and later on
in chapters two and three:
1. in chapter two (subsection 2.3.1) I will illustrate the various ways plausibility is achieved already at the inner level (off-line) of thinking of the abductive
human agent; I will also consider the so-called strategical plausibility, where
abductions are adopted without any need of the empirical inductive tests;
2. in chapter three (section 3.6) I will describe how the on-line interplay between
internal and external representations, both mimetic and creative, guarantees
to abductive cognition a continuous multimodal confrontation with respect to
something external to the individual brain activity, thanks to the dynamical interaction between the meaningful semiotic internal resources and devices and
the externalized semiotic materiality already stocked in the environment. It is in
this interplay that both the abductive result and its plausibility grow;
3. in this light the experimental test properly involved in the Peircean evaluation
phase, which for many scholars reflects in the most acceptable way the idea of
abduction as inference to the best explanation, enters a subclass of the processes
of adoption of abductive hypotheses. Hence, this experimental test can be acceptably considered external to the nature of abductive cognition, and inductive
in its essence.
20
1 Theoretical and Manipulative Abduction
Let us come back to the problem of evaluation. In a subclass of cognitive tasks,
especially the ones that aim at honoring the rational or epistemic value of empirical
evidence and of scientific mentality or methods (for example in science and medical diagnosis), to achieve the best explanation involves having or establishing a set
of criteria for evaluating the competing explanatory hypotheses reached by creative
or selective abduction, also contemplating the experimental test. The combinatorial
explosion of alternatives that has to be considered makes the task of finding the best
explanation (as I have already said, in the sense of the provisionally most acceptable explanation) very costly. Peirce surely thinks abduction has to be explanatory,
but also capable of experimental verification (that is evaluated inductively, cf. the
model above), and economic (this includes the cost of verifying the hypothesis, its
basic value, and other factors). Evaluation has a multi-dimensional and comparative
character. Following Peirce the economics of abduction is driven in turn by three
common factors: the cost of testing [Peirce, 1931-1958, 1.120], the intrinsic appeal
of the hypothesis, e.g., its simplicity, [5.60 and 6.532], where simplicity seems to
be a matter of naturalness [2.740]; and the consequences that a hypothesis might
have for future research, especially if the hypothesis proposed were to break down
[7.220].
Consilience [Thagard, 1988] can measure how much a hypothesis explains, so it
can be used to determine whether one hypothesis explains more of the evidence (for
instance, in diagnosis empirical or patient data) than another: thus, it deals with a
form of corroboration. In this way a hypothesis is considered more consilient than
another if it explains more “important” (as opposed to “trivial”) data than the others
do. In inferring the best explanation, the aim is not the sheer amount of data explained, but its relative significance. The assessment of relative importance presupposes that an inquirer has a rich background knowledge about the kinds of criteria
that concern the data. The evaluation is strongly influenced by Ockham’s razor: simplicity too can be highly relevant when discriminating between competing explanatory hypotheses; for example, it deals with the problem of the level of conceptual
complexity of hypotheses when their consiliences are equal.
Explanatory criteria are needed because the rejection of a hypothesis requires
demonstrating that a competing hypothesis provides a better explanation. Clearly,
in some cases – for instance when choosing scientific hypotheses or theories, where
the role of “explanation” is dominant – conclusions are reached according to rational criteria such as consilience or simplicity. In [Magnani, 2001b, chapter four]
I have illustrated that in the case of selecting diagnostic hypotheses the epistemic
reasons are dominant, whereas, in the case of selecting therapies, epistemic reasons
are of course intertwined with pragmatic and ethical reasons, which will play a very
important role. Hence, in reasoning to the best explanation, motivational, ethical or
pragmatic criteria cannot be neglected. Indeed the context suggests that they are unavoidable: as we have just mentioned, this is for example true in some part of medical reasoning (in therapy planning), but scientists that must discriminate between
competing scientific hypotheses or competing scientific theories have to recognize
that sometimes they too are conditioned by motivationally biasing their inferences
1.3 What Is Abduction?
21
to the best explanation. Some epistemologists, like [Kuhn, 1962] and [Feyerabend,
1975], argued that in science these extra-rational motivation are unavoidable.
For example, the so-called theory of explanatory coherence [Thagard, 1989;
Thagard, 1992] introduces seven ideal principles of plausibility that occurs in the
acceptation of new hypotheses and theories in science;31 the theory is susceptible to
be treated at the computational level using a local connectionist network.
Josephson has stressed that evaluation in abductive reasoning has to be referred
to the following criteria
1.
2.
3.
4.
How a hypothesis surpasses the alternatives.
How the hypothesis is good in itself.
Its confidence in the accuracy of the data.
How thorough was the search for alternative explanations [Josephson, 1998].
There is no agreement about which preference criteria to adopt. [Hendricks and
Faye, 1999], speak, in the case of science, about correctness (concerning the world
that it is investigating), empirical adequacy, simplicity (different kinds of), unification, consistency, practical usability, economy. [Poole and Rowen, 1990] list several
criteria that have been proposed in the literature and it can be shown that some of
these preference criteria are conflicting, i.e. in the same situation, they favor different conjectures. The problem is that all the proposed criteria do not work in all
situations: they are in some sense context dependent. For instance, the (syntactic)
criterion of minimality described by the sentential models of abduction (cf. the following section), is useless when the conjecture at hand is (syntactically) as simple
as the conflicting conjectures.
We can also use mathematical probability to select among hypotheses evaluating
them (Bayes’s Theorem itself can be viewed as a modality for weighing alternative
hypotheses [Krauss et al., 1999], of course in case the appropriate knowledge of
probabilities is present).32
The epistemological model (ST-model) I have previously illustrated should also
be regarded as a very simple and schematic illustration of scientific theory change.
In this case selective abduction is replaced by creative abduction and there exists
a set of competing theories instead of diagnostic hypotheses. Furthermore the language of background scientific knowledge should be regarded as open: in the case
of competing theories, as they are studied using the epistemology of theory change,
we cannot – contrary to Popper’s initial viewpoint [Popper, 1959] – reject a theory
simply because it fails occasionally. If for example such a theory is simpler and
31
32
The theory also fruitfully applies, with slight modifications, to many other fields like conceptual combination; adversarial problem-solving, when one has to infer an opponent’s intentions;
analogical reasoning; jury decisions in murder trials: contemporary debates about why the dinosaurs became extinct; psychological experiments on how beginning students learn physics;
ethical deliberation; emotional decision.
On the relationiships between probabilism and explanationism and on the fact that probabilism
is not appropriate to model abductive reasoning of actual individual human agents cf. [Gabbay
and Woods, 2005, chapter six].
22
1 Theoretical and Manipulative Abduction
explains more significant data than its competitors, then it can be accepted as the
best explanation.33
As already stressed, in accordance with the epistemological model previously
illustrated, medical reasoning may be broken down into two different phases: first,
patient data is abstracted and used to select hypotheses, that is hypothetical solutions
of the patient’s problem (selective abduction phase); second, these hypotheses provide the starting conditions for forecasts of expected consequences which should be
compared to the patient’s data in order to evaluate (corroborate or eliminate) those
hypotheses which they come from (deduction-induction cycle).
If we consider the epistemological model as an illustration of medical diagnostic
reasoning, the modus tollens is very efficacious because of the fixedness of language
that expresses the background medical knowledge: a hypothesis that fails can nearly
always be rejected immediately.
When Buchanan illustrates the old epistemological method of induction by elimination (and its computational meaning, evident if we add a “heuristic search”, to
limit the exhaustive enumeration of the derived hypotheses), first advanced by Bacon and Hooke and developed later on by John Stuart Mill, he is referring implicitly
to my epistemological framework in terms of abduction, deduction and induction,
as illustrative of medical diagnostic reasoning:
The method of systematic exploration is [. . . ] very like the old method of induction by
elimination. Solutions to problems can be found and proved correct, in this view, by
enumerating possible solutions and refuting all but one. Obviously the method is used
frequently in contemporary science and medicine, and is as powerful as the generator
of possibilities. According to Laudan, however, the method of proof by eliminative
induction, advanced by Bacon and Hooke, was dropped after Condillac, Newton, and
LeSage argued successfully that it is impossible to enumerate exhaustively all the hypotheses that could conceivably explain a set of events. The force of the refutation
lies in the open-endedness of the language of science. Within a fixed language the
method reduces to modus tollens [. . . ]. The computational method known as heuristic search is in some sense a revival of those old ideas of induction by elimination,
but with machine methods of generation and search substituted for exhaustive enumeration. Instead of enumerating all sentences in the language of science and trying each one in turn, a computer program can use heuristics enabling it to discard
large classes of hypotheses and search only a small number of remaining possibilities
[Buchanan, 1985, pp. 97–98].
33
Rigourously speaking, [Gabbay and Woods, 2005, p. 137] usefully point out the following
general result concerning abduction, which further stresses its ignorance preserving character:
“If (H) is the conclusion of and abductive inference and H is subsequently shown to be false, this
discredits neither the conclusion C(H) nor the conclusion H c . Corollary 5.12(a) This shows the
importance of recognizing that the conclusions of abductions imbed (often implicitly) temporal
parameters.” [The meaning of the notations C(H) and H c is explained in the following chapter,
subsection 2.1.1].
1.4 Sentential Abduction
1.4
23
Sentential Abduction
Sentential abduction can be rendered in different ways. For example, in the syllogistic framework we have just described abduction is considered like something
propositional and as a type of fallacious reasoning. If we want to model abduction
in a computational logic-based system, the fundamental operation is search [Thagard, 1996]. When there is a problem to solve, we usually face several possibilities
(hypotheses) and we have to select the suitable one (cf. selective abduction, above).
Accomplishing the assigned task requires that we have to search through the space
of possible solutions to find the desired one. In this situation we have to rely on
heuristics, that are rules of thumb expressed in sentential terms that help in arriving at satisfactory choices without considering all the possibilities. An example of
simple heuristic could be a rule like “Wear green socks with white pants but not
with blue pants”. The famous concept of heuristic search, which is at the basis of
many computational systems based on propositional rules (cf. chapter two, section
2.7) can perform this kind of sentential abduction (selective). Of course other computational tools can be used to this aim, like neural and probabilistic networks, and
frames-like representations.
Another important way of modeling abduction in a sentential way resorts to the
development of suitable logical systems, that in turn are computationally exploitable
in the area of the so-called logic programming (cf. section 1.4.1, below).
Many attempts have been made to model abduction by developing some formal
tools in order to illustrate its computational properties and the relationships with
the different forms of deductive reasoning (see, for example, [Bylander et al., 1991;
Console et al., 1991; Console and Torasso, 1991; Coz and Pietrsykowski, 1986;
Raedt and Bruynooghe, 1991; Jackson, 1989; Kakas et al., 1993; Konolige, 1992;
Josephson and Josephson, 1994; Levesque, 1989; O’Rorke, 1994; Poole, 1988;
Reiter, 1987; Reiter and de Kleer, 1991; Shanahan, 1989]).
Some of the formal models of abductive reasoning, for instance [Boutilier and
Becher, 1995], are based on the theory of the epistemic state of an agent [Alchourrón et al., 1985; Gärdenfors, 1988; Gärdenfors, 1992], where the epistemic
state of an individual is modeled as a consistent set of beliefs that can change by
expansion and contraction (belief revision framework).34
Deductive models of abduction may be characterized as follows. An explanation
for β relative to background theory T will be any α that, together with T , entails
β (normally with the additional condition that α ∪ T be consistent). Such theories
are usually generalized in many directions: first of all by showing that explanations entail their conclusions only in a defeasible way (there are many potential
explanations), thus joining the whole area of so-called nonmonotonic logic or of
probabilistic treatments; second, trying to show how some of the explanations are
relatively implausible, elaborating suitable technical tools (for example in terms
of modal logic) able to capture the notion of preference among explanations (cf.
Figure 1.4).
34
Levi’s theory of suppositional reasoning is also related to the problem of “belief change”
[Levi, 1996].
24
1 Theoretical and Manipulative Abduction
DEDUCTIVE MODELS
OF ABDUCTION
Generalizations
An explanation for E
relative to background
theory T will be any D that,
together with T, entails E
(normally with the
additional condition that
{D} ‰ 7 be consistent)
Explanations are relatively
implausible. Suitable technical
tools able to capture the notion of
preference among explanations
Some of the explanations entail their
conclusion only in a defeasible way
(there are many potential
explanations) - Nonmonotonicity -
Fig. 1.4 Deductive models of abductive reasoning
Hence, we may require that an explanation makes the observation simply sufficiently probable [Pearl, 1988] or that the explanations that are more likely will be
the “preferred” explanations: the involvement of a cat in breaking the glass can be
considered less probable than the effect of wind. Finally, the deductive model of
abduction does not authorize us to explain facts that are inconsistent with the background theory notwithstanding the fact that these explanations are very important
and ubiquitous, for instance in diagnostic applications, where the facts to be explained contradict the expectation that the system involved is working according to
specification.
[Boutilier and Becher, 1995] provide a formal account of the whole question
in term of belief revision: if believing A is sufficient to induce belief in B, then
A (epistemically) explains B; the situation can be semantically illustrated in terms
of an ordering of plausibility or normality which is able to represent the epistemic state of an agent. The conflicting observations will require explanations that
compel the agent to withdraw its beliefs (hypotheses), and the derived conditional
logic is able to account for explanations of facts that conflict with the existing beliefs. The authors are able to reconstruct, within their framework, the two main
paradigms of model-based diagnosis, abductive [Poole, 1988; Poole, 1991], and
1.4 Sentential Abduction
25
IS SUCH THAT D IS
NO LONGER HELD
WITHOUT ADDING
NEW FACTS
EXPANSION
K + D
CONTRACTION
K - D
REVISION
K·D
REGARDLESS OF
WHETHER THE LARGER
SET IS CONSISTENT
BELIEF CHANGE
BELIEF
REVISION HAPPENS WHEN K ² ™D,
THAT IS WHEN THE NEW D IS
INCONSISTENT WITH K AND WE
WANT TO MAINTAIN CONSISTENCY
SOME BELIEFS OF K MUST BE
WITHDRAWN BEFORE D CAN BE
ACCOMODATED: K · D
Fig. 1.5 Belief-revision
consistency-based [de Kleer et al., 1990; Reiter, 1987], providing an alternative
semantics for both in terms of a plausibility ordering over possible worlds.
Let us resume the kinds of change considered in the original belief revision
framework (see Figure 1.5). The expansion of a set of beliefs K taken from some
underlying language (considered to be the closure of some finite set of premise KB,
or knowledge base, so K = Cn(KB)) by a piece of new information A is the belief
set K + A = Cn(K ∪ A). The addition happens “regardless” of whether the larger set
is consistent. The case of revision happens when K |= ¬A, that is when the new A is
inconsistent with K and we want to maintain consistency: some beliefs in K must be
withdrawn before A can be accommodated: K · A. The problem is that it is difficult
to detect which part of K has to be withdrawn. The least “entrenched” beliefs in K
should be withdrawn and A added to the “contracted” set of beliefs. The loss of information has to be as small as possible so that “no belief is given up unnecessarily”
[Gärdenfors, 1988]. Hence, inconsistency resolution in belief revision framework is
captured by the concept of revision. Another way of belief change is the process of
contraction. When a belief set K is contracted by A, the resulting belief set K + A is
such that A is no longer held, without adding any new fact.35
35
[Aliseda, 1997; Aliseda, 2000] makes use of the belief revision framework to construct a theory
of the epistemic transition between the states of doubt and belief able to account for many
aspects of abductive reasoning. On the relationships between belief revision dynamics in data
bases and abduction cf. [Aravindan and Dung, 1995].
26
1 Theoretical and Manipulative Abduction
After having explained the distinction between predictive explanations and
“might” explanations, that merely allow an observation, and do not predict it,
Boutilier and Becher show in the cited article how model-based diagnoses can be
accounted for in terms of their new formal model of belief revision.
The abductive model-based reasoning36 [Poole, 1988; Poole, 1991; Brewka,
1989] illustrated by some models, such as Poole’s Theorist, allows many possible explanations, weak and predictive (so presenting a paraconsistent behavior: a
non-predictive hypothesis can explain both a proposition and its negation). This old
model, embedded in the new formal framework, acquires the possibility of discriminating certain explanations as preferred to others.
Reiter’s consistency-based diagnosis [Reiter, 1987] is devoted to ascertain why a
correctly designed system is not working according to its features. Because certain
components may fail, the system description also contains some abnormality predicates (the absence of them will render the description inconsistent with an observation of an incorrect behavior). The consistency-based diagnosis concerns any set of
components whose abnormality makes the observation consistent with the description of the system. A principle of parsimony is also introduced to capture the idea of
preferred explanations/diagnoses. Since the presence of fault models renders Reiter’s
framework incorrect, new more complicated notions are introduced in [de Kleer et
al., 1990], where the presence of a complete fault model ensures that predictive explanations may be given for “every” abnormal observation. Without any description
of correct behavior any observation is consistent with the assumption that the system works correctly. Hence, a complete model of correct behavior is necessary if we
want the consistency-based diagnosis to be useful.
The idea of consistency that underlies some of the recent deductive consistencybased models of selective abduction (diagnostic reasoning) is the following: any
inconsistency (anomalous observation) refers to an aberrant behavior that can usually be accounted for by finding some set of components of a system that, if behaving abnormally, will entail or justify the actual observation. The observation is
anomalous because it contradicts the expectation that the system involved is working
according to specification. This types of deductive model go beyond the mere treatment of selective abduction in terms of preferred explanations and include the role
of those components whose abnormality makes the observation (no longer anomalous) consistent with the description of the system [Boutilier and Becher, 1995;
Magnani, 2001a].
Without doubt the solution given by Boutilier and Becher furnishes a more
satisfying qualitative account of the choice among competing explanations than
Gärdenfors’ in terms of “epistemic entrenchment”37 which tries to capture the idea
of an ordering of beliefs according to our willingness to withdraw them when
36
37
Please distinguish here the technical use of the attribute model-based from the epistemologicalcognitive one I am introducing in this chapter.
Which of course may change over time or with the state of belief.
1.4 Sentential Abduction
27
necessary. Moreover, the new formal account in terms of belief revision is very powerful in shedding new light on the old model-based accounts of diagnostic reasoning.
The framework of belief revision is sometimes called coherence approach [Doyle,
1992]. In this approach, it is important that the agent holds some beliefs just as long
as they are consistent with the agent’s remaining beliefs. Inconsistent beliefs do
not describe any world, and so are unproductive; moreover, the changes must be
epistemologically conservative in the sense that the agent maintains as many of its
beliefs as possible when it adjusts its beliefs to the new information. It is contrasted
to the foundations approach, according to which beliefs change as the agent adopts
or abandons satisfactory reasons (or justifications). This approach is exemplified by
the well-known “reason maintenance systems” (RMS) or “truth maintenance systems” (TMS) [Doyle, 1979], elaborated in the area of artificial intelligence to cooperate with an external problem solver. In this approach, the role of inconsistencies
is concentrated on the negations able to invalidate justifications of beliefs; moreover, as there are many similarities between reasoning with incomplete information
and acting with inconsistent information, the operations of RMS concerning revision directly involve logical consistency, seeking to solve a conflict among beliefs.
The operations of dependency-directed backtracking (DDB) are devoted to this aim:
RMS informs DDB whenever a contradiction node (for instance a set of beliefs) becomes believed, then DDB attempts to remove reasons and premises, only to defeat
nonmonotonic assumptions: “If the argument for the contradiction node does not
depend on any of these (i.e., it consists entirely of monotonic reasons), DDB leaves
the contradiction node in place as a continuing belief” [Doyle, 1992, p. 36], so leaving the conflicting beliefs intact if they do not depend on defeasible assumptions,
and presenting a paraconsistent behavior.
Both in the coherence and foundations approach the changes of state have to be
epistemologically conservative: as already said above the agent maintains as many
of its beliefs as possible when it adjusts its beliefs to the new information, thus following Quine’s idea of “minimun mutilation” [Quine, 1979]. We have now to notice
some limitations of the formal models in accounting for other kinds of inconsistencies embedded in many reasoning tasks.
This kind of sentential frameworks exclusively deals with selective abduction (diagnostic reasoning)38 and relates to the idea of preserving consistency. Exclusively
considering the sentential view of abduction does not enable us to say much about
creative processes in science, and, therefore, about the nomological and most interesting creative aspects of abduction. It mainly refers to the selective (diagnostic)
aspects of reasoning and to the idea that abduction is mainly an inference to the best
explanation [Magnani, 2001b]: when used to express the creative events it is either
empty or replicates the well-known Gestalt model of radical innovation. It is empty
because the sentential view stops any attempt to analyze the creative processes: the
38
As previously indicated, it is important to distinguish between selective (abduction that merely
selects from an encyclopedia of pre-stored hypotheses), and creative abduction (abduction that
generates new hypotheses).
28
1 Theoretical and Manipulative Abduction
event of creating something new is considered so radical and instantaneous that its
irrationality is immediately involved.39
Already in the Peircean syllogistic and sentential initial conception of abduction – as the fallacy of affirming the consequent, we immediately see it is perfectly
compatible with the Gestalt model of discovery. In the syllogistic model the event
of creating something new (for example a new concept) is considered external to
the logical process, so radical and instantaneous that its irrationality is immediately
involved. In this case the process is not considered as algorithmic: “the abductive
suggestion comes to us like a flash. It is an act of insight, although of extremely
fallible insight” [Peirce, 1931-1958, 5.181]. Moreover, Peirce considers abduction
as “a capacity of guessing right”, and a “mysterious guessing power” common to all
scientific research [Peirce, 1931-1958, 6.530].
Notwithstanding its non-algorithmic character it is well known that for Peirce
abduction is an inferential process (for an explanation of the exact meaning of the
word “inference” cf. below section 1.5). Hence abduction has to be considered as
a kind of ampliative inference that, as already stressed, is not logical and truth preserving: indeed valid deduction does not yield any new information, for example
new hypotheses previously unknown: abduction
[. . . ] is logical inference [. . . ] having a perfectly definite logical form. [. . . ] The form
of inference, therefore, is this:
The surprising fact, C, is observed;
But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true [Peirce, 1931-1958, 5.188-189, 7.202].
C is true of the actual world and it is surprising, a kind of state of doubt we are not
able to account for by using our available knowledge. C can be simply a novel phenomenon or may be in conflict with the background knowledge, that is anomalous.
To conclude, if we want to provide a suitable framework for analyzing the most
interesting cases of conceptual change in science we do not have to limit ourselves
39
Research into the logic of abduction has increased over recent years. I have edited special issues of journals and proceedings which present various articles on this subject. [Reyes et al.,
2006] propose a notion of abductive problems, N-abductive, which helps to provide an effective procedure for finding abductive solutions in first-order logic, by means of a modification
of Beth’s tableaux. [Carnielli, 2006] shows that the robust logics of formal inconsistency, a
particular category of paraconsistent logics which permit the internalization of the concepts of
consistency and inconsistency inside the object language, provide simple and yet powerful techniques for automatic abduction; moreover, the whole procedure is capable of automatization by
means of the tableau proof-procedures available for such logics. [Inoue and Sakama, 2006]
focus on the problem of identifying the equivalence of two abductive theories represented
in first-order logic. [Bharathan and Josephson, 2006] suggest taking advantage of the specific
structure of abductive reasoning to identify revision candidates among earlier beliefs, to propose specific revisions, to select among possible revisions, and to make the requisite changes to
the system of beliefs; these adjustments are performed through meta-abductive processing over
the recorded steps in an abductive agent’s reasoning trace. Finally, on algorithms for diagnostic reasoning cf. [Luan et al., 2006; Shangmin et al., 2007], on abduction and counterfactuals
and conditionals cf. [Pizzi, 2006; Pizzi, 2007], on abduction and fallacies cf. [Woods, 2007;
Woods, 2010].
1.4 Sentential Abduction
29
to the sentential view of theoretical abduction but we have to consider a broader
inferential one which encompasses both sentential and what I call model-based sides
of creative abduction (see, for details, section 1.5 below). The abductive inference
includes all the operations whereby hypotheses and theories are constructed [Peirce,
1931-1958, 5.590] (see also [Hintikka, 1998]).
1.4.1
Abduction and Induction in Logic Programming
The syllogistic account of abduction we described above is the starting point of
much research in AI and logic programming devoted to perform tasks such as
diagnosis in medical reasoning and planning. In these logical and computational
accounts abduction and induction are considered as separate forms of reasoning
related to different tasks. Consequently, the distinction is very variable, contextdependent and different from the one we have seen operating in Peircean texts
(where, as illustrated in subsection 1.3.2, abduction is especially – but not only viewed as hypothesis generation and induction as a logic of hypothesis evaluation).
In a classical book edited by [Flach and Kakas, 2000b], many interesting contributions are dedicated to the analysis of the distinction between abductive and
inductive reasoning.40 Usually in these types of research abductive hypotheses are
considered as providing explanations, and inductive hypotheses as providing generalizations: this explains, for example, why diagnosis is generally considered in
AI like abductive and concept learning from examples inductive.41 Usually abduction is regarded as reasoning from specific observations to their explanations, and
induction as a Millian enumerative induction from samples to general statements.
In the case of the abductive logic programming (ALP), and assuming a common first-order language, possible abductive hypotheses are built from specific nonobservable predicates Δ called abducibles (suitably distinguished from observable
predicates). The problem is to be able to “select” among the so-called abductive
extensions T (Δ p) of of T in which the given observation to be explained holds,
by selecting the corresponding formula Δ . On the contrary, in the case of inductive
logic programming (ILP) the problem is to “select” a generalizing hypothesis able
to entail additional observable information on unobserved individuals (that is predictions), finding new individuals for which the addition of the hypothesis to our
knowledge is necessary to derive some observable properties for them [Console and
Saitta, 2000]. In the first case the abductive explanation Δ needs a given theory T ,
so it is “relative” to a “certain” theory T from which it is produced. In the case of
induction the explanation does not depend on a particular theory: we can say that
“all the beans from this bag are white” (Peirce’s example, see above, subsection
1.3.1, this chapter), is an explanation for why the observed beans from the bag are
white: this explanation does is in accordance with a particular model of the “world
of beans” [Flach and Kakas, 2000a].
40
41
Cf. also the clear article by [Console et al., 1991].
An overview on the relationships between abduction and induction is given in [Bessant,
2000].Cf. also the various contributions given by Abe; Christiansen; Inoue and Haneda;
Mooney; Poole; Psillos; Sakama; Yamamoto, in [Flach and Kakas, 2000b].
30
1 Theoretical and Manipulative Abduction
Moreover, we can say that abductions explain a phenomenon by indicating enabling conditions like causes (this explains the fact that abduction needs a domain
theory, often a causal theory, while induction does not):42
If we want to explain, for instance, that the light appears in a bulb when we turn a
switch on, an inductive explanation would say that this is because it happened hundreds of time before, whereas the abductive one can supply an explanation in terms
of the electric current flowing into the bulb filament. If, at some moment, turning the
switch on does not let the light bulbs starts burning, the inductive explanation just fails,
whereas the abductive one can supply hints for understanding what happened and for
suggesting remedies [Console and Saitta, 2000].
Hence, the two kinds of explanations are very different and distinct, induction firstly
aims at providing generalizations, abduction explanations of particular observations.
In Console and Saitta’s terms, abductive reasoning extends the intension of known
individuals (because abducible properties are rendered true for these individuals,
for example by providing new situated “samples”, which offer chances for further
knowledge – cf. above the considerations I have illustrated at p. 14), without having a genuine generalization impact on the observables (it does not increase their
extension).43
Another interpretation of the distinction between abduction and induction is
given by [Josephson, 2000]. Following his point of view all inferences to the best explanation have to be considered as kinds of “smart” reasoning. In Josephson’s terms
induction and abduction are not distinct processes: the inductive generalization is
a type of inference that points to some best explanation, so it can be considered as
a kind of abduction (he agrees with the use of the term abduction according to the
second meaning we previously illustrated, the one including generating – or selecting – and evaluating hypotheses). “Smart” inductive generalizations (or inductive
hypotheses) do not explain “particular” observations but the frequencies with which
the observations emerge, like in the well known AI case of “concept learning from
examples”: “An observed frequency is explained by giving a causal story that explains how the frequency came to be the way it was. This causal story typically
42
43
The role of the causal-hypothetical reasoning is central in modern science: Galileo was already
perfectly aware of this fact. He insists that interesting conclusions which reach far beyond experience can be derived from few experiments because “[. . . ] the knowledge of a single fact
acquired through a discovery of its cause prepares the mind to understand and ascertain other
facts without need to recourse to experiment” [Galilei, 1914, p. 296]: in the case of his study
of projectiles, once we know that their path is a parabola, we can derive using only pure mathematics, that their maximum range is 45◦ . Moreover, Newton says, using the ancient notion of
“analysis”: “By this way of analysis we may proceed from compounds to ingredients, and from
motions to the forces producing them; and in general, from effects to their causes, and from
particular causes to more general ones, [. . . ] and the synthesis consists in assuming the causes
discovered, and established as principles, and by them explaining the phenomena proceeding
from them, and proving the explanations” [Newton, 1721, p. 380 ff.].
Further results on the interaction and/or integration of abduction and induction in AI complex
theory development tasks are given in [Michalski, 1993] – in terms of coexistence; [Dimopoulos
and Kakas, 1996; Ourston and Mooney, 1994] – in terms of cooperation; [O’Rorke, 1994;
Thompson and Mooney, 1994; Kakas and Riguzzi, 1997] – on the role of inducing and learning
in abductive theories.
1.5 Model-Based Creative Abduction
31
includes both the method of drawing the sample, and the population frequency in
some reference class”.
When inductive hypothesis are “smart” or “good” they are so because they are
inferences to the best generalization-explanation of the sample frequencies, so they
can be considered as a kind of abduction. As a consequence of his ideas on abduction
and induction, Josephson concludes by arguing that the computational programs for
inductive generalizations have to be constructed abductively.
1.5
1.5.1
Model-Based Creative Abduction
Conceptual Change and Creative Reasoning in Science
The sentential models of theoretical abduction are limited, because they do not capture various reasoning tasks [Magnani, 1999]:44
1. the role of statistical explanations, where what is explained follows only probabilistically and not deductively from the laws and other tools that do the explaining;
2. the sufficient conditions for explanation;
3. the fact that sometimes the explanations consist of the application of schemas
that fit a phenomenon into a pattern without realizing a deductive inference;
4. the idea of the existence of high-level kinds of creative abductions;
5. the existence of model-based abductions (cf. the following section);
6. the fact that explanations usually are not complete but only furnish partial accounts of the pertinent evidence [Thagard and Shelley, 1997];
7. the fact that one of the most important virtues of a new scientific hypothesis
(or of a scientific theory) is its power of explaining new, previously unknown
facts: “[. . . ] these facts will be [. . . ] unknown at the time of the abduction, and
even more so must the auxiliary data which help to explain them be unknown.
Hence these future, so far unknown explananda, cannot be among the premises
of an abductive inference” [Hintikka, 1998], observations become real and explainable only by means of new hypotheses and theories, once discovered by
abduction.
We will see in the following subsection that it is in terms of model-based abductions
(and not in terms of sentential abductions) that we have to think for example of the
case of a successful synthesis of two earlier theoretical frameworks which might even
have seemed incompatible. The old epistemological view sees Einstein’s theory as an
attempt to “explain” certain anomalies and facts such as the Michelson-Morley experiment: “The most instructive way of looking at Einstein’s discovery is to see it as
44
Important developments in the field of logical models of abduction – also touching some related problems in artificial intelligence (AI) and devoted to overcome the limitations above –
are illustrated in [Flach and Kakas, 2000b] and in [Gabbay and Kruse, 2000; Gabbay and
Woods, 2005; Gabbay and Woods, 2006]. Cf. also the recent papers contained in the collections
[Magnani et al., 2002a; Magnani, 2006c].
32
1 Theoretical and Manipulative Abduction
a way of reconciling Maxwell’s electromagnetic theory with Newtonian mechanics
[. . . ] it would be ridiculous to say that Einstein’s theory ‘explains’ Maxwell’s theory any more than it ‘explains’ Newton’s laws of motion” [Hintikka, 1998, p. 510].
This kind of abductive movement does not have that immediate explanatory effect
illustrated by the sentential models of abduction: the new framework usually does
not “explain” the previous ones but provides a very radical new perspective.
If we want to deal with the nomological and most interesting creative aspects of
abduction we are first of all compelled to consider the whole field of the growth of
scientific knowledge cited above.
We have anticipated that abduction has to be an inference permitting the derivations of new hypotheses and beliefs. Some explanations consist of certain facts (initial conditions) and universal generalizations (that is scientific laws) that deductively
entail a given fact (observation), as showed by Hempel in his law covering model
of scientific explanation [Hempel, 1966]: in this case the argument starts with the
true premises and deduces the explained event. If T is a theory illustrating the background knowledge (a scientific or common sense theory) the sentence α explains
the fact (observation) β just when α ∪ T |= β , it is difficult to govern the question
involving nomological and causal aspects of abduction and explanation in the framework of the belief revision illustrated in the previous section: we would have to deal
with a kind of belief revision that permits us to alter a theory with new conditionals.
We may also see belief change (cf. the above section 1.4) from the point of view
of conceptual change, considering concepts either cognitively, like mental structures
analogous to data structures in computers, or, epistemologically, like abstractions or
representations that presuppose questions of justification. Belief revision is able to
represent cases of conceptual change such as adding a new instance, adding a new
weak rule, adding a new strong rule (see [Thagard, 1992], that is, cases of addition
and deletion of beliefs, but fails to take into account cases such as adding a new partrelation, adding a new kind-relation, adding a new concept, collapsing part of a kindhierarchy, reorganizing hierarchies by branch jumping and tree switching, in which
there are reorganizations of concepts or redefinitions of the nature of a hierarchy.
Let us consider concepts as composite structures akin to frames of the following
sort:
CONCEPT:
A kind of:
Subkinds:
A part of:
Parts:
Synonyms:
Antonyms:
Rules:
Instances:
It is important to emphasize (1) kind and part-whole relations that institute hierarchies, and (2) rules that express factual information more complex than simple slots.
To understand the cases of conceptual revolutions we need to illustrate how concepts
1.5 Model-Based Creative Abduction
33
can fit together into conceptual systems and what is involved in the replacement of
such systems. Conceptual systems can be viewed as ordered into kind-hierarchies
and linked to each other by rules.
Adding new part-relations occurs when in the part-hierarchy new parts are discovered: an example is given by the introduction of new molecules, atoms, and subatomic particles. Thomson’s discovery that the “indivisible” atom contains electrons
was very sensational.
Adding new kind-relations occurs when it is added a new superordinate kind
that combines two or more things previously taken to be distinct. In the nineteenth
century scientists recognized that electricity and magnetism were the same and constructed the new concept of electromagnetism. Another case is shown by differentiation, that is the making of a new distinction that generates two kinds of things (heat
and temperature were considered the same until the Black’s intervention).
The last three types of conceptual change can be illustrated by the following
examples. The Newtonian abandon of the Aristotelian distinction between natural
and unnatural motion exemplifies the collapse of part of the kind-hierarchy. Branch
jumping occurred when the Copernican revolution involved the recategorization of
the earth as a kind of planet, when previously it had been considered special, but
also when Darwin reclassified humans as a kind of animal. Finally, we have to say
that Darwin not only reclassified humans as animals, he modified the meaning of
the classification itself. This is a case of hierarchical tree redefinition:
Whereas before Darwin kind was a notion primarily of similarity, his theory made
it a historical notion: being of common descent becomes at least as important to
being in the same kind as surface similarity. Einstein’s theory of relativity changed
the nature of part-relations, by substituting ideas of space-time for everyday notions
of space and time [Thagard, 1992, p. 36].
These last cases are the most evident changes occurring in many kinds of creative
reasoning in science, when adopting a new conceptual system is more complex than
mere belief revision. Related to some of these types of scientific conceptual change
are different varieties of model-based abductions. In these cases the hypotheses
“transcend” the vocabulary of the evidence language, as opposed to the cases of
simple inductive generalizations: the most interesting case of creative abduction is
called by [Hendricks and Faye, 1999] trans-paradigmatic abduction. This is the case
where the fundamental ontological principles given by the background knowledge
are violated, and the new discovered hypothesis transcends the immediate empirical
agreement between the two paradigms, like for example in the well-known case of
the abductive discovery of totally new physical concepts during the transition from
classical mechanics to quantum mechanics.
To conclude, I have already said that, if we want to provide a suitable framework
for analyzing the most interesting cases of conceptual change in science we do not
have to limit ourselves to the sentential view of abduction but we have to consider
a broader inferential one which encompasses both sentential and what I call modelbased sides of creative abduction.
34
1 Theoretical and Manipulative Abduction
1.5.2
Model-Based Abduction and Its External Dimension
The last cases of creative reasoning in science we have just illustrated demonstrate
the radical conjectural character of the new concepts and the incommensurability as
regarding previous ones, that is the cases in which “revolutionary” changes happen
and the most “counterinductive” acts can become visible. The analysis of modelbased conceptual change helps us to study the revolutionary changes of science:
different varieties of what I call model-based abduction are related to some of these
types of conceptual change.
From Peirce’s philosophical point of view, all thinking is in signs, and signs can
be icons, indices or symbols. Moreover, all inference is a form of sign activity,45
where the word sign includes “feeling, image, conception, and other representation”
[Peirce, 1931-1958, 5.283], and, in Kantian words, all synthetic forms of cognition.46 That is, a considerable part of the thinking activity is model-based. Of course
model-based reasoning acquires its peculiar creative relevance when embedded in
abductive processes, so that we can individuate a model-based abduction. Hence,
we must think in terms of model-based abduction (and not in terms of sentential abduction) to explain complex processes like scientific conceptual change. Different
varieties of model-based abductions [Magnani, 1999] are related to the high-level
types of scientific conceptual change (see, for instance, [Thagard, 1992]).
For Peirce [Anderson, 1986] a Kantian keyword is synthesis, where the intellect constitutes in its forms and in a harmonic way all the material delivered by the
senses. Surely Kant did not consider synthesis as a form of inference but, notwithstanding the obvious differences,47 I think synthesis can be related to the Peircean
concept of inference, and, consequently, of abduction. After all, when describing the
ways the intellect follows to unify and constitute phenomena through imagination
Kant himself makes use of the term rule “Thus we think a triangle as an object, in
that we are conscious of the combination of the straight lines according to a rule by
which such an intuition can always be represented” [Kant, 1929, A140, B179-180,
p. 182], and also of the term procedure “This representation of a universal procedure of imagination in providing an image for a concept, I entitle the schema of
this concept” [Kant, 1929, A140, B179-180, p. 182]. We know that rules and procedures represent the central features of the modern concept of inference. Moreover,
according to Peirce, the central question of philosophy is “how synthetical reasoning
is possible [. . . ]. This is the lock upon the door of philosophy” [Peirce, 1931-1958,
5.348], and the mind presents a tendency to unify the aspects which are exhibited
by phenomena: “the function of conception is to reduce the manifold of sensuous
impressions to unity” [Peirce, 1931-1958, 1.545].
45
46
47
Cf. also [Fischer, 2001].
Also in the perspective of Thom’s catastrophe theory, it is interesting to stress that signs are
forms in space-time in its Euclidean validity, as the basic framework of all human experience.
Consequently, “their spatio-temporal localization is one of the first factors to consider” [Thom,
1980, p. 270]. Cf. also this, book, chapter eight.
For example Peirce considers space and time themselves as products of synthesis and not as
forms of intuition [Davis, 1972].
1.5 Model-Based Creative Abduction
35
Most of these forms of constitution of phenomena are creative and, moreover,
characterized in a model-based way. Let me show some examples of model-based
inferences. It is well known the importance Peirce ascribed to diagrammatic thinking, as shown by his discovery of the powerful system of predicate logic based
on diagrams or “existential graphs”. As we have already stressed, Peirce considers inferential any cognitive activity whatever, not only conscious abstract thought;
he also includes perceptual knowledge and subconscious cognitive activity [Davis,
1972]. For instance in subconscious mental activities visual representations play an
immediate role.
We may also see belief change from the point of view of conceptual change, considering concepts either cognitively, like mental structures analogous to data structures in computers, or, epistemologically, like abstractions or representations that
presuppose questions of justification. Belief revision is able to represent cases of
conceptual change such as adding a new instance, adding a new weak rule, adding
a new strong rule [Thagard, 1992], that is, cases of addition and deletion of beliefs, but fails to take into account cases such as adding a new part-relation, adding
a new kind-relation, adding a new concept, collapsing part of a kind-hierarchy, reorganizing hierarchies by branch jumping and tree switching, in which there are
reorganizations of concepts or redefinitions of the nature of a hierarchy.
We should remember, as Peirce noted, that abduction plays a role even in relatively simple visual phenomena. Visual (or iconic) abduction [Magnani et al., 1994;
Magnani, 1996], a special form of non verbal abduction, occurs when hypotheses are instantly derived from a stored series of previous similar experiences. It
covers a mental procedure that tapers into a non-inferential one, and falls into the
category called “perception”. Philosophically,48 visual perception is viewed by
Peirce as a fast and uncontrolled knowledge-production procedure. Perception, in
this philosophical perspective, is a vehicle for the instantaneous retrieval of knowledge that was previously structured in our mind through more structured inferential processes. Peirce says: “Abductive inference shades into perceptual judgment
without any sharp line of demarcation between them” [Peirce, 1955c, p. 304]. By
perception, knowledge constructions are so instantly reorganized that they become
habitual and diffuse and do not need any further testing: “[. . . ] a fully accepted,
simple, and interesting inference tends to obliterate all recognition of the uninteresting and complex premises from which it was derived” [Peirce, 1931-1958, 7.37].
Many visual stimuli – that can be considered the “premises” of the involved abduction – are ambiguous, yet people are adept at imposing order on them: “We
readily form such hypotheses as that an obscurely seen face belongs to a friend of
ours, because we can thereby explain what has been observed” [Thagard, 1988, p.
53]. This kind of image-based hypothesis formation can be considered as a form
of what I have called visual [Magnani et al., 1994; Magnani, 1996] (or iconic)
abduction. Of course such subconscious visual abductions of everyday cognitive
behavior are not of particular importance but we know that in science they may
48
In philosophical tradition visual perception was viewed very often like a kind of inference [Kant,
1929; Fodor, 1983; Gregory, 1987; Josephson and Josephson, 1994]. On visual perception as
abduction and its semi-encapsulated character cf. subsection 5.5.2, chapter five of this book.
36
1 Theoretical and Manipulative Abduction
be very significant and lead to interesting new discoveries [Magnani et al., 1994;
Shelley, 1996]. If perceptions are abductions they are withdrawable, just like the
scientific hypotheses abductively found. They are “hypotheses” about data we can
accept (sometimes this happens spontaneously) or carefully evaluate.
One more example is given by the fact that the perception of tone arises from the
activity of the mind only after having noted the rapidity of the vibrations of the sound
waves, but the possibility of individuating a tone happens only after having heard
several of the sound impulses and after having judged their frequency. Consequently
the sensation of pitch is made possible by previous experiences and cognitions stored
in memory, so that one oscillation of the air would not produce a tone.
To conclude, for Peirce all knowing is inferring and inferring is not instantaneous, it happens in a process that needs an activity of comparisons involving many
kinds of models in a more or less considerable lapse of time.49 As I will illustrate in
the first two sections 5.1 and 5.2 of chapter five this is not in contradiction with the
fact that for Peirce the inferential and abductive character of creativity is based on
the instinct (the mind is “in tune with nature”) but does not have anything to do with
irrationality and blind guessing. [Hanson, 1958, pp. 85-92] perfectly recognizes the
model-based side of abductive reasoning, when he relates (and reduces) it to the activity of “interpretation” (“pattern of discovery”) resorting to the well-known example of reversible perspective figures of Gestalt psychology. Unfortunately, this kind
of analysis inhibits the possibility of gaining further knowledge about model-based
reasoning. I think Hanson is inclined to consider the abductive event as instantaneous and not susceptible to further cognitive and epistemological examination.
All sensations or perceptions participate in the nature of a unifying hypothesis,
that is, in abduction, in the case of emotions too:
Thus the various sounds made by the instruments of the orchestra strike upon the ear,
and the result is a peculiar musical emotion, quite distinct from the sounds themselves.
This emotion is essentially the same thing as a hypothetic inference, and every hypothetic inference involved the formation of such an emotion [Peirce, 1931-1958, 2.643].
Also this example surely suggests that abductive movements have interesting extratheoretical effects (see the following chapter).50 Human beings and animals have
evolved in such a way that now they are able to recognize habitual and recurrent
events and to “emotionally” deal with them, like in cases of fear, that appears to be
a quick explanation that some events are dangerous. During the evolution such abductive types of recognition and explanation settled in their nervous systems: we can
abduce “fear” as a reaction to a possible external danger, but also when affronting a
different types of evidence, like in the case of “reading a thriller” [Oatley, 1996].
49
50
This corresponds to Peirce’s “philosophical” point of view, which delineates a very particular
meaning of the word “inference”, as illustrated above.
Considering emotions as abductions, [Oatley and Johnson-Laird, 2002] have proposed a cognitive theory of emotions largely based on Peircean intuitions. A different aim is pursued by
[O’Rorke and Ortony, 1992; O’Rorke, 1994]: using a computational tool implemented in PROLOG, AbMaL, and the situation calculus framework, they provide an abductive theory showing
how it is possible to construct explanations of emotional states.
1.5 Model-Based Creative Abduction
37
In all these examples Peirce is referring to a kind of hypothetical activity that is
inferential but not verbal, where “models” of feeling, seeing, hearing, etc., are very
efficacious when used to build both habitual abductions of everyday reasoning and
creative abductions of intellectual and scientific life (see Figure 1.6).
CONCEPTUAL
CHANGES
SIMULATIVE
REASONING
ANALOGY
VISUAL-ICONIC
REASONING
THOUGHT
EXPERIMENT
MODEL-BASED
ABDUCTION
PERCEPTION
AND
SENSE ACTIVITY
VISUAL
IMAGERY
DEDUCTIVE
REASONING
INFERENCES
Fig. 1.6 Model-based abduction
Following Nersessian [1995; 1999b], the term “model-based reasoning” is used
to indicate the construction and manipulation of various kinds of representations,
not mainly sentential and/or formal, but mental (visual imagistic, analogical, etc.)
and/or related to external mediators.51 She proposes the so-called cognitive history
and philosophy of science approach, which affords a reframing of the problem of
51
See also the recent analysis of the role of models in science given by [Giere, 1988; Giere,
1999; Harris, 1999; Suarez, 1999]. For an account on the role of models in the history of
recent philosophy of science cf. [Bailer-Jones, 1999]. [Zytkow, 1999; Winsberg, 1999] describe
some aspects of model construction in automated computational systems aimed at reproducing
scientific reasoning. On the mediating role of scientific models between theories and the real
world cf. [Morgan and Morrison, 1999]. Further, differences in novice and expert reasoning
skills in solving scientific problems (cf., e.g., [Chi et al., 1981]) provide evidence that skills in
modeling is something that develops with learning [Ippolito and Tweney, 1995]. More recent
research can be found in [Magnani, 2006f; Magnani and Li, 2007]. Moreover, Nersessian relates
model-based reasoning to some aspects of reasoning in terms of “mental models” described
by [Johnson-Laird, 1988; Johnson-Laird, 1993], and recently enriched her perspective in the
framework of distributed cognition cf. [Nersessian and Chandrasekharan, 2009; Nersessian and
Patton, 2009].
38
1 Theoretical and Manipulative Abduction
conceptual formation and change in science that not only provides philosophical
insights but also pays attention to the practices employed by real human agents in
constructing, communicating and replacing representation of a domain. Common
examples of model-based reasoning are constructing and manipulating visual representations, thought experiment, analogical reasoning, but also the so-called “tunnel
effect” [Cornuéjols et al., 2000], occurring when models are built at the intersection
of some operational interpretation domain – with its interpretation capabilities – and
a new ill-known domain.
Although controversy arises as to whether there is any form of representation
other than strings of symbols, it is possible, following [Johnson-Laird, 1983] to
assume the existence of at least three kinds of mental representations:
1. propositional representations (strings of symbols such as “the pot is on the
table”);
2. mental models (structural analogs of real world or imagined situations, such as
a pot being on a table);
3. images (a mental model from a specific perspective, such as looking down on
the pot on the table from above).
We have to remember that visual and analogical reasoning are productive in scientific concept formation too, where the role they play in model-based abductive reasoning is very evident; scientific concepts do not pop out of heads, but are elaborated
in a problem-solving process that involves the application of various procedures:
this process is a reasoned process. Visual abduction, but also many kinds of abductions involving analogies, diagrams, thought experimenting, visual imagery, etc. in
scientific discovery processes, can be just called model-based. Additional considerations about the intersections between abduction and model-based reasoning (especially in experiment and thought experiment) are illustrated by [Gooding, 1990;
Gooding, 2006]: the ability to integrate information from various sources is crucial
to scientific inference and typical of all kinds of model-based reasoning also when
models and representations are “external”, like verbal accounts, drawings, various
artifacts, narratives, etc.
We know that scientific concept formation has been ignored because of the accepted view that no “logic of discovery” – either deductive, inductive, or abductive
algorithms for generating scientific knowledge – is possible.52 The methods of discovery involve use of heuristic procedures (Peirce was talking of creative abduction
52
It is well-known that Popper (and 3most of the philosophy of science tradition) confined scientific discovery to the realm of irrationality: “[. . . ] there is not such thing as a logical method
of having new ideas, or a logical reconstruction of this process. My view may be expressed by
saying that every discovery contains ‘an irrational element’, or a ‘creative intuition’, in Bergson’s sense” [Popper, 1959, p. 32]. This is also the case of the celebrated distinction between
“context of discovery” and “context of justification” [Reichenbach, 1938] I have quoted at the
beginning of this chapter. Rational analysis is only possible within the context of justification
(verification, corroboration, falsification).
1.5 Model-Based Creative Abduction
39
as the capacity and the “method” of making good conjectures);53 cognitive psychology, artificial intelligence, and computational philosophy have established that
heuristic procedures are reasoned (see the following section). Analogical reasoning is one such problem-solving procedure, and some reasoning from imagery is
a form of analogical reasoning: [Holyoak and Thagard, 1995] elaborated an analysis of analogical reasoning that encompasses psychological, computational, and
epistemological aspects. We have to remember that, among the various kinds of
model-based reasoning, analogy received particular attention from the point of view
of computational models designed to simulate aspects of human analogical thinking:
for example, Thagard, et al. have developed ARCS (Analog Retrieval by Constraint
Satisfaction; 1990) and ACME (Analogical Mapping by Constraint Satisfaction;
Holyoak and Thagard, 1989), computational programs that are built on the basis of
a multiconstraint theory.54 [Holyoak and Thagard, 1995].
Finally, by recognizing the role of model-based abduction the analysis of conceptual change can overcome the negative issues that come from the reductionist
theory of meaning and from the related incommensurability thesis, and illustrate the
various grades of commensurability that can be found when dealing with the roles of
model-based abduction in science. [Nersessian, 1998] exploits the representational
and constructive virtues of model-based reasoning and makes use of Giere’s general
idea that “modeling is not at all ancillary to doing science, but central to constructing accounts of the natural world” [1999]: she illustrates how model-based abduction can explain that concept transformation and creation involves the construction
of fluid and evolving frameworks that guarantee commensurability at many levels.
Manipulative abduction [Magnani, 2001b] – contrasted with theoretical abduction – happens when we are thinking through doing and not only, in a pragmatic
sense, about doing. For instance, when we are creating geometry constructing and
manipulating a triangle, like in the case given by Kant in the “Transcendental Doctrine of Method”. So the idea of manipulative abduction (cf. Figure 1.7) goes beyond
the well-known role of experiments as capable of forming new scientific laws by
means of the results (nature’s answers to the investigator’s question) they present,
or of merely playing a predictive role (in confirmation and in falsification). Manipulative abduction refers to an extra-theoretical behavior that aims at creating communicable accounts of new experiences to integrate them into previously existing
systems of experimental and linguistic (theoretical) practices. As I said above, the
existence of this kind of extra-theoretical cognitive behavior is also testified by the
53
54
Analogy and abduction are separate types of reasoning practices, mutually independent both
structurally and procedurally, but they are extremely useful in hypothesis-search in hypothesis
selection tasks [Gabbay and Woods, 2005, p. 287].
On analogy cf. also the contributions by [Kolodner, 1993] (analogy as a form of case-based
reasoning in AI), [Davies and Goel, 2000; Nersessian et al., 1997; Davies et al., 2009] (visual
analogy in AI); [Gentner, 1982; Gentner, 1983; Gentner et al., 1997] (analogies and metaphors
in cognitive science and history of science), [Shelley, 1999] (analogy in archaeology). Many
theoretical and computational accounts of analogical reasoning have stressed the transfer of
relational knowledge. Causal and functional relationships have been the focus of many theories [Holyoak and Thagard, 1995; Holyoak and Thagard, 1997; Bhatta and Goel, 1997;
Falkenhainer, 1990; Winston, 1980] .
40
1 Theoretical and Manipulative Abduction
Fig. 1.7 Manipulative abduction
many everyday situations in which humans are perfectly able to perform very efficacious (and habitual) tasks without the immediate possibility of realizing their
conceptual explanation.55 In the following sections manipulative abduction will be
considered from the perspective of the relationship between unexpressed knowledge
and external representations.
I would like to reiterate that it is important to note that my epistemological distinction between theoretical and manipulative abduction is based on the possibility
of separating the two aspects in actual cognitive processes, relying on the differentiation between off-line (theoretical, when only inner aspects are at stake) and on-line
(manipulative, where the interplay between internal and external aspects is fundamental). As Wheeler has recently observed, some thinkers like Esther Thelen and
Andy Clark have raised doubts about the on-line/off-line distinction “[. . . ] on the
grounds that no intelligent agent is (they claim) ever wholly on-line or wholly offline” [Wheeler, 2004, p. 707, footnote 14]. I contend that, even if manipulative/online cases exist in great numbers, there are also cognitive processes that seem to fall
into the class of off-line thinking, as we can simply introspectively recognize. Anyway, the distinction above is always rewarding from the epistemological perspective
as a way of classifying and analyzing different cognitive levels, and it is endowed
with an indisputable conceptual and explanatory usefulness.56
55
56
[Rivera and Rossi Becker, 2007] have recently applied the ST-model above and especially my
concept of manipulative abduction in the analysis of abductive/inductive reasoning of preservice
elementary majors on patterns that consist of figural and numerical cues. Cf. also above footnote
24 at p. 14. Model-based reasoning and abduction in Felix Klein’s heuristics are described in
[Glas, 2009].
An extreme case in which we see cognitive processes that seem to occur “completely” outside
is that of a PC that performs a sophisticated AI program. In chapter two (section 3.7) I call
this kind of artifact “mimetic mind”; in this case we must not forget that such an artifact still
represents a cognitive “prosthesis” for the human brain, and so its cognitive performance still
operates at the level of an on-line environment that also includes a human agent. In this cognitive
sense the artifact is, in principle, no different from the mere use of a notebook for memorizing
or of a hammer for building some piece of furniture.
1.6 Manipulative Abduction
1.6
1.6.1
41
Manipulative Abduction
Unexpressed Knowledge, Knowledge Creation, and
External Mediators
The power of model-based abduction mainly depends on its ability to supply a
certain amount of important information, unexpressed at the level of available data
from the propositional point of view. It also has a fundamental role in the process
of transformation of knowledge from its tacit to its explicit forms, and in the subsequent elicitation and use of knowledge. Let us describe how this happens.
As pointed out by Polanyi in his epistemological investigation, a large part of
knowledge is not explicit, but tacit: we know more than we can tell and we can know
nothing without relying upon those things which we may not be able to tell [1966].
Polanyi’s concept of knowledge is based on three main theses: first, discovery cannot
be accounted for by a set of articulated rules or algorithms; second, knowledge is
public and also to a very great extent personal (i.e. it is constructed by humans and
therefore contains emotions, “passions”); third, an important part of knowledge is
tacit.
Hence, two levels of knowledge, mutually exclusive but complementary, as they
interact in creative tasks, underlie every activity: there is a kind of knowledge we
can call focal, that is the knowledge about the object or phenomenon in focus; and
another kind of knowledge, masked under the first one, and often used as a tool
to handle or improve what is being focused, we can call tacit. The first one is the
knowledge that is transmissible through any systematic language, since it can be
relatively easily formulated by means of symbols and it can be digitalized. Tacit
knowledge, on the other hand, is characterized by the fact that it is personal, context specific, usually characterized as derived from direct experience, and therefore
hard to elicit and communicate. It is a “non-codified, disembodied know-how that
is acquired via the informal take-up of learned behavior and procedures” [Howells,
1996, p. 92].
[Fleck, 1996, p. 119] describes this form of knowledge as “a subtle level of understanding often difficult to put into words, a trained recognition and perception”.
Tacit knowledge is wholly embodied in the individual, rooted in practice and experience, expressed through skillful execution, and can become useful by means of
watching and doing forms of learning and exploitation.
As Polanyi contends, human beings acquire and use knowledge by actively creating and organizing their own experience: tacit knowledge is the practical knowledge
used to perform a task. The existence of this kind of not merely theoretical knowing
behavior is also testified by the many everyday situations in which humans are perfectly able to perform very efficacious (and habitual) tasks without the immediate
possibility of realizing their conceptual explanation. In some cases the conceptual
account for doing these things was at one point present in memory, but now has
deteriorated, and it is necessary to reproduce it, in other cases the account has to be
constructed for the first time, like in creative experimental settings in science.
42
1 Theoretical and Manipulative Abduction
[Hutchins, 1995] illustrates the case of a navigation instructor that performed an
automatized task for 3 years involving a complicated set of plotting manipulations
and procedures. The insight concerning the conceptual relationships between relative and geographic motion came to him suddenly “as lay in his bunk one night”.
This example explains that many forms of learning can be represented as the result
of the capability of giving conceptual and theoretical details to already automatized manipulative executions. The instructor does not discover anything new from
the point of view of the objective knowledge about the involved skill, however,
we can say that his conceptual awareness is new from the local perspective of his
individuality.
We can find a similar situation also in the process of scientific creativity. In the
cognitive view of science, it has been too often underlined that conceptual change
just involves a theoretical and “internal” replacement of the main concepts. But
usually researchers forget that a large part of these processes are instead due to
practical and “external” manipulations of some kind, prerequisite to the subsequent
work of theoretical arrangement and knowledge creation. When these processes are
creative we can speak of manipulative abduction (cf. above). Scientists sometimes
need a first “rough” and concrete experience of the world to develop their systems,
as a cognitive-historical analysis of scientific change [Nersessian, 1992; Gooding,
1990] has carefully shown.
The prevailing perspective among philosophers is that the processes of discovery
and the consequent new incoming scientific representations are too mysterious to
be understood. This view receives support from numerous stories of genius’ discoveries, such as Archimedean eureka-experiences. Such accounts neglect periods
of intense and often arduous thinking activity, often performed by means of experiments and manipulative activity on external objects; these are periods that prepare
such “instantaneous” discoveries. It is also important to understand that the scientific process is complex and dynamic: new representations do not emerge completely
codified from the heads of scientists, but are constructed in response to specific
problems by the systematic use of heuristic procedures – as pointed out by Herbert
Simon’s view on the “problem-solving process” [Simon, 1977].
Traditional examinations of how problem-solving heuristics create new representations in science have analyzed the frequent use of analogical reasoning, imagistic
reasoning, and thought experiment, from an internal point of view. However, attention has not been focalized on those particular kinds of heuristics that resort to the
existence of extra-theoretical ways of thinking – thinking through doing [Magnani,
2002b]. Indeed many cognitive processes are centered on external representations,
as a means to create communicable accounts of new experiences ready to be integrated into previously existing systems of experimental and linguistic (theoretical)
practices (cf. chapter three of this book).
Interesting insights can arise regarding these problems studying them from a different contrasting approach, which moves away from Simon’s paradigm, but which
can offer a rational solution to the problem of creativity and conceptual change in
terms of mathematical models: the dynamic approach [Port and van Gelder, 1995].
The traditional computational view treats cognition as a process that computes
1.6 Manipulative Abduction
43
internal symbolic representations of the external world. But this approach is considered too reductive, since it is based on the functionalist hypothesis (which cannot
render the external dimension of cognition), and on a computation of static entities.
It is useful to integrate it with a dynamical modeling of cognition, which is able
to describe abductive processes as dynamical entities “unfolding” in real time (we
can also gain a better cognitive-historical perspective) [Magnani and Piazza, 2005].
From this point of view it is possible to model the terms (objects or propositions) that
constitute abduction by considering the attractors in a dynamical system. This can
be achieved by topologically specifying the semantic content of the inferential process through the spatial relations between its defining attractors. We can therefore
consider the process of progressive development of “new” concepts and replacement
of old ones in terms of temporal evolving patterns defined by interactions between
topological configurations of attractors.57
Moreover, a central point in the dynamical approach is the importance assigned
to the “whole” cognitive system: cognitive activity is in fact the result of a complex
interplay and simultaneous coevolution, in time, of the states of mind, body, and
external environment. Even if, of course, a large portion of the complex environment
of a thinking agent is internal, and consists in the proper software composed of the
knowledge base and of the inferential expertise of the individual, nevertheless a
“real” cognitive system is composed by “distributed cognition” among people and
some “external” objects and technical artifacts [Hutchins, 1995; Norman, 1993].58
A recent special issue of the journal Pragmatics & Cognition, devoted to the
theme of “distributed cognition”, addresses many of the puzzling theoretical problems still open to debate. In particular the article by [Sutton, 2006] usefully emphasizes how distributed cognition is related to the “extended mind hypothesis”
[Clark and Chalmers, 1998] and other similar approaches in terms of embodied,
embedded, situated, and dynamical cognition and active and vehicle externalism,
which of course present subtle nuances, that I nevertheless cannot account for here.
Sutton nicely presents a taxonomy of the distributed resources that are studied in
these fields of research: 1) external cultural tools, artifacts, and symbol systems;
2) natural environment features suitably endowed with cognitive value; 3) interpersonal and social distribution or cognitive “scaffolding”; 4) embodied capacities
and skills interwoven in complex ways with our use of technological, natural, and
social resources of the previous cases; 5) internalized cognitive artifacts. For Sutton the last two cases concern the analysis of the complex wholes made up when
embodied brains couple with “cognition” amplifiers like objects – technologies for
example, and other people, through a process I will mention in chapter three (subsection 3.6.4) “re-embodiment of the mind”, as a kind of neural recapitulation of
cognitive features – for example linguistic and model-based – found and distributed
outside.
57
58
On abduction, dynamic systems theory, and morphogenetical models cf. chapter eight of this
book.
[Skagestad, 1993] stresses the role of this coevolution in cognition in the framework of an
analysis of Popperian writing on evolutionary epistemology and Peircean semiotics.
44
1 Theoretical and Manipulative Abduction
The external distributed resources have culturally specific different degrees of
stability and so various chances to be re-internalized, varying from the very stable and reliable, like words and phrases of “natural” language and certain symbols, to others which are more evanescent and transient. Only when they are stable
can we properly speak of the establishment of an “extended mind”, like Wilson
and Clark contend. Finally, internal and external resources (that is neural and environmental) are not identical but complementary – in this sense human beings can
be appropriately considered “cyborgs” [Clark, 2003]. By showing their interaction
from an epistemological and cognitive perspective I will illustrate in chapter three
of this book various aspects of their interplay taking advantage of the concept of
abduction.59
In the recent [Clark, 2008, p. 13], a deep analysis of various aspects of embodiment, environmental embedding, and of the so-called “extended mind hypothesis”
is presented: Clark definitely contends that mind “leaches into body and world” (p.
29): “Inner neural processes [. . . ] are often productively entangled with the gross
bodily and extra-bodily processes of storage, representation, materialization, and
manipulation” (p. 169). Embodiment, action, and situation are fundamental in human thought and behavior. The first chapter of Clark’s new book also focuses on
the so-called Principle of Ecological Assembly (PEA), which states that the cognizer tends to recruit “whatever mix of problem-solving resources will yield and
acceptable result with a minimum effort”. This recruitment process does not make
a special distinction between neural, bodily, and environmental resources except
insofar as these somehow affect the whole effort involved. The operation is not operated “in the neural system alone, but in the whole embodied system located in
the world. [. . . ] the embodied agent is empowered to use active sensing and perceptual coupling in ways that simplify neural problem-solving by making the most
of environmental opportunities and information freely available in the optic array”
(p.1̃4).
In the case of the construction and examination of diagrams in geometrical reasoning, specific experiments serve as states and the implied operators are the manipulations and observations that transform one state into another. The geometrical
outcome depends upon practices and specific sensorimotor activities60 performed on
a non-symbolic object, which acts as a dedicated external representational medium
supporting the various operators at work. There is a kind of an epistemic negotiation
between the sensory framework of the geometer and the external reality of the diagram [Magnani, 2002a]. This process involves an external representation consisting
of written symbols and figures that for example are manipulated “by hand”. The
59
60
The role of external representations and resources – I call moral mediators – in ethics is described in my recent [Magnani, 2007d]. A detailed treatment of the theoretical and cognitive
controversies concerning the extended mind hypothesis and the role of external representations
is given in the recent collection [Schantz, 2004] and in [Clark, 2008, chapters five and six].
“The agent’s control architecture (e.g. nervous system) attends to and processes streams of
sensory stimulation, and ultimately generates sequences of motor actions which in turn guide the
further production and selection of sensory information. [In this way] ‘information structuring’
by motor activity and ‘information processing’ by the neural system are continuously linked to
each other through sensorimotor loops” [Lungarella and Sporns, 2005, p. 25].
1.6 Manipulative Abduction
45
cognitive system is not merely the mind-brain of the person performing the geometrical task, but the system consisting of the whole body (cognition is embodied) of
the person plus the external physical representation. In geometrical discovery the
whole activity of cognition is located in the system consisting of a human together
with diagrams.61
An external representation can modify the kind of computation that a human
agent uses to reason about a problem: the Roman numeration system eliminates, by
means of the external signs, some of the hardest parts of the addition, whereas the
Arabic system does the same in the case of the difficult computations in multiplication. The capacity for inner reasoning and thought results from the internalization
of the originally external forms of representation. In the case of the external representations we can have various objectified knowledge and structures (like physical symbols – e.g. written symbols, and objects – e.g. three-dimensional models,
shapes and dimensions), but also external rules, relations, and constraints incorporated in physical situations (spatial relations of written digits, physical constraints
in geometrical diagrams and abacuses) [Zhang, 1997]. The external representations
are contrasted with the internal representations that consist in the knowledge and
the structure in memory, as propositions, productions, schemas, models, prototypes,
images.
The external representations are not merely memory aids: they can give people
access to knowledge and skills that are unavailable to internal representations, help
researchers to easily identify aspects and to make further inferences, they constrain
the range of possible cognitive outcomes in a way that some actions are allowed and
others forbidden. The mind is limited because of the restricted range of information
processing, the limited power of working memory and attention, the limited speed
of some learning and reasoning operations; on the other hand the environment is
intricate, because of the huge amount of data, real time requirement, uncertainty
factors. Consequently, we have to consider the whole system, consisting of both internal and external representations, and their role in optimizing the whole cognitive
performance of the distribution of the various subtasks. In this case humans are not
“just bodily and sensorily but also cognitively permeable agents” [Clark, 2008, p.
40]. It is well-known that in the history of geometry many researchers used internal mental imagery and mental representations of diagrams, but also self-generated
diagrams (external) to help their thinking.
1.6.2
External Representations and Epistemic Mediators
I have illustrated above the notion of tacit knowledge and I have proposed an extension of that concept. From the perspective of a more adequate and updated account
61
[Elveton, 2005] provides a survey concerning the problem of embodiment considered as addressing a kind of practical intelligence in contrast to a disembodied, symbol manipulating intelligence
[Brooks, 1991]; a comparison of the recent cognitive perspectives with robotics and the classical philosophical insights given by Cassirer, Husserl and Heidegger is also illustrated. [Dourish,
2001] usefully demonstrates the importance of the concept of embodiment in human-computer
interaction (HCI) and in the design of computational tools, technologies, and systems.
46
1 Theoretical and Manipulative Abduction
of cognition surely there is something more important beyond the tacit knowledge
“internal” to the subject – considered by Polanyi as personal, embodied and context
specific. We can also speak of a sort of tacit information “embodied” into the whole
relationship between our mind-body system and suitable external representations.
An information we can extract, explicitly develop, and transform in knowledge contents, to solve problems, as it was already manifest, for instance, in the geometrical
problem contained in the Meno [Plato, 1977], even if philosophers know perfectly
that Plato considered this activity to be just the result of reminiscence and not of
discovery [Magnani, 2001b, chapter 1].
As I have already stressed, Peirce considers inferential any cognitive activity
whatever, not only conscious abstract thought; he also includes perceptual knowledge and subconscious cognitive activity. For instance in subconscious mental activities visual representations play an immediate role. Peirce gives an interesting
example of model-based abduction related to sense activity: “A man can distinguish
different textures of cloth by feeling: but not immediately, for he requires to move
fingers over the cloth, which shows that he is obliged to compare sensations of
one instant with those of another” [Peirce, 1931-1958, 5.221]. This surely suggests
that abductive movements have also interesting extra-theoretical characters and that
there is a role in abductive reasoning for various kinds of manipulations of external
objects. I would like to reiterate that for Peirce all knowing is inferring and inferring
is not instantaneous, it happens in a process that needs an activity of comparisons
involving many kinds of models in a more or less considerable lapse of time.
All these considerations suggest, then, that there exist a creative form of thinking through doing,62 fundamental as much as the theoretical one. It is what I have
called manipulative abduction (cf. above). As already said manipulative abduction
happens when we are thinking through doing and not only, in a pragmatic sense,
about doing. Of course the study of this kind of reasoning is important not only in
delineating the actual practice of abduction, but also in the development of programs
computationally adequate to rediscover, or discover for the first time, for example,
scientific hypotheses and mathematical theorems or laws.
Various templates of manipulative behavior exhibit some regularities. The activity of manipulating external things and representations is highly conjectural and
neither immediately explanatory nor necessarily immediately non-explanatory and
instrumental63 these templates are “hypotheses of behavior” (creative or already
cognitively present in the scientist’s mind-body system, and sometimes already applied) that abductively enable a kind of epistemic “doing”. Hence, some templates
of action and manipulation can be selected in the set of the ones available and prestored, others have to be created for the first time to perform the most interesting
creative cognitive accomplishments of manipulative abduction.
62
63
In this way the cognitive task is achieved on external representations used in lieu of internal
ones. Here action performs an epistemic and not a merely performative role, relevant to abductive reasoning.
I will illustrate these two non Peircean sorts of abductive cognition in the following chapter.
1.6 Manipulative Abduction
47
Fig. 1.8 Conjectural templates I
Some common features of the tacit templates of manipulative abduction (cf.
Figure 1.8), that enable us to manipulate things and experiments in science are related to: 1. sensibility towards the aspects of the phenomenon which can be regarded
as curious or anomalous; manipulations have to be able to introduce potential inconsistencies in the received knowledge (Oersted’s report of his experiment about electromagnetism is devoted to describe some anomalous aspects that did not depend on
any particular theory of the nature of electricity and magnetism); 2. preliminary sensibility towards the dynamical character of the phenomenon, and not to entities and
their properties, common aim of manipulations is to practically reorder the dynamic
sequence of events into a static spatial one that should promote a subsequent bird’seye view (narrative or visual-diagrammatic); 3. referral to experimental manipulations that exploit artificial apparatus to free new possibly stable and repeatable
sources of information about hidden knowledge and constraints (Davy well-known
set-up in terms of an artifactual tower of needles showed that magnetization was
related to orientation and does not require physical contact). Of course this information is not artificially made by us: the fact that phenomena are made and manipulated
does not render them to be idealistically and subjectively determined; 4. various contingent ways of epistemic acting: looking from different perspectives, checking the
different information available, comparing subsequent events, choosing, discarding, imaging further manipulations, re-ordering and changing relationships in the
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1 Theoretical and Manipulative Abduction
world by implicitly evaluating the usefulness of a new order (for instance, to help
memory).64
In this kind of action-based abduction the suggested hypotheses are inherently
ambiguous until articulated into configurations of real or imagined entities (images,
models or concrete apparatus and instruments). In these cases only by experimenting, can we discriminate between possibilities: they are articulated behaviorally and
concretely by manipulations and then, increasingly, by words and pictures. [Gooding, 1990] refers to this kind of concrete manipulative reasoning when he illustrates
the role in science of the so-called “construals” that embody tacit inferences in procedures that are often apparatus and machine based. The embodiment is of course
an expert manipulation of objects in a highly constrained experimental environment,
and is directed by abductive movements that imply the strategic application of old
and new templates of behavior mainly connected with extra-theoretical components,
for instance emotional, esthetical, ethical, and economic.65
The hypothetical character of construals is clear: they can be developed to
examine further chances, or discarded, they are provisional creative organization of
experience and some of them become in their turn hypothetical interpretations of experience, that is more theory-oriented, their reference is gradually stabilized in terms
of established observational practices. Step by step the new interpretation – that at
the beginning is completely “practice-laden” – relates to more “theoretical” modes
of understanding (narrative, visual, diagrammatic, symbolic, conceptual, simulative), closer to the constructive effects of theoretical abduction. When the reference
is stabilized the effects of incommensurability with other stabilized observations
can become evident. But it is just the construal of certain phenomena that can be
64
65
The problem of manipulative abduction and of its tacit features is strongly related to the
whole area of recent research on embodied reasoning (cf. [Anderson, 2003; Elveton, 2005]),
but also to the studies on external representations and situated robotics (cf. [Clancey, 2002;
Agree and Chapman, 1990; Brooks and Stein, 1994]). The role of manipulative abduction in
ethical reasoning is illustrated in [Magnani, 2007d]. Further aspects of experiment design and
its relationship with the problem of communication in science during the transition from the
personal to the public domain are given in [Gooding and Addis, 1999]: only a small subset of
many observations and measurements performed by individuals of research teams acquire the
status of real and public phenomena. Moreover, additional properties of the agent in a scientific
experimental setting are described: 1. ability to discriminate between observed results, 2. ability
to make judgments about the likelihood of the occurrence of a result, 3. flexibility of the agent’s
change in perception of the world and his consequent capacity to respond to new information, 4.
degrees of competence to build an experiment and observe the results, from novices to experts.
[Tweney, 2006] has recently emphasized the importance of externalized cognitive artifacts used
in the service of the “seeing” of scientists. In turn they are distributed “in the strong sense that
not all of the agentive movement of thought is localized solely within an individual skin”. I think
a further light on the role of construals is shed by Franklin who usefully analyzes the so-called
“exploratory experiments” that prior to theorizing investigate the world “without premature
reflection of any great subtlety, like Bacon says [2000, p. 210], and where there is no particular
hypothesis being pursued. They serve “[. . . ] to find interesting patterns of activity from which
the scientists could later generate a hypothesis” [Franklin, 2005, p. 894].
1.6 Manipulative Abduction
49
shared by the sustainers of rival theories.66 [Gooding, 1990] shows how Davy and
Faraday could see the same attractive and repulsive actions at work in the phenomena they respectively produced; their discourse and practice as to the role of
their construals of phenomena clearly demonstrate they did not inhabit different,
incommensurable worlds in some cases. Moreover, the experience is constructed,
reconstructed, and distributed across a social network67 of negotiations among the
different scientists by means of construals.68
Gooding introduces the so called experimental maps69 that are the epistemological two-dimensional tools that we can adopt to illustrate the conjecturing (abductive)
role of actions from which scientists “talk and think” about the world. They are particularly useful to stress the attention to the interaction of hand, eye, and mind inside
the actual four-dimensional scientific cognitive process. The various procedures for
manipulating objects, instruments and experiences will be in their turn reinterpreted
in terms of procedures for manipulating concepts, models, propositions, and formalisms. Scientists’ activity in a material environment first of all enables a rich perceptual experience that has to be reported mainly as a visual experience by means
of the constructive and hypothesizing role of the experimental narratives.
It is indeed interesting to note that in mathematics model-based and manipulative
abductions are present. For example, I will illustrate in the following chapter and in
chapter three that it is clear that in geometrical construction all these requirements
are fulfilled. Geometrical constructions present situations that are curious and “at
the limit”. These are constitutively dynamic, artificial, and offer various contingent
ways of epistemic acting, like looking from different perspectives, comparing subsequent appearances, discarding, choosing, re-ordering, and evaluating. Moreover,
they present some of the features indicated below, typical of all abductive epistemic
mediators, not only of the ones which play a scientific role in manipulative reasoning: simplification of the task and the capacity to get visual information otherwise
unavailable.
66
67
68
69
The theory of manipulative abduction can support Thagard’s statement that oxygen and phlogiston proponents could recognize experiments done by each others [Thagard, 1992]: the assertion
is exhibited as an indispensable requisite for his coherence-based epistemological and computational theory of comparability at the level of intertheoretic relations and for the whole problem
of the creative abductive reasoning to the best explanation cited in the previous chapter.
Cf. [Minski, 1985; Thagard and Shelley, 1997].
[Gooding and Addis, 2008] further analyze the role of various kinds of experiments – ranging
from the idealized crucial ones to those that are exploratory and/or controversial – like mediating models in the framework of an agent-based approach. Every agent or actor can investigate a
world of experiments and other agents, in a setting where eventually scientists invent and negotiate ways of representing aspects of the world they are investigating. The process is “adaptive”
and “inherently social” and inference is seen as a continuous activity of belief-revision where
the distributed and collaborative aspects are acknowledged. In this perspective experiments are
seen as mediating between at least four sets of objects: hypotheses, procedures, physical setups
and observable outcomes.
Circles denote concepts (mentally represented) that can be communicated, squares denote things
in the material world (bits of apparatus, observable phenomena) that can be manipulated – lines
denote actions.
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1 Theoretical and Manipulative Abduction
These construals aim at arriving to a shared understanding overcoming all conceptual conflicts. As I said above they constitute a provisional creative organization
of experience: when they become in their turn hypothetical interpretations of experience, that is more theory-oriented, their reference is gradually stabilized in terms of
established and shared observational practices that also exhibit a cumulative character. It is in this way that scientists are able to communicate the new and unexpected
information acquired by experiment and action.
To illustrate this process – from manipulations, to narratives, to possible theoretical models (visual, diagrammatic, symbolic, mathematical) – we need to consider
some observational techniques and representations made by Faraday, Davy, and Biot
concerning Oersted’s experiment about electromagnetism. They were able to create
consensus because of their conjectural representations that enabled them to resolve
phenomena into stable perceptual experiences. Some of these narratives are very interesting. For example, Faraday observes: “[. . . ] it is easy to see how any individual
part of the wire may be made attractive or repulsive of either pole of the magnetic
needle by mere change of position [. . . ]. I have been more earnest in my endeavors
to explain this simple but important point of position, because I have met with a great
number of persons who have found it difficult to comprehend”. Davy comments: “It
was perfectly evident from these experiments, that as many polar arrangements may
be formed as chord can be drawn in circles surroundings the wire”. Expressions like
“easy to see” or “it was perfectly evident” are textual indicators inside the experimental narratives of the stability of the forthcoming interpretations. Biot, in his turn,
provides a three-dimensional representation of the effect by giving a verbal account
that enables us to visualize the setup: “suppose that a conjunctive wire is extended
horizontally from north to south, in the very direction of the magnetic direction in
which the needle reposed, and let the north extremity be attached to the copper pole
of the trough, the other being fixed to the zinc pole [. . . ]” and then describes what
will happen by illustrating a sequence of step in a geometrical way:
Imagine also that the person who makes the experiment looks northward, and consequently towards the copper or negative pole. In this position of things, when the wire is
paced above the needles, the north pole of the magnet moves towards the west; when
the wire is placed underneath, the north pole moves towards the east; and if we carry
the wire to the right or the left, the needle has no longer any lateral deviation, but is
loses its horizontality. If the wire be placed to the right hand, the north pole rises; to
the left, its north pole dips [. . . ].70
It is clear that the possibility of “seeing” interesting things through the experiment
depends from the manipulative ability to get the correct information and to create
the possibility of a new interpretation (for example a simple mathematical form)
of electromagnetic natural phenomena, so joining the theoretical side of abduction.
Step by step, we proceed until Faraday’s account in terms of magnetic lines and
curves.
70
The quotations are from [Faraday, 1821-1822, p. 199], [Davy, 821, pp. 282–283] and [Biot,
1821, p. 282-283] , cited by [Gooding, 1990, pp. 35–37].
1.6 Manipulative Abduction
51
The whole activity of manipulation is in fact devoted to building various external
epistemic mediators.71 Therefore, manipulative abduction represents a kind of redistribution of the epistemic and cognitive effort to manage objects and information
that cannot be immediately represented or found internally (for example exploiting
the resources of visual imagery).72
It is difficult to establish a list of invariant behaviors that are able to illustrate
manipulative abduction in science. As illustrated above, certainly the expert manipulation of objects in a highly constrained experimental environment implies the
application of old and new templates of behavior that exhibit some regularities. The
activity of building construals is highly conjectural and not immediately or necessarily explanatory: these templates are hypotheses of behavior (creative or already
cognitively present in the scientist’s mind-body system, and sometimes already applied) that abductively enable a kind of epistemic “doing”. Hence, some templates
of action and manipulation can be selected in the set of the ones available and prestored, others have to be created for the first time to perform the most interesting
creative cognitive accomplishments of manipulative abduction.
Moreover, I think that a better understanding of manipulative abduction at the
level of scientific experiment could improve our knowledge of induction, and its
distinction from abduction: manipulative abduction could be considered as a kind
of basis for further meaningful inductive generalizations. Different generated construals can give rise to different inductive generalizations.
If we see scientific discovery like a kind of opportunistic ability of integrating73
information from many kinds of simultaneous constraints to produce explanatory
hypotheses that account for them all, then manipulative abduction will play the role
of eliciting possible hidden constraints by building external suitable experimental
structures.
From the point of view of everyday situations manipulative abductive reasoning
and epistemic mediators exhibit other very interesting templates (we can find the
first three in geometrical constructions) (cf. Figure 1.9): 5. action elaborates a simplification of the reasoning task and a redistribution of effort across time [Hutchins,
1995], when we need to manipulate concrete things in order to understand structures which are otherwise too abstract [Piaget, 1974], or when we are in presence of
71
72
73
This expression, I have introduced in [Magnani, 2001b], is derived from the cognitive anthropologist Hutchins, who coined the expression “mediating structure” to refer to various external tools that can be built to cognitively help the activity of navigating in modern but also
in “primitive” settings. Any written procedure is a simple example of a cognitive “mediating
structure” with possible cognitive aims, so mathematical symbols and diagrams: “Language,
cultural knowledge, mental models, arithmetic procedures, and rules of logic are all mediating
structures too. So are traffic lights, supermarkets layouts, and the contexts we arrange for one
another’s behavior. Mediating structures can be embodied in artifacts, in ideas, in systems of social interactions [. . . ]” [Hutchins, 1995, pp. 290–291] that function as an enormous new source
of information and knowledge. [Sterelny, 2004, p. 249] maintains that “epistemic tools support
open-ended and counterfactually robust dispositions to succeed” and further stresses their social
character.
It is difficult to preserve precise spatial and geometrical relationships using mental imagery, in
many situations, especially when one set of them has to be moved relative to another.
On the role of opportunistic reasoning in design cf. [Simina and Kolodner, 1995].
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redundant and unmanageable information; 6. action can be useful in presence of incomplete or inconsistent information – not only from the “perceptual” point of view
– or of a diminished capacity to act upon the world: it is used to get more data to
restore coherence and to improve deficient knowledge; 7. action enables us to build
external artifactual models of task mechanisms instead of the corresponding internal
ones, that are adequate to adapt the environment to the agent’s needs: experimental
manipulations exploit artificial apparatus to free new possible stable and repeatable
sources of information about hidden knowledge and constraints. 8. action as a control of sense data illustrates how we can change the position of our body (and/or of
the external objects) and how to exploit various kinds of prostheses (Galileo’s telescope, technological instruments and interfaces) to get various new kinds of stimulation: action provides some tactile and visual information (e.g., in surgery), otherwise
unavailable.
Fig. 1.9 Conjectural templates II
Also natural phenomena can play the role of external artifactual models: under
Micronesians’ manipulations of their images, the stars acquire a structure that “becomes one of the most important structured representational media of the Micronesian system” [Hutchins, 1995, p. 172]. The external artifactual models are endowed
with functional properties as components of a memory system crossing the boundary between person and environment (for example they are able to transform the
tasks involved in allowing simple manipulations that promote further visual inferences at the level of model-based abduction). The cognitive process is distributed
1.6 Manipulative Abduction
53
between a person (or a group of people) and external representation(s), and so obviously embedded and situated in a society and in a historical culture.74
So external well-built structures (Biot’s construals for example) and their contents in terms of new information and knowledge, will be projected onto internal
structures (for instance models, or symbolic – mathematical – frameworks) so joining the constructive effect of theoretical abduction. The interplay consists of a superimposition of internal and external, where the elements of the external structures
gain new meanings and relationships to one another, thanks to the constructive explanatory inner activity (for instance Faraday’s new meanings in terms of curves
and lines of force). This interplay expresses the fact that both internal and external
processes are part of the same epistemic ecology.75
Not all epistemic and cognitive mediators are preserved, saved, and improved,
as in the case of the ones created by Galileo at the beginning of modern science
(see the following subsection). For example, in certain non epistemological everyday emergency situations some skillful mediators are elaborated to face possible
dangers, but, because of the rarity of this kind of events, they are not saved and stabilized. [Hutchins, 1995, pp. 317–351] describes the interesting case of the failure
of an electrical device, the gyrocompass, crucial for navigation, and the subsequent
creation of substitutive contingent cognitive mediators. These cognitive mediators
consisted of additional computations, redistributions of cognitive roles, and finally,
of the discovery of a new shared mediating artifact in terms of divisions of labor –
the so-called modular sum that is able to face the situation.
Finally, we have to observe that many external things that usually are cognitively inert can be transformed into epistemic or cognitive mediators. For example
we can use our body: we can talk with ourselves, exploiting in this case the selfregulatory character of this action, we can use fingers and hands for counting.76 We
can also use external “tools” like writing, narratives, others persons’ information,77
concrete models and diagrams, various kinds of pertinent artifacts. Hence, not all of
the cognitive tools are inside the head, sometimes it is useful to use external objects
and structures as cognitive or epistemic devices. We indicated above that Micronesian navigator’s stars, that are natural objects, become very complicated epistemic
74
75
76
77
Modeling mechanisms of manipulative abduction is also related to the possibility of improving
technological interfaces that provide restricted access to controlled systems, so that humans have
to compensate by reasoning with and constructing internal models. New interfaces resources for
action, related to task-transforming representations, can contribute to overcome these reasoning
obstacles [Kirlik, 1998]. Further details on this issue will be provided in chapter six of this book.
It is [Hutchins, 1995, p. 114] that uses the expression “cognitive ecology” when explaining the
role of internal and external cognitive navigation tools. More suggestions on manipulative abduction can be derived by the contributions collected in [Morgan and Morrison, 1999], dealing
with the mediating role of scientific models between theory and the “real world”.
Another example is given by the gestures that are also activated in talking, sometimes sequentially, sometimes in an overlapping fashion. On this problem cf. the updated critical survey given
by [Clark, 2008, chapter six].
The results of an empirical research that show the importance of collaborative discovery in
scientific creative abduction and in explanatory activities are given in [Okada and Simon, 1997].
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1 Theoretical and Manipulative Abduction
artifacts, when inserted in the various cognitive manipulations (of seeing them)
related to navigation.
1.6.3
Segregated Knowledge and the “World of Paper”
I said that in the last part of the XX century the problem of the incommensurability
of meaning has distracted the epistemologists from the procedural, extra-sentential
and extra-theoretical aspects of scientific practice (cf. subsection 1.2.1 above). This
is surprising especially if we consider that the emphasis on concrete manipulative
reasoning in case of “construals”, that embody tacit inferences in procedures that
are often apparatus and machine based, is already clearly granted at the beginnings
of modern science.
It is a very common philosophical view to assert that modern science uses experiment to get new information about the world, even if it is not always completely
clear the manipulative character of this activity. The new world of the new knowledge has to be totally different from the one merely “of paper” of the Aristotelian
tradition. An unbelievable amount of knowledge that was segregated had to be released. Accentuating the role of observational manipulations Galileo says:
The anatomist showed that the great trunk of nerves, leaving the brain and passing
through the nape, extended on down the spine and then branched out through the whole
body, and that only a single strand as fine as a thread arrived at the heart [Galilei, 1989,
p. 63].
Manipulating the cadaver, the anatomist is able to get new, not speculative, information that the Peripatetic philosopher immediately refuses:
The philosopher, after considering for awhile, answered: “You have made me see this
matter so plainly and palpably that if Aristotle’s text were not contrary to it, stating
clearly that the nerves originate in the heart, I should be forced to admit it to be true”
(ibid.).
Ipse dixit: no room for the experience. Galileo-Salviati begs of Simplicius: “So put
forward the arguments and demonstrations, Simplicius, [. . . ] but not just texts and
bare authorities, because our discourses must relate to the sensible world and not
the one of paper” [Galilei, 1989, p. 68].
Manipulating observations to get new data, and “actively” building experiments,
like the famous one from the leaning tower, sometimes with the help of artifacts, is
the essence of the new way of knowing. Galileo says: “All these facts were discovered and observed by me many days ago with the aid of a spyglass which I devised,
after first being illuminated by divine grace. Perhaps other things, still more remarkable, will in time be discovered by me or by other observers with the aid of such
an instrument” [Galilei, 1957, p. 28]. Attaching a scale marked with equally spaced
horizontal and vertical lines to his telescope, and manipulating objects “idealizing”
them and not considering interesting and non influential factors, Galileo was able to
record the daily histories of the four “starlets” accompanying Jupiter and to show
1.6 Manipulative Abduction
55
that the data was consistent with the abduction that the starlets were indeed moons
orbiting Jupiter with a constant period.
With Galileo’s achievements, we observe that human scientific thinking is related
to the manipulation of a material and experimental environment that is no longer
natural. Knowledge is finally seen as something cognitively distributed across scientists, their internal “minds”, and external artifacts and instruments. Experiments
and instruments embody in their turn external crystallization of knowledge and practice. Modern science is made by this interplay of internal and external. Bacon too
was very clear about this distribution of epistemic tasks:
Those who handled sciences have been either men of experiment or men of dogmas.
The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes a
middle course: it gathers its material from the flowers of the garden and of the field,
but transforms and digests it by a power of its own [Bacon, 2000, p. 52].
An immediate consequence of Galileo’s and Bacon’s ideas is the critique of the
authority, that advocated the knowledge relevance of a “world of paper”. Gooding observes: “It is ironical that while many philosophers admire science because
it is empirical as well as rational, philosophical practice confines it to the literary
view that Galileo rejected” [Gooding, 1990, p. xii]. Galileo’s “book of nature” and
his systematic use of the telescope are the revolutionary epistemic mediators78 that
characterize the cognitive power of the new way of producing intelligibility.
Changes in the modalities of distributing epistemic assignments are never without costs. We can just remark, even if well-known, that Galileo’s new management
of information and knowledge by means of inventing and stabilizing these mediators
was not without individual and violent social costs. Because of the new knowledge
provided, Dialogue was prohibited, and he was sentenced (1633 – the admonition is
of 1616) to life imprisonment by the Holy Office with the added task of having to recite once a week for three years the seven penitential psalms. He read his abjuration
and was released to the custody of the Archibishop of Siena; his daughter, Sister
Maria Celeste was given permission to recite the psalms in his stead [van Helden,
1989]. The deterioration of the scientific climate and the decline of telescopic astronomy in Italy were the obvious immediate consequences. Notwithstanding the
problems, these new epistemic mediators, that are at the roots of the tradition of
scientific knowledge, were preserved, saved, and subsequently improved.
It is well known that recent philosophy of science has paid great attention to the
so-called theory-ladenness of scientific facts (Hanson, Popper, Lakatos, Kuhn): in
this light the formulation of observation statements presupposes significant knowledge, and the search for important observable facts in science is guided by that
knowledge. It is absolutely true that theory is able to lead us to abduce new facts,
but we cannot forget that a lot of new information is reached by observations and
experiments, as fruit of various kinds of artifactual manipulations. Robert Hooke,
using microscope to look at small insects, with practical interventions illuminated
78
Together with the exploitation of mathematical models.
56
1 Theoretical and Manipulative Abduction
his specimens from different directions to establish which features remained invariant under such changes and discovered that some disagreements about data were apparent [Chalmers, 1999, p. 22]. Galileo did not have a theory about Jupiter’s moons
to test when he used his telescope, but the manipulations of the new technology offered a lot of new information. In these cases it is only later that theory is able to
contribute new meanings to experimental results.
Following the so-called “new experimentalism” [Ackermann, 1989], we can say
that “experiment” has a “life of its own” [Hacking, 1983], independent of theory.
Hacking declares:
Experimental work provides the strongest evidence for scientific realism. This is not
because we test hypotheses about entities. It is because entities that in principle cannot
be “observed” are regularly manipulated to produce new phenomena and to investigate
other aspects of nature. They are tools, instruments not for thinking, but for doing
(p. 262).
We are even able to manipulate the old “philosopher’s favorite theoretical entity”,
the electron, and it is only in the early stages of our discovery of that entity, that
we may merely test the hypothesis that it exists. We already said that a great part of
the recent philosophy of science is theory-dominated: data is always considered as
theory-laden. Many histories of scientific facts are written, in this light, to emphasize theory and disregard the experimental and technological aspects of research:
experiments do not have an autonomous significance and the explanation of their
characteristics, aims and results is made in terms of theoretical issues unknown to
the experimenter. For instance: the experiment is considered significant only as a
means to test a theory under scrutiny. Hacking provides an interesting analysis of
Lakatos’ treatment of Michelson’s experiment: Hacking’s description of this experiment tells us that it does not pursue any programme Lakatos writes about and it
has a relative autonomy as regards theory. Classic positivism, pragmatism and kantism, the philosophies of science of Carnap, Popper, Lakatos, Feyerabend, Putnam,
van Fraassen and others are characterized by a “single-minded obsession with representation and thinking and theory, at the expense of intervention and action and
experiment” (p. 131).
Contrarily to a great part of the recent epistemological tradition, we have to follow Hacking and stress the attention on manipulative abduction and epistemic mediators also from the cognitive point of view. Creating an external cognitive support
is very important to increase the possibility to get new information, to extend scientific knowledge, but also to improve and simplify many kinds of reasoning. Scientific thinking, like everyday thinking, has not to be viewed only like an internal
speculative cognitive process, which occurs in a detached contemplation.
Hacking considers also the problem of realism by analyzing what we can use to
intervene in the world to affect something else, or what the world can use to affect us. He shows, with the help of many interesting and sophisticated laboratory
examples – some of them full of historical interest – that the significance of experiments sometimes has little to do with theory and representation. Entities whose
causal powers are well understood are used as tools to investigate (and to intervene
in) nature:
1.7 Mirroring Hidden Properties through Optical Diagrams
57
Understanding some causal properties of electrons, you guess how to build a very ingenious complex device that enables you to line up the electrons the way you want,
in order to see what will happen to something else. [. . . ] Electrons are no longer
ways of organizing our thoughts or saving the phenomena that have been observed.
They are ways of creating phenomena in some other domain of nature. Electrons are
tools (p. 263).
Concepts become tools endowed with absolutely unexpected outcomes. The experimentalists use various strategies for establishing the experimental effects without
any recourse to theory. These strategies correspond to the expert manipulation of
objects in a highly constrained experimental environment, we said directed by abductive movements that imply the application of old and new extra-theoretical templates of expert behavior. As possible creative organizations of experience some of
them become in their turn hypothetical interpretations of experience, that is more
theory-oriented, their reference is gradually stabilized in terms of established observational practices. Step by step the new interpretation relates to more “theoretical”
modes of abductively understanding (visual, diagrammatic, symbolic, conceptual,
simulative).
In this light it is not surprising that [Mayo, 1996], in her defense of experimentalism, has stressed attention to the possibility of delineating progress in science
in terms of accumulation of experimental knowledge and expertise. She adds more
arguments to the thesis of autonomy of experimental results illustrating many examples where the experiments are shown not as merely related to confirmation and
falsification. In some cases they not only serve as a falsification of the assertion, but
also to delineate new effects and ideas not previously known; moreover, they can
bear on the comparison of radically different theories:79 to resume, they can trigger
revolutionary creative abductions, enabling us to learn from errors. To exemplify the
positive role played by errors Mayo illustrates the famous case of the observation
of the questionable features of Uranus’s orbit that created problems for Newtonian
theory: the detection of the source of this difficulty led to the discovery of Neptune.
1.7
Mirroring Hidden Properties through Optical Diagrams
It is well-known that in the whole history of geometry many researchers used internal mental imagery and mental representations of diagrams, but also self-generated
diagrams (external) to help their thinking [Otte and Panza, 1999]. For example, it
is clear that in geometrical construction many of the requirements indicated by the
manipulative templates (cf. above subsection 1.6.2) are fulfilled. Indeed iconic geometrical constructions present situations that are curious and “at the limit”. Because
of their iconicity, they are constitutively dynamic, artificial, and offer various contingent ways of epistemic acting, like looking from different perspectives, comparing
subsequent appearances, discarding, choosing, re-ordering, and evaluating. Moreover, they present the features typical of manipulative reasoning illustrated above,
79
I already stressed at the beginning of this subsection the role played by construals of phenomena
to overcome the problem of incommensurability.
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such as the simplification of the task and the capacity to get visual information
otherwise unavailable.
We have seen that manipulative abduction is a kind of abduction, usually modelbased and so intrinsically “iconic”, that exploits external models endowed with delegated (and often implicit) cognitive and semiotic roles and attributes. We can say
that 1) the model (diagram) is external and the strategy that organizes the manipulations is unknown a priori; 2) the result achieved is new (if we, for instance, refer
to the constructions of the first creators of geometry), and adds properties not contained before in the concept (the Kantian to “pass beyond” or “advance beyond” the
given concept, [Kant, 1929, A154-B193/194, p. 192] I will describe in the following
chapter, section 2.8).80
Hence, in the construction of mathematical concepts many external representations are exploited, both in terms of diagrams and of symbols. I am interested in
my research in the diagrams which play various iconic roles: an optical role – microscopes (that look at the infinitesimally small details), telescopes (that look at
infinity), windows (that look at particularly situation), a mirror role (to externalize
rough mental models), and an unveiling role (to help to create new and interesting
mathematical concepts, theories, and structures).81 I also describe them as the epistemic mediators (cf. above) able to perform various abductive tasks (discovery of
new properties or new propositions/hypotheses, provision of suitable sequences of
models able to convincingly verifying theorems, etc.).82
An interesting epistemological situation I have recently studied is the one concerning the cognitive role played by some special epistemic mediators in the field
of non-standard analysis, an “alternative calculus” invented by Abraham Robinson
[1966], based on infinitesimal numbers in the spirit of Leibniz method.83 It is a kind
of calculus that uses an extension of the real numbers system R to the system R∗
containing infinitesimals smaller in the absolute value than any positive real number. I maintain that in mathematics diagrams play various roles in a typical abductive
way. Two of them are central:
• they provide an intuitive and mathematical abductive explanation facilitating the
understanding of concepts difficult to grasp, that appear hidden, obscure, and/or
epistemologically unjustified, or that are not expressible from an intuitive point
of view;
• they help create new previously unknown concepts, playing a non-explanatory
abductive role, as I will illustrate in the following chapter of this book.
80
81
82
83
Other interesting applications of the concept of abduction in mathematical discovery and in the
manipulation of symbols are illustrated in [Heeffer, 2007; Heeffer, 2009]. On the Cardano’s
abductive discovery of negative numbers and negative solution to a linear problem cf. [Heeffer,
2007].
The epistemic and cognitive role of mirror and unveiling diagrams in the discovery of nonEuclidean geometry is also illustrated in [Magnani, 2002a]. Cf. also the following chapter,
sections 2.9 and 2.11.
Elsewhere I have presented some details concerning the role of optical diagrams in the calculus
[Magnani and Dossena, 2005; Dossena and Magnani, 2007].
Further updated details concerning Leibniz’s mathematics and philosophy of infinitesimals are
ilustrated in [Mancosu, 1996].
1.7 Mirroring Hidden Properties through Optical Diagrams
59
Optical diagrams play a fundamental explanatory (and didactic) role in removing
obstacles and obscurities and in enhancing mathematical knowledge of critical situations. They facilitate new internal representations and new symbolic-propositional
achievements. In the example I have studied in the area of the calculus, the extraordinary role of the optical diagrams in the interplay standard/non-standard analysis
is emphasized. In the case of our non-standard analysis examples, some new diagrams (microscopes within microscopes) provide new mental representations of
the concept of tangent line at the infinitesimally small regions. Hence, external representations which play an “optical” role can be used to provide us with a better
understanding of many critical mathematical situations and, in some cases, to more
easily discover (or rediscover) sophisticated properties.
The role of an “optical microscope” that shows the behavior of a tangent line
is illuminating. In standard analysis, the change dy in y along the tangent line is
only an approximation of the change Δ y in y along the curve. But through an
optical microscope, that shows infinitesimal details, we can see that dy = Δ y and
then the quotient Δ y/Δ x is the same of dy/dx when dx = Δ x is infinitesimal (see
Figure 1.10 and, for more details, [Magnani and Dossena, 2005]). This removes
some difficulties of the representation of the tangent line as limit of secants, and
introduces a more intuitive conceptualization: the tangent line “merges” with the
curve in an infinitesimal neighborhood of the contact point.
1
0
0
1
1111
0000
Δy
00
11
11111
00000
11
00
00
11
11
00
Δx
0000
1111
00
1
01
1
0
Δy 1
0
1
0
1
00
1
111
01000
1
0
1
dy
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Fig. 1.10 An optical diagram shows an infinitesimal neighborhood of the graph of a real
function
Only through a second more powerful optical microscope “within” the first (I
call this kind of epistemic mediators microscopes within microscopes) (again, see
Figure 1.10), we can see the difference between the tangent line and the curve.
Under the first diagram, the curve looks like the graph of
f (a)x,
i.e., a straight line with the same slope of its tangent line;84 under the second, the
curve looks like
84
This is mathematically justified in [Magnani and Dossena, 2005].
60
1 Theoretical and Manipulative Abduction
1 f (a).
2
This suggests nice new mental representations of the concept of tangent lines:
through the optical lens, the tangent line can be seen as the curve, but through a
more powerful optical lens the graph of the function and the graph of the tangent
are distinct, straight, and parallel lines. The fact that one line is either below or above
the other, depends on the sign of f (a), in accordance with the standard real theory:
if f (x) is positive (or negative) in a neighborhood, then f is convex (or concave)
here and the tangent line is below (or above) the graph of the function.
However, this easily mirrors a sophisticated hidden property. Let f be a two times
differentiable function and let a be a flex point of it. Then f (a) = 0 and so the
second microscope shows again the curve as the same straight line: this means that
the curve is “very straight” in its flex point a. Of course, we already know this
property – the curvature in a flex point of a differentiable two times function is null
– which comes from standard analysis, but through optical diagrams we can find it
immediately and more easily (the standard concept of curvature is not immediate).
To conclude, I have already noted that some diagrams could also play an unveiling role, providing new light on mathematical structures: it can be hypothesized that
these diagrams can lead to further interesting creative results.
I stated that in mathematics diagrams play various roles in a typical abductive
way. We can add that:
f (a)x −
• they are epistemic mediators able to perform various more or less creative abductive tasks in so far as
• they are external representations which provide explanatory and non-explanatory
abductive results.
Summary
In this chapter we have seen that, to solve the problem of the so-called “logic of
discovery”, we need to clarify the meaning of concepts like creativity and discovery.
Following Peircean ideas, I have stressed that recent computational modeling is very
useful in a strictly pragmatical sense. We can produce and implement actual and
then possible, rational models of creative reasoning and scientific discovery. In this
intellectual framework a new paradigm, aimed at unifying the different perspectives,
is provided by the fundamental concept of abduction. Many “working” abductive
processes can be found and studied that are rational, unambiguous and perfectly
communicable. I have maintained that the concepts of sentential, model-based and
manipulative abduction are important not only in delineating the actual practice of
abduction but also in the development of computationally adequate programs used
to rediscover, or discover for the first time, for example, scientific hypotheses and
mathematical theorems or laws.
It is clear that the manipulation of external objects helps human beings in their
creative tasks. I have illustrated the strategic role played by the so-called traditional
1.7 Mirroring Hidden Properties through Optical Diagrams
61
concept of “implicit knowledge” in terms of the cognitive and epistemological concept of manipulative abduction, considered as a particular kind of abduction that
exploits external models endowed with delegated (sometimes implicit) cognitive
roles and attributes. Abductive manipulations operate on models that are external
and the strategy that organizes the manipulations is unknown and a priori. In the
case of creative manipulations of course the result achieved is also new and adds
properties not previously contained in the premises of reasoning. For example, in
scientific practice there are many procedural, extra-sentential and extra-theoretical
aspects indispensable to providing knowledge and information which are otherwise
hard to grasp. By making them explicit we can rationally and positively integrate
the previously existing scientific encyclopaedia. Enhancement of analysis of these
important human skills can increase knowledge on inferences involving creative,
analogical, spatial and simulative aspects, both in science and everyday situations,
thereby extending epistemological, computational, and psychological theory. It is
from this point of view that I have also described what I have called epistemic mediators and the templates of epistemic doing. These are able to illustrate the first
features of the performance of various abductive tasks and refer to various external
tools (and their manipulation) that can be built to cognitively help the activity of
scientists.
At the end of the chapter I have also described some results in the specific domain of calculus, were diagrams which play an optical role such as microscopes,
“microscopes within microscopes”, telescopes, and windows, a mirror role (to externalize rough mental models) or an unveiling role (to help create new and interesting mathematical concepts, theories, and structures) are studied. They play the role
of epistemic mediators able to perform the explanatory abductive task of endowing
difficult mathematical concepts with new “intuitive” meanings and of providing a
better understanding of the calculus through a non-standard model of analysis. I also
maintain that they can be used in many other different epistemological and cognitive situations (other examples in the field of mathematical discovery will be given
in the following chapter, section 2.8. 85
85
Another interesting application of the concept of manipulative abduction I have studied is in the
area of chance discovery [Magnani et al., 2002b]: concrete manipulations of the external world
constitute a fundamental passage in chance discovery. By a process of manipulative abduction
it is possible to build prostheses that furnish a kind of embodied and unexpressed knowledge
that plays a key role in the subsequent processes of scientific comprehension and discovery but
also in the extraction of the “unexpected” in ethical thinking and in moral deliberation.).
Chapter 2
Non-explanatory and Instrumental Abduction
Plausibility, Implausibility, Ignorance Preservation
In chapter one I have illustrated the basic distinction between theoretical and manipulative abduction and the other main features of abductive cognition. Further important cognitive and logico-epistemological considerations have to be added. First
of all the fact that abduction is a procedure in which something that lacks classical
explanatory epistemic virtue can be accepted because it has virtue of another kind:
[Gabbay and Woods, 2005] contend that abduction presents an ignorance preserving (but also an ignorance mitigating) character. From this perspective abductive
reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved
nor left intact. Abductive reasoning is an ignorance-preserving accommodation of
the problem at hand.
The chapter also introduces the basic distinction between the schematic representation of abduction which I have illustrated in chapter one (section 1.3), that
[Gabbay and Woods, 2005] call AKM-schema, and the GW -schema, they propose
in their recent book on abduction. The analysis and criticism of the GW -schema
provides an opportunity to illustrate non-explanatory and [radical] instrumentalist
aspects of abductive cognition. Examples of the non-explanatory features of abduction are present in logic and mathematical reasoning. The chapter gives an analysis
of how the importance of non-explanatory abduction in logical and mathematical
reasoning is clearly even if implicitly envisaged by Gödel. Furthermore, physics often aims at discovering physical dependencies which can be considered explanatorily undetermined. In this case abduction exhibits an instrumental aspect. In section
2.6 I contend that this character is sometimes related to the conventional nature of
the involved hypotheses.
The new non-explanatory and instrumentalist aspects of abduction in turn lead
to reconsideration, in a broader sense, of the role of plausibility in abductive cognition. Plausibility which occurs at the level of basic inner inferences of the real
human agent is related to considerations of relevance or how characteristic a certain behavior is and can be called [Gabbay and Woods, 2005, p. 209] “propositional”. However, there is also a “strategic” sense of plausibility that has to be taken
into account, the one which occurs in the case of instrumental abduction, where
L. Magnani: Abductive Cognition, COSMOS 3, pp. 63–143.
c Springer-Verlag Berlin Heidelberg 2009
springerlink.com 64
2 Non-explanatory and Instrumental Abduction
plausibility is no longer linked to standard characteristicness. For example, in scientific reasoning, an abductive hypothesis can be highly implausible from the “propositional” point of view and nevertheless it can be adopted for its instrumental virtues,
such as in the Newtonian case of action-at-a-distance. Highly implausible hypotheses from the “propositional” point of view can be conjectured because of their high
“instrumental” plausibility, where a different role of characteristicness is at stake.
The chapter further examines interesting cases of abduction that can be usefully
labeled non-explanatory and/or instrumentalist, showing how often the abductive
procedures are characterized by a mixture of explanatory, non-explanatory and instrumental aspects. The analysis of these cases is also an opportunity to demonstrate
that contradictions and inconsistencies are fundamental in abductive reasoning, especially in science, and that abductive reasoning is appropriate for “governing” inconsistencies, both at the empirical and theoretical/conceptual level. The importance
of the role of the so-called “preinventive forms” is also addressed.
Hence, contradiction is fundamental in abductive reasoning and it has a preference for strong hypotheses which are more easily falsified than weak ones.
Moreover, hard hypotheses may be more easily weakened than weak ones, which
subsequently prove more difficult to strengthen. Hypotheses may however be unfalsifiable, such as in the case of hypotheses which are fruit of “radical” instrumentalist
abduction. In this case, it is impossible to find a contradiction from the empirical
point of view but also from the theoretical point of view, in some area of the related conceptual systems. Notwithstanding this fact, it is sometimes necessary to
construct methods for rejecting the unfalsifiable hypothesis at hand by resorting to
some external form of negation. It would have to be an “external” criterion in order to avoid any arbitrary and subjective elimination, which could be rationally or
epistemologically unjustified.
I contend that this problem of unfalsifiable hypotheses is strictly linked to the
issue of non-explanatory and instrumentalist abduction, taking advantage of the
analysis of hypothesis withdrawal in Freudian analytic reasoning and in Poincaré’s
conventionalism of the principles of physics. From the point of view of instrumentalist abduction my example concerning the conventional principles of physics shows
a cognitive situation where such hypotheses are not subject to discharge except for
their instrumental value, since the abduced hypothesis, fruit of a radically instrumentalist abduction, fails all tests that would reveal it as having the requisite classical epistemic value.
The last part of the chapter is devoted to illustrating the problem of the extratheoretical dimension of cognition from the perspective of the famous discovery of
non-Euclidean geometries. This case study is particularly appropriate to the present
chapter because it shows relevant aspects of diagrammatic abduction, which involve
intertwined processes of both explanatory and non-explanatory abduction acting at
the model-based level in what I call mirror and unveiling diagrams. Finally, the
section 2.7 also deals with the epistemologically very interesting computational AI
applications that involve the abductive processes in scientific discovery and mathematical reasoning and creativity: some programs expressly devoted to the simulation
of geometrical reasoning are illustrated.
2.1 Is Abduction an Ignorance-Preserving Cognition?
2.1
2.1.1
65
Is Abduction an Ignorance-Preserving Cognition?
The Ignorance Preserving Character of Abduction
It is clear that “[. . . ] abduction is a procedure in which something that lacks epistemic virtue is accepted because it has virtue of another kind” [Gabbay and Woods,
2005, p. 62]. For example: “Let S be the standard that you are not able to meet
(e.g., that of mathematical proof). It is possible that there is a lesser epistemic standard S (e.g., having reason to believe) that you do meet” [Woods, 2010, chapter eight]. Focusing attention on this cognitive aspect of abduction [Gabbay and
Woods, 2005] contend that abduction (basically seen as a scant-resource strategy, which proceeds in absence of knowledge) presents an ignorance preserving
(but also an ignorance mitigating) character. Of course “[. . . ] it is not at all necessary, or frequent, that the abducer be wholly in the dark, that his ignorance be
total. It needs not be the case, and typically isn’t, that the abducer’s choice of a
hypothesis is a blind guess, or that nothing positive can be said of it beyond the
role it plays in the subjunctive attainment of the abducer’s original target (although
sometimes this is precisely so)” (cit.). Abductive reasoning is a response to an
ignorance-problem: one has an ignorance-problem when one has a cognitive target that cannot be attained on the basis of what one currently knows. Ignorance
problems trigger one or other of three responses. In the first case, one overcomes
one’s ignorance by attaining some additional knowledge (subduance). In the second instance, one yields to one’s ignorance (at least for the time being) (surrender).
In the third instance, one abduces [Woods, 2010, chapter eight] and so has a positive and reasoned basis for new action even if in the presence of the constitutive
ignorance.
From this perspective the general form of an abductive inference can be rendered
as follows. Let α be a proposition with respect to which you have an ignorance
problem. Putting T for the agent’s epistemic target with respect to the proposition
α at any given time, K for his knowledge-base at that time, K ∗ for an immediate accessible successor-base of K that lies within the agent’s means to produce
in a timely way,1 R as the attainment relation for T , as the subjunctive conditional relation, H as the agent’s hypothesis, K(H) as the revision of K upon the
addition of H, C(H) denotes the conjecture of H and H c its activation. The general structure of abduction can be illustrated as follows (GW-schema, cf. below
subsection 2.1.3):
1
“K ∗ is an accessible successor to K to the degree that an agent has the know-how to construct
it in a timely way; i.e., in ways that are of service in the attainment of targets linked to K. For
example if I want to know how to spell ‘accommodate’, and have forgotten, then my target can’t
be hit on the basis of K, what I now know. But I might go to my study and consult the dictionary.
This is K ∗ . It solves a problem originally linked to K” [Woods, 2010, chapter eight].
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2 Non-explanatory and Instrumental Abduction
1. T !α
[setting T is an epistemic
target with respect to a
proposition α ]
2. ¬(R(K, T )
[fact]
[fact]
3. ¬(R(K ∗ , T )
4. H ∈ K
[fact]
[fact]
5. H ∈ K ∗
6. ¬R(H, T )
[fact]
7. ¬R(K(H), T )
[fact]
8. If H were true then it would be the case that [fact]
R(K(H), T )
[fact]
9. H meets further conditions S1 , ....Sn
10. Therefore, C(H)
[sub-conclusion, 1-9]
[conclusion, 1-10]
11. Therefore, H c
It is easy to see that the distinctive epistemic feature of abduction is captured by the
schema. It is a given that H is not in the agent’s knowledge-set. Nor is it in its immediate successor. Since H is not in K, then the revision of K by H is not a knowledgesuccessor set to K. Even so, H (K(H), T ) . So we have an ignorance-preservation,
as required (cf. [Woods, 2010, chapter eight]).
[Note: Basically, line 9. indicates that H has no more plausible or relevant rival
constituting a greater degree of subjunctive attainment. Characterizing the Si is the
most difficult problem for abductive cognition, given the fact that in general there
are many possible candidate hypotheses. It involves for instance the consistency and
minimality constraints (lines 4 and 5 of the standard schema below in subsection
2.1.3, p. 70). I will illustrate below (cf. subsection 2.3.1) that, in the case of inner
processes in organic agents, this process is largely implicit, and so also linked to
unconscious ways of inferring, or, in Peircean terms, to the activity of the instinct
[Peirce, 1931-1958, 8.223] and of what Galileo called the lume naturale [Peirce,
1931-1958, 6.477], that is the innate fair for guessing right.
However, in more hybrid and multimodal (not merely inner) abductive processes
(cf. chapter four, section 4.1), such as in the case of manipulative abduction, the
assessment is reached – and constrained – taking advantage of the gradual acquisition of further external information with respect to future interrogation and control, even if not due to actual experimental tests. At least three kinds of actions
are involved in these abductive processes (and we would have to also take into account the motoric aspect of inner “thoughts” too, cf. chapter four, section 4.4, p.
233). In this interplay the cognitive agent further triggers internal thoughts “while”
modifying the environment and so (i) acting on it (thinking through doing). In this
case the “motor actions” directed to the environment have to be intended as part
and parcel of the whole embodied abductive inference, and so have to be distinguished from the final (ii) “actions” as fruit of the reached abductive result. In this
perspective the proper experimental test involved in the Peircean evaluation phase,
which for many researchers reflects in the most acceptable way the idea of abduction as inference to the best explanation, just constitutes a special subclass of the
processes – which involve another kind (iii) of actions – of adoption of abductive
2.1 Is Abduction an Ignorance-Preserving Cognition?
67
hypotheses, and should be considered ancillary to the nature of abductive cognition,
and inductive in its essence.
Finally, C(H) is read “It is justified (or reasonable) to conjecture that H” and H c is
its activation, as the basis for planned “actions”, in the sense I have just illustrated.]
In sum, T cannot be attained on the basis of K. Neither can it be attained on the
basis of any successor K ∗ of K that the agent knows then and there how to construct.
H is not in K: H is a hypothesis that when reconciled to K produces an updated
K(H). H is such that if it were true, then K(H) would attain T . The problem is that
H is only hypothesized, so that the truth is not assured. Accordingly Gabbay and
Woods contend that K(H) presumptively attains T . That is, having hypothesized
that H, the agent just “presumes” that his target is now attained. Given the fact that
presumptive attainment is not attainment, the agent’s abduction must be considered
as preserving the ignorance that already gave rise to her (or its, in the case for example of a machine) initial ignorance-problem. Accordingly, abduction does not have
to be considered the “solution” of an ignorance problem, but rather a response to
it, in which the agent reaches presumptive attainment rather than actual attainment.
C(H) expresses the conclusion that it follows from the facts of the schema that H is
a worthy object of conjecture. It is important to note that in order to solve a problem
it is not necessary that an agent actually conjectures a hypothesis, but it is necessary
that she states that the hypothesis is worthy of conjecture.
It is remarkable that in the above schema
[. . . ] R(K(H), T ) is false and yet that H (K(H), T ) is true. Let us examine a case.
Suppose that your target T is to know whether α is true. Suppose that, given your
present resources, you are unable to attain that target. In other words, neither your K
nor your K ∗ enables you to meet your target. Let H be another proposition that you
don’t know. So K(H) is not a knowledge-set for you. On the principle that you can’t
get to know whether α on the basis of what you don’t know, K(H) won’t enable you
to attain T either. This is a point of some subtlety. Pages ago, weren’t we insisting that
there are contexts – autoepistemic contexts – in which not knowing something is a way
of getting to know something else? No, we said that not knowing something was a way
of getting to presume something else. But just to be clear, let us point out that in the
GW-schema α and H are not candidates for the autoepistemic inference of α from H
or K(H). So R(K(H), T ) is false. H (K(H), T ) is different. It says, subjunctively,
that if H were true, then the result of adding H to K would attain T . Clearly this can be
true while, for the same H, K and T , R(K(H), T ) is false [Woods, 2010, chapter eight].
Finally, considering H justified to conjecture is not equivalent to considering it justified to send H to trial. H c denotes the decision to release H for further premissory
work in the domain of enquiry in which the original ignorance-problem arose, that
is the activation of H as a positive basis for action. Woods usefully observes:
There are lots of cases in which abduction stops at line 10, that is, with the conjecture
of the hypothesis in question but not its activation. When this happens, the reasoning
that generates the conjecture does not constitute a positive basis for new action, that is,
for acting on that hypothesis. Call these abductions partial as opposed to full. Peirce
has drawn our attention to an important subclass of partial abductions. These are cases
in which the conjecture of H is followed by a decision to submit it to experimental test.
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2 Non-explanatory and Instrumental Abduction
Now, to be sure, doing this is an action. It is an action involving H but it is not a case
of acting on it. In a full abduction, H is activated by being released for inferential work
in the domain of enquiry within which the ignorance-problem arose in the first place.
In the Peircean cases, what counts is that H is withheld from such work. Of course,
if H goes on to test favourably, it may then be released for subsequent inferential
engagement [Woods, 2009].
We have to remember that this last process is not abductive, it is inductive, as Peirce
contended and I illustrated in the previous chapter. Woods adds: “Now it is quite true
that epistemologists of a certain risk-averse bent might be drawn to the admonition
that partial abduction is as good as abduction ever gets and that complete abduction,
inference-activation and all, is a mistake that leaves any action prompted by it without an adequate rational grounding. This is not an unserious objection, but I have no
time to give it its due here. Suffice it to say that there are real-life contexts of reasoning in which such conservatism is given short shrift, in fact is ignored altogether.
One of these contexts is the criminal trial at common law” [Woods, 2009].
Here it cannot be said that testability is intrinsic to abduction, such as in the
case of the ST-model illustrated above in subsection 1.4 of chapter one, and in the
case of some passages of Peirce’s writings.2 This action, which in turn involves
degrees of risk proportioned to the strength of the conjecture, is strictly cognitive/epistemic and inductive in itself, for example an experimental test, is an intermediate step to release the abduced hypothesis for inferential work in the domain
of enquiry within which the ignorance-problem arose in the first place.
Through abduction the basic ignorance – that does not have to be considered
total “ignorance” – is neither solved nor left intact: it is an ignorance-preserving
accommodation of the problem at hand. As I have already stressed, in a defeasible
way, further action can be triggered either to find further abductions or to “solve”
the ignorance problem, possibly leading to what it is usually called the inference
to the best explanation. It is clear that in this framework the inference to the best
explanation – if considered as a truth conferring achievement – cannot be a case
of abduction, because abductive inference is constitutively ignorance preserving. In
this perspective the inference to the best explanation also involves – for example –
the generalizing and evaluating role of induction. Of course it can be said that the
requests of originary thinking are related to the depth of the abducer’s ignorance.
2.1.2
Truth Preserving and Ignorance Preserving Inferences
From an agent-based perspective on logic similar to one adopted by Gabbay and
Woods,3 which pays attention to psychological/subjective aspects and strongly
stresses the ignorance preserving character of the logic of abduction, Jean Yves
Girard’s annotations about the logics which model abduction can acquire further
clarification. Girard says “‘Epistemic’ logics are supposed to illustrate ‘abductive’
2
3
When abduction stops at line 10., the agent is not prepared to accept K(H), because of supposed
adverse consequences.
On this agent-based perspective cf. also chapter seven, this book.
2.1 Is Abduction an Ignorance-Preserving Cognition?
69
principles of reasoning: from the fact that we don’t know, one deduces something.
[. . . ] Epistemic logics are based upon the identification between ‘not to know’ and
‘to know not’. If such an identification would be possible, it would suffice to add
relevant axioms. One sees that this is impossible, since then, G being not provable,
this fact would be provable (what is expressed by G), contradiction” [Girard, 2006,
pp. 104–105]. Girard refers to the inconsistency of these systems as a corollary of
Gödel theorem, and further stresses the problems created by the nonmonotonic logics of abduction, which, he says, without any hesitation, add a principle of the sort
if ¬A is not provable, then A is provable”. The conclusion is strong:
Granted adequate precautions, these systems are consistent and complete, so what do
you complain about? They are simply non-deductive, because there is no way to activate the additional principle. One is no longer dealing with a formal system, since
there is no way to know that something is not provable (this is already wrong in a deductive system, so in such a doohickey, good luck!). By the way, let us directly refute
the algorithm analog of “non-monotonicity”. One wants to answer any query and the
“solution” is as follows: if the algorithm yields an answer, say “yes”, answer “yes”, if
it says “no”, answer “no”, if it keeps silent answer whatever you like, “yes” or “no”,
nay “I don’t know”. This is impossible, because Turing’s undecidability of the halting
problem precisely tells us that there is no algorithmic way of knowing that one does
not know [Girard, 2006, p. 105].
In sum, it seems that entering nonmonotonic logic of abduction means leaving deduction and demonstrative reasoning, at least in Girard’s rigid sense. The ignorance
preserving approach to abduction and its logics de facto acknowledges Girard’s conclusion regarding the entire old-fashioned perspective on deductive logic: “What we
logicians manipulate under the name true” is but an empty shell. A last word: one
should not forget either that Gödel formula, this over-ornate artifact, before meaning ‘I am not provable’, says ‘I mean nothing”’ [Girard, 2006, pp. 106]. Indeed, the
ignorance preserving approach permits us to further appreciate Girard’s view. Following Girard, we can say that, in a sense, abductive logics like the nonmonotonic
ones, certainly formalize ignorance preserving inferences, but the truth preserving
character of deductive logic is achieved at the cost of skipping the problem of the
multifaceted ignorance of cognitive agents. Truth preserving inferences involve a
kind of ideal intersubjectivity, that is the fact that certain propositions A, B, . . . “share
the same point of view” [Girard, 2007, p. 64], and it is at this price that deductive
logic can say that the truth of A and of A → B implies the truth of B.
“In terms of intersubjectivity, logic still testimonies the caprices of ‘common
knowledge’: no doubts about the fact that at this level the constitution of the subject
is not admitted, everything is already available, and it is only necessary to select
dispersed pieces of information” [Girard, 2007, pp. 64–65]. Nevertheless, the subjective side of truth implies that a theorem can also be true or false depending on
the point of view. The idea of making cooperative A and B implies that they share
something at the level of sense. This is basically (inter)subjective and expressed by a
shared perspective on truth: it is with respect to this common point of view that truth
is preserved. This subtle relativity to a “point of view” can be extended to the case
of abduction: if deductive logic preserves truth, abduction preserves ignorance, but
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2 Non-explanatory and Instrumental Abduction
in both cases the preservation depends on some common contingent perspectives
respectively on truth and ignorance.
2.1.3
AKM and GW Schemas of Abduction
The schematic representation of abduction I have illustrated in chapter one
(section 1.3) expresses what [Gabbay and Woods, 2005] call AKM-schema,4 which
is contrasted to their own (GW -schema), which I have basically explained in the
subsection 2.1.1 above.
The AKM can be illustrated as follows:
1. E
2. K E
3. H E
4. K(H) is consistent
5. K(H) is minimal
6. K(H) E
7. Therefore, H.
[Gabbay and Woods, 2005, pp. 48–49].
where of course the conclusion operator cannot be classically interpreted.
Consequentialism and explanationism are the two main characters of this
schema, which certainly grasps fundamental aspects of abduction. The target has
to be an explanation and K(H) bears R pres [that is the relation of presumptive attainment] to T only if there is a proposition V and a consequence relation such that
K(H) V , where V represents a payoff proposition for T . In turn, in this schema
explanations are interpreted in consequentialist terms. If E is an explanans and E an explanandum the first explains the second only if (some authors further contend if and only if) the first implies the second. It is obvious to add that the AKM
schema embeds a D-N (deductive-nomological) interpretation of explanation, as I
have already stressed in [Magnani, 2001b, p. 39]. Moreover, the fact that abduction
is a procedure in which something that lacks traditional epistemic virtue (at least
in the sense epistemic virtues are intended in the epistemological tradition) is accepted because it has virtue of another kind, that is its ignorance preservation, (cf.
above subsection 2.1.1) is tacitly recognized in the AKM model (and also in Peirce’s
philosophy), but only explicitly illustrated in the GW one.
I have said in the first chapter of this book that the AKM schema embeds the
D-N model (the Hempel’s law covering model of scientific explanation [Hempel,
1966]): an additional remark has to be added. The D-N model presents a classical
logical structure and consequently the idea of explanation it involves is not in itself
abductive, as clearly pointed out by Gabbay and Woods
4
For A they refer to Aliseda [Aliseda, 1997; Aliseda, 2006], for K to Kowalski [Kowalski, 1979],
Kuipers [Kuipers, 1999], and Kakas et al. [Kakas et al., 1993], for M to Magnani [Magnani,
2001b] and Meheus [Meheus et al., 2002].
2.2 Non-explanatory Abduction
71
If explanation is taken in the D-N sense, then no successful explanationist abduction
can embody the D-N notion of explanation unless the explanationism in question is
subjunctive. [. . . ] The explanations it captures also stand or fall independently of the
epistemic states or interests of any agent (so the epistemic version is not intrinsic to the
model). But when abduction enters the picture, it does so with the requisite structure
and the necessary impairments or omissions of the agent’s K-set. The requirements
necessary for the explanationist hitting of an abductive target T make it impossible
for the abducer to produce a D-N explanation of the state of affairs embraced by this
target. The best he can do in this regard is produce a subjunctive D-N explanation,
putting it loosely [Gabbay and Woods, 2005, p. 93].
However, this requirement is not sufficient: “Even so, it is a fateful turn. [. . . ] There
are senses of explanation for which the constraints of subjunctivity are redundant.
Another way of saying this is that there are conceptions of explanations that are
themselves subjunctivist in character, and for which, therefore, the subjunctivizing consequences of abductive employment amount to the transportation of coal to
Newcastle” [Gabbay and Woods, 2005, p. 93].
2.2
Non-explanatory Abduction
[Gabbay and Woods, 2005] contend – and I agree with them – that abduction is
not intrinsically explanationist, like for example its description in terms of inference to the best explanation would suggest. Not only that, abduction can also be
merely instrumental. This conviction constitutes the main reason for proposing the
GW -schema, which offers a representation of abductive cases not captured by that
of the AKM-schema. In the following sections and subsections I will describe some
non-explanatory (and instrumental) aspects of abduction that are explicitly acknowledged by the GW schema. In my previous book on abduction [Magnani, 2001b]
I made some examples of abductive reasoning that basically are non-explanatory
and/or instrumentalist without clearly acknowledging it. The contribution of Gabbay and Woods to the analysis of abduction has the logical and epistemological
merit of having clarified these basic aspects of abduction, until now disregarded in
the literature. Their distinction between explanatory, non-explanatory and instrumental abduction is orthogonal to mine in terms of the theoretical and manipulative
(including the subclasses of sentential and model-based) and further allows us to
explore fundamental features of abductive cognition.
Hence, if we maintain that E explains E only if the first implies the second,
certainly the reverse does not hold. This means that various cases of abduction are
consequentialist but not explanationist [other cases are neither consequentialist nor
explanationist]:
It merits emphasis that not all T ’s either specify or have payoff propositions. If, for
example, the target is to justify a recondite principle of logic L, it may suffice to produce a derivation of some obvious proposition of arithmetic A in which that logical
principle occurs non-redundantly as premisses. Following Russell [. . . ] we might well
take this as grounds on which to hypothesize that the recondite principle L is indeed
72
2 Non-explanatory and Instrumental Abduction
justified. But it is as well to note that nowhere in this scenario is there any question that
the abduction requires (or permits) that L itself is a payoff proposition for T or that L
is in the counterdomain of any consequence relation on display in the abduction. Let
the proof that does not deliver the goods for A be schematized as
P1
..
.
Pn
A
Assume now that if L is added as premiss, the proof goes through. In other words,
whereas {P1 , ..., Pn } doesn’t suffice for A, {P1 , ..., Pn , L} does. For this to be so, there
must be a consequence relation on {P1 , ..., Pn, L}, A. But A is not the payoff for T .
Rather {P1 , ..., Pn, K} is. And this is itself neither a proposition nor the consequent of
any consequence relation of which the abduction must take note. We repeat: sometimes
T has a payoff proposition; sometimes it specifies this proposition; and sometimes
this proposition is required to be in the counterdomain of a consequence relation the
abduction must take note of. When these facts obtain, it is essential that the abductive
enterprise take them into account. When they do not obtain, there is nothing to take
into account; and no schema should posit them unduly [Gabbay and Woods, 2005, pp.
51-52].
Non-explanatory modes of abduction are clearly exploited in the “reverse mathematics” pioneered by Harvey Friedman and his colleagues, e.g., [Friedman and
Simpson, 2000], where propositions can be taken as axioms because they support
the axiomatic proofs of target theorems. The target of reverse mathematics is to answer this fundamental question: What are the appropriate axioms for mathematics?
The problem is to discover which are the appropriate axioms for proving particular theorems in central mathematical areas such as algebra, analysis, and topology
(cf. [Simpson, 1999]). The idea of reverse mathematics originates with Russell’s
notion of the regressive method in mathematics [Russell, 1973], and is also present
in some remarks of [Gödel, 1944; Gödel, 1990a].5 [Gabbay and Woods, 2005, p.
128] conclude, following Russell, that regressive abduction is both instrumental
and non-explanatory, and quote a Gödel’s passage, which confirms their statement:
[. . . ] even disregarding the intrinsic necessity of some new axiom, and even in case it
has no intrinsic necessity at all, a probable decision about its truth is possible also in
another way, namely inductively by studying its “success”. Success here means fruitfulness in consequences, in particular, “verifiable” consequences, i.e., consequences
demonstrable without the new axioms, whose proofs with the help of the new axiom,
however, are considerably simpler and easier to discover, and make it possible to contract into one proof many different proofs [Gödel, 1990a, pp. 476–477] .6
5
6
For more details about this, see [Irvine, 1989], who also compares Russell’s regressive method
to Peirce’s abduction.
I will further illustrate Gödel’s implicit acknowledgment of the role of abduction in logic in the
following subsection.
2.2 Non-explanatory Abduction
73
Furthermore, often in physics the target is the discovery of physical dependencies
which [Gabbay and Woods, 2005, pp. 122–123] consider explanatorily undetermined. In this case abduction can exhibit an instrumental aspect.7 I will contend in
section 2.6 below that this character is sometimes related to the conventional nature
of the involved hypotheses. Moreover, also in many AI approaches based on logic
programming and belief revision (cf. above, chapter one, subsections 1.4 and 1.4.1)
explanationism tends to disappear and abduction is mainly considered as proof theoretic and algorithmic: “On this view, an H is legitimately dischargeable to the extent
to which it makes it possible to prove (or compute) from a database a formula not
provable (or computable) from it as it is currently structured. This makes it natural
to think of AI-abduction in terms of belief-revision theory, of which belief-revision
according to explanatory force is only a part” [Gabbay and Woods, 2005, p. 88].
However, the explanatory character is subsumed in these AI approaches as a philosophical conception.
2.2.1
Gödel and Abduction
I aim at further illustrating that the importance of non-explanatory abduction in
logic and mathematics is clearly envisaged by Gödel. In the two essays of 1944 and
1947 “Russell’s Mathematical Logic” and “What is Cantor’s Continuum Problem?”
[Gödel, 1944; Gödel, 1990b] and in the “Supplement” to the Second Edition of the
1947 essay [Benacerraf and Putnam, 1964, pp. 258–273], Gödel’s ontology reveals
itself as a space for reflection which allows us to rescue Cantor’s classical analysis
and set theory and to account for a possible expansion of the latter.
Gödel’s ontology is articulated into a conceptual strategy with three levels of
analysis: 1) the ontological extent of formal systems and mathematics; 2) the analogy between mathematics and logic on the one hand and natural sciences on the
other; 3) the elaboration of an original notion of mathematical intuition to be understood as an activity of the constitution of mathematical objects, which we can
interpret as essentially abductive.
Gödel considers “[...] mathematical objects to exist independently of our constructions and our having an intuition of them individually” (“What is Cantor’s. . . ”,
in [Benacerraf and Putnam, 1964, p. 262]). Mathematical entities, the objects of
mathematical reality, are those studied by that area of mathematics called mathematical logic, i.e. “[. . . ] classes, relations, combinations of symbols, etc., instead of
numbers, functions, geometric figures, etc.” (“Russell’s Mathematical. . . ”, in [Benacerraf and Putnam, 1964, p. 211]. Moreover, all those objects from other areas of
mathematics which one tries to derive “[. . . ] actually from a very few logical concepts and axioms” (ibid., p. 212) are entities too, such as for example, those of the
Principia and in general those contained in formal systems meant to represent the
entities themselves, that is the objects of mathematical reality.
7
Other authors, and myself in [Magnani, 2001b, p. 17], disregarded this aspect and rather thought
in this case we deal with a different kind of explanation, i.e simple non causal explanation.
74
2 Non-explanatory and Instrumental Abduction
We can, therefore, maintain that logical and mathematical objects transcend their
own representation. Gödel is obviously interested in spotting the ontological constitution of the entities of mathematical logic: this is, by the way, of such great
importance because not only does mathematical logic aim at achieving a representation and a foundation of mathematics, but “[. . . ] it is a science prior to all others,
which contains the ideas and principles underlying all sciences” (ibid., p. 211).
Seeking a theory of knowledge adequate to address the issue of a Platonistrealist ontology, Gödel develops an analogy between logic and natural sciences already found in Russell’s Introduction to Mathematical Philosophy [Russell, 1919].
Gödel finds in Russell the comparison between the axioms of logic and mathematics
and the laws of nature and consequently the comparison between logical evidence
(which [Wang, 1987, p. 303], calls “semi-perception”; for Gödel, in fact, logical evidence is “something like a perception”) and sense perception. In this way, axioms
do not appear to receive their evidence immediately themselves but, rather, their
justification lies (exactly as is the case of hypotheses in physics) in the fact that they
render possible an inference of more elementary “logical evidence”, i.e., somehow
relatable to sense perceptions. We can now make explicit that this inference is a
kind of non-explanatory and instrumental abduction (plausibility at play is a mixed
one, propositional and strategic, see the following section). Gödel’s concept of the
axiomatic method certainly goes beyond the concept of formal systems, since he
regards classical physics, for instance, as an axiomatic system.
Logical axioms are, therefore, considered to be similar to physical hypotheses.
Their hypothetical make-up indicates that they are meant to discover a world of
mathematical objects and at the same time to make of these objects an original
intelligibility and an original representability. I contend that the activity which is
thought by Gödel to be operating in logic (and in mathematics) is to be considered
as an abductive activity of the construction of a knowledge of mathematical objectivity. This is shown within an inferential process that allows to guess the axioms
from which an argument can be traced back to the “logical evidence” (as similar to
“sense perception”), which is similar to the process occurring in physics and natural
sciences, though with a different degree of plausibility.
For Gödel, an example of this process is the case in which, in order to solve
some arithmetical problems, it is deemed necessary to use very general principles,
“[. . . ] assumptions essentially transcending arithmetic, i.e., the domain of the kind
of elementary indisputable evidence that may be most fittingly compared with sense
perception” [Benacerraf and Putnam, 1964, p. 213]. This is also the case when, in
order to solve set theory problems (which are, so to speak, far from the ‘evident”
level of arithmetic), it is necessary to enrich the available theories using “[. . . ] new
axioms based on some hitherto unknown idea” (ibid.). In my opinion the exploration
of the analogy between mathematics and logic on the one hand and natural sciences
on the other, does not superimpose a trivial theory of knowledge of a hypotheticaldeductive type on the basic Platonist ontology, but rather serves to complicate it
further with Kantian considerations, as we shall see below.
In the “Supplement” to the Second Edition of “What is Cantor’s Continuum Problem?”, Gödel clearly and profoundly points out the actual philosophical structure of
2.2 Non-explanatory Abduction
75
the gnoseological medium which integrates with the basic Platonist ontological conception. Following through the analogy between logic and natural sciences, Gödel
specifies the relationship between logical objects and the elementary level of “evidence”, which, as we have seen above, had been held to be analogous with sense
experience and sense perception in physics: “[. . . ] despite their remoteness from
sense experience, we do have something like a perception also of the objects of
set theory, as is seen from the fact axioms force themselves upon us as being true”
(‘Supplement’ to the Second Edition of “What is Cantor’s. . . ”, [Benacerraf and Putnam, 1964, p. 271].
Sense perceptions, in the specific meaning they acquire in the case of logic and
mathematics, trigger off a process of theory germination, just like perceptions themselves that, in the specific meaning they acquire in the case of physics and natural
sciences, cause an abductive movement of hypothesis generation (Gödel, who does
not refer to the concept of abduction, calls this movement inductive). More precision is needed: the abductive movement from “this type of perception” toward the
generality of theories and logical concepts encounters, in its turn, the categorizing
effect of another element which Gödel, after some hesitation, clearly indicates as
“mathematical intuition”.
Mathematical intuition is actually an activity of the constitution of mathematical objects themselves: “It should be noted that mathematical intuition need not be
conceived of as a faculty giving an immediate knowledge of the objects concerned.
Rather, it seems that, as in the case of physical experience, we form our ideas also
of those objects on the basis of something else which is immediately given” (ibid.).
Mathematical intuition does not therefore provide an immediate knowledge of its
own object: it forms itself upon a basis, an original datum that “it” “is immediately
given”. And, moreover, a very important consideration, this datum “is not, or not
primarily, the sensations” (ibid).
Sense perceptions in logic and mathematics, as already observed, contain something different from physical ones. Gödel explains himself very precisely: “That
something besides the sensations actually is immediately given follows [. . . ] from
the fact that even our ideas referring to physical objects contain constituents qualitatively different from sensations or mere combinations of sensations, e.g., the idea
of concept itself, whereas, on the other hand, by our thinking we cannot create any
qualitatively new elements, but only reproduce and combine those that are given”
(ibid., pp. 271-272). These “constituents” are the basis/premise of the abductive
inference.
With the statement concerning thinking, which reminds us of Kant’s assertion
regarding the incapability of concept constituting the object itself, it is possible to
define the specific feature of that sense perception level (“evidence”, “given”) which
operates in mathematical and logical knowledge or, more generally, the set of abstract aspects already present at the empirical level; in fact Gödel is once again
very clear: “[. . . ] the ‘given’ underlying mathematics is closely related to the abstract elements contained in our empirical ideas” (ibid., p. 272). And again: “It by
no means follows, however, that the data of this second kind, because they cannot
be associated with actions of certain things upon our sense organs, are something
76
2 Non-explanatory and Instrumental Abduction
purely subjective, as Kant asserted. Rather they, too, may represent an aspect of objective reality” (ibid.). At this point, the reasoning comes to an end: these abstract
elements, besides representing an aspect of the objective reality, “[. . . ] as opposed
to the sensations [. . . ] may be due to another kind of relationship between ourselves
and reality” (ibid).
According to Gödel’s philosophy, mathematical entities are therefore formed, and
so abductively guessed, on the basis of something else which is immediately given,
which is both their starting point and point of arrival. The gnoseological framework
is given by an intuition as an abductive constitution of the mathematical object, but
– it is important to note – not from a fixed and rigid perspective, but according to
the image of a continuous and progressive activity (e.g., by means of the continuous
introduction of new axioms and of the actual operations of constructivist proofs)
which, starting from a given basis (the constituents qualitatively different from sensations), returns, having in the meantime produced the categorical and ontological
representation of the true entities.
Gödel recognizes the continuing expansion of the results of our intuition and
provides an illustration of this dynamic and progressive activity referring to the concept of set, that is “of synthetic nature”, “[. . . ] there is a close relationship between
the concept of set [. . . ] and the categories of pure understanding in Kant’s sense.
Namely, the function of both is ‘synthesis’, i.e., the generating of unities out of manifolds” (ibid., footnote 40). The immediately given, therefore, does not consist of a
merely sensuous manifold, but a manifold complicated by the presence of abstract
elements and therefore different from data typical of sense perception, which are
conceivable in the gnoseological process of the constitution of the physical object.8
Kant’s considerations are for Gödel the ideal place from which to draw suggestions for a gnoseology which is adaptable to the requirement of a philosophy of
logic. We can say that knowledge which represents mathematical and logical entities thus becomes the product of an abductive activity which, as seen above, is
dynamic, progressive and iterative. But we cannot say that the abduced axioms have
a clear explanatory function. If, therefore, the systems which are elaborated are
many (and consequently the proofs change according to the systems in which they
are activated), the fundamental feature of logic with regard to mathematics becomes
relative, without falling into conventionalism or pragmatism.
8
[Ladrière, 1981, pp. 296–297] provides an interpretation which I share, using analogies to
Kant’s Critique of Pure Reason: the original datum we spoke about coincides with transcendental schematism, where schemas are spotted, not as the data of an intuition, but as something
intermediate which, on the one hand, result as being homogeneous with the category and, on
the other, with the phenomenon, in order to render possible the application of the former to the
latter. The schemas, therefore, are considered as deriving from a sort of vision that is neither
merely conceptual nor merely sensible, but which is precisely transcendental imagination. This
interpretation proves to be more satisfactory than the one provided by [Wang, 1987, pp. 295–
304] who, not recognizing the different status of the given underlying logical and mathematical
objects as a level which can be linked to transcendental schemas, undervalues the exclusively
Kantian nature of Gödel’s argument and must use the less appropriate notion of Husserl’s Wesenschau. I have proposed a new interpretation in terms of abduction of some aspects of Kantian
schematism in my book [Magnani, 2001c, chapter two].
2.3 Instrumental Abduction
2.3
77
Instrumental Abduction
Gabbay and Woods maintain we can face a kind of abduction that, basically,
• is not plausibilist
at least in the sense we have considered in the first chapter.
They say: “It is not uncommon for philosophers to speak of the contribution
made by the hypothesis of action-at-a-distance as one of explaining otherwise unexplainable observational data. [. . . ] Like numerous instances of D-N explanation,
Newtonian explanations need convey no elucidation of their explicanda. They need
confer no jot of further intelligibility to them. The action at-a-distance equation
serves Newton’s theory in a wholly instrumental sense. It allows the gravitational
theory to predict observations that it would not otherwise be able to predict” [Gabbay and Woods, 2005, pp. 118-119]. In this case Newtonian explanations are seen
as epistemically agnostic conjectures, that is they lack the classical epistemic virtues
envisaged by the neopositivistic tradition. These abductions are secured by instrumental considerations and accepted because doing so enables one’s target to be hit.
They cannot be discharged because of their possible implausibility, for example on
the basis of empirical disconfirmation.
We have to note that in some sense all abductions embed instrumental factors. In
the general case, one accepts because doing so enables ones target to be attained,
notwithstanding that lacks the relevant epistemic virtue. However, in cases such
as Newtons, is selected notwithstanding that it is considered to be epistemically
hopeless. [Gabbay and Woods, 2005, p. 119] call this extreme kind of abduction
radically instrumental).
2.3.1
On Propositional and Strategic Plausibility and Abduction
Abductive reasoning occurs in a situation of “scant resources in quest of comparatively modest targets” [Gabbay and Woods, 2005, p. 58]. I have illustrated above
that presumptive abductive hypotheses have to be relevant, plausible, and an economical substitute for any kind of potential exhaustive exploration, cheaper than
the acquisition of relevant new knowledge. Hence, plausibility (which is traditionally considered similar to “reasonableness”) is a central issue concerning hypothesis
generation, choice, and selection in biological abducers like for example human beings and animals but also in artefactual abducers like ideal logical, probabilistic and
computational agents.9 In the case of organic agents plausibility processes are of
course largely implicit, and so also linked to unconscious ways of inferring, or, in
Peircean terms, to the activity of the instinct [Peirce, 1931-1958, 8.223] and of what
Galileo called the lume naturale [Peirce, 1931-1958, 6.477], that is the innate fair
for guessing right.10
9
10
The different character of abduction in human and in logical and computational agents is illustrated in chapter six of this book.
On the relationships between instinct and abduction in the framework of other related Peircean
themes cf. chapter five, sections 5.1 and 5.2.
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2 Non-explanatory and Instrumental Abduction
In the case of theoretical abduction, that is in the abductive processes basically
performed thanks to the inner cognitive resources of human agents faced with
some problems, some aspects concerning the role of plausibility have to be clearly
stressed, taking advantage of the remarks made by [Gabbay and Woods, 2005, chapter seven]. In this case a key role is played by the following aspects, which are
intertwined with the role of the candidate spaces and of the resolution procedures
for filtrating them:
•
•
•
•
•
surprise,
relevance,
characteristicness,
plausibility,
resolution.
Surprise refers to unexpected and uncharacteristic events that create problems which
demand a solution (often anomalies, or just events/problems that urge explanations
or solutions). These events are marked by both an epistemic disadvantage and an
emotional rating.11 Through a “filtration structure” [Gabbay and Woods, 2005, p.
212], human agents internally form a space of candidates, usually very small, found
by means of an automatic inner exploration of the information and knowledge stored
and available in memory: in this process of successive filtering a reduction from
sets of potential explainer/solutions to the considerable actual ones is already at
play. Relevance12 dominates at this level, and the task is reached by applying –
through relevance filters – further, helpful inner information to information which
is considered important with respect to the problem at hand (abduction always aims
– we have said – at reaching the best state of ignorance). Then plausibility enters
the process, in which some candidates are rejected (judged less plausible, or clearly
implausible, and thus irrelevant), often based on information that licenses defaults
(generalizations for example)13 for the agent. Resolution is the elimination of all
candidates but one.
Looking for a plausibility logic able to illuminate the whole process [Gabbay
and Woods, 2005, p. 202] stress the role of the “Auto Rule”, which they illustrate
in the following way, when speaking of a simple abductive situation involving the
married couple Sarah and Harry: “The Auto Rule. To the extent possible, favours the
option that has an element of autoepistemic backing. For example, in the case we
are investigating, the generality claims about Sarah’s never coming home early, is
likely to be underwritten by two factors of autoepistemic significance. One is that if
11
12
13
[Thagard, 2002b] already clearly stressed the central role of the emotion of surprise in finding
problems and anomalies in scientific reasoning (and of the emotion of satisfaction caused by a
discovery!).
A further useful distinction between topical, full-use, irredundancy and probabilistic relevance
is introduced in [Gabbay and Woods, 2005, pp. 239–250].
Defaults are generalizations that tolerate exceptions and so are complicatedly linked to genericity and normalcy, and, in turn, to characteristicness, given the fact that generic claims also
concern what is characteristic. Further details about the relationships between genericity, normalcy, default, characteristicness, common knowledge, and presumption – which in various
ways qualify plausibility – are laid out in [Gabbay and Woods, 2005, pp. 213–238] .
2.3 Instrumental Abduction
79
it were indeed true that Sarah never comes home early, this is something that Harry
would know. And if today were to be an exception to that rule, this too is something
that Harry may well have knowledge of.” The rule is presumptive “Given that a candidate hypothesis is not known to be true, it is presumed to be untrue” (ibid.). The
Auto Rule favors the most plausible hypothesis going beyond its characteristicness,
which is often unconvincing. Characteristicness can fail because human beings obey
to the conservative Quinean principle of minimal mutilation, so that a hypothesis
should not be too strange. Cognitive psychologists have carried out some interesting empirical work on these issues but I think they are far from reaching general
results.14
Until now I have described aspects of plausibility which are occurring at the
level of basically inner inferences of the real human agent, and which are related to
considerations of relevance and characteristicness: this kind of plausibility is called
“propositional” by [Gabbay and Woods, 2005, p. 209]. There is also a “strategic”
sense of plausibility that has to be taken into account, the one which is occurring
in the case of instrumental and radically instrumental abduction (cf. above in this
section), where plausibility is no longer linked to characteristicness. To make an example in the case of scientific reasoning, an abductive hypothesis can be highly implausible from the “propositional” point of view and nevertheless it can be adopted
for its instrumental virtues, such as in the Newtonian case of action-at-a-distance.
Highly implausible hypotheses from the “propositional” point of view can be conjectured because of their high instrumental plausibility, where a different role of
characteristicness is at stake. I will illustrate below (subsection 2.6.2)15 the case of
the principle of physics (and of their conventional character): they are conjectured
and adopted, beyond their (classical) epistemic plausibility – indeed they are a priori
unfalsifiable – in so far as they are endowed with an instrumental epistemic value.
It is “characteristic” in physics to adopt unifying and simple principles, and this is
plausible in a “strategic” sense. Another striking example is the following, illustrated by Gabbay and Woods, where propositional plausibility is low and strategic
plausibility high:
Planck conjectured quanta for their contribution to the unification of the laws of black
body radiation. He did so notwithstanding the extreme propositional implausibility of
the existence of quanta. Even so, Planck thought it reasonable to proceed against the
grain of this implausibility. Quanta were nothing like anything then known to physics;
so they were uncharacteristic of what physics quantified over in 1900. Planck’s was a
conjecture grounded in its instrumental yield. It was, we say, a strategically plausible
conjecture to make. Why would this be so? It would be so, as we saw earlier, because
it is characteristic of the laws of physics to admit unification under the appropriate
conditions. [. . . ] Planck reasoned that black body radiation is such that it should be expected that it is subject to unified laws, and because such unifications are characteristic
of physics, he made a conjecture that would achieve it [Gabbay and Woods, 2005, p.
218].
14
15
In hypothesis search and selection tasks the role of analogy is also very important, cf. above
subsection 1.5 of chapter one.
Cf. also [Magnani, 2001b, chapter seven].
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2 Non-explanatory and Instrumental Abduction
We have to remember that, in the case of real human agents plausibility assessment is of course largely inner and implicit, and it is unmediated by explicit and
conscious reflections in terms of plausibility, characteristicness, and relevance, such
as the ones that can be illustrated in the ideal epistemological and logico-cognitive
reconstruction or in the functions of automatic abductive agents.16
In more hybrid (multimodal) abductive processes (cf. chapter four, section 4.1),
such as in the case of manipulative abduction, of course the whole propositional
plausibility assessment is reached – and constrained – taking advantage of the gradual acquisition of new external information with respect to future interrogation and
control. In this interplay the cognitive agent further triggers internal plausibility
thoughts “while” actively modifying the environment (thinking through doing). Indeed, as I have already noted in subsection 1.3.2 of the previous chapter, already
at the generation/selection phase of genuine abduction many embodied processes –
so to say – of a kind of confrontation (if not exactly of evaluation) with something
external to the individual brain, even if not due to experimental tests, can be present,
so that we can say that abduction considered as a way of forming hypotheses is
of course immediately a generation/selection of “plausible” hypotheses. The role
of these continuous stages of confrontation/coordination with external constrained
(and fertile) cognitive offerings has been pointed out thanks to the concept of manipulative abduction, which takes into account the external dimension of abductive
reasoning. Let me reiterate that in this perspective the proper experimental test involved in the Peircean evaluation phase, which for many researchers reflects in the
most acceptable way the idea of abduction as inference to the best explanation, just
represents a particular subclass of the processes of adoption of abductive hypotheses, and should be considered ancillary to the nature of abductive cognition, and
inductive in its essence.
Some researchers could not be as convinced as Gabbay and Woods about the
GW characterization of abduction, especially where it is not intrinsically explanatory. They advert to the observation by Gödel and others that putative mathematical
axioms are sometimes endorsed because they help to prove conclusions that are
accepted on other grounds. It could be maintained that such axioms are still explanatory in the broad sense that they are defeasible and must compare well with
the alternatives. 1. The fact that the conclusions are accepted on other grounds suggests the plausibility of the putative axiom. 2. When constructing a proof, does a
mathematician not try to select the best concepts or axioms to apply, among a set
of alternatives? If so, then there is a kind of inference to the best proof occurring.
3. Old proofs and mathematical ideas are sometimes revisited and revised by later
mathematicians. Some are found to be invalid. No proof is necessarily above revision, suggesting their defeasibility in practice. 4. If old proofs or ideas are revised,
then they are, in effect, in competition with alternatives, suggesting that there is a
kind of inference to the best proof at work in the overall process of mathematics
(or logic).
16
Automatic abductive agents are described below in section 2.7.
2.4 Governing Inconsistencies in Science through Explanatory
81
I have to note that – in these last cases – plausibility considerations are certainly
still at play, but they range from various degrees that involve less “propositional”
and more “strategical” and instrumental aspects, so that propositional plausibility
is lower and strategic plausibility higher. These cases are far from the clear ones of
explanatory abduction that are for example occurring in science and in various kinds
of diagnosis. In non-explanatory abduction the cognitive virtues can be more strategical than epistemological, at least if we attribute to the word “epistemological” the
standard meaning that neopositivistic tradition established through the specific “explanatory” tone of the D-N law-covering model of scientific explanation. To avoid
misunderstandings it has to be stressed that also strategic and instrumental considerations “can” have other epistemological virtues related to scientific rationality, like
it is in the case of the action at distance (cf. p. 64) or in the other cases (for example,
the unifying principles of physics) I will describe in the following sections.
2.4
Governing Inconsistencies in Science through Explanatory,
Non-explanatory, and Instrumental Abduction
In chapters six and seven of my previous book on abduction [Magnani, 2001b] I
have illustrated other interesting cases of abductions that can be usefully and basically labeled non-explanatory and instrumentalist. Taking advantage of the role of
inconsistencies in abductive reasoning, in the following I am summarizing my argument, showing how often the complex abductive procedures are characterized by
a mixture of explanatory, non-explanatory, and instrumental aspects.
We have seen that for Peirce abduction is an inferential process in a very particular and wide semiotic sense (cf. chapter one, section 1.5). The aspect of surprise I
have described in the previous subsection is central for Peirce: abduction is logical
inference [. . . ] having a perfectly definite logical form. [. . . ] The form of inference,
therefore, is this:
• The surprising fact, C, is observed;
• But if A were true, C would be a matter of course,
• Hence, there is reason to suspect that A is true [Peirce, 1931-1958, 5.188189,7202].
C is true of the actual world and it is surprising, a kind of state of doubt we are not
able to account for using our available knowledge. Philosophers of science in the
last century have illustrated that inconsistencies and anomalies often play this role
of surprise in the growth of scientific knowledge.
Hence, contradictions and inconsistencies are fundamental in abductive reasoning, and abductive reasoning is appropriate for “governing” inconsistencies: this
section illustrates abductive reasoning in order to classify and analyze the different
roles played by inconsistencies in different reasoning tasks and in scientific discovery. The special sensitivity to anomalies and inconsistencies, which is an undoubted
endowment of human beings and many animals, becomes institutionalized in scientific mentality, and an important part of the scientific method. The aim of this
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section is to identify aspects of inconsistencies not covered by certain formalisms
and to suggest extensions to present thinking, but also to delineate the first features
of a broader constructive framework able to include abduction and to provide constructive solutions to some of the limitations of its formal models. There are many
ways of “governing” inconsistencies: from the methods activated in diagnostic settings and consistency-based models (cf. chapter one, section 1.4) to the typical ones
embedded in some forms of creative reasoning, from the interpretations in terms
of conflicts and competitions to the actions performed on empirical and conceptual
anomalies, from the question of generating inconsistencies by radical innovation
to the connectionist treatment of coherence. The conclusions presented here aim at
representing a step forward in the understanding of the use of inconsistencies in
creative abductive reasoning both in scientific and practical settings.
In different theoretical changes we witness different kinds of discovery processes
operating. Discovery methods are data-driven (generalizations from observation
and from experiments) (induction), explanation-driven (explanatory abduction), and
coherence-driven (formed to overwhelm contradictions) [Thagard, 1992]. Sometimes there is a mixture of such methods: for example, a hypothesis devoted to
overcome a contradiction is found by explanatory abduction. The detection of an
anomaly usually demonstrates that an explanation is needed.17 The next move of
the process of explanation is to obtain a possible explanation. Therefore, contradiction and its reconciliation play an important role in philosophy, in scientific theories and in all kinds of problem-solving. It is the driving force underlying change
(thesis, antithesis and synthesis) in the Hegelian dialectic and the main tool for advancing knowledge (conjectures and refutations – [Popper, 1963] – and proofs and
counter-examples – [Lakatos, 1976] – in the Popperian philosophy of science and
mathematics).18
Following Quine’s line of argument against the distinction between necessary and
contingent truths [Quine, 1979], when in science a contradiction arises, consistency
can be restored by rejecting or modifying any assumption which contributes to the
derivation of contradiction: no hypothesis is immune from possible alteration. Of
course there are epistemological and pragmatic limitations: some hypotheses contribute to the derivation of useful consequences more often than others, and some
participate more often in the derivation of contradictions than others. For example,
when faced with abduced hypotheses which we have decided to release for further
premissory work (H c ) (cf. section 2.1.1), it might be useful to abandon the hypotheses which contribute least to the derivation of useful consequences leading to
(empirical or theoretical) contradictions. If contradictions continue and the assessed
utility of the hypotheses changes, it may be necessary to backtrack, reinstate a previously abandoned hypothesis and abandon another.
17
18
In the last sections of this chapter I will describe the paradigmatic case of the anomaly of the
postulate of parallels, which brings together explanatory and non-explanatory aspects.
Also psychoanalysis relates creative thinking to something contradictory: creative expression is
explained in terms of sublimation of unconscious conflicts, as Freud demonstrated in his famous
analysis of the symbolic meanings of the works of Leonardo da Vinci [Freud, 1916].
2.4 Governing Inconsistencies in Science through Explanatory
83
Hence, the derivation of inconsistency contributes to the search for alternative,
and possibly new, hypotheses: for each assumption which contributes to the derivation of a contradiction there exists at least one alternative new system obtained by
abandoning or modifying the assumption.
Anomalies result not only from direct conflicts between inputs and system knowledge but also from conflicts between their ramifications: “[. . . ] noticing a particular
anomaly may require building long inference chains tracing ramifications until a
contradiction is found” [Leake, 1992, p. xiii]. Any explanation must be suitably
plausible and able to dominate the situation in terms of reasonable hypotheses.
Moreover, the explanation has to be relevant to the anomaly, and resolve the underlying conflict. Finally, in some cases of everyday (and practical) anomaly-driven
reasoning the explanation has to be useful, so it needs information that will point to
the specific faults that need repair (on the role of plausibility and abduction in inner
rehearsal of human agents cf. the previous subsection).
The classical example of a theoretical system that is opposed by a contradiction is
the case in which the report of an empirical observation or experiment contradicts a
scientific theory. Whether it is more beneficial to reject the report or the statement of
the theory depends on the whole effect on the theoretical system. It is also possible
that many alternatives might lead to non-comparable, equally viable, but mutually
incompatible, systems.19
Why were the photographic plates in Röntgen laboratory continually blackened?
Why does the perihelion of the Mercury planet advance? Why is the height of the
barometer lower at the high altitudes than at the low ones? These are examples of
problems that come from observation, but they are problematic in light of some
theory, that is unexpected and anomalous. The first was problematic because it was
tacitly supposed at that time that no radiation or emanation existed able to penetrate
the container of the photographic plates; the second because it conflicted with the
Newtonian theory; the third was problematic for the supporters of Galileo’s theories
because it contradicted the belief in the “force of vacuum” that was adopted as an
explanation of why the mercury does not fall from a barometer tube [Chalmers,
1999].
Dealing with the problem of withdrawing scientific paradigms Kuhn writes:
Discovery commences with the awareness of anomaly: i.e., with the recognition that
nature has somehow violated the paradigm-induced expectations that govern normal
science. It then continues with a more or less extended exploration of the area of
anomaly. And it closes only when the paradigm theory has been adjusted so that the
anomalous has become the expected. Assimilating a new sort of fact demands a more
than additive adjustment of theory, and until that adjustment is completed – until the
scientist has learned to see nature in a different way – the new fact is not quite a scientific fact at all. [Kuhn, 1962, p. 53, second edition].
19
Thagard proposes a very interesting computational account of scientific controversies in terms
of so-called explanatory coherence [Thagard, 1992] (cf. also chapter one, subsection 1.3.2, this
book), which improves on Lakatos’ classic one [1970], by explaining various aspects dealing
with the comparison of scientific theories.
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It is well-known that the recent falsificationist tradition in epistemology has focused
attention on the role of anomalies (that can give rise to falsifications) establishing a
sort of “received view” on the growth of scientific knowledge characterized by the
fundamental role played by anomalies: Newton’s theory is able to explain phenomena not touched on by Aristotle’s theory, such as correlations between the tides and
the location of the moon, and the variation in the force of gravity with respect to
height above sea level; in turn, Einstein was able to do the same with respect to the
Newtonian theory and its anomalies and falsifications.
As Lakatos argues, in a mature theory with a history of useful consequences, it
is generally better to reject an anomalous conflicting report than it is to abandon the
theory as a whole. The cases in which we have to abandon a whole theory are very
rare: a theory may be considered as a complex information system in which there is
a collection of cooperating individual statements some of which are useful and more
firmly held than others; propositions that belong to the central core of a theory are
more firmly held than those which are located closer to the border, where instead
rival hypotheses may coexist as mutually incompatible alternatives. Accumulating
reports of empirical observations can help in deciding in favor of one alternative
over another.
I have to remember that even without restoring consistency, an inconsistent system can still produce useful information. Of course from the point of view of classical logic we are compelled to derive any conclusion from inconsistent premises, but
in practice efficient proof procedures infer only “relevant” conclusions with varying degrees of accessibility, as reverberated by the criteria of non-classical relevant
entailment [Anderson and Belnap, 1975].
We may conclude by asserting that
1. contradiction, far from damaging a system, helps to indicate regions in which it
can be changed (and improved): it typically furnishes chances of “explanatory”
abductive reasoning, it becomes possible to resolve/explain the inconsistency;
2. we have to remember that not all the configurations of new concepts are
incoherence-driven and related to the highest case of creative abduction and creative analogical reasoning, ubiquitous in science, and more constructive than associative. For example, in conceptual combination in everyday reasoning, many
new concepts are formed in a coherence-driven way, where a kind of reconciliation of associations and thematic relations operates. Thagard presents the case
of the construction of the concept of “computational philosopher” where in order to understand the concept people need to make coherent sense of how a
“modifier” such as “computational” can apply to a “head” such as “philosopher” [Thagard, 1997a]. In science hypotheses are abductively formed also in
absence of triggering anomalies and inconsistencies, and in this case it is frequent to witness cases of non-explanatory (like for example in guessing new
axioms in mathematics – cf. below section 2.9.1) and of instrumental abduction
(like in the case of guessing conventions in physics – cf. below section 2.6.2);
there is also the intermediate case of guessing hypotheses that have an explanatory descent but, in so far as they are not falsifiable, their instrumental character
2.4 Governing Inconsistencies in Science through Explanatory
85
tends to overwhelm the explanatory one, such as in the case of “constructions”
during the Freudian psychoanalytic treatment: – cf. below 2.6;
3. of course contradiction is also a way of falsifying established hypotheses (H c ):
it has a preference for strong hypotheses which are more easily falsified than
weak ones; and moreover, hard hypotheses may more easily weakened than
weak ones, which prove difficult subsequently to strengthen. It is always better
to produce mistakes and then correct them than to make no progress at all.
We can see abductive inferences “[. . . ] as answers to the inquirer’s explicit or (usually) tacit questions put to some definite source of answers (information)” [Hintikka,
1998, p. 519] stressing the interrogative features of this kind of reasoning. If abduction is the making of a set of possible answers, the choice of the possible questions
is also decisive (and this choice of course is not indifferent as regards the further
process of finding answers). As already illustrated in chapter one (section 1.4)20
we may see belief change from the point of view of conceptual change, considering concepts either cognitively, like mental structures analogous to data structures
in computers, or, epistemologically, like abstractions or representations that presuppose questions of justification. Belief revision – even if extended by formal accounts
such as illustrated above in chapter one21 – is able to represent cases of conceptual
change such as adding a new instance, adding a new weak rule, adding a new strong
rule (see [Thagard, 1992, pp. 34–39]), that is, cases of addition and deletion of beliefs, but fails to take into account cases such as adding a new part-relation, adding
a new kind-relation, adding a new concept, collapsing part of a kind-hierarchy, reorganizing hierarchies by branch jumping and tree switching, in which there are
reorganizations of concepts or redefinitions of the nature of a hierarchy. These last
cases are the most evident changes occurring in many kinds of creative reasoning,
for example in science. Related to some of these types of conceptual change are
different varieties of inconsistencies (see Figure 2.1), as explained in the following
sections.
2.4.1
Empirical Anomalies and Explanatory Abduction
In chapter one (section 1.5) I argued that various logical accounts of abduction certainly illustrate much of what is important in abductive reasoning, especially the objective of selecting a set of hypotheses (diagnoses, causes) that are able to dispense
good (preferred) explanations of data (observations), but tend to fail in accounting
for many cases of explanations occurring in science or in everyday reasoning. For
example they do not capture 1) the role of statistical explanations, where what is explained follows only probabilistically and not deductively from the laws and other
tools that do the explaining; 2) the sufficient conditions for explanation; 3) the fact
that sometimes the explanations consist of the application of schemas that fit a phenomenon into a pattern without realizing a deductive inference; 4) the idea of the
20
21
Cf. also [Magnani, 1999].
Or developed by others, see for example, [Katsuno and Mendelzon, 1992; Cross and Thomason,
1992].
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2 Non-explanatory and Instrumental Abduction
CONCEPTUAL CHANGE
PROCESSES OF
DISCOVERY
FINDING
INCONSISTENCIES
GENERATING
INCONSISTENCIES
MAINTAINING
INCONSISTENCIES
CONTRADICTING,
CONFLICTING, FAILING
Fig. 2.1 Conceptual change and inconsistencies
existence of high-level kinds of creative abductions; 5) the existence of model-based
abductions (for instance visual and diagrammatic); 6) the fact that explanations usually are not complete but only furnish partial accounts of the pertinent evidence (see
[Thagard and Shelley, 1997]; ) 7) the fact that one of the most important virtues of
a new scientific hypothesis (or of a scientific theory) is its power of explaining new,
previously unknown facts.
Moreover, the recent logical accounts of abduction certainly elucidate many
kinds of inconsistency government, which nevertheless reduce to the act of finding
contradictions able to generate the withdrawal of some hypotheses, beliefs, reasons,
etc.: these contradictions always emerge at the level of data (observations), and consistency is restored at the theoretical level.22 This view may distract from important
aspects of other kinds of reasoning that involve intelligent abductive performances.
For example, empirical anomalies result from data that cannot currently be fully
explained by a theory. They often derive from predictions that fail, which implies
some element of incorrectness in the theory. In general terms, many theoretical constituents may be involved in accounting for a given domain item (anomaly) and
hence they are potential points for modification. The detection of these points involves defining which theoretical constituents are employed in the production of the
anomaly. Thus, the problem is to investigate all the relationships in the explanatory
area. In science, first and foremost, empirical anomaly resolution involves the localization of the problem at hand within one or more constituents of the theory. It is
then necessary to produce one or more new hypotheses to account for the anomaly,
and finally, these hypotheses need to be evaluated so as to establish which one
best satisfies the criteria for theory justification. Hence, anomalies require a change
in the theory, yet once the change is successfully made, anomalies are no longer
22
We have to remember that the logical models in some cases exhibit a sort of paraconsistent
behavior.
2.4 Governing Inconsistencies in Science through Explanatory
87
anomalous but in fact are now resolved. This can involve both transforming the domain knowledge and learning or discovering new schemas or rules endowed with
explanatory power. Also in the tradition of the machine discovery programs (cf.
below, section 2.7) failed predictions drive the mechanism which selects new experiments to guess new hypotheses [Zytkow, 1997]. The process is goal-driven. Of
course an explainer will use different information for the objective of predicting a
situation than for repairing or preventing it with a good explanation.
General strategies for anomaly resolution, as well as for producing new ideas and
for assessing theories, have been studied by [Darden, 1991] in her book on reasoning
strategies from Mendelian genetics. Anomaly resolution presents four aspects: 1)
confirmation that the anomaly exists, 2) localization of the problem (not considering
the cases where the anomaly either is an uninteresting monster or is outside the
scope of the theory), 3) generation of one or more new hypotheses to account for the
anomaly, that is, conceptual changes in the theory, 4) evaluation and assessment of
the hypotheses chosen. Abductive steps are present at the third level (that normally
is activated when step 2 fails to manage the anomaly): in this case we are trying
to eliminate the already confirmed anomaly (step 1) in a creative way. At this level
there are various kinds of conceptual changes: from the simple ones related to the
possible alteration (deletion, generalization, simplification, complication, “slight”
changes, proposal of the opposite, etc.), or addition of a new component of the
theory, to the construction and discovery of a new “theoretical component” [Darden,
1991, pp. 269–275].
Let us relate this taxonomy to the cases of scientific conceptual change illustrated above and in the previous chapter. Darden’s alterations and additions can be
assimilated to the cases of conceptual change such as adding a new instance, adding
a new weak rule, adding a new strong rule (that is, cases of addition and deletion
of beliefs), adding a new part-relation, adding a new kind-relation, adding a new
concept. On the contrary, Darden’s case about the discovery of a new “theoretical
component” relates to changes where there is collapse of part of a kind-hierarchy,
the reorganization of hierarchies by branch jumping and tree switching, in which
there are reorganizations of concepts or redefinitions of the nature of a hierarchy.
We have seen that these last cases are the most evident changes occurring in many
kinds of creative reasoning in science, when adopting a new conceptual system is
more complex than mere belief revision: different varieties of model-based abductions are related to some of these types of scientific conceptual change.
Darden reminds to us that geneticists sometimes abandoned hypotheses on the
basis of falsifying evidence (this is another way – unsuccessful resolution, unresolved anomaly – of seeing the problem of anomalies, already indicated at the step
“alter a component-deletion”). And, of course, as clearly illustrated by Lakatos (see
section 2.4 above) an anomalous observation statement can be rejected and the theory which it clashes retained. This is for example the case of the Copernicus’ theory
that was retained and the naked-eye observation of the sizes of Venus and Mars,
which were in contradiction with that theory, eliminated.
Moreover, as taught by the recent epistemological tradition, and especially by
Lakatos’ falsificationism [1970], in science new creative abduced hypotheses (or
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2 Non-explanatory and Instrumental Abduction
new theories), originating from a case of anomaly resolution, have to lead to novel
predictions. Galileo reported that the moon was not a smooth sphere but full of
craters and mountains. His Aristotelian opponent had to admit that observation that
nevertheless configured a terrible anomaly for the notion, common to many Aristotelians and coming from the ancient times, that the celestial bodies are perfect
spheres. The hypothesis created by the Aristotelian to explain this anomaly is ad
hoc: he advocated that there is an invisible substance on the moon, which fills the
craters and covers the mountains so that the moon’s aspect is absolutely spherical.
Unfortunately, this modified theory of the moon did not lead to new testable consequences, and thus is not scientifically acceptable, following the falsificationist point
of view.23
2.4.2
Conceptual Anomalies, Explanatory, and Non-explanatory
Abduction
Empirical anomalies are not alone in generating impasses, there are also the socalled conceptual anomalies. To illustrate more features of a theory of the role of
inconsistencies in (especially “model-based”) abduction we can present the case of
conceptual problems as triggers for hypotheses. The so-called conceptual problems
represent a particular form of anomaly. In addition, resolving conceptual problems
may involve satisfactorily answering questions about the nature of theoretical entities. Nevertheless such conceptual problems do not arise directly from data, but
from the nature of the claims in the principles or in the hypotheses of the theory. It
is far from simple to identify a conceptual problem that requires a resolution, since,
for example, a conceptual problem concerns the adequacy or the ambiguity of a
theory, and yet also its incompleteness or (lack of) evidence.
The formal sciences are especially concerned with conceptual problems. Let’s
consider an example deriving from the well-known case of the non-Euclidean revolution, which plays a remarkable role in illustrating some actual transformations in
rational conceptual systems. The discovery of non-Euclidean geometries involves
some interesting cases of visual abductive reasoning. It demonstrates a kind of
visual abduction, as a strategy for anomaly resolution related to an interplay between explanatory and productive visual thinking, but also to the active role of nonexplanatory abduction (cf. below sections 2.9 and 2.11).
Since ancient times the fifth postulate has been held to be not evident. This “conceptual problem” (just an anomaly) has caused much suspicion about the reliability
of the whole theory of parallels, consisting of the theorems that can be only derived
with the help of the fifth postulate. The recognition of this anomaly was fundamental to the development of the great non-Euclidean revolution. Two thousand years
of attempts to resolve the anomaly have generated many more-or-less fallacious
23
On the relationship between falsificationism (Popperian and Lakatosian) and conventionalism
(at least in the ingenious case of Poincaré), cf. below section 2.6.2.
2.4 Governing Inconsistencies in Science through Explanatory
89
demonstrations of the fifth postulate (for example, a typical attempt was that of trying to prove the fifth postulate from the others), until the discovery of non-Euclidean
geometries [Greenberg, 1974].
At the end of this chapter I will present some details derived from the historical
discovery of non-Euclidean geometries which illustrate the relationships between
strategies for anomaly resolution and visual thinking: I consider how Lobachevsky’s
strategy for resolving the anomaly of the fifth postulate was to manipulate the symbols, rebuild the principles, and then to derive new proofs and provide a new mathematical apparatus. The failure of the demonstrations of his predecessors induced
Lobachevsky to believe that the difficulties that had to be overcome were due to
causes other than those which had until then been focused on. I will show how
some of the hypotheses created by Lobachevsky were mostly image-based trying to
demonstrate that visual abduction is relevant to hypothesis formation in mathematical discovery, in an interplay between explanatory and non-explanatory steps.
The fact that inconsistencies may occur also at the theoretical level is further
emphasized if we consider that in science or in legal reasoning [Thagard and Shelley,
1997], hypotheses are mainly layered, contrarily to the case of diagnostic reasoning,
where we have a set of data that can be explained by a given set of diseases (that is
with the explanation consisting of a mapping from the latter to the former). Hence,
the organization of hypotheses is more complex than the one illustrated in formal
models, and abduction is not only a matter of mapping from sets of hypotheses to a
set of data.
In many “explanatory” abductive settings there are hypotheses that explain other
hypotheses so that the selection or creation of explanations is related to these relationships.24 In this case the plausibility of the hypothesis comes not only from what
it explains, but also from it itself being explained. The Darwinian hypothesis stating that “Species of organic beings have evolved” gains plausibility from the many
pieces of evidence it helps to explain. Moreover, it receives plausibility from above,
from being explained by the hypothesis of natural selection, in its turn explained by
the hypothesis concerning the struggle for existence. The principle of special relativity and the principle of the constancy of the speed of light explain (in this case
the explanatory relation is “deductive”) the Lorentz transformation, which explains
the negative result of the Michelson-Morley experiment, but also they explain the
convertibility of mass and energy which explains the nuclear transmutations detected by Rutherford in 1919. Hence the two principles explain the two experiments
above by means of the intermediate layered hypotheses of Lorentz transformation
and mass/energy conversion, but we also know the two principles directly explain
the Fizeau experiment concerning the speed of light in a flowing fluid [Einstein,
1961]. In the tradition of machine discovery programs the question of layered hypotheses could be related to the one of postulating hidden structures where some
hidden hypotheses can trigger discovery of other hypotheses at a higher level.
24
This kind of hierarchical explanations has also been studied in the area of probabilistic belief
revision [Pearl, 1988].
90
2.4.3
2 Non-explanatory and Instrumental Abduction
Generating Inconsistencies by Radical Innovation
The case of conceptual change such as adding a new part-relation, adding a new
kind-relation, adding a new concept, collapsing part of a kind-hierarchy, reorganizing hierarchies by branch jumping and tree switching, in which there are reorganizations of concepts or redefinitions of the nature of a hierarchy are the most evident
changes occurring in many kinds of creative abduction, for instance in the growth
of scientific knowledge.
In Against Method [Feyerabend, 1975], Feyerabend attributes a great importance
to the role of contradiction. He establishes a “counterrule” which is the opposite
of the neoposititivistic one that it is “experience”, or “experimental results” which
measures the success of our theories, a rule that constitutes an important part of
all theories of corroboration and confirmation. The counterrule “[. . . ] advises us
to introduce and elaborate hypotheses which are inconsistent with well-established
theories and/or well-established facts. It advises us to proceed counterinductively”
[Feyerabend, 1975, p. 20]. Counterinduction is seen more reasonable than induction, because appropriate to the needs of creative reasoning in science: “we need
a dream-world in order to discover the features of the real world we think we inhabit” (p. 29). We know that counterinduction, that is the act of introducing, inventing, and generating new inconsistencies and anomalies, together with new points of
view incommensurable with the old ones, is congruous with the aim of inventing
“alternatives” (Feyerabend contends that “proliferation of theories is beneficial for
science”), is very important in all kinds of creative abductive reasoning.
When a scientist introduces a new hypothesis, especially in the field of natural
sciences, he is interested in the potential rejection of an old theory or of an old
knowledge domain. Consistency requirements in the framework of deductive models of abduction, governing hypothesis withdrawal in various ways, would arrest
further developments of the new abduced hypothesis. In the scientist’s case there
is not the deletion of the old concepts, but rather the coexistence of two rival and
competing views.
Consequently we have to consider this competition as a form of epistemological,
and non logical inconsistency. For instance two scientific theories are conflicting
because they compete in explaining shared evidence.
The problem has been studied in Bayesian terms but also in connectionist ones,
using the so-called theory of explanatory coherence ([Thagard, 1992], cf. also footnote 19, above), which deals with the epistemological reasons for accepting a whole
set of explanatory hypotheses conflicting with another one. In some cognitive settings, such as the task of comparing a set of hypotheses and beliefs incorporated in
a scientific theory with the one of a competing theory, we have to consider a very
complex set of criteria (to ascertain which composes the best explanation), that goes
beyond the mere simplicity or explanatory power. The minimality criteria included
in some of the formal accounts of abduction, or the idea of the choice among preferred models cited in section 1.4 of chapter one, are not sufficient to illustrate more
complicated cognitive situations.
2.4 Governing Inconsistencies in Science through Explanatory
2.4.4
91
Maintaining Inconsistencies: Static and Dynamic Aspects
As noted above, when we create or produce a new concept or belief that competes
with another one, we are compelled to maintain the derived inconsistency until the
possibility of rejecting one of the two becomes feasible. We cannot simply eliminate a hypothesis and then substitute it with one inconsistent with it, because until
the new hypothesis comes in competition with the old one, there is no reason to
eliminate the old one. Other cognitive and epistemological situations present a sort
of paraconsistent behavior: a typical kind of inconsistency maintenance is the wellknown case of scientific theories that face anomalies. As noted above, explanations
are usually not complete but only furnish partial accounts of the pertinent evidence:
not everything has to be explained.
Newtonian mechanics is forced to cohabit with the anomaly of perihelion of
Mercury until the development of the theory of relativity, but it also has to stay
with its false prediction about the motion of Uranus. In diagnostic reasoning too,
it is necessary to make a diagnosis even if many symptoms are not explained or
remain mysterious. In this situation we again find the similarity between reasoning in the presence of inconsistencies and reasoning with incomplete information
already stressed. Sometimes scientists may generate the so-called auxiliary hypotheses [Lakatos, 1970], justified by the necessity of overcoming these kinds of inconsistencies: it is well-known that the auxiliary hypotheses are more acceptable if able
to predict or explain something new (the making of the hypothesis of the existence
of another planet, Neptune, was a successful way – not an ad hoc maneuver – of
eliminating the anomaly of the cited false prediction).
To delineate the first features of a constructive cognitive and formal framework
that can handle the coexistence of inconsistent theories (and unify many of the
themes concerning the limitations of formal models of abductions previously illustrated) we have first of all to be able to deal with the treatment of non sentential
representations (that is model-based representations).
Moreover, I think that the problem of coexistence of inconsistent scientific theories and of reasoning from inconsistencies in scientific creative processes leads to
analyze the characters of what I call the best possible information of a situation.
It is also necessary to distinguish between the dynamic and the static sides of the
best possible information. If we stress the sequential (dynamic) aspects we are more
oriented to analyze anomalies as triggers for hypotheses: as illustrated by the traditional deductive models of abduction, the problem concerns the abductive steps of
the sequential comprehension and integration of data into a hypothetical structure
that represents the best explanation for them. Analogously, as we will see in the
case of conceptual anomalies in geometry (this chapter, sections 2.8, 2.9, and 2.11),
the “impasse” can also be a trigger for a whole process of model-based abduction.
On the contrary, if we consider the holistic (static) aspects we are more interested
in the coexistence of inconsistencies as potential sources of different reasoned creative processes. In this last case we have to deal with explanatory model-based abduction and its possible formal treatment; some suggestions can be derived from
the area of paraconsistent and adaptive logic [Meheus, 1999; Meheus et al., 2002;
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2 Non-explanatory and Instrumental Abduction
Meheus and Batens, 2006], for instance handling hierarchies of inconsistent models
of a given representation.25
When the holistic representation concerns the relationship between two competing theories containing some inconsistencies, a formal framework can be given by
the connectionist tradition using a computational reconstruction of the epistemological concept of coherence, as already stated (see also the following section).
2.4.5
Contradicting, Conflicting, Failing, and Instrumental
Abduction
Considering the coherence of a conceptual system as a matter of the simultaneous
satisfaction of a set of positive and negative constraints leads to the connectionist
models (also in computational terms) of coherence [Thagard, 2002a]. In this light
logical inconsistency becomes a relation that furnishes a negative constraint and
entailment becomes a relation that provides a positive constraint. For example, as
already noted, some hypotheses are inconsistent when they simply compete, when
there are some pragmatic incompatibility relations, when there are incompatible
ways of combining images, etc. [Thagard and Shelley, 1997; Thagard and Verbeurgt,
1998].
From the viewpoint of the connectionist model of coherence, it spontaneously
allows the situations in which there is a set of accepted concepts containing an inconsistency, for example in the case of anomalies: the system at hand may at any
rate have a maximized coherence, when compared to another system. Moreover, another interesting case is the relation between quantum theory and general relativity,
which individually have enormous explanatory coherence. According to the eminent
mathematical physicist Edward Witten “[. . . ] the basic problem in modern physics
is that these two pillars are incompatible”. Quantum theory and general relativity
may be incompatible, but it would be premature given their independent evidential
support to suppose that one must be rejected [Thagard, 1992, p. 223].
A situation that is specular to inconsistency maintenance (cf. previous section)
is given when two theories are not intertranslatable but observationally equivalent,
as illustrated by the epistemology of conventionalist tradition. In these cases they
are unconcerned by inconsistencies (and therefore by crucial experiments, they are
unfalsifiable) but have to be seen as rivals. The incommensurability thesis shows interesting relationships with the moderate and extreme conventionalism. If theories
that are not intertranslatable, that is incommensurable, function in certain respects
as do observationally equivalent theories (and they are unconcerned by crucial experiments), the role of observational and formal-structural invariants in providing
comparability is central: it is impossible to find a contradiction in some areas of
the conceptual systems they express. I think that it is necessary to study in general
the reasons able to model the demise of such observationally equivalent “conventional” theories, showing how they can be motivationally abandoned. This problem
25
See also the analysis of the relationships between inconsistency, generic modeling, and conceptual change given in [Nersessian, 1999a].
2.5 A Note on Preinventive Forms, Disconfirming Evidence, Unexpected Findings
93
has been frequently stressed from the beginnings of research in automated discovery (cf. section 2.7): if many hypothetical patterns are discovered, all justified by
their observational consequences, we are looking for the reasons to claim that one
of them is the best [Zytkow and Fischer, 1996].
Moreover these theories can be seen as rivals in some sense not imagined in
traditional philosophy of science. We already stressed that in these cases the role of
observational and formal-structural invariants in providing comparability is central:
it is impossible to find a contradiction in some area of the conceptual systems they
express.
I have already said that contradiction has a preference for strong hypotheses
which are more easily falsified than weak ones. Moreover, hard hypotheses may
be more easily weakened than weak ones, which subsequently prove difficult to
strengthen. Some hypotheses may however be unfalsifiable: they exhibit an instrumental abductive force and present various degrees of strategic plausibility (cf.
above subsection 2.3.1). In this case, it is impossible to find a contradiction from the
empirical, but also theoretical point of view, in the conceptual systems in which they
are incorporated. Notwithstanding this fact, it is sometimes necessary to construct
ways of rejecting the unfalsifiable hypothesis at hand by resorting to some external
forms of negation, (external because we want to avoid any arbitrary and subjective
elimination), which would be rationally or epistemologically unjustified. As I have
already anticipated, in the section 2.6 I will consider a kind of abduced instrumental
“weak” hypothesis that is hard to negate and the ways to make this easy. I will explore whether negation as failure can be employed to model hypothesis withdrawal
in Freudian analytic reasoning, where “constructions” are hypotheses which oscillate between explanatory and instrumental roles, and in Poincaré’s conventionalism
of the principles of physics, where the abduced hypotheses (called “conventions”)
are essentially instrumental.
2.5
A Note on Preinventive Forms, Disconfirming Evidence,
Unexpected Findings
I have said that intuitively an anomaly is something surprising, as Peirce already
knew “The breaking of a belief can only be due to some novel experience” [Peirce,
1931-1958, 5.524] or “[. . . ] until we find ourselves confronted with some experience contrary to those expectations” [Peirce, 1955b, 7.36] (cf. this chapter, section
2.4).26 I have said that many biological organisms are very sensitive to anomalies,
therefore it is not strange that something anomalous can be found in those kinds
of structures the cognitive psychologists call preinventive. Cognitive psychologists
have described many kinds of preinventive structures and described their desirable
properties, that constitute particularly interesting ways of “irritating” the mind and
stimulating creativity.
26
Classical cognitive considerations on inconsistencies in reasoning can be found in [Schank,
1982; Schank and Abelson, 1987].
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2 Non-explanatory and Instrumental Abduction
Preinventive structures are very important from the point of view of creative abduction, because of the propulsive role they play. [Finke et al., 1992] list the following preinventive cognitive structures:27 visual patterns and objects forms (one can
generate two dimensional patterns resulting in creative products such as new types
of symbols and artistic design or three-dimensional forms resulting in new inventions and spatial analogies); mental blend (two distinct entities are fused to create
something new, one might imagine combining a lion with an ostrich to create a type
of animal); exemplars of unusual or hypothetical categories (they show emergent
features that lead to new and unexpected discoveries, for example, in attempting
to construct a member of the category “alien creatures that inhabit a planet different from the earth”, one might imagine a creature that resemble earth creatures in
some respect but not others); mental models that represent various mechanical or
physical systems (sometimes incomplete, unstable, and even unscientific), as well
as conceptual systems; various kinds of verbal combinations (they can lead to poetic
and other literary and narrative explorations, cf. subsection 7.8.4 of chapter seven).
Moreover, some musical forms or actions schemas can be identified, as well as also
other possibilities.
Some particular attributes of these structures are very important in contributing
to discovery: novelty, ambiguity (ambiguous visual patterns are often interpreted in
various creative ways), implicit meaningfulness (they seem to have hidden meanings: “a general perceived sense of ‘meaning’ in the structure [. . . ] potential for
inspiring or eliciting new and unexpected interpretations” [Finke et al., 1992, p.
23], emergence (referred to the extension in the preinventive structures of unexpected relations and features), incongruity (that refers to conflict or contrast among
elements).28 Examples of creative reinterpretations of the preinventive form in
experiments on spanning the object categories are given in Figures 2.2 and 2.3.
Fig. 2.2 A preinventive form in experiments on spanning the object categories, constructed
c
using the bracket, hook, and half-sphere. (From [Finke et al., 1992, p. 84], 1992
Massachusetts Institute of Technology, by permission of The MIT Press).
27
28
Cf. also [Finke, 1990].
Already exploited by Koestler’s theory of bisociation [1964], divergence refers to the possibility of finding various uses and meanings in the same structure, like in the case of a hammer, an
unambiguous form that can be used in many ways. As can be easily seen, all these properties
can be considered from the single theoretical point of view of the presence of something anomalous. All properties refer to a kind of detected surprise that can open the abductive exploratory
processes of creativity.
2.5 A Note on Preinventive Forms, Disconfirming Evidence, Unexpected Findings
95
Fig. 2.3 Possible reinterpretations of the preinventive form given in Figure 2.2, spanning
eight object categories (left to right): lawn lounger (furniture), global earrings (personal
items), water weigher, (scientific instruments) portable agitator (appliances), water sled
(transportation), rotating masher (tool and utensils), ring spinner (toys and games), and
c
slasher basher (weapons). (From [Finke et al., 1992, p. 85], 1992
Massachusetts Institute
of Technology, by permission of The MIT Press).
[Koslowski, 1996] studies scientific reasoning observing the principles and strategies people use in generating and testing hypotheses in every day situations. In
some situations subjects reason in a scientific way to a greater extent than considered in the existing literature. She illustrates experiments with subjects dealing with
hypothesis-testing and examines how hypotheses (possible explanations) are generated and how they vary in credibility as a function of various sorts of evidence about
the considered phenomena. Moreover, the experiments concern the ways in which
humans deal with evidence or information “[. . . ] that disconfirms or is anomalous
to or at least unanticipated by an explanation” to focus on situations where there is
the opportunity to engage hypothesis revision (or hypothesis withdrawal).
The results are quite interesting and show that theoretical concerns play a prominent role in recognizing the importance of the anomalies: subjects manage hypothesis revision as theory dependent in a scientific legitimate way; when the alternative
explanatory hypotheses involved are in terms of causal (theoretical) mechanisms
96
2 Non-explanatory and Instrumental Abduction
– and not simply stated in terms of covariation with data – subjects are able to
treat them as defeasible and to modify them in ways that are theoretically motivated [Klahr and Dunbar, 1988], not simply using ad hoc maneuvers. Decisions
about whether to revise or reject as well as decisions about type of revisions that
would considered as justified are highly theory-dependent and involve much more
that merely information about covariation. In turn, ignoring the importance of the
theoretical component (or mechanism), can underestimate subjects’ willingness to
reject hypotheses when rejection would be appropriate (this is the reason why these
subjects have sometimes been regarded as poor scientists, like in the case described
in Wason’s task, [Wason, 1960].29
Finally, the empirical research by [Dunbar, 1995; Dunbar, 1999], in many molecular biology and immunology laboratory in US, Canada and Italy, has demonstrated
the central role of the unexpected in creative abductive reasoning. Scientists expect
the unexpected. By experimentally looking at the so-called “in vivo science” Dunbar
analyzes three activities that are seen as the most important in scientific model building: analogical reasoning, attention given to unexpected findings (that is anomalies,
errors, inconsistencies), experimental design, and distributed reasoning.
First of all scientists frequently use analogy where there is not a simple answer
to a particular problem, and distant analogies are not so widespread as supposed,
they are primarily used to explain concepts to others, but not in creative scientific
reasoning.
Secondly, it is well know that the recent discoveries of naked DNA and Buckey
balls, but also the old well-known of penicillin, nylon, and gravitation are charged to
the unexpected: in the “in vivo” science we can see the unexpected is very common,
for example it is a regular occurrence that the outcome of an experiment does not
match the scientists’ prediction. The scientists have to evaluate which findings are
caused by methodological errors, faulty assumptions, and chance events. At the local
level of experimentation in real scientific laboratories this research constitutes a kind
of confirmation of the Popperian ideas on hypotheses falsification, made in that case
at the macro-level of the whole growth of scientific knowledge. The hypotheses
are activated to deal with such problematic findings, usually local analogies and
model-based abductions, which can give rise to generalizations, causal explanation,
visualizations, etc., for finding the common features of the unexpected findings, and
possibly discover more general and deep explanations.
Third, experimental design is shown to have interesting cognitive components,
illustrating the fact that sometimes the experiments are locally built independently
of the hypotheses being tested. The problem is related to the role of manipulative
abduction I described in chapter one, showing how we can find methods of constructivity based on external models and action-based reasoning in scientific and
everyday reasoning, like the one embedded in experimental activity. Dunbar says
29
On the role of conceptual change in childhood and in “intuitive” theories see [Carey, 1985;
Carey et al., 1996]. Analogies and differences between scientific and ordinary thought are illustrated in [Kuhn, 1991; Kuhn, 1996]. [Ram et al., 1995] argue that a creative outcome is not
an outcome of extraordinary mental processes, but of mechanisms that are on a continuum with
those used in ordinary thinking.
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
97
scientists aim firstly at ensuring a robust internal structure of the experiment, optimizing the likelihood experiments will work, performing cost/benefits analysis on
possible design components, ensuring acceptance of results in case of negotiation
with other scientists of the community involved, and, finally, preferring experiments
that have both conditions and control conditions [Dunbar, 1999, p. 95].
Finally, we have to remember that science happens, particularly at the “critical” moments, in a situation of distributed reasoning (see also [Thagard, 1997b])
by a group of scientists and not individual scientists. Abductive reasoning (to produce multiple hypotheses) and generalization are the main cognitive events that
occur during social interactions among scientists. As I have already stressed in
the previous chapter (section 1.6) and I will more clearly illustrate in the following chapters, real people (and so scientists) are some kinds of cognitive-epistemic
“mediating structures” incorporating possible objective cognitive aims: epistemic
structures can be embodied in artifacts, in ideas, but also in systems of social
interactions.
2.6
Withdrawing Unfalsifiable Hypotheses Found through
Explanatory and Instrumental Abduction
In the previous sections I have illustrated that contradiction is fundamental in abductive reasoning and that it has a preference for strong hypotheses which are more
easily falsified than weak ones. Moreover, hard hypotheses may be more easily
weakened than weak ones, which prove difficult subsequently to strengthen. Unfortunately, abductive hypotheses may be unfalsifiable and basically instrumental,
such as in the case of hypotheses which are fruit of a radical instrumentalist abduction. In this case, it is impossible to find a contradiction from the empirical point
of view but also from the theoretical point of view, in some area of the related conceptual systems. Notwithstanding this fact, it is sometimes necessary to construct
ways of rejecting the unfalsifiable hypothesis at hand by resorting to some external
forms of negation, external because we want to avoid any arbitrary and subjective
elimination, which would be rationally or epistemologically unjustified.
In the following sections I will consider a kind of “weak” hypothesis in science
that is hard to negate and the ways for making it easy. In these cases, the subject(s)
can rationally decide to withdraw his hypotheses, and to activate abductive reasoning, even in contexts where it is impossible to find “explicit” contradictions; moreover, thanks to the new information reached simply by finding this kind of negation,
the subject is free to abduce new hypotheses. I will explore whether negation as failure can be employed to model hypothesis withdrawal in Freudian analytic reasoning
and in Poincaré’s conventionalism of the principles of physics. The first case shows
how conventions can be motivationally abandoned, the second one explains how the
questioned problem of the probative value of clinical findings in psychoanalysis can
be solved.
98
2.6.1
2 Non-explanatory and Instrumental Abduction
Negation as Failure in Query Evaluation
Computer and AI scientists have suggested an interesting technique for negating
hypotheses and accessing new ones: negation as failure. The objective of this section is to consider how the use of negation as failure may be relevant to hypothesis
withdrawal. There has been little research into the weak kinds of negating hypotheses, despite abundant reports that hypothesis withdrawal is crucial in everyday life
and also in certain kinds of diagnostic or epistemological settings, such as medical
reasoning and scientific discovery [Magnani, 2001b, chapters two and four].
NEGATION AS
FAILURE
We have to deal with a
PROOF such as the
following
FROM PROVING P
INFER ¬P
THE “PROOF THAT P IS NOT
PROVABLE” IS THE
EXHAUSTIVE BUT
UNSUCCESSFUL SEARCH FOR
A PROOF OF P.
¬ ACQUIRES THE NEW
MEANING OF “FAIL TO PROVE”
Fig. 2.4 Negation as failure
In the cases of conceptual change I describe, inferences are made using this kind
of negation as a fundamental tool for advancing knowledge: new conclusions are
issued on the basis of the data responsible for the failure of the previous ones. I plan
to explore whether this kind of negation can be employed to model hypothesis withdrawal in Poincaré’s conventionalism of the principles of physics and in Freudian
analytic reasoning.
I consider this kind of logical account of negation, studied by researchers into
logic programming, to be very important also from the epistemological point of
view. Negation as failure is active as a “rational” process of withdrawing previouslyabduced hypotheses in everyday life, but also in certain subtle kinds of diagnostic
(analytic interpretations in psychoanalysis) and other epistemological settings. Contrasted with classical negation, with the double negation of intuitionistic logic, and
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
99
with the philosophical concept of Aufhebung,30 negation as failure shows how a
subject can decide to withdraw his hypotheses, while maintaining the “rationality”
of his argumentations, in contexts where it is impossible to find contradictions.
The statements of a logical database are a set of Horn clauses which take the
form:
R(t1 , ...,tn ) ← L1 ∧ L2 ∧ ... ∧ Lm
(m ≥ 0, n ≥ 0, where R(t1 , ...,tn ) – conclusion – is the distinguished positive literal31
and L1 ∧L2 ∧...∧Lm – conditions – are all literals, and each free variable is implicitly
universally quantified over the entire implication). In more conventional notation
this would be written as the disjunction
R(t1 , ...,tn ) ∨ ¬L1 ∨ ¬L2 ∨ ... ∨ ¬Lm
where any other positive literal of the disjunctive form would appear as a negated
precondition of the previous implication.
Let us consider a special query evaluation process for a logical database that
involves the so-called negation as failure inference rule [Clark, 1978]. We can build
a Horn clause theorem prover augmented with this special inference rule, such that
we are able to infer ¬P when every possible proof of P fails.
We know that a relational database only contains information about true instances
of relations. Even so, many queries involve negation and we can answer them by
showing that certain instances are false. For example, let’s consider this simple case:
to answer a request for the name of a student not taking a particular course, C, we
need to find a student, S, such that the instance (atomic formula) Takes(S,C) is false.
For a logical database, where an atomic formula which is not explicitly given may
still be implied by a general rule, the assumption is that an atomic formula is false
if we fail to prove that it is true. To prove that an atomic formula P is false we do
an exhaustive search for a proof of P. If every possible proof of P fails, we can infer
¬P. The well-known PROLOG programming language [Roussel, 1987] uses this
method of manipulating negation.
We have to deal with a proof such as the following:
from proving P infer ¬P
where the “proof that P is not provable” [Clark, 1978, p. 120] is the exhaustive but
unsuccessful search for a proof of P. Here the logical symbol ¬ acquires the new
meaning of “fail to prove” (Figure 2.4).
Clark proposes a query evaluation algorithm based essentially on ordered linear
resolution for Horn clauses (SLD) augmented by the negation as failure inference
rule “¬P may be inferred if every possible proof of P fails” (SLDNF).32
30
31
32
[Toth, 1991] models negation exploiting this Hegelian concept which he considers very significant for explaining non-Euclidean revolution.
A literal is an atomic formula or the negation of an atomic formula.
The links between negation as failure, completed databases [Clark, 1978, p. 120], and the closed
world assumption have been classically studied in great detail. A survey can be found in [Lloyd,
1987].
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2 Non-explanatory and Instrumental Abduction
What is the semantic significance of this kind of negation? Can we interpret a
failed proof of P as a valid first order inference that P is false? Clark’s response
resorts to reconciling negation as failure with its truth functional semantics: if we
can demonstrate that every failed attempt to prove P using the database of clauses
B, is in effect a proof of ¬P using the completed33 database C(B), then “negation
as failure” is a derived inference rule for deductions from C(B): the explicit axioms
of equality and completion laws are therefore necessary at the object level in order
to simulate failure of the matching algorithm at the meta-level. A negated literal
¬P will be evaluated by recursively entering the algorithmic query evaluator (as an
ordered linear resolution proof procedure, as stated above) with the query P. If every
possible path for P ends in failure (failure proofs that can be nested to any depth),
we return with ¬P evaluated as true.
[Clark, 1978] has shown that for every meta-language proof of ¬P obtained by
a Horn clause theorem prover (query evaluation) augmented with negation as failure there exists a structurally similar object-language proof of ¬P. He has proved
that a query evaluation with the addition of negation as failure will only produce
results that are implied by first order inference from the completed database, that
is, the evaluation of a query should be viewed as a “deduction” from the completed
database (correctness of query evaluation). Consequently negation as failure is a
sound rule for deductions from a completed database.
Although the query evaluation with negation as failure process is in general not
complete, its main advantage is the efficiency of its implementation. There are many
examples in which the attempt to prove neither succeeds nor fails, because it goes
into a loop. To overcome these limitations it is sufficient to impose constraints on the
logical database and its queries, and add loop detectors to the Horn clause problem
solver: by this method the query evaluation process is guaranteed to find each and
every solution to a query. However, because of the undecidability of logic, no query
evaluator can identify all cases in which a goal is unsolvable. A best theorem prover
does not exist and there are no limitations on the extent to which a problem solver
can improve its ability to detect loops and to establish negation as failure.
2.6.2
Withdrawing Conventions and Instrumental Abduction
We will now consider some aspects dealing with Poincaré’s famous conventionalism of the principles of physics and the possibility of negating conventions. From the
point of view of radical instrumentalist abduction this example is striking because it
shows how these abduced principles fail all tests that would reveal them as having a
traditional epistemic value, so that they are not subject to discharge except for their
instrumental value. An extension of Poincaré’s so-called geometric conventionalism, according to which the choice of a geometry is only justified by considerations
of simplicity, in a psychological and pragmatic sense (“commodisme”), is the generalized conventionalism, expressing the conventional character of the principles of
physics:
33
The notion of database completion can be found in [Clark, 1978], and in all textbooks on logic
for computer science.
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
101
The principles of mathematical physics (for example, the principle of conservation of
energy, Hamilton’s principle in geometrical optics and in dynamics, etc.) systematize
experimental results usually achieved on the basis of two (or more) rival theories, such
as the emission and the undulation theory of light, or Fresnel’s and Neumann’s wave
theories, or Fresnel’s optics and Maxwell’s electromagnetic theory, etc. They express
the common empirical content as well as (at least part of) the mathematical structure
of such rival theories and, therefore, can (but need not) be given alternative theoretical
interpretations [Giedymin, 1982, pp. 27–28].
From the epistemological point of view it is important to stress that the conventional
principles usually survive the demise of theories and are therefore responsible for
the continuity of scientific progress: in a sense they show a radical instrumental
character Moreover, they are not empirically falsifiable; as stated by Poincaré in
Science and Hypothesis:
The principles of mechanics are therefore presented to us under two different aspects.
On the one hand, they are truths founded on experiment, and verified approximately
as far as almost isolated systems are concerned; on the other hand they are postulates
applicable to the whole of the universe and regarded as rigorously true. If these postulates possess a generality and a certainty which the experimental truths from which
they were deduced lack, it is because they reduce in final analysis to a simple convention that we have a right to make, because we are certain beforehand that no experiment can contradict it. This convention, however, is not absolutely arbitrary; it is not
the child of our caprice. We admit it because certain experiments have shown us that it
will be convenient, and thus is explained how experiment has built up the principles of
mechanics, and why, moreover, it cannot reverse them [Poincaré, 1902, pp. 135–136].
Following Poincaré we can say that conventional principles of mechanics derive
abductively from experience, as regards their “genesis”, but cannot be falsified by
experience because they contribute to “constitute” the experience itself, in a proper
Kantian sense. The experience has only suggested their adoption because they are
convenient: there is a precise analogy with the well-known case of geometrical conventions, but also many differences, which pertain the “objects” studied.34
Poincaré seeks also to stress that geometry is more abstract than physics, as
is revealed by the following speculations about the difficulty of “tracing artificial
frontiers between the sciences”:
34
The conventional principles of mechanics should not be confused with geometrical conventions:
“The experiments which have led us to adopt as more convenient the fundamental conventions
of mechanics refer to bodies which have nothing in common with those that are studied by geometry. They refer to the properties of solid bodies and to the propagation of light in a straight
line. These are mechanical, optical experiments” [Poincaré, 1902, pp. 136–137], they are not,
Poincaré immediately declares, “des expériences de géométrie” (ibid.): “And even the probable
reason why our geometry seems convenient to us is, that our bodies, our hands, and our limbs
enjoy the properties of solid bodies. Our fundamental experiments are pre-eminently physiological experiments which refer, not to the space which is the object that geometry must study, but
to our body - that is to say, to the instrument which we use for that study. On the other hand, the
fundamental conventions of mechanics and experiments which prove to us that they are convenient, certainly refer to the same objects or to analogous objects. Conventional and general
principles are the natural and direct generalisations of experimental and particular principles”
(ibid.)
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2 Non-explanatory and Instrumental Abduction
Let it not be said that I am thus tracing artificial frontiers between the sciences; that I
am separating by a barrier geometry properly so called from the study of solid bodies. I
might just as well raise a barrier between experimental mechanics and the conventional
mechanics of general principles. Who does not see, in fact, that separating these two
sciences we mutilate both, and that what will remain of the conventional mechanics
when it is isolated will be but very little, and can in no way be compared with that
grand body of doctrine which is called geometry [Poincaré, 1902, pp. 137–138] .
I believe that the meaning of this passage refers primarily to the fact that physics cannot be considered completely conventional because we know that the conventional
“principles” are derived from the “experimental laws” of “experimental mechanics”,
and then absolutized by the “mind”. Second, Poincaré wants to demonstrate how geometry is more abstract than physics: geometry does not require a rich experimental
reference as physics does, geometry only requires that experience regarding its genesis and as far as demonstrating that it is the most convenient is concerned. Here
we are very close to Kant’s famous passage about the synthetical a priori character
of the judgments of (Euclidean) geometry, and of the whole of mathematics: “The
science of mathematics presents the most splendid example of the extension of the
sphere of pure reason without the help of the experience” [Kant, 1929, A712-B740,
p. 576].
Even when separated from the reference to solid bodies, Euclidean geometry
maintains all its conceptual pregnancy, as a convention that, in a proper Kantian
sense, “constitutes” the ideal solid bodies themselves. This is not the case of the
conventional principles of mechanics when separated from experimental mechanics:
“[. . . ] what will remain of the conventional mechanics [. . . ] will be very little” if
compared “[. . . ] with that grand body of doctrine which is called geometry”.
Poincaré continues:
Principles are conventions and definitions in disguise. They are, however, derived from
experimental laws, and these laws have, so to speak, been erected into principles to
which our mind attributes an absolute value. Some philosophers have generalized far
too much. They have thought that the principles were the whole of science, and therefore that the whole of science was conventional. This paradoxical doctrine, which is
called nominalism, cannot stand examination. How can a law become a principle?
[Poincaré, 1902, p. 138].
If the experimental laws of experimental physics are the source of the conventional
principles themselves, conventionalism escapes nominalism.
As stated at the beginning of this section, conventional principles survive the
demise (falsification) of theories in such a way that they underlie the incessant spectacle of scientific revolutions: “It is the mathematical physics of our fathers which
has familiarized us little by little with these various principles; which has habituated
us to recognize them under the different vestments in which they disguise themselves” [Poincaré, 1905, p. 95]. Underlying revolutions of physics, conventional
principles guarantee the historicity and the growth of science itself. Moreover, the
conventional principles surely imply “[. . . ] firstly, that there has been a growing tendency in modern physics to formulate and solve physical problems within powerful,
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
103
and more abstract, mathematical systems of assumptions [. . . ]; secondly, the role
of conventional principles has been growing and our ability to discriminate experimentally between alternative abstract systems which, with a great approximation,
save the phenomena has been diminishing (by comparison to the testing of simple
conjunctions of empirical generalizations)” [Giedymin, 1982, p. 28].
Moreover, as stated above, they are not empirically falsifiable: “The principles of
mechanics [. . . ] reduce in final analysis to a simple convention that we have a right
to make, because we are certain beforehand that no experiment can contradict it”
[Poincaré, 1902, p. 136].
Up to now I have considered in details how the conventional principles guarantee
the revolutionary changes of physics and why they cannot be considered arbitrary,
being motivated by – and abduced from – the experimental laws of the “experimental physics”, that is by experience. Although arbitrary and conventional, the
conventional principles too can be substituted by others. This is the main problem
treated by Poincaré in the last passages of Chapter IX, “The Future of Mathematical
Physics”, in The Value of Science. Already the simple case of “linguistic” changes
in science “[. . . ] suffices to reveal generalizations not before suspected” [Poincaré,
1905, p. 78]. By means of the new discoveries, scientists arrive at a point where
they are able to “[. . . ] admire the delicate harmony of numbers and forms; they
marvel when a new discovery opens to them an unexpected perspective” [Poincaré,
1905, p. 76], a new perspective that is always provisional, fallible, open to further
confirmations or falsifications when compared to rival perspectives.
We have seen how the conventional principles of physics guarantee this continuous extension of experience thanks to the various perspectives and forms expressed by experimental physics. However, because conventional, “no experiment
can contradict them”. The experience only suggested the principles, and they, since
absolute, have become constitutive just of the empirical horizon common to rival
experimental theories.
Poincaré observes:
Have you not written, you might say if you wished to seek a quarrel with me – have you
not written that the principles, though of experimental origin, are now unassailable by
experiment because they have become conventions? And now you have just told us that
the most recent conquests of experiment put these principles in danger. Well, formerly
I was right and today I am not wrong. Formerly I was right, and what is now happening
is a new proof of it [Poincaré, 1905, p. 109].
Poincaré appeals to a form of weak negation, just as Freud did when dealing with
the problem of withdrawing constructions in the analytic setting (cf. the following
subsection). Let us follow the text. To pursue his point, Poincaré illustrates the attempts to reconcile the “calorimetric experiment of Curie” with the “principle of
conservation of energy”:
This has been attempted in many ways; but there is among them one I should like
you to notice; this is not the explanation which tends to-day to prevail, but it is one
of those which have been proposed. It has been conjectured that radium was only an
intermediary, that it only stored radiations of unknown nature which flashed through
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2 Non-explanatory and Instrumental Abduction
space in every direction, traversing all bodies, save radium, without being altered by
this passage and without exercising any action upon them. Radium alone took from
them a little of their energy and afterward gave it out to us in various forms [Poincaré,
1905, pp. 109–110] .
At this point Poincaré resolutely asserts: “What an advantageous explanation, and
how convenient! First, it is unverifiable and thus irrefutable. Then again it will serve
to account for any derogation whatever to Mayer’s principle; it answers in advance
not only the objection of Curie, but all the objections that future experimenters might
accumulate. This new and unknown energy would serve for everything” (p. 110).
Now Poincaré can show how this ad hoc hypothesis can be identified with the nonfalsifiability of the conventional principle of the conservation of energy:
This is just what I said, and therewith we are shown that our principle is unassailable
by experiment. But then, what have we gained by this stroke? The principle is intact,
but thenceforth of what use is it? It enabled us to foresee that in such and such circumstance we could count on such total quantity of energy; it limited us; but now that this
indefinite provision of new energy is placed at our disposal, we are no longer limited
by anything [Poincaré, 1905, p. 110].
Finally, Poincaré’s argumentation ends by affirming negation as failure: “[. . . ] and,
as I have written in ‘Science and Hypothesis’, if a principle ceases to be fecund,
experiment without contradicting it directly will nevertheless have condemned it”
(ibid.) (cf. Figure 2.5).
Let us now analyze this situation from the epistemological point of view: the
conventional principle has to be withdrawn when it “ceases to be fecund” and so because it is no longer endowed with an acceptable degree of strategical plausibility,
or when it seems that we have failed to prove it. It is clear that the principle exhibits
in this case a kind of strategic, rather than propositional, plausibility, as I have described in subsection 2.3.1. Remember that for a logic database the assumption is
that an atomic formula is false if we fail to prove that it is true. More clearly: as
stated above, every conventional principle, suitably underlying some experimental
laws, generates expectations with regard to the subsequent evidences of nature. I
analogously consider as the proof of a conventional principle the fact that we can
increasingly extend and complete the experimental laws related to it, adding the new
(expected) evidence that “emerges” from the experimental research. If, after a finite
period of time, nature does not provide this new “evidence” that is able to increase
the fecundity of the conventional principle, this failure leads to its withdrawal: “[. . . ]
experiment without contradicting it directly will nevertheless have condemned it”.
Analogously to the Freudian case of constructions I will illustrate in the following
subsection the “proof that a principle is not provable”35 is the unsuccessful search
for a proof of the principle itself. Here too, the logical symbol ¬ acquires the new
meaning of “fail to prove” in the empirical sense.
Let us resume: if the old conventional principle does not produce new experimental “evidence” to underpin it, it is legitimate to abandon the principle, when
35
Please keep in mind I am making an analogy between “not provable” and “not empirically
fecund”.
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
105
convenient: the opportunity to reject the old principle will happen just by exploiting
the experimental evidence which, even if not suitable for contradicting it (Poincaré
says, it is “unassailable by experiment”), is nevertheless suitable as a basis for conceiving a new alternative principle, generated by new creative abductions.
We can now interpret Popper’s ideas about conventionalism in a different way.
Popper writes: “Thus, according to the conventionalist view, it is not possible to
divide systems of theories into falsifiable and non-falsifiable ones; or rather, such
a distinction could be ambiguous. As a consequence, our criterion of falsifiability
must turn out to be useless as a criterion of demarcation” [Popper, 1959, p. 81]. In
the light of Poincaré’s theory of the principles of physics that we have just illustrated, the nominalistic interpretation of conventionalism given by Popper (see also
[Popper, 1963]) appears to be very reductive. Moreover, Popper’s tendency to identify conventions with ad hoc hypotheses (a very bad kind of auxiliary hypotheses)
is shown to be decidedly unilateral, since, as is demonstrated by the passages, immediately above, the adhocness is achieved only in a very special case, when the
conventional principle is epistemologically exhausted.
Physics
Hypotheses
Principles of Physics
Conventions
Negation
as failure
Abduction
(Extending experimental
evidence related to the
conventional principle)
Deduction
Evidence
Expected
evidence
Fig. 2.5 Withdrawing conventions
In some sense Poincaré was already aware of the following fact, subsequently
clearly acknowledged by Popper: the introduction of auxiliary hypotheses must not
diminish the degree of falsifiability or testability (that will have to be performed by
means of “severe tests”) of the scientific theory in question, but, on the contrary,
should increase it [Popper, 1959, p. 83]. The example of an unsatisfactory (ad hoc)
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auxiliary hypothesis given by Popper is the “[. . . ] contraction hypothesis of Fitzgerald and Lorentz which had no falsifiable consequences but merely served to restore
the agreement between theory and experiment – mainly the findings of Michelson
and Morley” [Popper, 1959, p. 83].
In turn Lakatos’ revision of falsificationism in terms of the theory of research
programs [Lakatos, 1970] has definitely established that modified hypotheses (by
means of auxiliary assumptions) have to be more falsifiable than the original versions, they have to lead to new testable consequences (and, moreover, independently
testable, to use Popper’s phrase – [Popper, 1959, p. 193]; progress in “scientific
programs” is heavily related to the existence of novel predictions: one program is
superior to another insofar as it is a more successful predictor of novel phenomena.
Something analogous – but in a more indirect way – operates in the case of the
conventional principles described by Poincaré: it seems that conventionalism, at
least in the Poincaré’s case, does not treat all hypotheses like “stratagems”, as maintained by Popper. Hypothetical conventional principles are unfalsifiable and should
be withdrawn only when exhausted, when their indirect production of “novel” evidence is finished. Consequently, Poincaré’s conventionalism is not simply a theory
of adhocness, in the nominalistic Popperian sense.
As regards instrumentalist abduction my example of the conventional principles
of physics shows a cognitive situation that Gabbay and Woods synthetically illustrate in the following way: “Proposition 5.7 (Discharging radically instrumentalist
hypotheses) Since the hypothesis of a radically instrumentalist abduction fails all
tests that would reveal it as having the requisite epistemic value, such hypotheses
are not subject to discharge except for their instrumental value” [Gabbay and Woods,
2005, p. 120].
2.6.3
Withdrawing Constructions and Explanatory and
Instrumental Abduction
First of all I will illustrate how it is possible to explain the epistemological status
of Freud’s method of clinical investigation in terms of a special form of negation as
failure. I am not dealing here with the highly controversial problem of the epistemological status of psychoanalytic clinical theories (comprehensively analyzed in the
classical [Grünbaum, 1984]): it is well-known that clinical data have no probative
value for the confirmation or falsification of the general hypotheses of psychoanalytic clinical theories of personality, because, given that they depend completely on
the specific nature of the clinical setting, they are devoid of the independence that
characterizes observations endowed with scientific value.
Furthermore, because of the lack of probative value in the patient’s clinical data
with regard to the analyst’s interpretations, any therapeutic gains from analysis may
be considered to have been caused not by true insightful self-discovery but rather by
placebo effects induced by the analyst’s powers of suggestion. If the probative value
of the analysand’s responses is negated, then Freudian therapy might reasonably be
considered to function as an emotional corrective (performed by a positive “transference” effect) and not because it enables the analysand to acquire self-knowledge;
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
107
instead he or she capitulates to proselytizing suggestion, which operates the more insidiously since under the pretense that analysis is nondirective. Suggestion is indeed
responsible for the so-called epistemical contamination of the patient’s responses.
Freud asks the patient to believe in the analyst’s theoretical retrodictions of significant events in his early life and these theoretical retrodictions are communicated
to him as constructions – actually they are explanatory abductions derived on the
basis of some present evidence furnished by the patient:
The analyst finishes a piece of construction and communicates it to the subject of the
analysis so that it may work upon it; he then constructs a further piece out of the
fresh material pouring in upon him, deals with it in the same way and proceeds in this
alternating fashion until the end [Freud, 1953-1974, vol, 23, 1937, pp. 260–261].
The aim is to provoke the previously-cited true insightful self-discovery that guarantees the cure [Freud, 1953-1974, vol. 18, 1920, p. 18]. A single construction is
built as a “sequence” of the interpretations (that have an obvious abductive character) that issue from clinical data found in the clinical setting, epistemologically
characterized by “transference” and “countertransference”:
“Interpretation” applies to something that one does to some single element of the material, such as an association or a parapraxis. But it is a “construction” when one lays
before the subject of the analysis a piece of his early history that he has forgotten, in
some such way as this: “Up to your nth year you regarded yourself as the sole and
unlimited possessor of your mother; then came another baby and brought you grave
disillusionment. Your mother left you for some time, and even after her reappearance
she was never again devoted to you exclusively. Your feelings towards your mother
became ambivalent, your father gained a new importance for you,” and so on [Freud,
1953-1974, vol. 23, 1937, p. 261].
A construction can be considered as a kind of “explanatory” “history” or “narrative” abductively obtained of the analysand’s significant early life events, which is
never complete, but that can be rendered more and more comprehensive by adding
new interpretations. This abductive process, I call selective, presents a constitutive
uncertainty due to its nonmonotonicity (cf. chapter one, section 1.3, this book), the
analyst may always withdraw his or her interpretations (constructions) when new
evidence arises. Every construction is generated by a “double” abduction: first of
all the analyst has to select a suitable general psychoanalytic hypothesis, apply it
to some “single element of the material” to produce an interpretation, then he/she
has to select each of these general hypotheses in such a way that the sequence of
the generated interpretations can give rise to a significant and consistent construction. Every “abduced” construction, suitably connected with some other clinical
psychoanalytical hypotheses, generates expectations with regard to the analysand’s
subsequent responses and remarks.
Let us remember that Habermas considers therapy as due to a sort of Hegelian
causality of fate: the analyst applies what Habermas calls “general interpretations”36
[Habermas, 1968, p. 279] to the analysand’s clinical data. This application generates
36
They correspond to general “schemes” of possible constructions.
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2 Non-explanatory and Instrumental Abduction
particular interpretations that combine into a “narrative” (Freud’s “construction”).
Within the scientophobic framework of Habermas’s philosophy this application is
regarded as “hermeneutic”, because the constructions are presumed to be expressed
in the “intentional” and motivational language of desires, affects, fantasies, sensations, memories, etc. We can more easily consider them abduction without resorting
to the hermeneutical lexicon.
Of course the analyst aims at building the most complete construction. The problem here is the analyst cannot propose to the analysand any construction he wants,
without some form of external testing. As stated above, the objection most often
raised against psychoanalysis is that “[. . . ] therapeutic success is nonprobative because it is achieved not by imparting veridical insight but rather by the persuasive
suggestion of fanciful pseudoinsights that merely ring verisimilar to the docile patient” [Grünbaum, 1984, p. 138]. In one of his last papers, “Constructions in analysis” [Freud, 1953-1974, vol, 23, 1937, pp. 257–269], Freud reports that “a certain
well-known man of science” had been “at once derogatory and unjust” because
He said that in giving interpretations to a patient we treat him upon the famous principle of “Heads I win, tails you lose” [In English in the original]. That is to say, if the
patient agrees with us, then the interpretation is right, but if he contradicts us, that is
only a sign of his resistance, which again shows that we are right. In this way we are
always in the right against the poor helpless wretch whom we are analysing, no matter
how he may respond to what we put forward [Freud, 1953-1974, vol, 23, 1937, p. 257].
Freud looks for a criterion for justifying, in the clinical setting, the abandonment of
constructions that have been shown to be inadequate (it is interesting to note that
in the cited article Freud emphasizes the provisional role of constructions referring
to them also as “hypotheses” or “conjectures”). This is the fundamental epistemological problem of the method of clinical investigation: Freud is clear in saying that
therapeutic success will occur only if incorrect analytic constructions, spuriously
confirmed by “contaminated” responses from the patient, are discarded in favor of
new correct constructions (that are constitutively provisional) derived from clinical data not distorted by the patient’s compliance with the analyst’s communicated
expectations.
Freud then proceeds “[. . . ] to give a detailed account of how we are accustomed
to arrive at an assessment of the ‘Yes’ or ‘No’ [considered as “direct evidences”]
of our patients during analytic treatment – of their expression of agreement or of
denial” (p. 257).
Analytic constructions cannot be falsified by dissent from the patient because
“[. . . ] it is in fact true that a ‘No’ from one of our patients is not as a rule enough
to make us abandon an interpretation as incorrect” (p. 257). It might seem to Freud
that patient dissent from an interpretation can be always discounted as inspired by
neurotic resistance. It is only “in some rare cases” that dissent “turns out to be the
expression of legitimate dissent” (p. 262). A “patient’s ‘No’ is no evidence of the
correctness of a construction, though it is perfectly compatible with it” (p. 263).
Rather, a patient’s ‘No’ might be more adequately related to the “incompleteness”
of the proposed constructions: “[. . . ] the only safe interpretation of his ‘No’ is that
it points to incompleteness” (p. 263).
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
109
Even if a patient’s verbal assent may result from genuine recognition that the analyst’s construction is true, it may nevertheless be spurious because it derives from
neurotic resistance, as already seen in his or her dissent. Assent is “hypocritical”
when it serves “[. . . ] to prolong the concealment of a truth that has not been discovered” (p. 262). On the other hand, assent is genuine and not hypocritical when
patient’s verbal assent will be followed and accompanied by new memories: “The
‘Yes’ has no value unless it is followed by indirect confirmations, unless the patient,
immediately after his ‘Yes’, produces new memories which complete and extend
the construction” (p. 262) .
Since “Yes” and “No” do not have any importance to test a construction it is
necessary to see other facts, such as “the material” that has “come to light” after
having proposed a construction to the patient:
[. . . ] what in fact occurs [. . . ] is rather that the patient remains as though he were
untouched by what has been said and reacts to it with neither a “Yes” nor a “No”. This
may possibly mean no more than that his reaction is postponed; but if nothing further
develops we may conclude that we have made a mistake and we shall admit as much
to the patient at some suitable opportunity without sacrificing any of our authority
(pp. 261–262).
Let us now analyze this situation from the epistemological point of view: the analyst has to withdraw the construction (a narrative complex hypothesis) when he
has failed to prove it. Remember that for a logic database the assumption is that an
atomic formula is false if we fail to prove that it is true. More precisely: as stated
above, every construction, suitably connected with some other clinical psychoanalytical hypotheses, generates expectations with regard to the analysand’s subsequent
responses and remarks. We consider the fact that we can continuously extend and
complete a construction by adding the new (expected) material that “has come to
light” from the patient as proof of the construction validity. If the patient does not
provide this new “material” which is able to extend the proposed construction, this
failure leads to the withdrawal of the construction itself. So the “proof that a construction is not provable” is the unsuccessful search for a proof of the construction
itself. Here the logical symbol ¬ acquires the new meaning of “fail to prove” in the
empirical sense.37
Let us resume: if the patient does not provide new “material” which extends the
proposed construction, “if”, as Freud declares, “[. . . ] nothing further develops we
may conclude that we have made a mistake and we shall admit as much to the
patient at some suitable opportunity without sacrificing any of our authority”. The
“opportunity” of rejecting the proposed construction “will arise” just
[. . . ] when some new material has come to light which allows us to make a better
construction and so to correct our error. In this way the false construction drops out, as
if it has never been made; and indeed, we often get an impression as though, to borrow
the words of Polonius, our bait of falsehood had taken a carp of truth (p. 262).
37
Again, please keep in mind in this case I am making an analogy between “not provable” and
“not empirically fecund”.
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2 Non-explanatory and Instrumental Abduction
Theories
Hypotheses
Interpretations
Constructions
Negation
as failure
Abduction
(Extending constructions)
Deduction
Observed
material
Expected
material
Fig. 2.6 Withdrawing constructions
A new cycle very similar to the one previously started with the assumption of the
first construction takes place: a new construction (derived by applying new clinical
psychoanalytical hypotheses and schemes) is provisionally conceived on the basis
of the new material that came to light when the analyst was seeking to extend the
old one (“we often get an impression as though [. . . ] our bait of falsehood had taken
a carp of truth”) (cf. Figure 2.6). The inferential process is clearly nonmonotonic: in
an initial phase we have some material coming from the patient and which provides
the background for an initial abduced construction; in a second phase we have to
add to the initial construction the material which emerges after having communicated to the patient the first construction. If in this second phase the new material
is not suitable for extending the first construction, the negation as failure compels
the analyst to withdraw and reject the construction. The whole process is nonmonotonic because the increase of material does not generate an increase in (the number
of) constructions: the old construction is abandoned (“the false construction drops
out, as if it has never been made”).
I should stress that the epistemological role of what Freud calls “indirect confirmations” or disconfirmations of analytic constructions is in my opinion negligible.
These patient responses, other than verbal assent or dissent, Freud declares, “are in
every respect trustworthy” (p. 263). Examples are when a patient has a mental association whose content is similar to that of the construction, or when a patient commits a parapraxis as part of a direct denial. Moreover, when a masochistic patient is
averse to “receiving help from the analyst”, an incorrect construction will not affect
his symptoms, but a correct one will produce “[. . . ] an unmistakable aggravation of
2.6 Withdrawing Unfalsifiable Hypotheses Found through Explanatory
111
his symptoms and of his general condition” (p. 265). The indirect confirmations, in
Freud’s opinion, provide a “[. . . ] valuable basis for judging whether the construction
is likely to be [further] confirmed in the course of analysis” (p. 264).
We should not confuse the kind of transformations of “No” in “Yes” (or vice
versa) that pertains to the “indirect confirmations” or disconfirmations, with the
above-described extension of constructions toward the most complete one on the
basis of new (expected) material that emerges. In conclusion, a patient’s “Yes” or
“No”, whether direct or indirect, has no role to play in withdrawing constructions.
I think that these cases do not have any function in the process of abandoning a
construction because they always keep open the possibility of extending it: moreover, the indirect confirmations or disconfirmations do not increase the acceptability of constructions. In my opinion, we should not consider Freud as an inductivist,
despite his emphasis on these kind of indirect evidence.
Moreover, as stated by Grünbaum, who tends to consider Freudian description
of clinical method as inductive, this presumption of the consilience of clinical
inductions is “spurious” because
[. . . ] the independence of the inferentially concurring pieces of evidence is grievously
jeopardized by a shared contaminant: the analyst’s influence. For each of seemingly
independent clinical data may well be more or less alike confounded by the analyst’s
suggestion as to conform to his construction, at the cost of their epistemic reliability or probative value. For example a “confirming” early memory may be compliantly produced by the patient on the heels of giving docile assent to an interpretation
[Grünbaum, 1984, p. 277].
The second section of “Constructions in analysis” concludes with a very explicit
affirmation of nonmonotonicity:
Only the further course of the analysis enables us to decide whether our constructions
are correct or unserviceable. [. . . ] an individual construction is anything more than a
conjecture which awaits examination, confirmation or rejection. We claim no authority
for it, we require no direct agreement from the patient, nor do we argue with him if at
first he denies it. In short, we conduct ourselves on the model of a familiar figure in
one of Nestroy’s farces – the manservant who has a single answer on his lips to every
question or objection: “It will all become clear in the course of future developments”
(p. 265).
But I have shown that Freud considers important only the rejection achieved by
negation as failure. The epistemological aim is not to validate a construction by
extensions provided by new material or by indirect confirmations or disconfirmations. Freud aims to reject it. Perhaps in Freud’s considerations there are some ambiguities in perceiving the asymmetry between falsification and confirmation, but
it would seem that my interpretation of Freud as a special falsificationist can be
maintained without fear of distorting his methodological intention. Freud is a special type of “falsificationist” because negation as failure guarantees the possibility
of freely withdrawing an abduced construction and substituting it with a rival and
better one. In the computational case, negation as failure is achieved by suitable
algorithms related to the knowledge that is handled (see above, subsection 2.6.1).
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2 Non-explanatory and Instrumental Abduction
In the human and not computational case, negation as failure is played out in the
midst of the analyst-analysand interaction, where transference and countertransference are the human epistemological operators and “reagents”. Negation as failure is
therefore a limitation on the dogmatic and autosuggestive exaggerations of (pathological) countertransference.
We can say again, from the point of view of instrumentalist abduction that my
example shows a cognitive situation that Gabbay and Woods synthetically illustrate
in the following way and that we have already quoted: “Proposition 5.7 (Discharging
radically instrumentalist hypotheses) Since the hypothesis of a radically instrumentalist abduction fails all tests that would reveal it as having the requisite epistemic
value, such hypotheses are not subject to discharge except for their instrumental
value” [Gabbay and Woods, 2005, p. 120]. In this Freudian case the explanatory
aspects of hypothetical interpretations and constructions shades in their final radical instrumentalist/strategic character. They are only indirectly activated for further
explanatory premissory work; so to say, they are always constitutively taken on
epistemological explanatory sufferance because no other chances are practicable,
and their main epistemic (instrumental, strategic) virtue – which guarantees they
are withdrawable – is stimulating the emergence of new material able to enrich the
construction.38
2.7
Automatic Abductive Scientists
Paul Thagard [1988] illustrates four kinds of abduction that have been implemented
in PI, a system devoted to explaining in computational terms the main problems
of the traditional philosophy of science, such as scientific discovery, explanation,
evaluation, etc. He distinguishes between simple, existential, rule-forming, and analogical abduction. Simple abduction generates hypotheses about individual objects.
Existential abduction postulates the existence of previously unknown objects, such
as new planets. Rule-forming abduction generates rules that explain laws. Analogical abduction uses past cases of hypothesis formation to construct hypotheses
similar to existing ones. If the pure philosophical task is to state correct rules of
reasoning in an abstract and objective way, the use of computer modeling may be a
rare tool to investigate abduction in science because of its rational correctness. The
increase in knowledge provided by this intellectual interaction is manifest.
Early works on machine scientific discovery, such as the well-known Logic Theorist [Newell et al., 1957], DENDRAL, in chemistry [Lindsay et al., 1980], and
AM, in mathematics, [Lenat, 1982], have shown that heuristic search in combinatorial spaces is an advantageous and general framework for automating scientific
38
Other interesting examples of instrumentalist abduction in science are illustrated in [Gabbay
and Woods, 2005, p. 120]: the axiom of choice – which has an abductive role in proofs of
Löwenheim-Skolem theorem, Planck’s discovery of the quantum hypothesis (cf. above p. 79),
and the hypothesis of gravitons.
2.7 Automatic Abductive Scientists
113
discovery39. In these programs abduction is mainly rendered in a sentential way,
using rules and heuristics.
There are many ways for identifying a commonality in computational scientific
discovery programs that will take a next step beyond the acknowledged general –
but weak – framework of heuristic search (cf. also [Tweney, 1990]. For example,
[Valdés-Pérez, 1999], characterizes discovery in science as the generation of novel,
interesting, plausible, and intelligible knowledge about the objects of study. Looking
for a common general pattern he analyzes four machine discovery programs that
match those requirements in different ways:
1. MECHEM, which hypothesizes reaction mechanisms in chemistry based on the
available experimental evidence [Zeigarnik et al., 1997]
2. ARROSMITH, which notices connections between drugs or dietary factors and
diseases in medicine [Swanson and Smalheiser, 1997]
3. GRAFFITI, which makes conjectures in graph theory and other similar
mathematical fields [Fajtlowicz, 1988]
4. MDP/KINSHIP, which delineates the classes within a classification in linguistics [Pericliev and Valdés-Pérez, 1998].
In turn [Boden, 1992] expecially stresses the distinction between classical programs
able to re-produce historical cases of scientific discovery in physics (BACON systems and GLAUBER, [Langley et al., 1987]), and systems able to perform new
discoveries (DENDRAL and AM, cited above). Other authors (for example, [Shunn
and Klahr, 1995], who constructed the program ACT-R) emphasize the distinction
between computational systems that address the process of hypothesis formation
and evaluation (BACON; PHINEAS, [Falkenhainer, 1990]; AbE, [O’Rorke et al.,
1990]; ECHO, [Thagard, 1989; Thagard, 1992]; TETRAD, [Glymour et al., 1987];
MECHEM), those that address the process of experiment (like DEED, [Rajamoney,
1993]; DIDO, [Scott and Markovitch, 1993]), and, finally, those that address both
the processes (like KEKADA, [Kulkarni and Simon, 1988]; SDDS, [Klahr and Dunbar, 1988], LIVE, [Shen, 1993], and others).
All these AI systems explicitly or implicitly perform epistemological tasks. From
the point of view of the task of abduction it is interesting to note that some of
them model a kind of sentential creative abduction, others are dealing with modelbased creative abduction, and there are also the ones related to model the activity of
experiment (that relate to the problem of what I call “manipulative abduction”).
Sentential creative abduction. In the first case we have to note that systems
like BACON, GLAUBER, built in terms of heuristic search, notwithstanding they
39
Already in 1995 the AAAI Society organized a Spring Symposium on “Systematic Methods
of Scientific Discovery” and in 1997 the Journal Artificial Intelligence devoted a special issue
to “Machine Discovery” (91, 1997, – [Okada and Simon, 1997]). Classical books where the
reader can find the description of the most interesting research and the description of historical
machine discovery programs are [Langley et al., 1987], and [Shrager and Langley, 1990]. Cf.
also [Zytkow, 1992] (Proceedings of MD-92 Workshop on “Machine Discovery”), and [Colton,
1999] (Proceedings of AISB’99). In 1990 AAAI Society already organized a Spring Symposium
on the problem of “automated abduction”, devoted to the illustration of many computational
programs able to perform various abductive tasks.
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2 Non-explanatory and Instrumental Abduction
perform outputs that can be presented as a fruit of the creative abductive task of reproducing well-known past discovery of physics, they actually execute a selective
abduction: starting from given data, they just have to “select” among a pre-stored encyclopedia of mathematical equations capable of explaining the data. Consequently
they are similar, because of the epistemology of their architecture, to the computational programs devoted to perform diagnostic reasoning in medicine (cf. [Magnani,
2001b, chapter four]).
Model-based creative abduction. In the second case the programs are capable
of performing model-based abductions: for example by providing causal and analogical reasoning, like the previously cited AbE (theory revision in science), CHARADE (discovery of the causes of scurvy) [Corruble and Ganascia, 1997], CDP
(discovery of urea cycle, [Grasshoff and May, 1995]), GALATEA (explanation
tasks) [Davies and Goel, 2000], PROTEUS [Davies et al., 2009] (analogical reasoning), PHINEAS, that exploits the representational resources of qualitative physics
[Forbus, 1984; Forbus, 1986]. to perform analogical reasoning in liquid flow.40 AbE
and PHINEAS explicitly and directly refer to abductive tasks, other programs employ the word induction, even if they are achieving a more complicated task than
mere generalization from data.41 A system that explicitly addresses model-based
abduction (the so-called generic modeling) in science is TORQUE [Nersessian et
al., 1997], devoted to perform tasks of visualizations able to account for various
cases of discovery in science (Faraday, Maxwell).42
More recent AI programs have been built to simulate abduction in mathematical and geometrical reasoning. This is the case of ARCHIMEDES ([Lindsay, 1994;
Lindsay, 1998; Lindsay, 2000b; Lindsay, 2000a], cf. also the last section of this
chapter, section 2.12), which realizes cases of manipulative diagrammatic abduction in elementary geometry, and HR [Colton, 1999; Pease et al., 2005], which
creates new concepts in the field of algebra also taking advantage of Lakatosian
epistemology of formal reasoning. [Trickett and Trafton, 2007] recently stressed the
role of conceptual simulation in the so called “what if” reasoning (mental experiment, thought experiment, inceptions, mental simulations) in scientists’ strategies to
resolve informational uncertainty. Actually the analysis illustrates the abductive role
played by a wide range of model-based and manipulative ways of discovering in science. For a recent survey of the relationships between computation and the problem
40
41
42
A system that aims at constructing causal hypotheses is TETRAD [Glymour et al., 1987], but it
manipulates numeric data – and not model-based types of reasoning – and is deeply entrenched
in a probabilistic framework.
On the ambiguities and relationships between abduction and induction cf. chapter one, subsection 1.4.1 and chapter seven, section 7.4.
Other tools that could be proven useful in the area of abduction and machine discovery come
from the field of genetic algorithms and evolving neural networks (cf. [Pennock, 1999; Pennock,
2000]), where creative reasoning is studied improving Darwinian mechanisms described by
evolutionary theories, and may be from the very recent so-called DNA computers [Boneh et al.,
1996].
2.7 Automatic Abductive Scientists
115
of scientific explanation and discovery in philosophy of science cf. [Thagard and
Litt, 2008]. .43
Manipulative abduction. In the third case, when dealing with the simulation of
experiment, the computational programs join the area of manipulative abduction.
An interesting and neglected point of contention about human reasoning is whether
or not concrete manipulations of external objects influence the generation of hypotheses, for example in science: in the following chapter I will delineate the first
features of what I call manipulative abduction showing how we can find methods
of constructivity in scientific and everyday reasoning based on external models and
“epistemic mediators”. Manipulation of external objects in scientific experiments
realizes a kind of epistemic mediation, also exploiting the cognitive resources of
human body and its performances. The discovery programs that address the process
of experiment constitute the first attempt to automatize these abilities, that could
further extend the interest of machine discovery in science also to the whole area of
robotics.44
It is well known that epistemology and logic are not alone in investigating reasoning. Reasoning is also a major subject of investigation in AI cognitive psychology,
and the whole area of cognitive science. Epistemological (and logical) theories of
reasoning, when implemented in a computer, become AI programs. The theories and
the programs are, quite literally, two different ways of expressing the same thing.
43
44
Recent workshops and conferences that cover computational AI applications that involve abductive processes have been organized worldwide. Here a list of the more recent ones: AAAI
Symposium on Automated Scientific Discovery, Stanford, November 2008; International Joint
Workshop on Computational Creativity (IJWCC2008), Madrid, Spain, September, 2008; Fourth
Joint Workshop on Computational Creativity (ECAI2006), London, UK, June 2007; Workshop
Abduction and Induction in AI and Scientific Modeling (ECAI2006), Riva del Garda, Italy, August 2006; Third Joint Workshop on Computational Creativity (ECAI2006), Riva del Garda,
Italy, August 2006; Fourth International Workshop on Computational Models of Scientific Reasoning and Applications (CMSRA-IV) Lisbon, Portugal, September 2005; The Second Joint
International Workshop on Computational Creativity (IJCAI’05, International Joint Conference
of Artificial Intelligence), UK, August 2005; Workshop on Chance Discovery: from Data Interaction to Scenario Creation, The 22nd International Conference on Machine Learning (ICML
2005), Bonn, Germany, August 2005; Computational Creativity 2004, at the Seventh European
Conference on Case-Based Reasoning (ECCBR-04), Madrid, Spain, 2004; The 6th International
Conference on Discovery Science, Sapporo, Japan, 2003; The Third International Workshop on
Computational Models of Scientific Reasoning and Applications (III CMSRA), Buenos Aires,
Argentina, 2003. To update knowledge about recent research in the interesting field of AI the
reader is directed to the web pages related to the events above. Of particular interest to the problem of manipulative abduction are the studies on natural language and visual interpretation in
the context of human-robot interaction as a mathematical abductive process, where every potential interpretation has an associated set of relevant manipulative actions that an agent should
perform in every reasoning and epistemic decision step and decision about of reasoning.
[Clark, 2008, p. 202] is rather optimistic about the possibility that in the near future classical artificial intelligence and robotics will be able to include aspects related to embodiment, action, and
situatedness: “The increasingly popular image of functional, computational, and informationprocessing approaches to mind as flesh-eating demons is thus subtly misplaced. For rather than
necessarily ignoring the body, such approaches may instead help target larger organizational
wholes in ways that help reveal where, why, how, and even how much [. . . ] embodiment and
environmental embedding really matter for the construction of mind and experience”.
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2 Non-explanatory and Instrumental Abduction
After all, theories of reasoning are about rules for reasoning and these are rules
telling us to do certain things in certain circumstances. Writing a program allows us
to state such rules precisely.
Some philosophers might insist that, between epistemology (and logic) and cognitive psychology, there is little, if any connection. The basis for such claims is
that epistemology and logic are normative while psychology is descriptive. That is,
psychology is concerned with how scientists do reason, whereas epistemology and
logic with how scientists ought to reason. One of the central dogmas of philosophy
is that you cannot derive an ought from an is.45
Nevertheless, this kind of ought might be called a “procedural ought”. The apparent normativity of epistemology and logic is just a reflection of the fact that epistemology and logic are concerned with rules for how to do something. It would be
considerably unreasonable to design a computational model of scientific discovery
and reasoning without taking into account how scientists actually reason, what scientists know, and what data scientists can acquire. Nevertheless, the general goal is
not the complete simulation of scientists themselves, but rather the achievement of
discoveries about the world, using methods that extend human cognitive capacities.
The goal is to build prosthetic scientists: just as telescopes are designed to extend
the sensory capacity of humans, computational models of scientific discovery and
reasoning are designed to extend our cognitive capacities. This cooperation should
prove very fruitful from an educational perspective too: reciprocally clarifying both
philosophical and AI theories of reasoning will provide new and very interesting
didactic tools.
2.8
Geometrical Construction Is a Kind of Manipulative
Abduction
Let’s quote an interesting passage by Peirce about constructions. Peirce says that
mathematical and geometrical reasoning “[. . . ] consists in constructing a diagram
according to a general precept, in observing certain relations between parts of that
diagram not explicitly required by the precept, showing that these relations will hold
for all such diagrams, and in formulating this conclusion in general terms. All valid
necessary reasoning is in fact thus diagrammatic” [Peirce, 1931-1958, 1.54]. Not
dissimilarly Kant says that in geometrical construction “[. . . ] I must not restrict my
attention to what I am actually thinking in my concept of a triangle (this is nothing
more than the mere definition); I must pass beyond it to properties which are not
contained in this concept, but yet belong to it” [Kant, 1929, A718-B746, p. 580].
We have seen that manipulative abduction is a kind of, usually model-based,
abduction that exploits external models endowed with delegated (and often implicit)
cognitive roles and attributes. 1. The model (diagram) is external and the strategy
that organizes the manipulations is unknown a priori. 2. The result achieved is new
(if we, for instance, refer to the constructions of the first creators of geometry), and
45
Chapter seven of this book analyzes in details this gap between “ideal” or “institutional” models
of reasoning and concrete inferences in “beings-like-us”.
2.8 Geometrical Construction Is a Kind of Manipulative Abduction
117
adds properties not contained before in the concept (the Kantian to “pass beyond”
or “advance beyond” the given concept [Kant, 1929, A154-B194, p. 192]).46
Humans and other animals make a great use of perceptual reasoning and kinesthetic and motor abilities. We can catch a thrown ball, cross a busy street, read
a musical score, go through a passage by imaging if we can contort out bodies to the way required, evaluate shape by touch, recognize that an obscurely
seen face belongs to a friend of ours, etc. Usually the “computations” required
to achieve these tasks are not accessible to a conscious description. Mathematical reasoning uses language explanations, but also non-linguistic notational devices and models. Geometrical constructions represent an example of this kind of
extra-linguistic machinery we know as characterized in a model-based and manipulative – abductive – way. Certainly a considerable part of the complicated
environment of a thinking agent is internal, and consists of the proper software
composed of the knowledge base and of the inferential expertise of that individual.
Nevertheless, I have already pointed out, any cognitive system consists of a “distributed cognition” among people and “external” technical artifacts [Hutchins, 1995;
Zhang, 1997].
In the case of the construction and examination of diagrams in geometry, a sort
of specific “experiments” serve as states and the implied operators are the manipulations and observations that transform one state into another. The mathematical outcome is dependent upon practices and specific sensorimotor activities performed on
a non-symbolic object, which acts as a dedicated external representational medium
supporting the various operators at work. There is a kind of an epistemic negotiation between the sensory framework of the mathematician and the external reality
of the diagram. This process involves an external representation consisting of written symbols and figures that are manipulated “by hand”. The cognitive system is
not merely the mind-brain of the person performing the mathematical task, but the
system consisting of the whole body (cognition is embodied) of the person plus the
external physical representation. For example, in geometrical discovery the whole
activity of cognition is located in the system consisting of a human together with
diagrams.
An external representation can modify the kind of computation that a human
agent uses to reason about a problem: the Roman numeration system eliminates,
by means of the external signs, some of the hardest parts of the addition, whereas
the Arabic system does the same in the case of the difficult computations in multiplication [Zhang, 1997]. All external representations, if not too complex, can be
transformed in internal representations by memorization. But this is not always necessary if the external representations are easily available. Internal representations
can be transformed in external representations by externalization, that can be productive “[. . . ] if the benefit of using external representations can offset the cost associated with the externalization process” (ibid., p. 181). Hence, contrarily to the old
view in cognitive science, not all cognitive processes happen in an internal model
46
Of course in the case we are using diagrams to demonstrate already known theorems (for instance in didactic settings), the strategy of manipulations is already available and the result is
not new. Further details on this issue are illustrated in chapter three.
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2 Non-explanatory and Instrumental Abduction
Fig. 2.7 Galley division, XVI Century, from an unpublished manuscript of a Venetian monk.
The title of the work is Opus Artimetica D. Honorati veneti monachj coenobij S. Lauretij.
of the external environment. The information present in the external world can be
directly picked out without the mediation of memory, deliberation, etc. Moreover,
various different external devices can determine different internal ways of reasoning and cognitively solve the problems, as is well-known. Even a simple arithmetic
task can completely change in presence of an external tool and representation. In
the Figure 2.7 an ancient external tool for division is represented.
Following the approach in cognitive science related to the studies in distributed
cognition, I contend that in the construction of mathematical concepts many external representations are exploited, both in terms of diagrams and of symbols. I
have been interested in my research in diagrams which play an optical role47– microscopes (that look at the infinitesimally small details), telescopes (that look at
infinity), windows (that look at a particular situation), a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting
mathematical concepts, theories, and structures).
Moreover optical diagrams play a fundamental explanatory (and didactic) role in
removing obstacles and obscurities (for example the ambiguities of the concept of
infinitesimal)48 and in enhancing mathematical knowledge of critical situations (for
example the problem of parallel lines, cf. the following sections). They facilitate new
internal representations and new symbolic-propositional achievements. The mirror and unveiling diagrammatic representation of mathematical structures activates
perceptual operations (for example identifying the interplay between conflicting
structures: for example how the parallel lines behave to infinity). These perceptual
operations provide mirror and unveiling diagrammatic representations of mathematical structures.
To summarize we can say mathematics diagrams play various roles in a typical
abductive way; moreover, they are external representations which, in the cases I
47
48
This method of visualization was invented by [Stroyan, 2005] and improved by [Tall, 2001].
Chapter one, this book, section 1.7.
2.9 Mirror Diagrams: Externalizing Mental Models to Represent Imaginary Entities
119
will present in the following sections, are devoted to provide explanatory and nonexplanatory abductive results. Two of them are central:
• they provide an intuitive and mathematical explanation able to help the understanding of concepts difficult to grasp or that appear obscure and/or epistemologically unjustified. I will present in the following section some mirror diagrams
which provided new mental representations of the concept of parallel lines.
• they help abductively create new previously unknown concepts that are nonexplanatory, as illustrated in the case of the discovery of the non-Euclidean
geometry.
2.9
Mirror Diagrams: Externalizing Mental Models to
Represent Imaginary Entities
I have already said that empirical anomalies result from data that cannot currently
be fully explained by a theory. They often derive from predictions that fail, which
implies some element of incorrectness in the theory. In general terms, many theoretical constituents may be involved in accounting for a given domain item (anomaly)
and hence they are potential points for modification. The detection of these points
involves defining which theoretical constituents are employed in the explanation of
the anomaly. Thus, the problem is to investigate all the relationships in the explanatory area.
As illustrated in section 2.4, first and foremost, anomaly resolution involves the
localization of the problem at hand within one or more constituents of the theory, it
is then necessary to produce one or more new hypotheses to account for the anomaly,
and, finally, these hypotheses need to be evaluated so as to establish which one best
satisfies the criteria for theory justification. Hence, anomalies require a change in the
theory. We know that empirical anomalies are not alone in generating impasses. The
so-called conceptual problems represent a particular form of anomaly (cf. above in
this chapter). Resolving conceptual problems may involve satisfactorily answering
questions about the status of theoretical entities: conceptual problems arise from the
nature of the claims in the principles or in the hypotheses of the theory. Usually it
is necessary to identify the conceptual problem that needs a resolution, for example
by delineating how it can concern the adequacy or the ambiguity of a theory, and
yet also its incompleteness or (lack of) evidence.
I have also already illustrated that formal sciences are especially concerned with
conceptual problems. The discovery of non-Euclidean geometries presents an interesting case of visual/spatial abductive reasoning, where both explanatory and
non-explanatory aspects are intertwined. First of all it demonstrates a kind of visual/spatial abduction, as a strategy for anomaly resolution connected to a form of
explanatory and productive visual thinking. Since ancient times the fifth postulate
has been held to be not evident. This “conceptual problem” has generated many
difficulties about the reliability of the theory of parallels, consisting of the theorems that can be only derived with the help of the fifth postulate. The recognition of
this anomaly was crucial to the development of the non-Euclidean revolution. Two
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2 Non-explanatory and Instrumental Abduction
thousand years of attempts to resolve the anomaly have produced many fallacious
demonstrations of the fifth postulate: a typical attempt was that of trying to prove
the fifth postulate from the others. Nevertheless, these attempts have also provided
much theoretical speculation about the unicity of Euclidean geometry and about the
status of its principles.
Here, I am primarily interested in showing how the anomaly is recognizable. A
postulate that is equivalent to the fifth postulate states that for every line l and every
point P that does not lie on l, there exists a unique line m through P that is parallel
to l. If we consider its model-based (diagrammatic) counterpart (cf. Figure 2.8),
the postulate may seem “evident” to the reader, but this is because we have been
conditioned to think in terms of Euclidean geometry. The definition above represents
the most obvious level at which ancient Euclidean geometry was developed as a
formal science – a level composed of symbols and propositions.
Fig. 2.8
Furthermore, when we also consider the other fundamental level, where modelbased aspects (diagrammatic) are at play, we can immediately detect a difference
between this postulate and the other four if we regard the first principles of geometry as abstractions from experience that we can in turn represent by drawing
figures on a blackboard or on a sheet of paper or on our “visual buffer” [Kosslyn
and Koenig, 1992] in the mind. We have consequently a double passage from the
sensorial experience to the abstraction (expressed by symbols and propositions) and
from this abstraction to the experience (sensorial and/or mental).
We immediately discover that the first two postulates are abstractions from
our experiences drawing with a straightedge, the third postulate derives from our
2.9 Mirror Diagrams: Externalizing Mental Models to Represent Imaginary Entities
121
experiences drawing with a compass. The fourth postulate is less evident as an abstraction, nevertheless it derives from our measuring angles with a protractor (where
the sum of supplementary angles is 180◦, so that if supplementary angles are congruent to each other, they must each measure 90◦ ) [Greenberg, 1974, p. 17].
In the case of the fifth postulate we are faced with the following serious problems:
1) we cannot verify empirically whether two lines meet, since we can draw only
segments, not lines. Extending the segments further and further to find if they meet
is not useful, and in fact we cannot continue indefinitely. We are forced to verify
parallels indirectly, by using criteria other than the definition; 2) the same holds
with regard to the representation in the “limited” visual buffer. The “experience”
localizes a problem to solve, an ambiguity, only in the fifth case: in the first four
cases our “experience” verifies without difficulty the abstraction (propositional and
symbolic) itself. In the fifth case the formed images (mental or not) are the images
that are able to explain the “concept” expressed by the definition of the fifth postulate
as problematic (an anomaly): we cannot draw or “imagine” the two lines at infinity,
since we can draw and imagine only segments, not the lines themselves.
The selected visual/spatial image or imagery derived from the propositional and
symbolic level of the definition is nothing more than the explanation of the anomaly
of the definition itself. As stated above, the image demonstrates a kind of visual
abduction, as a strategy for anomaly localization related to a form of explanatory
visual/spatial thinking.
Once the anomaly is detected, the way to anomaly resolution is opened up – in
our case, this means that it becomes possible to discover non-Euclidean geometries.
That Euclid himself did not fully trust the fifth postulate is revealed by the fact that
he postponed using it in a proof for as long as possible – until the twenty-ninth
proposition. As is well-known, Proclus tried to solve the anomaly by proving the
fifth postulate from the other four. If we were able to prove the postulate in this way,
it would become a theorem in a geometry which does not require that postulate (the
future “absolute geometry”) and which would contain all of Euclid’s geometry.
Without showing all the passages of Proclus’s argument [Greenberg, 1974, p.
119-121] we need only remember that the argument seemed correct because it was
proved using a diagram. Yet we are not allowed to use that diagram to justify a
step in a proof. Each step must be proved from stated axioms or previously proven
theorems. We may visualize parallel lines as railroad tracks, everywhere equidistant
from each other, and the ties of the tracks as being perpendicular to both parallels.
Yet this imagery is valid only in Euclidean geometry. In the absence of the parallel
postulate we can only consider two lines as “parallel” when, by the definition of
“parallel”, they do not possess any points in common. It is not possible implicitly
to assume that they are equidistant; nor can it be assumed that they have a common
perpendicular. This is an example in which a selected abduced image is capable
of compelling you to make a mistake, and in this way it was used as a means of
evaluation in a proof: we have already stated that in this case it is not possible to use
that image or imagery to justify a step in a proof because it is not possible to use
that image or imagery that attributes to experience more than the experience itself
can deliver.
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2 Non-explanatory and Instrumental Abduction
For over two thousand years some of the greatest mathematicians tried to prove
Euclid’s fifth postulate. For example, Saccheri’s strategy for anomaly resolution in
the XVIII century was to abduce two opposite hypotheses.49 of the principle, that
is, to negate the fifth postulate and derive, using new logical tools coming from
non-geometrical sources of knowledge, all theorems from the two alternative hypotheses by trying to detect a contradiction. The aim was indeed that of demonstrating/explaining that the anomaly is simply apparent. We are faced with a kind
of explanatory abduction. New axioms are hypothesized and adopted in looking for
outcomes which can possibly help in explaining how the fifth postulate is unique and
so not anomalous. At a first sight this case is similar to the case of non-explanatory
abduction pointed out at p. 72, speaking of reverse mathematics, but the similarity
is only structural (i.e. guessing “new axioms”): in the case of reverse mathematics
axioms are hypothesized to account for already existing mathematical theories and
do not aim at explanatory results.
The contradiction in the elliptic case (“hypothesis of obtuse angle”, to use the
Saccheri’s term designing one of the two future elementary non-Euclidean geometries) was found, but the contradiction in the hyperbolic case (“hypothesis of the
acute angle”) was not so easily discovered: having derived several conclusions that
are now well-known propositions of non-Euclidean geometry, Saccheri was forced
to resort to a metaphysical strategy for anomaly resolution: “Proposition XXXIII.
The ‘hypothesis’ of acute angle [that is, the hyperbolic case] is absolutely false, because repugnant to the nature of the straight line” [Saccheri, 1920]. Saccheri chose
to state this result with the help of the somewhat complicated imagery of infinitely
distant points: two different straight lines cannot both meet another line perpendicularly at one point, if it is true that all right angles are equal (fourth postulate) and
that two different straight lines cannot have a common segment. Saccheri did not ask
himself whether everything that is true of ordinary points is necessarily true of an
infinitely distant point. In Note II to proposition XXI some “physico-geometrical”
experiments to confirm the fifth postulate are also given, invalidated unfortunately
by the same incorrect use of imagery that we have observed in Proclus’s case. In this
way, the anomaly was resolved unsatisfactorily and Euclid was not freed of every
fleck: nevertheless, although he did not recognize it, Saccheri had discovered many
of the propositions of non-Euclidean geometry [Torretti, 1978, p. 48].
In the following sections I will illustrate the example of Lobachevsky’s discovery of non-Euclidean geometry where we can see the abductive role played in a
discovery process by new considerations concerning visual sense impressions and
productive imagery representations.
2.9.1
Internal and External Representations
Lobachevsky was obliged first of all to rebuild the basic Principles and to this end, it
was necessary to consider geometrical principles in a new way, as neither ideal nor a
priori. New interrelations were created between two areas of knowledge: Euclidean
49
On the strategies adopted in anomaly resolution cf. [Darden, 1991, pp. 272–275].
2.9 Mirror Diagrams: Externalizing Mental Models to Represent Imaginary Entities
123
geometry and the philosophical tradition of empiricism/sensualism. In the following
section I will describe in detail the type of abduction that was at play in this case.
Lobachevsky’s target is to perform a geometrical abductive process able to create the
new and very abstract concept of non-Euclidean parallel lines. The whole epistemic
process is mediated by interesting manipulations of external mirror diagrams.
I have already said that for over two thousand years some of the greatest mathematicians tried to prove Euclid’s fifth postulate. Geometers were not content merely
to construct proofs in order to discover new theorems and thereby to try to resolve
the anomaly (represented by its lack of evidence) without trying to reflect upon the
status of the symbols of the principles underlying Euclidean geometry represent.
Lobachevsky’s strategy for resolving the anomaly of the fifth postulate was first
of all to manipulate the symbols, second to rebuild the principles, and then to derive new proofs and provide a new mathematical apparatus; of course his analysis
depended on some of the previous mathematical attempts to demonstrate the fifth
postulate. The failure of the demonstrations – of the fifth postulate from the other
four – that was present to the attention of Lobachevsky, lead him to believe that the
difficulties that had to be overcome were due to causes traceable at the level of the
first principles of geometry.
We simply can assume that many of the internal visualizations of the working geometers of the past were spatial and imaginary because those mathematicians were
precisely operating with diagrams and visualizations. By using internal representations Lobachevsky has to create new external visualizations and to adjust them
tweaking and manipulating [Trafton et al., 2005] the previous ones in some particular ways to generate appropriate spatial transformations (the so-called geometrical
constructions).50 In cognitive science many kinds of spatial transformations have
been studied, like mental rotation and any other actions to improve and facilitate
the understanding and simplification of the problem. It can be said that when a spatial transformation is performed on external visualizations, it is still generating or
exploiting an internal representation.
Spatial transformations on external supports can be used to create and transform
external diagrams and the resulting internal/mental representations may undergo
further mental transformations. Lobachevsky mainly takes advantage of the transformation of external diagrams to create and modify the subsequent internal images.
So mentally manipulating both external diagrams and internal representations is extremely important for the geometer that uses both the drawn geometrical figure and
her own mental representation. An active role of these external representations, as
epistemic mediators able to favor scientific discoveries – widespread during the ancient intuitive geometry based on diagrams – can be curiously seen at the beginning
of modern mathematics, when new abstract, imaginary, and counterintuitive nonEuclidean entities are discovered and developed.
There are in vivo cognitive studies performed on human agents (astronomers and
physicists) about the interconnection between mental representations and the external scientific visualizations. In these studies “pure” spatial transformations, that
50
I maintain that in general spatial transformations are represented by a visual component and a
spatial component [Glasgow and Papadias, 1992].
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2 Non-explanatory and Instrumental Abduction
is transformations that are performed – and based – on the external visualizations
dominate: the perceptual activity seems to be prevalent, and the mental representations are determined by the external ones. The researchers say that there is, in fact,
some evidence for this hypothesis: when a scientist mentally manipulates a representation, 71% of the time the source is a visualization, and only 29% of the time
it is a “pure” mental representation. Other experimental results show that some of
the time scientists seem to create and interpret mental representations that are different from the images in the visual display: in this case it can be hypothesized that
scientists use a comparison process to connect their internal representation with the
external visualizations [Trafton et al., 2005].
In general, during the comparison between internal and external representation
the scientists are looking for discrepancies and anomalies, but also equivalences and
coherent shapes (like in the case of geometers, as we will see below). The comparison between the transformations acted on external representations and their previously represented “internal” counterpart forces the geometer to merge or to compare
the two sides (some aspects of the diagrams correspond to information already represented internally as symbolic-propositional).51
External geometrical diagrams activate perceptual operations, such as searching
for objects that have a common shape and inspecting whether three objects lie on
a straight line. They contain permanent and invariant geometrical information that
can be immediately perceived and kept in memory without the mediation of deliberate inferences or computations, such as whether some configurations are spatially
symmetrical to each other and whether one group of entities has the same number of
entities as another one. Internal operations prompt other cognitive operations, such
as making calculations to get or to envision a result. In turn, internal representations
may have information that can be directly retrieved, such as the relative magnitude
of angles or areas.
2.10
Mirror Diagrams and the Infinite
As previously illustrated the failure of the demonstrations (of the fifth postulate
from the other four) of his predecessors induced Lobachevsky to believe that the
difficulties that had to be overcome were due to causes other than those which had
until then been focused on.
Lobachevsky was obliged first of all to rebuild the basic principles: to this end, it
was necessary to consider geometrical principles in a new way, as neither ideal nor
a priori. New interrelations were created between Euclidean geometry and some
claims deriving from the philosophical tradition of empiricism/sensualism.
51
Usually scientists try to determine identity, when they make a comparison to determine the
individuality of one of the objects; alignment, when they are trying to determine an estimation
of fit of one representation to another (e.g. visually inspecting the fit of a rough mental triangular
shape to an external constructed triangle); and feature comparison, when they compare two
things in terms of their relative features and measures (size, shape, color, etc.) [Trafton et al.,
2005].
2.10 Mirror Diagrams and the Infinite
2.10.1
125
Abducing First Principles through Bodily Contact
From this Lobachevskyan perspective the abductive attainment of the basic concepts
of any science is in terms of senses: the basic concepts are always acquired through
our sense impressions. Lobachevsky builds geometry upon the concepts of body and
bodily contact, the latter being the only “property” common to all bodies that we
ought to call geometrical. The well-known concepts of depthless surface, widthless
line and dimensionless point were constructed considering different possible kinds
of bodily contact and dispensing with, per abstractionem, everything but preserving
the contact itself: these concepts “[. . . ] exist only in our representation; whereas we
actually measure surfaces and lines by means of bodies” for “[. . . ] in nature there
are neither straight lines nor curved lines, neither plane nor curved surfaces; we find
in it only bodies, so that all the rest is created by our imagination and exists just in
the realm of theory” [Lobachevsky, 1897, Introduction]. The only thing that we can
know in nature is movement “[. . . ] without which sense impressions are impossible.
Consequently all other concepts, e.g. geometrical concepts, are generated artificially
by our understanding, which derives them from the properties of movement; this is
why space in itself and by itself does not exist for us” (ibid.).
It is clear that in this inferential process Lobachevsky performs a kind of modelbased abduction, where the perceptual role of sense impressions and their experience with bodies and bodily contact is cardinal in the generation of new concepts.
The geometrical concepts are “[. . . ] generated artificially by our understanding,
which derives them from the properties of movement”. Are these abductive hypotheses explanatory or not? I am inclined to support their basic “explanatory” character:
they furnish an explanation of our sensorial experience with bodies and bodily contact in ideal and abstract terms.
On the basis of these foundations Lobachevsky develops the so-called absolute
geometry, which is independent of the fifth postulate: “Instead of commencing geometry with the plane and the straight line as we do ordinarily, I have preferred to
commence it with the sphere and the circle, whose definitions are not subject to the
reproach of being incomplete, since they contain the generation of the magnitudes
which they define” [Lobachevsky, 1929, p. 361].)
This leads Lobachevsky to abduce a very remarkable and modern hypothesis
– anticipatory of the future Einstein’s theoretical atmosphere of general relativity
– which I consider to be largely image-based: since geometry is not based on a
perception of space, but constructs a concept of space from an experience of bodily
movement produced by physical forces, there could be place in science for two or
more geometries, governing different kinds of natural forces:
To explain this idea, we assume that [. . . ] attractive forces decrease because their effect
is diffused upon a spherical surface. In ordinary Geometry the area of a spherical surface of radius r is equal to 4r2 , so that the force must be inversely proportional to the
square of the distance. In Imaginary Geometry I found that the surface of the sphere is
(er − e−r )2 ,
126
2 Non-explanatory and Instrumental Abduction
and it could be that molecular forces have to follow that geometry [. . . ]. After all,
given this example, merely hypothetical, we will have to confirm it, finding other more
convincing proofs. Nevertheless we cannot have any doubts about this: forces by themselves generate everything: movement, velocity, time, mass, matter, even distances and
angles [Lobachevsky, 1897, p. 9].
Lobachevsky did not doubt that something, not yet observable with a microscope
or analyzable with astronomical techniques, accounted for the reliability of the new
non-Euclidean imaginary geometry. Moreover, the principles of geometry are held
to be testable and it is possible to prepare an experiment to test the validity of the
fifth postulate or of the new non-Euclidean geometry, the so-called imaginary geometry. He found that the defect of the triangle formed by Sirius, Rigel and Star
No. 29 of Eridanus was equal to 3.727 + 10−6 seconds of arcs, a magnitude too
small to be significant as a confirmation of imaginary geometry, given the range of
observational error. Gauss too had claimed that the new geometry might be true on
an astronomical scale. Lobachevsky says:
Until now, it is well-known that, in Geometry, the theory of parallels had been incomplete. The fruitlessness of the attempts made, since Euclid’s time, for the space
of two thousand years, aroused in me the suspicion that the truth, which it was desired to prove, was not contained in the data themselves; that to establish it the aid
of experiment would be needed, for example, of astronomical observations, as in the
case of other laws of nature. When I had finally convinced myself of the justice of my
conjecture and believed that I had completely solved this difficult question I wrote,
in 1826, a memoir on this subject Exposition succincte des principes de la Géométrie
[Lobachevsky, 1897, p. 5].
With the help of the explanatory abductive role played by the new sensualist considerations of the basic principles, by the empiricist view and by a very remarkable
productive visual hypothesis, Lobachevsky had the possibility to proceed in discovering the new theorems. Following Lobachevsky’s discovery the fifth postulate will
no longer be considered in any way anomalous – we do not possess any proofs of
the postulate, because this proof is impossible. Moreover, the new non-Euclidean
hypothesis is reliable: indeed, to understand visual thinking we have also to capture its status of guaranteeing the reliability of a hypothesis. In order to prove the
relative consistency of the new non-Euclidean geometries we should consider some
very interesting visual and mathematical “models” proposed in the second half of
XIX century (i.e. the Beltrami-Klein and Poincaré models), which involve new uses
of visual images in theory assessment.
In summary, the abductive process of Lobachevsky’s discovery can be characterized in the following way, taking advantage of the nomenclature introduced in the
previous and in the present chapter:
1. the inferential process Lobachevsky performs to rebuild the first principles of
geometry is prevalently a kind of manipulative and model-based abduction, endowed with an explanatory character: the new abduced principles furnish an
explanation of our sensorial experience with bodies and bodily contact in ideal
and abstract terms;
2.10 Mirror Diagrams and the Infinite
127
2. at the same time the new principles found offer the chance of further multimodal52 and distributed abductive steps (that is based on both on both visual and
sentential aspects, and on both internal and external representations) which are
mainly non-explanatory and provide unexpected mathematical results. These
further abductive processes:
a. first of all have to provide a different multimodal way of describing parallelism (both from a diagrammatical and propositional perspective, cf.
subsection 2.10.4 and Figure 2.11);
b. second, on the basis of the new concept of parallelism it will be possible to
derive new theorems of a new non-Euclidean geometrical system exempt
from inconsistencies just like the Euclidean system. Of course this process show a moderately instrumental character, more or less present in all
abductions (cf. below section 2.11).
Let us illustrate how Lobachevsky continues to develop the absolute geometry. The
immediate further step is to define the concept of plane, which is defined as the
geometrical locus of the intersections of equal spheres described around two fixed
points as centers, and, immediately after, the concept of straight line (for example
BB in the mirror diagram of the Figure 2.9) as the geometrical locus of the intersections of equal circles, all situated in a single plane and described around two fixed
points of this plane as centers. The straight line is so defined by means of “finite”
parts (segments) of it: we can prolong it by imaging a repeatable movement of rotation around the fixed points (cf. Figure 2.9) [Lobachevsky, 1829-1830, 1835-1838,
§25].
Fig. 2.9
Rectilinear angles (which express arcs of circle) and dihedral angles (which express spherical lunes) are then considered; and the solid angles too, as generic parts
of spherical surfaces – and in particular the interesting spherical triangles. π means
for Lobachevsky the length of a semicircumference, but also the solid angle that
52
Cf. below chapter four, this book.
128
2 Non-explanatory and Instrumental Abduction
Fig. 2.10
corresponds to a semisphere (straight angle). The surface of the spherical triangles
is always less than π , and, if π , coincides with the semisphere. The theorems about
the perpendicular straight lines and planes also belong to absolute geometry.
2.10.2
Expansion of Scope Strategy
We have to note some general cognitive and epistemological aspects which characterize the development of this Lobachevskyan absolute geometry.
Spherical geometry is always treated together with the plane geometry: the definitions about the sphere are derived from the ones concerning the plane when
we substitute the straight lines (geodetics in the plane) with the maximal circles
(geodetics in the spherical surface). Lobachevsky says that the maximal circle on
the sphere with respect to the other circles presents “properties” that are “similar”
to the ones belonging to the straight line with respect to all the segments in the plane
[Lobachevsky, 1829-1830, 1835-1838, §66]. This is an enhancement, by means of a
kind of analogical reasoning, reinforced by the external mirror diagrams, of the internal representation of the concept of straight line. The straight line can be in some
sense thought (because it is “seen” and “imagined” in the various configurations
provided by the external diagrams) as “belonging” to various types of surfaces, and
not only to the plane. Consequently, mirror diagrams not only manage consistency
requirements, they can also act in an additive way, providing new “perspectives”
and information on old entities and structures. The directly perceivable information
strongly guides the discoverer’s selections of moves by servicing the discovery strategy expansion-of-the-scope (of the concept of straight line). This possibility was not
indeed available at the simple level of the internal representation. The Figure 2.10
[Lobachevsky, 1829-1830, 1835-1838, §79] is another example of the exploitation
of the analogy plane/spherical surface by means of a diagram that exploits the perspective of the two-dimensional flat plane.
2.10 Mirror Diagrams and the Infinite
2.10.3
129
Infinite/Finite Interplay
In all the previous cases the external representations are constructions that have to
respect the empirical attitude described above: because of the fact that the geometrical bodies are characterized by their “finiteness” the external representation is just
a coherent mirror of finite internal images. The “infinite” can be perceived in the
“finite” constructions because the infinite is considered only as something potential
that can be just mentally and artificially thought: “defined artificially by our understanding”. As the modern axiomatic method is absent, the geometer has to conceptualize infinite situations exploiting the finite resources offered by diagrams. In front
of the question: “How is it that the finite human resources of internal representations
of human mind can conceptualize and formalize abstract notions of infinity?” – notions such as the specific ones embedded in the non-Euclidean assumptions – the
geometer is aware we perceive a finite world, act upon it, and think about it. Moreover, the geometer operates in “[. . . ] a combination of perceptual input, physical
output, and internal mental processes. All three are finite. But by thinking about the
possibility of performing a process again and again, we can easily reach out towards
the potential infinite” [Tall, 2001]. Lobachevsky states: “Which part of the lines
we would have to disregard is arbitrary”, and adds, “our senses are deficient” and
it is only by means of the “artifice” consisting of the continuum “enhancement of
the instruments” that we can overcome these limitations [Lobachevsky, 1829-1830,
1835-1838, §38]. Given this epistemological situation, it is easy to conclude saying that instruments are not just and only telescopes and laboratory tools, but also
diagrams.
Let us continue to illustrate the geometer’s inventions. In the Proposition 27 (a
theorem already proved by Euler and Legendre) of the Geometrical Researches
of the Theory of Parallels, published in 1840, [Lobachevsky, 1891], Lobachevsky
states that if A, B, and C are the angles of a spherical triangle, the ratio of the area of
the triangle to the area of the sphere to which it belongs will be equal to the ratio of
1
(A + B + C − π )
2
to four right angles; that the sum of the three right angles of a rectilinear triangle
can never surpass two right angles (Prop. 19), and that, if the sum is equal to two
right angles in any triangle, it will be so in all (Prop. 20).
2.10.4
Non-euclidean Parallelism: Coordination and
Inconsistency Detection
The basic unit is the manipulation of diagrams. Before the birth of the modern axiomatic method the geometers still and strongly have to exploit external diagrams,
to enhance their thoughts. It is impossible to mental imaging and evaluating the alternative sequences of symbolic calculations being only helped by the analytic tools,
such as various written equations and symbols and marks: it is impossible to do a
complete anticipation of the possible outcomes, due to the limited power of working
130
2 Non-explanatory and Instrumental Abduction
memory and attention. Hence, because of the complexity of the geometrical problem space and the limited power of working memory, complete mental search is
impossible or difficult. Geometers may use perceptual external biases to make decisions. Moreover, in those cognitive settings, lacking in modern axiomatic theoretical
awareness, certainly perceptual operations were epistemic mediators which need
less attentional and working memory resources than internal operations. “The directly perceived information from external representations and the directly retrieved
information from internal representation may elicit perceptual and cognitive biases,
respectively, on the selections of actions. If the biases are inconsistent with the task,
however, they can also misguide actions away from the goal. Learning effect can
occur if a task is performed more than once. Thus, the decision on actions can also
be affected by learned knowledge” [Zhang, 1997, p. 186].
The new external diagram proposed by Lobachevsky (the diagram of the drawn
parallel lines of Figure 2.11) [Lobachevsky, 1891] is a kind of analogous both
of the mental image we depict in the mental visual buffer and of the symbolicpropositional level of the postulate definition. It no longer plays the explanatory
role of showing an anomaly, like it was in the case of the diagram of Figure 2.8 (and
of other similar diagrams) during the previous centuries. I have already said I call
this kind of external tool in the geometrical reasoning mirror diagram. In general
this diagram mirrors the internal imagery and provides the possibility of detecting
anomalies, like it was in the case of the similar diagram of Figure 2.8. The external
representation of geometrical structures often activates direct perceptual operations
(for example, identify the parallels and search for the limits) to elicit consistency or
inconsistency routines. Sometimes the mirror diagram biases are inconsistent with
the task and so they can make the task more difficult by misguiding actions away
from the goal. If consistent, we have already said that they can make the task easier
by instrumentally and non-explanatorily guiding actions toward the goal. In certain
cases the mirror diagrams biases are irrelevant, they should have no effects on the
decision of abductive actions, and play lower cognitive roles.
In the case of the diagram of the parallel lines of the similar Figure 2.8 it was
used in the history of geometry to make both consistent and in-consistent the fifth
Euclidean postulate and the new non-Euclidean perspective (more details on this
epistemological situation are given in [Magnani, 2001c]).
I said that in some cases the mirror diagram plays a negative role and inhibits
further creative abductive theoretical developments. As I have already indicated (p.
121), Proclus tried to solve the anomaly by proving the fifth postulate from the other
four. If we were able to prove the postulate in this way, it would become a theorem in
a geometry which does not require that postulate (the future “absolute geometry”)
and which would contain all of Euclid’s geometry. We need only remember that
the argument seemed correct because it was proved using a diagram. In this case the
mirror diagram biases were consistent with the task of justifying Euclidean geometry
and they made this task easier by guiding actions toward the goal, but they inhibited
the discovery of non-Euclidean geometries [Greenberg, 1974, pp. 119–121]; cf. also
[Magnani, 2001c, pp. 166–167].
2.10 Mirror Diagrams and the Infinite
131
Fig. 2.11 Non-Euclidean parallel lines
In sum, contrarily to the diagram of Figure 2.8, the diagram of Figure 2.11 does
not aim at explaining anything given, it is fruit of a non-explanatory and instrumental abduction, as I have anticipated at p. 127: the new related principle/concept of
parallelism offers the chance of further multimodal and distributed abductive steps
(based on both visual and sentential aspects, and on both internal and external representations) which are mainly non-explanatory. On the basis of the new concept
of parallelism it will be possible to derive new theorems of a new non-Euclidean
geometrical system exempt from inconsistencies just like the Euclidean system (cf.
below section 2.11).
The diagram now favors the new definition of parallelism [Lobachevsky, 1891,
Prop. 16], which introduces the non-Euclidean atmosphere: “All straight lines which
in a plane go out from a point can, with reference to a given straight line in the same
plane, be divided in two classes – into cutting and not-cutting. The boundary lines
of the one and the other class of those lines will be called parallel to the given lines”
(p. 13).
The external representation is easily constructed like in Figure 2.11 of
[Lobachevsky, 1891, p. 13], where the angle HAD between the parallel HA and
the perpendicular AD is called the angle of parallelism, designated by Π (p) for
AD = p. If Π (p) is < 12 π , then upon the other side of AD, making the same angle
DAK = Π (p) will lie also a line AK, parallel to the prolongation DB of the line
DC, so that under this assumption we must also make a distinction of sides in parallelisms. Because of the fact that the diagrams can contemplate only finite parts of
straight lines it is easy to represent this new postulate in this mirror image: we cannot know what happens at the infinite neither in the internal representation (because
of the limitations of visual buffer), nor in the external representation: “[. . . ] in the
uncertainty whether the perpendicular AE is the only line which does not meet DC,
132
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
we will assume it may be possible that there are still other lines, for example AG,
which do not cut DC, how far so ever they may be prolonged” (ibid.). So the mirror
image in this case is seen as consistently supporting the new non-Euclidean perspective. The idea of constructing an external diagram of a non-Euclidean situation
is considered normal and reasonable. The diagram of Figure 2.11 is now exploited
to unveil new fruitful consequences.
A first analysis of the exploitation of what I call unveiling diagrams in the discovery of the notion of non-Euclidean parallelism is presented in the following section
related to the exploitation of diagrams at the stereometric level.53 Taking advantage
of the Lobachevskyan case I have illustrated that in mirror diagrams the coordination between perception and cognition is central, from both static and dynamic
(constructions) points of view; in the case of the abduced unveiling diagrams allocating and switching attention between internal and external representation govern
the reasoning strategy, by integrating internal and external representation in a more
dynamical and complicated way – essentially non-explanatory – as we will see in
the following section.
2.11
2.11.1
Unveiling Diagrams in Lobachevsky’s Discovery as
Gateways to Imaginary Entities
Euclidean/Non-euclidean Model Matching Strategy
Lobachevsky’s target is to perform a geometrical abductive process able to create
new and very abstract entities: the whole epistemic process is mediated by interesting manipulations of external unveiling diagrams. The first step toward the exploitation of what I call unveiling diagrams is the use of the notion of non-Euclidean
parallelism at the stereometric level, by establishing relationships between straight
lines and planes and between planes: Proposition 27 (already proved by Lexell and
Euler): “A three-sided solid angle equals the half sum of surface angles less a rightangle” (p. 24, Figure 2.12). Proposition 28 (directly derived from Prop. 27): “If
three planes cut each other in parallel lines, then the sum of the three surface angles
equals two rights” (p. 28), Figure 2.13. These achievements are absolutely important: it is established that for a certain geometrical configuration of the new geometry
(the three planes cut each other in parallel lines that are parallel in Lobachevskyan
sense) some properties of the ordinary geometry hold.
The important notions of oricycle and orisphere are now defined to search for
a possible symbolic counterpart able to express a foreseen consistency (as a justification) of the non-Euclidean theory. This consistency is looked at from the point
a view of a possible “analytic” solution, that is in terms of verbal-symbolic (not
diagrammatic) results (equations).
53
[Magnani and Dossena, 2005; Dossena and Magnani, 2007] illustrate that external representations like the ones I call unveiling diagrams can enhance the consistency of a cognitive process
but also provide more radically creative suggestions for new useful information and discoveries.
2.11 Unveiling Diagrams in Lobachevsky’s Discovery
133
Fig. 2.12
Fig. 2.13
Fig. 2.14
Such is the case of the Proposition 31. “We call boundary line (oricycle) that curve
lying in a plane for which all perpendiculars erected at the mid-ponts of chords are
parallel to each other. [. . . ] The perpendicular DE erected upon the chord AC at its
mid-point D will be parallel to the line AB, which we call the Axis of the boundary
line” (pp. 30-31), cf. Figure 2.14. Proposition 34. “Boundary surface54 we call that
surface which arises from the revolution of the boundary line about one of its axes,
which, together with all other axes of the boundary-line, will be also an axis of the
54
Also called limit sphere or orisphere.
134
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
Fig. 2.15
boundary surface” (p. 33). Moreover, the intersections of the orisphere by its diametral planes are limit circles. The limit circle arcs are called the sides, and the dihedral
angles between the planes of these arcs the angles of the “orisphere triangle”.
A part of the surface of the orisphere bounded by three limit circle arcs will be
called an orisphere triangle. From Prop. 28 follows that the sum of the angles of an
orisphere triangle is always equal to two right angles: “everything that is demonstrated
in the ordinary geometry of the proportionality of the sides or rectilinear triangles can
therefore be demonstrated in the same manner in the pangeometry”55 [Lobachevsky,
1929, p. 364] of the orisphere triangles if only we will replace the lines parallel to
the sides of the rectilinear triangle by orisphere arcs drawn through the points of one
of the sides of the orisphere triangle and all making the same angle with this side. To
conclude, the orisphere is a “partial” model of the Euclidean plane geometry.
The last constructions of the Lobachevskyan abductive process give rise to two
fundamental unveiling diagrams (cf. Figures 2.15 and 2.17) that accompany the
remaining proofs. They are more abstract and exploit “audacious” representations
in the perspective of three dimensional geometrical shapes.
The construction given in Figure 2.15 aims at diagrammatically “representing” a
stereometric non-Euclidean form built on a rectilinear right angled triangle ABC
to which the Theorem 28 above can be applied (indeed the parallels AA , BB ,
CC , which lie on the three planes are parallels in non-Euclidean sense), so that
Lobachevsky is able to further apply symbolic identifications; the planes make with
each other the angles Π (a) at AA , a right angle at CC , and, consequently Π (a ) at
BB .56 The diagram is enhanced by constructing a spherical triangle mnk, in which
55
56
Lobachevsky called the new theory “imaginary geometry” but also “pangeometry”.
Given that Lobachevsky designates the size of a line by a letter with an accent added, e.g.
x , in order to indicate this has a relation to that of another line, which is represented by the
same letter without the accent x, “which relation is given by the equation Π (x) + Π (x ) =π ”
(Prop. 35).
2.11 Unveiling Diagrams in Lobachevsky’s Discovery
135
Fig. 2.16
the sides are mn = Π (c), kn = Π (β ), mk = Π (a) and the opposite angles are Π (a),
Π (α ), 12 π realizing that with the “existence” of a rectilinear triangle with the sides
a, b, c (like in the case of the previous one) “we must admit” the existence of a
related spherical triangle (cf. Figure 2.16), etc. Not only, a boundary surface (orisphere) can be constructed, that passes through the point A with AA as axis, and
those intersections with the planes the parallels form a boundary triangle (that is
a triangle situated upon the given orisphere), whose sides are BC = p, C A = q,
B A = r, and the angles opposite to them Π (α ), Π (α ), 12 π and where consequently
(this follows from the Theorem 34):
p = r sin Π (a), q = r cos Π (a).
As I will illustrate in the following subsections in this way Lobachevsky is able to
further apply symbolic identifications and to arrive to new equations which consistently (and at the same time) connect Euclidean and non-Euclidean perspectives.
This kind of diagram strongly guides the geometer’s selections of moves by eliciting
what I call the Euclidean-inside non-Euclidean “model matching strategy”.
Inside the perspective representations (given by the fundamental unveiling
diagram of a non-Euclidean structure, cf. Figure 2.15), a Euclidean spherical triangle and the orisphere (and its boundary triangle where the Euclidean properties hold) are constructed. The directly perceivable information strongly guides
the geometer’s selections of moves by eliciting the Euclidean-inside non-Euclidean
“model matching strategy” I have quoted above. This maneuver also constitutes
an important step in the affirmation of the modern “scientific” concept of model.
We have to note that other perceptions activated by the diagram are of course
disregarded as irrelevant to the task, as it usually happens when exploiting external diagrammatic representations in reasoning processes. Because not everything in external representations is always relevant to a task, high level cognitive
mechanisms need to use task knowledge (usually supplied by task instructions)
to direct attention and perceptual processes to the relevant features of external
representations.
The different selected representational system – that still uses Euclidean icons –
determines in this case quite different possibilities of constructions, and thus different results from iconic experimenting. New results are derived in diagrammatic
reasoning through modifying the representational systems, adding new meaning to
them, or in reconstructing their systematic order.
136
2.11.2
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
Consistency-Searching Strategy
This external representation in terms of the unveiling diagram illustrated in
Figure 2.15 activates a perceptual reorientation in the construction (that is identifies possible further constructions); in the meantime the consequent new generated
internal representation of the external elements activates directly retrievable information (numerical values) that elicits the strategy of building further non-Euclidean
structures together with their analytic counterpart (cf. below the non-Euclidean
trigonometry equations). Moreover, the internal representation of the stereometric
figures activates cognitive operations related to the consistency-searching strategy.
In this process, new “imaginary” and strange mathematical entities, like the oricycle and the orisphere, are – non-explanatorily – abduced and unveiled, and related
to ordinary and unsuspected perceptive entities.
Finally, it is easy to identify in the proof the differences between perceptual and
other cognitive operations and the differences between sequential – the various steps
of the constructed unveiling diagram – and parallel perceptual operations. Similarly,
it is easy to distinguish between the forms that are directly perceptually inspected
and the elements that are mentally computed or computed in external symbolic
configurations.
To arrive to the second unveiling diagram the old diagram (cf. Figure 2.15) is
further enhanced by a new construction, by breaking the connection of the three
principal planes along the line BB , and by turning them out from each other so
that they, together with all the lines lying in them, come to lie in one plane, where
consequently the arcs p, q, r will unite to a single arc of a boundary-line (oricycle), which goes through the point A and has AA as its axis, in such a manner that
(Figure 2.17) on the one side will lie, the arcs q and p, the side b of the triangle,
which is perpendicular to AA at A, the axis CC going from the end of b parallel
to AA and through C the union point of p and q, the side a perpendicular to CC
at the point C, and from the end-point of a the axis BB parallel to AA which goes
Fig. 2.17
2.11 Unveiling Diagrams in Lobachevsky’s Discovery
137
through the end-point B of the arc p, etc. Finally, taking CC as axis, a new boundary line (an arc of oricycle) from the point C to its intersection with the axis BB is
constructed. What happens?
2.11.3
Loosing Intuition
In this case we see that the external representation completely looses its spatial intuitive interest and/or its capacity to simulate internal spatial representations: it is not
useful to represent it as an internal spatial model in order to enhance the problem
solving activity. The diagram of Figure 2.17 does not have to depict internal forms
coherent from the intuitive spatial point of view, it is just devoted to suitably “unveil” the possibility of further calculations by directly activating perceptual information that, in conjunction with the non-spatial information and cognitive operations
provided by internal representations in memory, determine the subsequent problem
solving behavior. This diagram does not have to prompt an internal “spatially” intuitively coherent model. Indeed perception often plays an autonomous and central
role, it is not a peripheral device. In this case the end product of perception and
motor operations coincides with the intermediate data highly analyzed, processed,
and transformed, that is prepared for high-level cognitive mechanisms in terms of
further analytic achievements (the equations).57
We have to note that of course it cannot be said that the external representation
would work independently without the support of anything internal or mental. The
mirror and unveiling diagrams have to be processed by perceptual mechanisms that
are of course internal. And in this sense the end product of the perceptual mechanisms is also internal. But it is not an internal model of the external representation
of the task: the internal representation is the knowledge and structure of the task
in memory; and the external representation is the knowledge and structure of the
task in the environment. The end product of perception is merely the situational information in working memory that usually only reflects a fraction (crucial) of the
external representation [Zhang, 1997]. At this point it is clear that the perceptual
operations generated by the external representations “mediated” by the unveiling
diagrams are central as mechanisms of the whole geometrical abductive and manipulative process; they are not less fundamental than the cognitive operations activated
by internal representations, in terms of images and/or symbolic-propositional. They
constitute an extraordinary example of complex and perfect coordination between
perceptual, motor, and other inner cognitive operations.
Let us conclude the survey on Lobachevsky’s route to an acceptable assessment
of its non-Euclidean theory. By means of further symbolic/propositional designations taken from both internal representations followed from previous results and
“externalized” calculations, the reasoning path is constrained to find a general “analytic” counterpart for (some aspects of) the non-Euclidean geometry (we skip the
exposition of this complicated passage – cf. [Lobachevsky, 1891]). Therefore we
obtain the equations.
57
In other problems solving cases, the end product of perception – directly picked-up – is the end
product of the whole problem solving process.
138
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
sin Π (c) = sin Π (a) sin Π (b)
sin Π (β ) = cos Π (α ) sin Π (a)
Hence we obtain, by mutation of the letters,
sin Π (α ) = cos Π (β ) sin Π (b)
cos Π (b) = cos Π (c) cos Π (α )
cos Π (a) = cos Π (c) cos Π (β )
that express the mutual dependence of the sides and the angles of a non-Euclidean
triangle. In these equations of plane non-Euclidean geometry we can pass over the
equations for spherical triangles. If we designate in the right-angled spherical triangle
(Figure 2.16) the sides Π (c), Π (β ), Π (a), with the opposite angles Π (b), Π (α ), by
the letters a, b, c, A, B, then the obtained equations take of the form of those which
we know as the equations of spherical trigonometry for the right-angled triangle
sin(a) = sin(c) sin(A)
sin(b) = sin(c) sin(B)
cos(A) = cos(A) sin(B)
cos(B) = cos(B) sin(A)
cos(c) = cos(a) cos(b).
The equations are considered to “[. . . ] attain for themselves a sufficient foundation for considering the assumption of imaginary geometry as possible” (p. 44).
The new geometry is considered exempt from possible inconsistencies together with
the acknowledgment of the reassuring fact that it presents a very complex system
full of surprisingly harmonious conclusions. A new contradiction which could have
emerged and which would have forced to reject the principles of the new geometry
would have been already contained in the equations above. Of course this is not true
from the point of view of modern deductive axiomatic systems and a satisfactory
model of non-Euclidean geometry has not yet been built (as Beltrami and Klein
will do with the so-called “Euclidean models of non-Euclidean geometry”).58 As
for now the argument rests on a formal agreement between two sets of equations,
one of which is derived from the new non-Euclidean geometry. Moreover, the other
set of equations does not pertain to Euclidean geometry; rather they are the equations
of spherical trigonometry that does not depend on the fifth postulate (as maintained
by Lobachevsky himself). Nevertheless, we can conclude that Lobachevsky is not
far from the modern idea of model.
We can say that geometrical diagrammatic thinking represented the capacity to
extend finite perceptual experiences to give known (Euclidean) and infinite unknown
(non-Euclidean) mathematical structures that appear consistent in themselves and
that have quite different properties each other.
58
On the limitations of the Lobachevskyan perspective cf. [Torretti, 1978] and [Rosenfeld, 1988].
2.12 Mechanizing Manipulative Abduction
139
Many commentators (and myself in [Magnani, 2001c]) contend that Kant did
not imagine that non-Euclidean concepts could in some way be constructed in intuition59(a Kantian expression which indicated our iconic external representation),
through the mediation of a model, that is preparing and constructing a Euclidean
model of a specific non-Euclidean concept (or group of concepts). Yet Kant also
wrote that “[. . . ] the use of geometry in natural philosophy would be insecure, unless the notion of space is originally given by the nature of the mind (so that if
anyone tries to frame in his mind any relations different from those prescribed by
space, he will labor in vain, for he will be compelled to use that very notion in
support of his figment)” [Kant, 1968, Section 15E].
[Torretti, 2003, p. 160] observes:
I find it impossible to make sense of the passage in parentheses unless it refers precisely to the activity of constructing Euclidean models of non-Euclidean geometries
(in a broad sense). We now know that one such model (which we ought rather to call
quasi-Euclidean,
√ for it would represent plane Lobachevskian geometry on a sphere
with radius −1) is mentioned in the Theorie der Parallellinien that Kant’s fellow
Königsbergian Johann Heinrich Lambert [Lambert, 1786] wrote about 1766. There is
no evidence that Kant ever saw this tract and the few extant pieces of his correspondence with Lambert do not contain any reference to the subject, but, in the light of
the passage I have quoted, it is not unlikely that Kant did hear about it, either from
Lambert himself, or from a shared acquaintance, and raised the said objection.
I agree with Torretti, Kant had a very wide perspective about the resources of
“intuition”, anticipating that a geometer would have been “compelled” to use the
notion of space “given by nature”, that is the one that is at the origins of our external representation, “in support of his figment”, for instance the non-Euclidean
Lobachevskyan abstract structures we have treated above in Figure 2.15, which
exhibits the non-Euclidean through the Euclidean.
2.12
2.12.1
Mechanizing Manipulative Abduction
Automatic Geometrical Constructions as
Extra-Theoretical Epistemic Mediators
A very interesting artificial intelligence computer program has been built,
ARCHIMEDES [Lindsay, 1994; Lindsay, 1998], that represents geometrical diagrams (points, line segments, polygons, and circles) both as pixels arrays and as
propositional statements.60 For example a triangle will be represented from a propositional description as a set of marked pixels in an array, together with a set of data
naming the given triangle and storing facts about it (for instance that it is right) and
constraints upon it (perhaps that it remains right throughout this use of the diagram).
59
60
We have seen how Lobachevsky did this by using the Figure 2.15.
This approach in computer science, involving the use of diagram manipulations as forms of
acceptable methods of reasoning, was opened by Gelernter’s Geometry Machine [Gelertner,
1959], but the diagrams played a very secondary role.
140
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
Hence, a computational equivalent of a physical diagram is represented, plus some
human propositional knowledge about it.
The program is able to manipulate and modify its own representations of diagrams,
that is it is able to make geometrical constructions (called “simulation constructions”):
adding parts or elements, moving components about, translating and rotating by preserving metric properties, of course subordinated to the given specific constraints and
to the whole structure of the two-dimensional space. Some knowledge of algebra is
added, and of the taxonomic hierarchy of geometric figures (all square are rectangles,
etc.); moreover, additional knowledge is also included, like side-angle-side congruency theorem and the sum of the interior angles of a triangle, knowledge of problem solving strategies and heuristics, knowledge of logic (for example: a universal
statement can be disproved by a single counterexample) [Lindsay, 2000a].
When the program manipulates the specific diagram, it records the new information that comes out, then it can for example detect sets of area equivalences, and so
on: for example, it is able to verify that a demonstration of the Pythagorean Theorem is correct, mirroring its truth in terms of constructions and manipulations. To
account for the universality of geometrical theorems and propositions many different methods for learning and “generalizing” the specific instance of the constructed
diagram are exploited [Lindsay, 1998, pp. 260-264].
These methods come from a kind of predicative knowledge “exogenous” of
course to the mere diagrammatic representation: generalization is not a possible
product of the pure diagrammatic understanding. For instance, one suggestion is
to break the problem into cases, to individuate a “representative” instance for each
case, and to demonstrate that this conclusion holds for each of these instances.61
Another one is to exploit the simulative aspects of constructions by “running experiments” that show how some parts of a diagram co-vary with changes in others: the
observation of the interaction of the diagrams parts as one property is varied allows
us to grasp and understand the “universal” value of some geometric relations and
results (for example congruency theorem, asymptotic behaviors, periodic relations,
and some symmetric relations). It is interesting to note that one of the construction
manipulations proposed by the program to verify the Pythagorean Theorem intends
to show that it is not true of (some examples of) non-right triangles.
An extension of the program (described in [Lindsay, 2000b]), aims at
autonomously building constructions that can demonstrate a given proposition,62
It accomplishes the further complex task of discovering conjectures that can lead to
the constructions of demonstrations, illustrating the possible role of diagrammatic
reasoning in creativity.63
61
62
63
A method already suggested by Johnson-Laird to deal with generalization using the so-called
“mental models” [Johnson-Laird, 1983].
The program is able to “discover demonstrations”, that is to find sequences of manipulations
that achieve a particular end, rather than simply verify them.
On the role of abduction in automated scientific discovery and machinery for generating hypotheses cf. the recent [Ray, 2007]. On the historical systems cf. the section “Automatic abductive scientists” above (section 2.7).
2.12 Mechanizing Manipulative Abduction
2.12.2
141
Automatic “Thinking through Doing”
Geometric constructions are certainly epistemic mediators that exploit the semantics of two dimensional diagrams (rather than the syntax of formal propositions)
to perform various manipulative abductive tasks (discover a new property or new
proposition/hypothesis, selecting suitable sequences of constructions as able to
convincingly verifying theorems, etc).
Hence, geometrical construction, one of the most ancient exploitations of twodimensional diagrams for both practical and mathematical problem solving, is
“embodied” in a computational program, that is, finally, in a machine. From the
epistemological point of view it is important to note that the program shows how it
is possible to delineate the rules and the procedures that underlie the diagrams as
models of propositions about space, that is able to capture the structure of space.
The kind of reasoning described is very rich and takes advantage of almost all the
resources of two-dimensional space (going beyond the simple use of topological
properties like in the case of Euler/Venn diagrams). Moreover, the physical diagram
necessarily (that is for the objective reasons of its materiality) preserves topological and geometric properties of two-dimensional space.64 . The following passage is
very clear:
Geometric diagrams [. . . ] are intended to reflect all structural properties of two dimensional space, although this requires that the observer ignore line width and so forth
and deal with the intended idealization. Since they are recorded in space (on a piece of
paper for example) the mapping is iconic. The intuitive structure of two- dimensional
space is partially captured by Euclid’s definitions, postulates and axioms. Although
it is now known that this is not the veridical description of actual space, for objects
of human scale it is adequate both for reasoning and for successful intercourse with
the environment, just as Newtonian mechanics is adequate for modeling physical processes that occur at a human scale though it is inaccurate at very large and very small
scale [. . . ] [Lindsay, 2000a].
We know that the structure of intuitive space is also embraced by analytic geometry.
Lindsay observes that, in general, it could be better to use an analytic representation
because conventional digital computers are “a natural match for numerical representation”. If we consider the various ways of representing geometrical diagrams
and their behavior – the analytic representation is an example – it is important to
point out their real cognitive nature. I think we have to agree with the following
position: “This does not mean, however, that diagrams represented numerically are
not really diagrams. What makes them diagrams is not bits or voltages or axioms or
CCD signals. What makes them diagrams is that they capture the structure of space.
This is another way of saying that they enforce constraints on the behavior of the
representations that reflect restrictions on the behavior of objects in space” (ibid.).
The computational embodiment generates a kind of “squared” epistemic mediator: geometrical constructions, as epistemic mediators, are further mediated. A mental performance not simply reproduced, like in more traditional AI systems, but just
64
This is not the case of the two-dimensional depictions of a three dimensional object (like in the
clear cases illustrated by Escher’s drawings) [Lindsay, 1998, p. 266].
142
2.11
Unveiling Diagrams in Lobachevsky’s Discovery
a way of “thinking through doing”, as illustrated by manipulative abduction. Humans can think using geometrical constructions also without “doing”, for instance
in the case of “thinking through drawing” at the level of imagination. Kant (and
Proclus) were perfectly clear when they referred to the role of imagination as the
condition of possibility of the empirical drawing itself [Magnani, 2001c].
It has been established that imagination is able to perform some tasks at intermediate levels of complexity. Humans, when working from an external physical
display, are aided by actual pencil shading or tracing. When working from mental images humans have greater difficulty keeping track of what has been inspected.
Moreover, in the case of imaginary geometrical representations (or in data structures
in a computer) we can use whatever rules we want (for instance the rules that reflect
the motion of rigid bodies but also the ones that violate them and do not happen –
or are not yet seen to happen – in the physical world). This of course does not mean
that the mind can imagine anything whatsoever, or everything with equal facility:
“[. . . ] human mind is indeed predisposed to handle certain types of imagery and
simulations better than others, presumably those kinds for which evolution has best
prepared us, especially the motion of rigid objects” [Lindsay, 1998, p. 267].
In the past some researchers emphasized the role of visualizations in geometrical
reasoning. For example in 1847 Byrne prepared an amazing and attractive edition
of the first six books (which range from the most elementary plane geometry to
the theory of proportions) of the Elements of Euclid “in which coloured diagrams
and symbols are used instead of letters for the greater ease of learners”.65 The aim
was to try to use as little text – and in particular, labels – as possible. Byrne considered the use of colors in geometrical constructions a suitable tool to this aim.
Interesting exploitations of the visual devices of the Internet are some Java applications/manipulations where it is possible to “construct by clicking”.66
Summary
In this chapter we have seen that, to better understand how abductive cognition
works, non-explanatory and instrumental aspects clearly have to be taken into account. I have stressed that Gabbay and Woods’ GW-model is very useful to this
end: it stimulates the analysis of many “working” abductive processes that have
non-explanatory and pragmatic/instrumental importance. From this perspective the
65
66
[Byrne, 1847]. See the web site http://sunsite.ubc. ca/DigitalMathArchive/ Euclid/byrne.html.
The home page provides links to other web sites where it is possible to find Java editions of Euclid and other “visual” information. The web site devoted to illustrating a list of many proofs of
Pythagoras’ theorem in Java is particularly interesting, where the user can “construct” geometrical demonstrations by clicking at the figures presented, moving points and features of geometrical diagrams (http://sunsite.ubc.ca/DigitalMathArchive/Euclid/java/html/pythagoras. html).
Cf. the Banchoff’s web page http://www.geom.umn.edu / banchoff/, where it is possible
to manipulate diagrams that correspond to mathematical problems. Joyce’s appealing Java
edition of Euclid where it is possible to “construct by clicking”, is given at the web site
http://aleph0.clarku.edu/ djoyce/java /elements/elements.html.
2.12 Mechanizing Manipulative Abduction
143
concept of plausibility, central to abductive reasoning, has been reshaped by stressing its “strategic” components, more pragmatically and in a less epistemologically
qualified manner.
Finally, I would like to reiterate the importance of the sections devoted to illustrating the concrete examples taken from the history and practice of epistemology, science, and mathematics, seen from the perspective of the interconnection
between explanatory, non-explanatory, and instrumental abduction. This analysis
also allowed me to shed new light on traditional epistemological concepts, which
are much better understood, such as in the case of falsification of the conventionalist
first principles of physics and regarding the problem of falsification of construction
in psychoanalytic interpretation. In these cases newly acquired knowledge about
abductive cognition better accounts for the role of contradiction and inconsistency
in creative reasoning. I also believe it can help us to overcome some consequences
of the old-fashioned assumptions typical of the epistemological tradition which resorted to affirmation of the different status of inferential processes at work in natural
and formal sciences.
The analysis of mirror and unveiling diagrams described at the end of the chapter,
taking advantage of the cognitive-epistemological reconstruction of the discovery of
non-Euclidean geometry, entails some general consequences concerning the epistemology of mathematics and formal sciences. The concept of mirror diagram plays
a fundamental explanatory role in the epistemology of removing obstacles and obscurities related to the ambiguities of the problem of parallel lines and, in general,
in enhancing mathematical knowledge regarding critical situations. In the case of
the more instrumental unveiling diagrams, the allocating and switching of attention between internal and external representation better reveals how to govern the
reasoning strategy at hand by integrating internal and external representation in a
more dynamic and complicated way. This account in terms of mirror and unveiling
diagrams seems empirically adequate to integrate findings from research on cognition and findings from historical-epistemological research into models of actual
mathematical practices. I contended that the assessment of the fit between cognitive findings and historical-epistemological practices helps to elaborate richer and
more realistic models of cognition and presents a significant advance over previous
epistemological work on actual mathematical reasoning and practice.
I also think that: i) the role of optical diagrams in a geometry teaching environment could be relevant. Experimental research could be performed on high school
geometry students devoted to detecting the didactic effects and learning improvements due to mirror and unveiling diagrams in producing abstract entities; ii) the
activity of zooming (especially in the case of magnification) of optical diagrams
could be studied in other areas of human abductive model-based reasoning, such as
the ones involving creative, analogical, and spatial inferences, both in science and
everyday situations so that this can extend the psychological theory.
Chapter 3
Semiotic Brains and Artificial Minds
How Brains Make Up Material Cognitive Systems
In chapter one the important role of external representations and epistemic mediators was stressed, when illustrating the concept of manipulative abduction, especially in the field of scientific reasoning. Further insight can be granted by some
considerations that also take into account Turing’s seminal ideas about human and
machine intelligence, some paleoanthropological results, and a Peircean semiotic
perspective.
Following Peirce’s semiotics, the interplay between internal and external representation can be further depicted taking advantage of what I call semiotic brains.
They are brains that make up a series of signs and that are engaged in making or
manifesting or reacting to a series of signs. Through this semiotic activity they are
at the same time engaged in “being minds” and thus in thinking intelligently. An
important effect of this semiotic brain activity is a continuous process of disembodiment of mind that exhibits a new cognitive perspective on the mechanisms underlying the semiotic emergence of meaning processes. To illustrate this process I will
take advantage of Turing’s comparison between the so-called “unorganized” brains
and “logical” and “practical” machines, and of some paleoanthropological results on
the birth of material culture, that provide an evolutionary perspective on the origin
of intelligent behaviors.
Then I will describe the centrality to semiotic cognitive information processes of
the disembodiment of mind from the point of view of the cognitive interplay between internal and external representations, both mimetic and creative, where the
problem of the continuous interaction between on-line – like in the case of manipulative abduction – and off-line (for example in inner rehearsal) intelligence can
properly be addressed (section 3.6.5). I consider this interplay critical in analyzing
the relation between meaningful semiotic internal resources and devices and their
dynamical interactions with the externalized semiotic materiality already stored in
the environment. This materiality plays a specific role in the interplay due to the fact
that it exhibits (and operates through) its own cognitive constraints. Hence, minds
are “extended” and artificial in themselves.
L. Magnani: Abductive Cognition, COSMOS 3, pp. 145–217.
c Springer-Verlag Berlin Heidelberg 2009
springerlink.com
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3 Semiotic Brains and Artificial Minds
From this perspective Turing’s “unorganized” brains can be seen as structures
that organize themselves through a semiotic activity that is reified in the external
environment and then re-projected and reinterpreted through new configurations
of neural networks and chemical processes. I will show how the disembodiment
of mind can nicely account for low-level semiotic processes of meaning creation,
bringing up the question of how higher-level processes could be comprised and
how they would interact with lower-level ones. To better explain these higher-level
semiotic mechanisms I will return to analysis of the role of model-based and manipulative abduction and of external representations. The example of elementary
geometry will also be examined, where many external things, usually inert from
the cognitive/semiotic point of view, can be transformed into what I have called
“epistemic mediators” (cf. [Magnani, 2001b] and the previous chapter of this book)
that then give rise – for instance in the case of scientific reasoning – to new signs,
new chances for “interpretants”, and thus to new interpretations. In this interplay
abduction can be seen as fully multimodal, in that both data and hypotheses can
have a full range of verbal and sensory representations. Some basic aspects of this
constitutive hybrid nature of abduction – involving words, sights, images, smells,
etc. but also kinesthetic experiences and other feelings such as pain – will be
investigated.1
Taking advantage of Turing’s comparison between “unorganized” brains and
“logical” and “practical” machines the concept of the mimetic mind is introduced.
This sheds new cognitive and philosophical light on the role of Turing’s machines
and computational modeling, outlines the decline of the so-called Cartesian computationalism and emphasizes the possible impact of the construction of new types
of universal “practical” machines, available over there, in the environment, as new
tools underlying the emergence of meaning processes. Language itself can be seen
as a mediating “ultimate artifact” (section 3.4.2): from this perspective the brain
would merely be a pattern completing device while language would be considered
an external resource/tool which is – through coevolution – obviously fitted to the
human brain helping and supporting it to enhance its cognitive capacities.
Finally, the thesis of this chapter being that the externalization/disembodiment
of mind is a significant cognitive perspective able to unveil some basic features of
abduction and creative/hypothetical thinking, its success in explaining the semiotic
interplay between internal and external representations (mimetic and creative) is
evident. This is also clear at the level of some intellectual issues stressed by certain results of psychoanalytic research and therapy, such as in the case of creative
meaning formation. To this aim I will focus on the epistemological status of the
psychoanalytic concepts of projections and introjections, and of the mythologization of external observation. Also taking advantage of the concept of manipulative
abduction, I will stress the role of some external artifacts (symbols, Mandala, ritual
tools) in what Jung calls “psychic energy flow”, where the mobility and disposability of psychic energy are seen as the secret of cultural development. I contend
1
On the concept of multimodal abduction cf. also the following chapter, section 4.1.
3.1 Turing Unorganized Machines
147
these artifacts are tools which can be usefully represented as memory mediators
that “mediate” and make available the story of their origin and the actions related to
them, which can be learnt and/or re-activated when needed. From this wide perspective symbols in psychoanalysis can be seen as memory mediators which maximize
abducibility, because they maximize recoverability, in so far as they are the best
possible expression of something not yet grasped by consciousness.
In summary, a key issue of the chapter is “What kind of brain could or would
use external representations as an aid or method of thinking?” The description of
cognitive mediators in the light of multimodal and manipulative abduction and the
introduction of the concept of maximization of abducibility try to furnish a first
answer.
3.1
Turing Unorganized Machines
If we decide to increase knowledge on the semiotic character of high-level types of
cognition it is first of all necessary to develop a model of creativity able to represent
not only “novelty” and “unconventionality”, but also some features commonly referred to as the entire creative process, such as the expert use of background knowledge and ontology (defining new concepts and their new meanings and searching
heuristically among the old ones) and the modeling activity developed in the so
called “incubation time” (generating and testing, transformations in the space of the
hypotheses). The philosophical concept of abduction I have illustrated in the first
two chapters is a candidate to solve this problem, and offers an approach to model
creative processes of meaning generation in a completely explicit and formal way,
which can fruitfully integrate the narrowness proper of a merely psychological approach, too experimentally human-oriented. I have already stressed that abductive
reasoning is active in many scientific disciplines but also in everyday reasoning: it is
essential in scientific discovery, medical and non medical diagnosis, generation of
causal explanations, generations of explanations for the behaviors of others, minds
interplay, when for example we attribute intentions to others, empathy, analogy,
emotions, as an appraisal of a given situation endowed with an explanatory or instrumental power, etc. I have illustrated in chapter one that the concept of manipulative abduction can nicely account for the relationship between meaningful behavior
and dynamical interactions with the environment. In the following sections we will
see in detail that at the roots of the creation of new meanings there is a process of
disembodiment of mind that exhibits a new cognitive description of the mechanisms
underling the emergence of meaning processes through semiotic “delegations” to
the environment.2
2
To illustrate the importance of the semiotic processes in complex cognitive systems [Loula et
al., 2009] describe an interesting digital ecosystem in which the emergence of self-organized
and adaptive symbol-based communication among distributed (and semiotic) artificial creatures
is simulated.
148
3.1.1
3 Semiotic Brains and Artificial Minds
Logical, Practical, Unorganized, and Paper Machines
Aiming at building intelligent machines Turing first of all provides an analogy
between human brains and computational machines. In “Intelligent Machinery”,
written in 1948 [Turing, 1969] maintains that “[. . . ] the potentialities of human intelligence can only be realized if suitable education is provided” (p. 3). The concept
of unorganized machine is then introduced, and it is maintained that the infant human cortex is of this nature.3 The argumentation is indeed related to showing how
such machines can be educated by means of “rewards and punishments”.
Unorganized machines are listed among different kinds of existent machineries:
- (Universal) Logical Computing Machines (LCMs). A LCM is a kind of discrete
machine Turing introduced in 1937 that has
[. . . ] an infinite memory capacity obtained in the form of an infinite tape marked out
into squares on each of which a symbol could be printed. At any moment there is one
symbol in the machine; it is called the scanned symbol. The machine can alter the
scanned symbol and its behavior is in part described by that symbol, but the symbols
on the tape elsewhere do not affect the behavior of the machine. However, the tape
can be moved back and forth through the machine, this being one of the elementary
operations of the machine. Any symbol on the tape may therefore eventually have
innings [Turing, 1992, p. 6].
This machine is called Universal if it is “[. . . ] such that if the standard description
of some other LCM is imposed on the otherwise blank tape from outside, and the
(universal) machine then set going it will carry out the operations of the particular
machine whose description is given” (p. 7). The importance of this machine resorts
to the fact that we do not need to have an infinity of different machines doing different jobs. A single one suffices: it is only necessary “to program” the universal
machine to do these jobs.
- (Universal) Practical Computing Machines (PCMs). PCMs are machines that
put their stored information in a form very different from the tape form. Given the
fact that in LCMs the number of steps involved tends to be enormous because of the
arrangement of the memory along the tape, in the case of PCMs “[. . . ] by means of
a system that is reminiscent of a telephone exchange it is made possible to obtain a
piece of information almost immediately by ‘dialing’ the position of this information in the store” (p. 8). Turing adds that “nearly” all the PCMs under construction
have the fundamental properties of the Universal Logical Computing Machines:
“[. . . ] given any job which could have be done on an LCM one can also do it on one
of these digital computers” (ibid.) so we can speak of Universal Practical computing
Machines.
3
I am taking advantage here of the concept of unorganized brain (and machine) to stress the
historical/epistemological interest of Turing’s discoveries. Of course the concept acquires a
specific meaning in the context of those Turing’s philosophical speculations that lead to the
proposal of the new idea of universal logical computing machine and to the related
computational- representational-understanding of the mind (CRUM). Therefore the concept is
obviously unrelated to current neuroscience results and only presents a philosophical concern.
3.1 Turing Unorganized Machines
149
- Unorganized Machines. Machines that are largely random in their constructions
are called “Unorganized Machines”: “So far we have been considering machines
which are designed for a definite purpose (though the universal machines are in a
sense an exception). We might instead consider what happens when we make up a
machine in a comparatively unsystematic way from some kind of standard components. [. . . ] Machines which are largely random in their construction in this way will
be called ‘Unorganized Machines’. This does not pretend to be an accurate term. It is
conceivable that the same machine might be regarded by one man as organized and
by another as unorganized.” (p. 9). They are machines made up from a large number
of similar units. Each unit is endowed with two input terminals and has an output
terminals that can be connected to the input terminals of 0 or more of other units.
An example of the so-called unorganized A-type machine with all units connected
to a synchronizing unit from which synchronizing pulses are emitted at more or less
equal intervals of times is given in Figure 3.1 (the times when the pulses arrive are
called moments and each unit is capable of having two states at each moment). The
so-called A-type unorganized machines are considered very interesting because they
are the simplest model of a nervous system with a random arrangement of neurons
(cf. the following section 3.2, “Brains as unorganized machines”).
Fig. 3.1 An example of the so-called unorganized A-type machine
- Paper Machines. “It is possible to produce the effect of a computing machine
by writing down a set of rules of procedure and asking a man to carry them out.
[. . . ] A man provided with paper, pencil and rubber, and subject to strict discipline,
is in effect a universal machine” (p. 9). Turing calls this kind of machine “Paper
Machine”.
3.1.2
Continuous, Discrete, and Active Machines
The machines described above are all discrete machines because it is possible to
describe their possible states as a discrete set, with the motion of the machines occurring by jumping from one state to another. However, Turing remarks that all
150
3 Semiotic Brains and Artificial Minds
machinery can be also regarded as continuous (where the states form a continuous
manifold and the behavior of the machine is described by a curve on this manifold) but “[. . . ] when it is possible to regard it as discrete it is usually best to do
so. Moreover machineries are called “controlling” if they only deal with information, and “active” if aim at producing some definite physical effect. A bulldozer will
be a continuous and active machine, a telephone continuous and controlling. But
also brains can be considered machines and they are – Turing says “probably” –
continuous and controlling but “very similar to much discrete machinery” (p. 5).
Brains very nearly fall into this class [discrete controlling machinery – when it is
natural to describe its possible states as a discrete set] and there seems every reason
to believe that they could have been made to fall genuinely into it without any change
in their essential properties. However, the property of being “discrete” is only an
advantage for the theoretical investigator, and serves no evolutionary purpose, so
we could not expect Nature to assist us by producing truly “discrete brains” (p. 6).4
Brains can be treated as machines but they can also be considered discrete
machines. The epistemological reason is clear: this is just an advantage for the “theoretical investigator” that aims at knowing what are intelligent machines, but certainly it would not be an evolutionary advantage. “Real” humans brains are of course
continuous systems, only “theoretically” they can be treated as discrete.
Following Turing’s perspective we have derived two new achievements about
machines and intelligence: brains can be considered machines, the simplest nervous
systems with a random arrangement of neurons can be considered unorganized machines, in both cases with the property of being “discrete”.
3.1.3
Mimicking Human Education
Turing also says:
The types of machine that we have considered so far are mainly ones that are allowed
to continue in their own way for indefinite periods without interference from outside.
The universal machines were an exception to this, in that from time to time one might
change the description of the machine which is being imitated. We shall now consider
machines in which such interference is the rule rather than the exception (p. 11).
Screwdriver interference is when parts of the machine are removed and replaced
with others, giving rise to completely new machines. Paper interference is when
mere communication of information to the machine modifies its behavior. It is clear
that in the case of the universal machine, paper interference can be as useful as
screwdriver interference: we are interested in this kind of interference. We can say
that each time an interference occurs the machine is probably changed. It has to be
noted that paper interference provides information that is both external and material.
Turing thought that the fact that human beings have already made machinery able
to imitate various parts of a man was positive in order to believe in the possibility
4
Further details on the so-called “discretization of knowledge” will be given in chapter eight,
section 8.1.1.
3.2 Brains as Unorganized Machines
151
of building thinking machinery: trivial examples are the microphone for the ear, and
the television camera for the eye. What about the nervous system? We can copy the
behavior of nerves with suitable electrical models and the electrical circuits which
are used in electronic computing machinery seem to have essential properties of
nerves because they are able to transmit information and to store it.
Education in human beings can model “education of machinery” “Mimicking
education, we should hope to modify the machine until it could be relied on to
produce definite reactions to certain commands” (p. 14). A graduate has had interactions with other human beings for twenty years or more and at the end of this
period “[. . . ] a large number of standard routines will have been superimposed on
the original pattern of his brain” (ibid.).
Turing maintains that
1. in human beings the interaction is mainly with other men and the receiving of
visual and other stimuli constitutes the main forms of interference;
2. it is only when a man is “concentrating” that he approximates a machine without
interference;
3. even when a man is concentrating his behavior is mainly conditioned by previous interference.
3.2
3.2.1
Brains as Unorganized Machines
The Infant Cortex as an Unorganized Machine
In many unorganized machines when a configuration5 is reached and possible interference suitably constrained, the machine behaves as one organized (and even
universal) machine for a definite purpose. Turing provides the example of a B-type
unorganized machine with sufficient units where we can find particular initial conditions able to make it a universal machine also endowed with a given storage capacity.
The set up of these initial conditions is called “organizing the machine” that indeed
is seen a kind of “modification” of a preexisting unorganized machine through external interference.
Infant brain can be considered an unorganized machine. Given the analogy previously established (cf. subsection above “Logical, Practical, Unorganized, and
Paper Machines), what are the events that modify it in an organized universal
brain/machine? “The cortex of an infant is an unorganized machinery, which can
be organized by suitable interference training. The organization might result in the
modification of the machine into a universal machine or something like it. [. . . ]
This picture of the cortex as an unorganized machinery is very satisfactory from
the point of view of evolution and genetics.” (p. 16). The presence of human cortex
is not meaningful in itself: “[. . . ] the possession of a human cortex (say) would be
virtually useless if no attempt was made to organize it. Thus if a wolf by a mutation
5
A configuration is a state of a discrete machinery.
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3 Semiotic Brains and Artificial Minds
acquired a human cortex there is little reason to believe that he would have any selective advantage” (ibid.). Indeed the exploitation of a big cortex (that is its possible
organization) requires a suitable environment: “If however the mutation occurred
in a milieu where speech had developed (parrot-like wolves), and if the mutation
by chance had well permeated a small community, then some selective advantage
might be felt. It would then be possible to pass information on from generation to
generation” (ibid.).
Hence, organizing human brains into universal machines strongly relates to the
presence of
1. speech (even if only at the level of rudimentary but meaningful parrot-like
wolves);
2. and a social setting where some “techniques” are learnt “[. . . ] the isolated man
does not develop any intellectual power. It is necessary for him to be immersed
in an environment of other men, whose techniques he absorbs during the first
twenty years of his life. He may then perhaps do a little research of his own and
make a very few discoveries which are passed on to other men. From this point
of view the search for new techniques must be regarded as carried out by human
community as a whole, rather than by individuals” (p. 23).
This means that a big cortex6 can provide an evolutionary advantage only in presence of that massive storage of meaningful information and knowledge on external
supports that only an already developed small community can possess. Turing himself considers this picture rather speculative but evidence from paleoanthropology
can support it, as I will describe in the following section.
Moreover, the training of a human child depends on a system of rewards and
punishments, that suggests that organization can occur only through two inputs.
The example of an unorganized P-type machine, that can be regarded as a LCM
without a tape and largely incompletely described, is given. Through suitable stimuli
of pleasure and pain (and the provision of an external memory) the P-type machine
can become an universal machine (p. 20).
When the infant brain is transformed in an intelligent one both discipline and
initiative are acquired: “[. . . ] to convert a brain or machine into a universal machine
is the extremest form of discipline. [. . . ] But discipline is certainly not enough in
itself to produce intelligence. That which is required in addition we call initiative.
[. . . ] Our task is to discover the nature of this residue as it occurs in man, and try
and copy it in machines” (p. 21).
Examples of problems requiring initiative are the following: “Find a number n
such that . . . ”, “see if you can find a way of calculating the function which will
6
[Evans et al., 2005] illustrate recent research in neurogenetics which shows the role of a gene,
Microcephalin, which regulates brain size and which has evolved under strong positive selection
in the evolution of primate lineage, leading to Homo sapiens and beyond. One genetic variant
of it in modern humans, which arose ∼37,000 years ago, increased in frequency too rapidly to
be compatible with neutral drift, so supporting the ongoing brain evolutionary plasticity of the
human brain.
3.3 From the Prehistoric Brains to the Universal Machines
153
enable us to obtain the values for arguments . . . .”. The problem is equivalent to that
of finding a program to put on the machine in question.
We have seen how a brain can be “organized”, in Turing’s sense, but how can that
brain be a creative brain able to account for the emergence of interesting meaning
processes?
3.3
From the Prehistoric Brains to the Universal Machines
I have said that what I call semiotic brains are brains that make up a series of
signs and that are engaged in making or manifesting or reacting to a series of signs:
through this semiotic activity they are at the same time engaged in “being minds”
and so in thinking intelligently. In this section I will illustrate the process of “disembodiment of mind” as an important aspect of this semiotic activity of brains.
We have seen in the previous section that following Turing’s point of view [1969]
a big cortex can provide an evolutionary advantage only in presence of a massive
storage of meaningful information and knowledge on external supports that only an
already developed small community of human beings can possess. Evidence from
paleoanthropology seems to support this perspective. Some research [Mithen, 1996;
Mithen, 1999; Humphrey, 2002; Lewis-Williams, 2002] in cognitive paleoanthropology – even if rather speculative – teaches us that high level and reflective consciousness in terms of thoughts about our own thoughts and about our feelings (that
is consciousness not merely considered as raw sensation) is intertwined with the development of modern language (speech) and material culture. After 250.000 years
ago several hominid species had brains as large as ours today, but their behavior
lacked any sign of art or symbolic behavior. If we consider high-level consciousness as related to a high-level organization – in Turing’s sense – of human cortex,
its origins can be related to the active role of environmental, social, linguistic, and
cultural aspects.7
Handaxes were made by Early Humans and firstly appeared 1,4 million years
ago, still made by some of the Neanderthals in Europe just 50.000 years ago. The
making of handaxes is seen as strictly intertwined with the development of consciousness. Many needed capabilities constitute a part of an evolved psychology
that appeared long before the first handaxes were manufactured. It seems humans
were pre-adapted for some components required to make handaxes [Mithen, 1996;
Mithen, 1999] (cf. Figure 3.2):
1. imposition of symmetry (already evolved through predators escape and social
interaction). It has been an unintentional by-product of the bifacial knapping
technique but also deliberately imposed in other cases. [Dennett, 1991] hypothesizes that the attention to symmetry may have developed through social interaction and predator escape, as it may allow one to recognize that one is being
7
[Logan, 2006] further stresses the coevolution of brain and culture and the supposed limits of
brain size due to obstetrical and mobility reasons and to the the expensiveness in terms of energy.
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3 Semiotic Brains and Artificial Minds
c
Fig. 3.2 From [Mithen, 1999, p. 286]. 1999
Massachusetts Institute of Technology, by
permission of The MIT Press.
directly stared at. It also seems that “Hominid handaxes makers may have been
keying into this attraction to symmetry when producing tools to attract the attention of other hominids, especially those of the opposite sex” [Mithen, 1999,
p. 287];
2. understanding fracture dynamics (for example evident from Oldowan tools and
from nut cracking by chimpanzees today);
3. ability to plan ahead (modifying plans and reacting to contingencies, such unexpected flaws in the material and miss-hits), still evident in the minds of Oldowan
tool makers and in chimpanzees;
4. high degree of sensorimotor control: “Nodules, preforms, and near finished artifacts must be struck at precisely the right angle with precisely the right degree
of force if the desired flake is to be detached” [Mithen, 1999, p. 285]. The origin of this capability is usually tracked back to encephalization – the increased
number of nerve tracts and of the integration between them allows for the firing
of smaller muscle groups – and bipedalism – that requires a more complex integrated highly fractionated nervous system, which in turn presupposes a larger
brain.
The combination of these four resources produced an important semiotic revolution: the birth of what Mithen calls technical intelligence of early human mind,
that is consequently related to the construction of handaxes and their new semiotic
values. Indeed they indicate high intelligence and good health. They cannot be compared to those artifacts made by animals, like honeycomb or spider web, deriving
from the iteration of fixed actions which do not require plastic consciousness and
intelligence.8
8
I will illustrate animal artifacts due to more “plastic” abductive endowments in chapter five.
3.3 From the Prehistoric Brains to the Universal Machines
3.3.1
155
Private Speech and Fleeting Consciousness
Two central factors play a fundamental role in the combination of the four resources
above:
• the exploitation of private speech (speaking to oneself) to trail between planning,
fracture dynamic, motor control and symmetry (also in children there is a kind of
private muttering which makes explicit what is implicit in the various abilities);
• a good degree of fleeting consciousness (thoughts about thoughts).
Of course they furnish a kind of blackboard where the four – previously distinct
– resources can be exploited all together and in their dynamic interaction. In the
meantime these two aspects obviously played a fundamental role in the development
of consciousness and thought:
So my argument is that when our ancestors made handaxes there were private mutterings accompanying the crack of stone against stone. Those private mutterings were
instrumental in pulling the knowledge required for handaxes manufacture into an emergent consciousness. But what type of consciousness? I think probably one that was
fleeting one: one that existed during the act of manufacture and that did not the endure.
One quite unlike the consciousness about one’s emotions, feelings, and desires that
were associated with the social world and that probably were part of a completely separated cognitive domain, that of social intelligence, in the early human mind [Mithen,
1999, p. 288].
This use of private speech can be certainly considered a semiotic internal “tool”
for organizing brains and so for manipulating, expanding, and exploring minds, a
tool that probably coevolved with another: talking to each other.9 Both private and
public language act as tools for thought and play a fundamental role in the evolution “opening up our minds to ourselves” and so in the emergence of new meaning
processes.
3.3.2
Material Culture as Distributed Cognition and Semiosis
Another semiotic tool appeared in the latter stages of human evolution, that played
a great role in the evolution of primitive minds, that is in the organization of human brains. Handaxes also are at the birth of material culture, so as new cognitive
chances can coevolve:
• the mind of some early humans, like the Neanderthals, were constituted by relatively isolated cognitive domains, [Mithen, 1999] calls different intelligences,
probably endowed with different degrees of consciousness about the thoughts
and knowledge within each domain (natural history intelligence, technical
9
On natural languages as cognitive artifacts cf. [Carruthers, 2002a; Clark and Chalmers, 1998;
Clark, 2003; Clark, 2005; Norman, 1993; Clowes and Morse, 2005], and below section 3.4.2.
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3 Semiotic Brains and Artificial Minds
c
Fig. 3.3 From [Mithen, 1999, p. 290]. 1999
Massachusetts Institute of Technology, by
permission of The MIT Press.
intelligence, social intelligence). These isolated cognitive domains became integrated also taking advantage of the role of public language (cf. Figure 3.3.);10
• degrees of high level consciousness appear, human beings need thoughts about
thoughts;
• social intelligence and public language arise.11
10
11
In this book I will address the problem of the origin of human language from many current perspectives related to philosophy, cognitive science, biology, and paleoanthropology, addressing
phylogenetic, ontogenetic, and learning issues. A general description of the various approaches
to the problem of the emergence of natural language is provided by [Számadó and Szathmáry,
1997].
Posed in the late 1980s [Whiten and Byrne, 1988; Whiten and Byrne, 1997; Byrne and Whiten,
1988], the “social brain hypothesis” (also called “Machiavellian intelligence hypothesis”)
holds that the relatively large brains of human beings and other primates reflect the computational demands of complex social systems and not only the need of processing information of ecological relevance: ability to manipulate information and not simply to remember
it, to recognize visual signals to identify other individuals, sufficient memory for faces and
to remember who has a relationship with whom, use of tactical deception, coalition, ability
to understand intentions, to hold false beliefs, and “mind-read”, known as “theory of mind”
etc. Language itself would have at a certain point grooming as a way of creating social cohesion as the size and complexity of the social group increased (cf. also [Dunbar, 1998;
Dunbar, 2003]).
3.3 From the Prehistoric Brains to the Universal Machines
157
It is extremely important to stress that material culture is not just the product of this
massive cognitive chance but also cause of it. “The clever trick that humans learnt
was to disembody their minds into the material world around them: a linguistic
utterance might be considered as a disembodied thought. But such utterances last
just for a few seconds. Material culture endures” [Mithen, 1999, p. 291].
In this perspective we acknowledge that material artifacts are tools for thoughts
as is language: tools (and their related new “signs”) for exploring, expanding, and
manipulating our own minds. In this regard the evolution of culture is inextricably
linked with the evolution of consciousness and thought.12
Early human brain becomes a kind of universal “intelligent” machine, extremely
flexible so that we did no longer need different “separated” intelligent machines
doing different jobs. A single one will suffice. As the engineering problem of producing various machines for various jobs is replaced by the office work of “programming” the universal machine to do these jobs, so the different intelligences
become integrated in a new universal device endowed with a high-level type of
consciousness.13
From this perspective the semiotic expansion of the minds is in the meantime
a continuous process of disembodiment of the minds themselves into the material
world around them. In this regard the evolution of the mind is inextricably linked
with the evolution of large, integrated, material cognitive semiotic systems. In the
following sections I will illustrate this extraordinary interplay between human brains
and the cognitive systems they make.
3.3.3
Semiotic Delegations through the Disembodiment of Mind
A wonderful example of meaning creation through disembodiment of mind is the
carving of what most likely is the mythical being from the last ice age, 30.000 years
ago, a half human/half lion figure carved from mammoth ivory found at Hohlenstein
Stadel, Germany.
An evolved mind is unlikely to have a natural home for this being, as such entities
do not exist in the natural world, the mind needs new chances: so whereas evolved
minds could think about humans by exploiting modules shaped by natural selection,
and about lions by deploying content rich mental modules moulded by natural selection and about other lions by using other content rich modules from the natural history
12
13
A further analysis of the domain specific mentality of Neanderthals, related to social behavior, natural world, and technology, contrasted with the cognitive “fluidity” of modern mind, is
illustrated in [Mithen, 2007].
On the relationship between material culture and the evolution of consciousness cf. [Donald,
1998; Donald, 2001; Dennett, 2003]. The fact that bigger brains found an evolutionary success
has been recently also related to the change in diet, caused by the fact that in Pliocene the climate
conditions began to change. Bigger brains (together with growth of body size and reduction in
the dentition) were important because they helped to solve dietary problems and to arrive to
higher quality diet: so the birth of social and material culture would be related to the problem
of solving dietary problems, brains are also required to retain a mental map of plant and food
supplies [Milton, 2006].
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3 Semiotic Brains and Artificial Minds
c
Fig. 3.4 From [Mithen, 1999, p. 293]. 1999
Massachusetts Institute of Technology, by
permission of The MIT Press.
cognitive domain, how could one think about entities that were part human and part
animal? Such entities had no home in the mind [Mithen, 1999, p. 291].
A mind consisting of different separated intelligences cannot come up with such
entity (Figure 3.4). The only way is to extend the mind into the material word,
building in the environment primitive scenarios14 and exploiting in a semiotic way
rocks, blackboards, paper, ivory, and writing, painting, and carving: “[. . . ] artifacts
such as this figure play the role of anchors for ideas and have no natural home within
the mind; for ideas that take us beyond those that natural selection could enable us
to possess” [Mithen, 1999, p. 291].
In the case of our figure we face with an anthropomorphic thinking created by the
material representation serving to semiotically anchor the cognitive representation
of supernatural being. In this case the material culture disembodies thoughts, that
otherwise will soon disappear, without being transmitted to other human beings,
and realizes a systematic semiotic delegation to the external environment. The early
human mind possessed two separated intelligences for thinking about animals and
people. Through the mediation of the material culture the modern human mind can
arrive to internally think about the new concept of animal and people at the same
time. But the new meaning occurred over there, in the external material world where
the mind picked up it.
14
Ohsawa proposed this term to explain some aspects of “chance discovery”. Cf. for example
[Nara and Ohsawa, 2004] that stress the attention on the activity of extracting chances through
communication of scenarios: given that a scenario is a time series of events under a given context, during a communication scenario drawings are generated, externalized (that is disembodied) and subsequently analyzed in the abductive process of chance discovery. [Abe et al., 2006]
usefully apply abduction to dynamic risk management in nursing, where rare chances (risks
or accidents) can be abduced as novel generated hypotheses. The set of nursing activities is
regarded as a scenario where risks and accidents are considered as a scenario violation.
3.4 Mimetic and Creative Representations
159
Artifacts as external semiotic objects allowed humans to loosen and cut those
chains on our unorganized brains imposed by our evolutionary past. Chains that
always limited the brains of other human beings, such as the Neanderthals. Loosing
chains and securing ideas to external objects was also a way to creatively re-organize
brains as universal machines for thinking.15
In the remaining part of this chapter I will describe the centrality to semiotic cognitive information processes of the disembodiment of mind from the point of view
of the cognitive interplay between internal and external representations. I consider
this interplay critical in analyzing the relation between meaningful semiotic internal
resources and devices and their dynamical interactions with the externalized semiotic materiality already stocked in the environment. Hence, minds are “extended”
and artificial in themselves.16 With the aim of explaining these higher-level mechanisms I will provide a cognitive framework where model-based and manipulative
abduction together with external representations and epistemic mediators play a
central role.
3.4
Mimetic and Creative Representations
We have seen that unorganized brains organize themselves through a semiotic activity that is reified in the external environment and then re-projected and reinterpreted
through new configurations of neural networks and chemical processes. I also think
the disembodiment of mind can nicely account for low-level semiotic processes of
meaning creation, bringing up the question of how could higher-level processes be
comprised and how would they interact with lower-level ones.
3.4.1
External and Internal Representations
We have said that through the mediation of the material culture the modern human
mind can arrive to internally think the new meaning of animals and people at the
15
16
Actually, the brains of the humans who made those artifacts were highly organized, not unorganized. I have to reiterate that my argumentation is related to the concept of unorganized brain
in its specific Turing’s sense. We do tend to think of early humans as being like our children but
they were perfectly viable adults.
To correctly place this view in present, general cognitive debate it is useful to read the book by
[Shapiro, 2004]. The author, speaking of the so-called “multiple realizability thesis” (that is: are
mental states multiply realizable?) offers a full and critical treatment of the various current theories that deal with the concept of multiple realizable mind, also treating topics like “envatment”
– mind as distinct from the body, embodied and extended mind – mind “beyond” and “outside”
the body, etc. The perspectives range from those which only see some creatures which are different to us in their physical composition as possessing a mind to the ones stating that every
suitable organized system, regardless of its physical composition, can have minds like ours. On
the multirealizability thesis cf. also [Polger, 2006] and the recent discussion, also related to the
so-called “separability thesis”, given by [Clark, 2008, chapter nine]. On the frequent misunderstandings and confusions in current discussions of multiple realization, cf. the clear criticisms
contained in [Polger, 2008].
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3 Semiotic Brains and Artificial Minds
same time. We can account for this process of disembodiment from an impressive
cognitive point of view.
I maintain that representations are external and internal. We can say that
- external representations are formed by external materials that express (through
reification) concepts and problems already stored in the brain or that do not have
a natural home in it;
- internalized representations are internal re-projections, a kind of recapitulations
(learning), of external representations in terms of neural patterns of activation in
the brain. They can sometimes be “internally” manipulated like external objects
and can originate new internal reconstructed representations through the neural
activity of transformation and integration.
This process explains why human beings seem to perform both computations of a
connectionist type17 such as the ones involving representations as
- (I Level) patterns of neural activation that arise as the result of the interaction
between body and environment (and suitably shaped by the evolution and the
individual history): pattern completion or image recognition,18
and computations that use representations as
- (II Level) derived combinatorial syntax and semantics dynamically shaped by
the various external representations and reasoning devices found or constructed
in the environment (for example geometrical diagrams); they are neurologically
represented contingently as pattern of neural activations that “sometimes” tend
to become stabilized structures and to fix and so to permanently belong to the I
Level above.
The I Level originates those sensations (they constitute a kind of “face” we think
the world has), that provide room for the II Level to reflect the structure of the
environment, and, most important, that can follow the computations suggested by
these external structures. It is clear we can now conclude that the growth of the brain
and especially the synaptic and dendritic growth are profoundly determined by the
environment.
When the fixation is reached the patterns of neural activation no longer need a
direct stimulus from the environment for their construction. In a certain sense they
can be viewed as fixed internal records of external structures that can exist also
in the absence of such external structures. These patterns of neural activation that
17
18
Here the reference to the word “connectionism” is used on the plausible assumption that all
mental representations are brain structures: verbal and the full range of sensory representations
are neural structures endowed with their chemical functioning (neurotransmitters and hormones)
and electrical activity (neurons fire and provide electrical inputs to other neurons). In this sense
we can reconceptualize cognition neurologically: for example the solution of an explanatory
problem can be seen as a process in which one neural structure representing an explanatory
target generates another neural structure that constitutes a hypothesis for the solution.
Andy Clark, adopting a connectionist perspective, maintains that human brain is essentially a
device for pattern-association, pattern-completion, and pattern-manipulation.
3.4 Mimetic and Creative Representations
161
constitute the I Level Representations always keep record of the experience that
generated them and, thus, always carry the II Level Representation associated to
them, even if in a different form, the form of memory and not the form of a vivid
sensorial experience. Now, the human agent, via neural mechanisms, can retrieve
these II Level Representations and use them as internal representations or use parts
of them to construct new internal representations very different from the ones stored
in memory (cf. also [Gatti and Magnani, 2005]).19
3.4.2
Language as the Ultimate Artifact
The example of recent cognitive theories concerning natural language is particularly
useful to illustrate the interplay between external and internal representations. Following [Clark, 1997, p. 218] language is an “ultimate artifact”. In this perspective
brain is just a pattern completing device (as I have illustrated introducing the I level
in the previous subsection), while language is an external resource/tool which is –
along a process of coevolution – obviously fitted to the human brain, helping and
supporting it to enhance its cognitive capacities [Wheeler, 2004]. Language is culturally passed from one generation to the next and is thus learnt again and again
just through exposure to a sample of it, and then suitably generalized.20 It is not
only an important part of the cognitive niche built by human beings a long time ago,
but it also formed a permanent artificial environment that in turn created a further
selective pressure in evolution, in the coevolutionary interplay between genes and
culture, as I will describe in chapter six: in a recent article [Clark, 2006, p. 370]
himself acknowledges that “language is a self-constructed cognitive niche” consisting of structures that “combine with appropriate culturally transmitted practices to
enhance problem-solving”.
Exactly like hammers and PCs are fitted to the human brain and to the structure
and capacities of human hands, language is a medium of communication and information and it “[. . . ] alters the nature of the computational tasks involved in various
kinds of problem solving” that affect human beings (and their brains) [Clark, 1997,
19
20
The role of external representations has already been stressed in some central traditions of cognitive science and artificial intelligence, from the area of distributed and embodied cognition
and of robotics [Brooks, 1991; Clark, 2003; Zhang, 1997] to the area of active vision and perception [Gibson, 1979; Thomas, 1999]). I also think this discussion about external and internal
representations can be used to extend and enhance the Representational Redescription model
introduced by [Karmiloff-Smith, 1992], which accounts for how these levels of representation
are generated in the infant mind. [Sterelny, 2004] lists some of the most important results we
can obtain thanks to external representations: they 1) ease memory burdens, 2) transform difficult cognitive problems into easier perceptual problems, 3) transform difficult perceptual problems into easier ones, 4) transform difficult learning problems into easier ones, 5) engineer
workspaces to complete tasks more rapidly and reliably.
On the importance of arbitrariness in natural languages cf. [Gasser, 2004]. Research acknowledging the fact that language understanding cannot be performed through the manipulations of
arbitrary symbols alone, but has to be based on the body interaction with the environment is
described in [Glenberg and Kaschak, 2003; Zwaan, 2004]. In this perspective language acquisition and meaning comprehension are partly achieved through the same simulative structures
used to plan and guide action [Svensson and Ziemke, 2004].
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3 Semiotic Brains and Artificial Minds
p. 193]. It is said that language scaffolds cognition for the mind [Clowes and Morse,
2005]. Basically, language is for Clark a cognitive tool that facilitates thought and
cognition through 1) memory augmentation, 2) environmental simplification, 3) coordination of activities through control of attention and resource allocation, 4) the
activity of transcending path-dependent learning (the learning of linguistic organisms is not constrained by complicated cognitive paths that are circumvented thanks
to language), 5) control loops (that act for our future behavior: for example writing plans difficult to keep in one’s head), 6) data manipulation and representation
[Bermúdez, 2003, p. 151]. From this perspective there is no innate domain-specific
language processing system, – like for example the one maintained by [Chomsky,
1986] and language does not deeply alter the “basic modes of representation and
computation” of the brain [Clark, 1997, p. 198].21
The acquisition of language is a kind of reprogramming of the computational
resources of the human brain in such a way that “[. . . ] our innate pattern-completing
neural architecture comes to simulate a kind of logic-like serial processing device”
[Wheeler, 2004, p. 696], without a substantial modification of the brain’s processing
architecture. Just like diagrams can help us in many cognitive tasks and especially
in mathematical reasoning (cf. below sections 3.6.1, 3.6.2 and 3.6.3) language helps
in various cognitive tasks, for instance as a sensory relay in human communication
(and in other various simulations of basic psychic endowments), when writing in
notebooks, building databases, organizing actions and plans, creating narratives and
theories, etc. Moreover, language helps us in a more internal modality, such as in
self-directed speech (silent, in auditory imagery, or aloud), when for example we
repeat some instructions to ourselves.22
In Clark’s words, “[. . . ] exposure to, or rehearsal [of spoken and written language, through visual, auditory, and haptic sensorial systems] [. . . ] always activates
or otherwise exploits many other kinds of internal representational or cognitive resources” that are able “to provide a new kind of cognitive niche whose features
and properties complement, but do not need to replicate the basic modes of operation and representation of the biological brain [Clark, 2006, pp. 370–371]. Various
experiments provide evidence that the adoption of language (and symbols) would
favor the de-coupling of the cognitive agent from the “immediate pull of the encountered scene” and would provide a “new realm of perceptible objects” which
simplify certain kinds of attentional, reasoning, and learning tasks (ibid.). For example, in the case of the use of external linguistic tags or symbols (for example
numbers), the brain is enabled – by re-presenting them when needed – to solve
problems previously seen as puzzling. Studies on writing as thinking show how
their coupling involves a kind of reciprocal influence, where inner and outer features
21
22
On the received view on language, the so-called “language myth” cf. [Love, 2004], who discusses Clark’s rejection of the idea that natural languages are codes and usefully analyzes some
aspects of Saussure’s and Harris’ perspectives. A computational framework for studying the
emergence of language and communication, which sees language as a heterogeneous set of artifacts implicated in cultural and cognitive activities is presented in [Cangelosi, 2007], also taking
into account social, sensorimotor, and neural capabilities of cognitive agents.
On the role of the so-called “inner rehearsal” cf. below subsection 3.6.5.
3.4 Mimetic and Creative Representations
163
have a causal influence on one another which is occurring over time [Harris, 1989;
Menary, 2007]: “The restructuring of thought which writing introduces depends
upon prising open a conceptual gap between sentence and utterance. [. . . ] Writing
is crucial here because autoglottic inquiry presupposes the validity of unsponsored
language. Utterances are automatically sponsored by those who utter them, even if
they merely repeat what has been said before. Sentences by contrast, have no sponsors: they are autoglottic abstractions. The Aristotelian syllogism like the Buddhist
panchakarani, presupposes writing” [Harris, 1989, p. 104].
Language would stabilize and discipline (or “anchor”, Clark says) intrinsically
fluid and context-sensitive modes of thought and reason:23 one of the fruitful qualities of connectionist or artificial neural-network models is their capability and their
need to be stabilized. Moreover, words act on mental off-line24 inner states affecting not only other internally represented words but also many other model-based
and sensorimotor representations and modes, between and within humans: “Words
and sentences act as artificial input signals, often (as in self-directed inner speech)
entirely self-generated, that nudge fluid natural systems of encoding and representation along reliable and useful trajectories”, where a “a semi-anarchic parallel organization of competing elements” (a metaphor taken from [Dennett, 1991]) is at play
and explains the origin of language. These elements take control at different times
in a distributed structure informed by “[. . . ] a wealth of options involving intermediate grades of intelligent and semi-intelligent orchestration, and of hierarchical and
semi-hierarchical control” [Clark, 2006, p. 372].25
Quoting Clark, we have stressed above that “exposure to, or rehearsal of [spoken
and written language, through visual, auditory, and haptic sensorial systems] [. . . ]
always activates or otherwise exploits many other kinds of internal representational
or cognitive resources” that are able “[. . . ] to provide a new kind of cognitive niche
whose features and properties complement, but do not need to replicate the basic
modes of operation and representation of the biological brain” [Clark, 2006, pp.
370–371].
23
24
25
I agree with [Bermúdez, 2003, p. 155] who, speaking of Clark’s approach says: “His view, I
suspect, is that the environmental simplification that language provides applies to a perceived
environment that is already parsed into objects or objects like entities” (on prelinguistic reification in animal cognition cf. chapter five, section 5.5, on the role of spatial cognition in reification
cf. chapter four, section 4.7).
On this concept cf. below subsection 3.6.5.
Interesting considerations on the scaffolding role of language in mathematical thought are presented in [Clark, 2008, chapter, section four]. The never-ending problem of the role of language in “necessarily” rendering thoughts possible, and even its role in any form of conceptual
thinking, or at least in the mere acquisition of thoughts or in scaffolding them and in making
communication, consciousness and mind-reading possible, is extensively treated in [Carruthers,
2002a]. Coherently with Clark’s contention which I have just described, the author maintains
that language is the medium for “non-domain specific thinking”, which fulfils the role of integrating the outputs of a variety of domain-specific conceptual faculties (or “central-cognitive
quasi-modules”). The opinion that embodiment in cognitive science undervalues concepts such
as conventions/norms, representations, and consciousness, as essential properties of language,
is provided by [Zlatev, 2007].
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The semantic approach to language can take advantage of this perspective in a
more traditional framework that does not take into account the concept of cognitive
niche, but is oriented towards a dynamic systems framework: [Logan, 2006, p. 153]
nicely expresses an analogous consideration. A word is “[. . . ] a strange attractor
for all the percepts associated with the concept represented by that word”, and a
concept can be characterized like an “artificial or virtual percept”. Instead of “[. . . ]
bringing the mountain or the percept of the mountain directly to the mind the word
brings the mind to the mountain through the concept of the mountain” so accessing
and capturing suitable memories. In the terms of dynamic systems approach [Logan, 2006, p. 155] “An attractor is a trajectory in phase space towards which all of
the trajectories of a non-linear dynamic system are attracted. The meaning of the
word [as an attractor] being uttered does not belong simply to the individual but to
the community to which the individual belongs [. . . ] and emerges in the context in
which it is being used”. The variability of the context explains that “The attractor
is a strange attractor because the meaning of a word never exactly repeats itself”
for instance because of the variability of the constraints imposed by the medium
at hand.26 According to the theory of dissipative systems [Prigogine and Stengers,
1984], spoken and syntaclilized language and abstract conceptual thinking can be
seen as having emerged at exactly the same time as the “bifurcation” of the brain
which shifted from the concrete percept-based thinking of prelingual hominids to
that of the fully fledged human species, Homo sapiens sapiens, providing an example of both punctuated equilibrium and a new order coming out of a chaotic linear
system. Of course Homo sapiens sapiens vestigially retains the perceptual-oriented
features of hominid brains.
In tune with this dynamic approach to semantics are the considerations made in
terms of the catastrophe theory: at the level of human individuals we can hypothesize that there exists an “[. . . ] isomorphism between the mental mechanisms which
ensure the stability of a concept Q, and the physical and material mechanisms which
ensure the stability of the actual object K represented by Q” [Thom, 1980, p. 248].
Here the semantic depth of a concept is characterized by the time taken by the mental mechanisms of analysis to reduce this concept to its representative sign. The
more complex the concept is, the more its stability needs regulator mechanisms, the
greater is its semantic density to an actual object, as obviously happens in the case
of nouns which refer to a substance: “The supreme prize is handed to animate beings, and most likely to man. An animal to live must periodically resort to a whole
spectrum of activities: eating, sleeping, moving,. . . etc. To these fundamental physiological activities are added (for man) mental activities almost as indispensable to
the meaning of being human: speaking, thinking, believing, . . . etc., which constitute
a form of regulation which superimposes itself at the beginning and on the presupposed” [Thom, 1980, p. 248].
26
Details on the concept of attractor are given in chapter four, section 4.7.4 and in chapter eight.
On the constraints imposed by the materiality of the external medium in the the process of
abductive formation of new meanings and in meaning change cf. below section 3.6.7.
3.5 Model-Based Abduction and Semiosis beyond Peirce
165
In the following section I will illustrate some fundamental aspects of the interplay
above in the light of basic semiotic aspects of general abductive reasoning (cf. also
section 1.3).
3.5
Model-Based Abduction and Semiosis beyond Peirce
I think there are two basic kinds of external representations active in the process of
externalization of the mind: creative and mimetic. Mimetic external representations
mirror concepts and problems that are already represented in the brain and need to
be enhanced, solved, further complicated, etc. so they sometimes can creatively give
rise to new concepts and meanings. In the examples I will illustrate in the following
sections it will be clear how for instance a mimetic geometric representation can
become creative and give rise to new meanings and ideas in the hybrid interplay
between brains and suitable cognitive environments, as “cognitive niches”27 that
consequently are appropriately reshaped.
What exactly is model-based abduction from a philosophical point of view? I
have already said that Peirce stated that all thinking is in signs, and signs can be
icons, indices, or symbols and that all inference is a form of sign activity, where the
word sign includes “feeling, image, conception, and other representation” [Peirce,
1931-1958, 5.283] (for details cf. [Kruijff, 2005]), and, in Kantian words, all synthetic forms of cognition. In this light it can be maintained that a considerable part
of the creative meaning processes is model-based. Moreover, a considerable part
of meaning creation processes (not only in science) occurs in the middle of a relationship between brains and external objects and tools that have received cognitive and/or epistemological delegations (cf. the previous section and the following
subsection).
Following this Peircean perspective about inference I think it is extremely useful
from a cognitive point of view to consider the concept of reasoning in a very broad
way (cf. also [Brent, 2000, p. 8]). We have three cases:
1. reasoning can be fully conscious and typical of high-level worked-out ways of
inferring, like in the case of scientists’ and professionals’ performances;
2. reasoning can be “acritical” [Peirce, 1931-1958, 5.108], which includes every
day inferences in conversation and in various ordinary patterns of thinking;
3. reasoning can resort to “[. . . ] operations of the mind which are logically analogous to inference excepting only that they are unconscious and therefore uncontrollable and therefore not subject to logical criticism” [Peirce, 1931-1958,
5.108].
Immediately Peirce adds a note to the third case: “But that makes all the difference in
the world; for inference is essentially deliberate, and self-controlled. Any operation
which cannot be controlled, any conclusion which is not abandoned, not merely as
27
This expression, Clark used in the different framework of the cognitive analysis of language
appears very appropriate also in this context [Pinker, 2003].
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soon as criticism has pronounced against it, but in the very act of pronouncing that
decree, is not of the nature of rational inference – is not reasoning” (ibid.).
As Colapietro clearly states [Colapietro, 2000, p. 140], it seems that for Peirce human beings semiotically involve unwitting trials and unconscious processes. Moreover, it seems clear that unconscious thought can be in some sense considered
“inference”, even if not rational; indeed, Peirce says, it is not reasoning. Peirce
further indicates that there are in human beings multiple trains of thought at once
but only a small fraction of them is conscious, nevertheless the prominence in
consciousness of one train of thought is not to be interpreted an interruption of
other ones.
In this Peircean perspective, which I adopt in this chapter, where inferential aspects of thinking dominate, there is no intuition, in an anti-Cartesian/anti-dualistic
way. We know all important facts about ourselves in an inferential abductive
way:
[. . . ] we first form a definite idea of ourselves as a hypothesis to provide a place in
which our errors and other people’s perceptions of us can happen. Furthermore, this
hypothesis is constructed from our knowledge of “outward” physical facts, such things
as the sounds we speak and the bodily movements we make, that Peirce calls signs
[Brent, 2000, p. 8].
Recognizing in a series of material, physical events, that they make up a series of
signs, is to know the existence of a “mind” (or of a group of minds) and to be absorbed in making, manifesting, or reacting to a series of signs is to be absorbed in
“being a mind”. “[. . . ] all thinking is dialogic in form” [Peirce, 1931-1958, 6.338],
both at the intrasubjective28 and intersubjective level, so that we see ourselves exactly as others see us, or see them exactly as they see themselves, and we see ourselves through our own speech and other interpretable behaviors, just others see us
and themselves in the same way, in the commonality of the whole process [Brent,
2000, p. 10].
As I will better explain later on in the following sections, in this perspective
minds are material like brains, in so far as they consist in intertwined internal and
external semiotic processes: Peirce clearly anticipated the “extended mind” hypothesis maintaining that “[. . . ] the psychologists undertake to locate various mental
powers in the brain; and above all consider it as quite certain that the faculty of
language resides in a certain lobe; but I believe it comes decidedly nearer the truth
(though not really true) that language resides in the tongue. In my opinion it is much
more true that the thoughts of a living writer are in any printed copy of his book than
they are in his brain” [Peirce, 1931-1958, 7.364].
28
“One’s thoughts are what he is ‘saying to himself’, that is saying to that other self that is just
coming to life in the flow of time. When one reasons, is that critical self that one is trying to
persuade: and all thought whatsoever is a sign, and is mostly in the nature of language” [Peirce,
1931-1958, 5.421].
3.5 Model-Based Abduction and Semiosis beyond Peirce
3.5.1
167
Man Is an External Sign
Peirce’s semiotic motto “man is an external sign” is very clear about the materiality
of mind and about the fact that the conscious self is a cluster actively embodied of
flowing intelligible signs:29
It is sufficient to say that there is no element whatever of man’s consciousness which
has not something corresponding to it in the word; and the reason is obvious. It is that
the word or sign which man uses is the man himself. For, as the fact that every thought
is a sign, taken in conjunction with the fact that life is a train of thoughts, proves that
man is a sign; so, that every thought is an external sign, proves that man is an external
sign. That is to say, the man and the external sign are identical, in the same sense in
which the words homo and man are identical. Thus my language is the sum total of
myself; for the man is the thought [Peirce, 1931-1958, 5.314].
It is by way of signs that we ourselves are semiotic processes – for example a more
or less coherent cluster of narratives. If all thinking is in signs it is not true that
thoughts are in us because we are in thoughts.30
The systemic perspective of the catastrophe theory31 also stresses the role of signs
in their creation of semiotic brains. In the structure of signs (as potential messages
for humans) there is always a kind of dynamic instability, which renders them less
probable than naturally created forms: “The imprint of a finger on the sand, the
tracing of a stylet on clay, are so many naturally fragile marks of man’s deliberate
acts” [Thom, 1980, p. 284]. Nevertheless, on being perceived by human organisms
– which consequently also “become” semiotic processes – these unstable structures
return to a normal stability, and in so doing they activate semantic values, generating
– mentally – the content signified by the message.
I think it is at this point clearer what I meant in section 1.5 of chapter one, when I
explained the concept of model-based abduction and said, adopting a Peircean perspective, that all thinking is in signs, and signs can be icons, indices, or symbols and
that, moreover, all inference is a form of sign activity, where the word sign includes
feeling, image, conception, and other representation. The model-based aspects of
human cognition are central, given the central role played for example by signs like
images and feeling in the inferential activity “[. . . ] man is a sign developing according to the laws of inference. [. . . ] the entire phenomenal manifestation of mind is a
sign resulting from inference” [Peirce, 1931-1958, 5.312 and 5.313].
Moreover, the “person-sign” is future-conditional, that is not fully formed in the
present but depending on the future destiny of the concrete semiotic activity (future thoughts and experience of the community) in which she will be involved. If
Peirce maintains that when we think we appear as a sign [Peirce, 1931-1958, 5.283]
and, moreover, that everything is present to us is a phenomenal manifestation of
29
30
31
Consciousness arises as “a sort of public spirit among the nerve cells” [Peirce, 1931-1958,
1.354]. The contemporary researcher on consciousness Donald fully acknowledges the “materiality of mind” [Donald, 2001, pp. 96-99].
It is similar to the situation of the dreamer who is so deeply involved in the dream (we say, “she
is lost in her dreams”) that she does not feel she is in the dream.
See also chapter eight of this book.
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ourselves, then feelings, images, diagrams, conceptions, schemata, and other representations are phenomenal manifestations that become available for interpretations
and thus are guiding our actions in a positive or negative way. They become signs
when we think and interpret them. It is well-known that for Peirce all semiotic experience – and thus abduction – is also providing a guide for action. Indeed the whole
function of thought is to produce habits of action.32
Let us summarize some basic semiotic ideas that will be of help in the further
clarification of the cognitive and computational features of model-based and manipulative abduction. One of the central property of signs is their reinterpretability.
This occurs in a social process where signs are referred to material objects.
As is well-known, for Peirce iconic signs are based on similarity alone, the psychoanalytic patient who thought he was masturbating when piloting the plane interpreted the cloche as an extension of his body, and an iconic sign of the penis;
an ape may serve as an icon of a human.33 Indexical signs are based on contiguity
and dynamic relation to the object, a sign which refers to an object that it denotes
by virtue of being “really affected” by that object: a certain grimace indicates the
presence of pain, the rise of the column of mercury in a thermometer is a sign of
a rise in temperature, indexical signs are also the footprints in the sand or a rap on
the door. Consequently we can say indexical signs “point”. A symbol refers to an
artificial or conventional (“by virtue of a law”) interpretation of a sign, the sign ∞
used by mathematicians would be an example of Peirce’s notion of symbol, almost
all words in language, except for occasional onomatopoeic qualities, are symbols in
this sense, associated with referents in a wholly arbitrary manner.34
We have to immediately note that from the semiotic point of view feelings too are
signs that are subject to semiotic interpretations at different levels of complexity.
Peirce considered feelings elementary phenomena of mind, comprising all that is
immediately present, such as pain, sadness, cheerfulness. He believes that a feeling
is a state of mind possessing its own living qualities independent of any other state
of the mind. Neither icon, index, nor symbol actually functions as a sign until it is
interpreted and recognized in a semiotic activity and code. To make an example,
it is the evolutionary kinship that makes the ape an icon of the man, in itself the
similarity of the two animals does not mean anything.
Where cognition is merely possible, sign action, or semiosis, is working. Knowledge is surely inferential as well as abduction, that like any inference requires three
32
33
34
On this issue cf. for example the contributions contained in a recent special issue of the journal
Semiotica devoted to abduction [Queiroz and Merrell, 2005].
Iconic signs preserve the relational structure governing their objects. This fact does not always
have to be interpreted as a mirror-like resemblance, it can be seen as a “relation of reason”
[Peirce, 1931-1958, 1.369] with the object. Rather, the structural relation would be better and
more generally grasped through the mathematical notion of homomorphism – between icons
and icons and their referents, as already indicated by [Barwise and Etchemendy, 1990; Stenning,
2000], and recently stressed by [Ambrosio, 2007]. A general homomorphic relationship would
also be more satisfactory to account for the case in which the manipulation of diagrams is able
to creatively convey new information and chances, like in the case of algebraic representations
which I will illustrate below in subsection 3.6.4.
On the role of symbols in mathematical abduction cf. [Heeffer, 2007].
3.5 Model-Based Abduction and Semiosis beyond Peirce
169
elements: a sign, the object signified, and the interpretant. Everywhere “A signifies
B to C”.
There is a continuous activity of interpretation and a considerable part of this
activity – as we will see – is abductive. The Peircean notion of interpretant plays
the role of explaining the activity of interpretation that is occurring in semiosis.
The interpretant does not necessarily refer to an actual person or mind, an actual
interpreter. For instance the communication to be found in a beehive35 where the
bees are able to communicate with the others by means of signs is an example of
a kind of “mindless” triadic semiosis: indeed we recognize that a sign has been
interpreted not because we have observed a mental action but by observing another
material sign. To make another example, the person recognizing the thermometer
as a thermometer is an interpretant, as she generates in her brain a thought. In this
case the process is conscious, but also unconscious or emotional interpretants are
widespread. Again, a person points (index) up at the sky and his companion looks
up (interpretant) to see the object of the sign. Someone else might call out “What
do you see up there?” that is also another interpretant of the original sign. As noted
by Brent “For Peirce, any appropriate response to a sign is acting as another sign of
the object originally signified. A sunflower following the sun across the sky with its
face is also an interpretant. Peirce uses the word interpretant to stand for any such
development of a given sign” [Brent, 2000, p. 12].
Semiosis is in itself a dynamic and interactive process that happens in time and
presupposes the notions of environment and agents. As anything can be seen as
a sign, the collection of potential signs may encompass virtually everything available within the agent, including all data gathered by its sensors. In the context of
the science of complexity semiosis can be depicted as an emergent property of a
semiotic system: emergent properties constitute a certain class of higher-level properties, related in a certain way to the microstructure of a class of system, that thus
become able to produce, transmit, receive, compute, and interpret signs of different
kinds. In this last sense they are more than simple reactive systems which in principle are not able to use something as a sign for something else [Gomes et al., 200;
Loula et al., 2009]. It has to be stressed that semiotic systems are obviously materially embodied because they can be only realized through physical implementation.
Finally, an interpretant may be the thought of another person, but may as well be
simply the further thought of the first person, for example in a soliloquy the succeeding thought is the interpretant of the preceding thought so that an interpretant is
both the interpretant of the thought that precedes it and the object of the interpretant
thought that succeeds it. In soliloquy sign, object, and interpretant are all present in
the single train of thought.
Interpretants, mediating between signs36 and their objects have three distinct levels in hierarchy: feelings, actions, and concepts or habits (that is various generalities
35
36
This kind of communication is studied in [Monekosso et al., 2004].
It has to be noted that for Peirce no sign is so general that it cannot be amended, hence all
general signs are to an extent incomplete. Consequently, a sign holds the chance of taking any
particular feature previously unknown to its interpreters, many of these new features remaining
inconsistent with other possibilities.
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as responses to a sign). They are the effect of a sign process. The interpretant produced by the sign can lead to a feeling (emotional interpretant), or to a muscular
or mental effort, that is to a kind of action – energetic interpretant (not only outward, bodily action, but also purely inward exertions like those “mental soliloquies
strutting and fretting on the stage of imagination” – [Colapietro, 2000, p. 142]. Finally, when it is related to the abstract meaning of the sign, the interpretant is called
logical,37 as a generalization requiring the use of verbal symbols. It is a further
development of semiosis in the hierarchy of iconic, enactive, and symbolic communication: in short, it is “an interpreting thought”, related for instance not only to the
intellectual activity but also to initiate the ethical action in so far as a “modification
of a person’s tendencies toward action” [Peirce, 1931-1958, 5.476].
The logical interpretants are able to translate percepts, emotions, unconscious
needs, and experience needs, and so to mediate their meanings to arrive to provisional stabilities. They can lead to relatively stable cognitive or intellectual habits
and belief changes as self-controlled achievements like many abductive conceptual
results, that Peirce considers the most advanced form of semiosis and the ultimate
outcome of a sign. Indeed abduction – hypothesis – is the first step toward the formation of cognitive habits: “[. . . ] every concept, every general proposition of the
great edifice of science, first came to us as a conjecture. These ideas are the first logical interpretants of the phenomena that suggested them, and which, as suggesting
them, are signs” [Peirce, 1931-1958, 5.480].38
Orthogonal to the classification of interpretants as emotional, energetic, and logical is the alternate classification given by Peirce: M. E. Q. Gonzalez and W. F. G.
Haselager interpretants can also be immediate, dynamic, and normal. Some interpreters consider this classification a different way of expressing the first one. It is
sufficient to note this classification can be useful in studying the formation of a subclass of debilitating and facilitating psychic habits [Colapietro, 2000, pp. 144–146]
and, I would add, of certain reasoning devices that are used by human agents.39 Colapietro proposes the concept of quasi-final interpretants – as related to the Peircean
normal interpretants – as “[. . . ] effective in the minimal sense that they allow the
conflict-ridden organism to escape being paralyzed agent: they permit the body-ego
to continue its ongoing negotiations with these conflicting demands, even if only
in a precarious and even debilitating manner. In brief, they permit the body-ego to
37
38
39
The logical interpretant is not “logical” in the sense in which deductive reasoning is studied by
a discipline called “logic”, but rather because it attributes a further meaning to the emotion or
to the mental effort that preceded it by providing a conceptual representation of that effort.
Habits also appear in organic and inorganic matter: “Empirically, we find that some plants take
habits. The stream of water that wears a bed for itself is forming a habit” [Peirce, 1931-1958,
5.492]. In human beings, it has to be stressed that Peirce’s habit is not a purely mental, rational,
or intellectual result of the semiotic process, but it is a mental representation that is always
connected to the somatic and motor level, and thus constitutively embodied. On the abductive
creative formation of habit as typical of self-organizing dynamic systems and processes, cf.
[Gonzalez and Haselager, 2005].
On the role of agency in distributed cognitive systems cf. also [Giere, 2006]. I have illustrated
the role of these kinds of – more or less conscious – reasoning processes in real “human-agents”,
as contrasted with the abstract templates of thinking as crystallized and stabilized in the socalled “ideal logical agents”, in [Magnani and Belli, 2006].
3.5 Model-Based Abduction and Semiosis beyond Peirce
171
go on” [Colapietro, 2000, p. 146]. For instance there are some sedimented unsconscious reactions of this type in immediate puzzling environments – later on useless
and stultifying in wider settings – but there also is the recurrent reflective and – provisionally – productive use of fallacious ways of reasoning like hasty generalizations
and other arguments [Woods, 2004].40
Some Peircean words about instinctual beliefs are very interesting and can be
stressed to further comprehend the character of the unconscious reactions above:
“[. . . ] our indubitable beliefs refer to a somewhat primitive mode of life” [Peirce,
1931-1958, 5.511] but it seems their authority is limited to that domain “While they
never become dubitable in so far as our mode or life remains that of somewhat primitive man, yet as we develop degrees of self-control unknown to that man, occasions
of actions arise in relation to which the original beliefs, if stretched to cover them,
have no sufficient authority” (ibid.).
3.5.2
Cultured Unconscious and External/Internal
Representations
In the perspective of the disembodiment of mind I have illustrated above in
section 3.3 we can also understand how both modern human beings and externalized
culture contain within them “implicit” traces of each of the previous stages of cognitive evolution. The first case of externalized distributed culture is evident: remains,
buildings, manuscripts, and so on, are fragments of ancient “cognitive niches” from
which we can retrieve cultural knowledge.
In the second case it can be hypothesized that much of what Freud attributes to
the unconscious is truly unconscious only in the cultural sense of the word, that is
formed by “things that are not expressed or are repressed at the level of culture”.
It has to be acknowledged that in recent cognitive science, and in the sense I have
attributed to it in the previous subsections on “man as an external sign” the unconscious is a solipsistic notion, not a cultural one and concerns a part of human mind
that is a priori outside the reach of consciousness, a golem, an “automaton world of
instincts and zombies”, like Donald eloquently says. An example is object vision:
“It serves up all the richness of the three-dimensional visual world of awareness,
gratis and fully formed. But we can never gain access to the mysterious region of
mind that delivers such images. It lies on the other side of cognition, permanently
outside the purview of consciousness” [Donald, 2001, pp. 286-287].
In the case of psychoanalysis unconscious is constructed by drives, intuitions,
and representations that are shaped by the brain/culture symbiosis and interplay and
so are not a priori inaccessible to awareness. It is interesting to remember that Jung
has also hypothesized the existence of a collective unconscious, that is that part of
individual unconscious we would share with others humans, shaped by the evolution
of the above interplay, which, so to say, “wired” in it archetypes, also very ancient,
that still would act in our present behavior. An example can be the “scapegoat”
mechanism, typical of ancient groups and societies, where a paroxysm of violence
40
Further details are illustrated in chapter seven of this book.
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would tend to focus on an arbitrary victim and a unanimous antipathy generated by
“mimetic desire” (and the related envy) would grow against him. The brutal elimination of the victim would reduce the appetite for violence that possessed everyone
a moment before, and leaves the group suddenly appeased and calm so granting the
equilibrium of the related social organization (for us repugnant, but not less useful
for those societies for this reason).41
Like Girard [1986] says, and many researchers maintain, this kind of archaic
brutal behavior, fruit of a conscious (at that time) cultural religious invention of our
ancestors is still present in civilized human conduct in rich countries, it is almost
always implicit and unconscious, for example in spontaneous and incognizant racist
and mobbing behaviors. Given the fact that these kinds of behavior are widespread
and partially unconsciously performed it is easy to understand how they can be
implicitly “learned” during infancy and then implicitly “wired” by the individual
in that cultured unconscious we humans collectively share with others. The result
is that they are there, available in our minds/brains, to be picked up and executed –
paradoxically, given the fact we are often convinced we are meant to be civil modern
human beings – as archaic forms of “social” behavior.
3.5.3
Duties, Abductions, and Habits
The Peircean theory of “habits” can help us understand duties as imposed on ourselves from a philosophical, evolutionary, and pragmatic viewpoint, a conception I
consider to be in tune with the idea of abduction that I am proposing in this chapter:
as I contended above, all semiotic experience – and thus abduction – also provides
a guide for action. For example, the logical interpretant, as a hypothetical fruit of
abductive thinking requiring the use of verbal symbols is in itself “an interpreting
thought”, related for instance not only to the intellectual activity but also to initiate
the ethical action in so far as a “modification of a person’s tendencies toward action” [Peirce, 1931-1958, 5.476]. Indeed the whole function of thought is to produce
habits of action, Peirce says that “[. . . ] conduct controlled by ethical reason tends
toward fixing certain habits of conduct, the nature of which [. . . ] does not depend
upon any accidental circumstances, and in that sense may be said to be destined”
[Peirce, 1931-1958, 5.430]. This philosophical attitude “[. . . ] does not make the
summum bonum to consist in action, but makes it to consist in that process of evolution whereby the existent comes more and more to embody those generals which
[. . . ] [are] destined, which is what we strive to express in calling them reasonable”
[Peirce, 1931-1958, 5.433]. This process, Peirce adds, is related to our “capacity
of learning”: increasing our “knowledge” will occur through time and generations,
“[. . . ] by virtue of man’s capacity of learning, and by experience continually pouring
over him” [Peirce, 1931-1958, 5.402 n. 2]. It is in this process of anthroposemiosis that civilization moves toward clearer understanding and greater reason. It is in
this process of anthroposemiosis, Peirce maintains, that we build highly beneficial
habits that help us to acquire various “ethical propensities”.
41
On this archaic mechanism and its effect in the violence that characterizes modern societies cf.
[Girard, 1977; Girard, 1986]. Cf. also subsection 8.6.2, chapter eight of this book.
3.5 Model-Based Abduction and Semiosis beyond Peirce
173
Not only abductions, but also reiterations originate ethical habits as logical interpretants, and in this case the interplay between internal and external representations
is still fundamental, related to the exercise of rational self-control and self-reproach
guilt feelings which can be further strengthened by direct commands to oneself:
“Reiterations in the inner world – fancied reiterations – if well-intensified by direct
effort, produce habits, just as do reiterations in the outer world; and these habits
will have power to influence actual behaviour in the outer world; especially, if each
reiteration be accompanied by a peculiar strong effort that is usually likened to issuing a command to one’s future self ” [Peirce, 1931-1958, 5.487]. Moreover, reiterations originate habits both through imaginary and actual exertions42 – for example
repeated outward actions – but also in a hybrid way, in the suitable combination
of the two (cf. above section 3.4, on the interplay between external and internal
representations).
Moreover, it may be useful to recall here what Peirce says about instinctual beliefs, we have already quoted above: “our indubitable beliefs refer to a somewhat
primitive mode of life” [Peirce, 1931-1958, 5.511], but their authority is limited
to such a primitive sphere. “While they never become dubitable in so far as our
mode of life remains that of somewhat primitive man, yet as we develop degrees
of self-control unknown to that man, occasions of action arise in relation to which
the original beliefs, if stretched to cover them, have no sufficient authority.” (ibid.)
The problem Peirce touches on here relates to the role of emotions in ethical reasoning: I agree with him that it is only in a constrained and educated – not primitive
– way that emotions like love, compassion, and good will, for example, can guide
us “morally.43
Anyway, a link between ethical rules and conventions and drives and instincts can
be hypothesized at a more basic level, as Damasio contends in the framework of a
neurological perspective: “Although such conventions and rules need be transmitted
only through education and socialization, from generation to generation, I suspect
that the neural representations of the wisdom they embody, and of the means to implement that wisdom, are inextricably linked to the neural representations of innate
regulatory biological processes” [Damasio, 1994, p. 125]. Of course in this perspective drives and instincts have to be considered not only innate but also acquired, like
in the case of educated emotions (cf. [Moorjani, 2000, p. 116]).
Natural entities exhibit different habits and various degrees, ways, and speeds
with which they abandon old habits and adopt (or integrate the old ones with) new
ones. Peirce says “The highest quality of mind involves greatest readiness to take
habits, and a great readiness to lose them” [Peirce, 1931-1958, 6.613]. Colapietro
observes that “[. . . ] this capacity entails a measure of consciousness below that of
the most acute sensations (e.g., intense pleasure or pain) but above that of our quasiautomatic reactions resulting from the unimpeded operation of effective habits in
familiar circumstances” [Colapietro, 2000, p. 139]. In this sense inanimate matter is
more reluctant than – for example – brains, to lose old habits and assume new ones,
42
43
“[. . . ] every sane person lives in a double world, the outer and the inner world, the world of
percepts and the world of fancies” [Peirce, 1931-1958, 5.487].
I defended this perspective in a recent book [Magnani, 2007d, chapter six].
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3 Semiotic Brains and Artificial Minds
but it is absolutely not exempt from habit-change. We must not forget that for Peirce
there is a real cosmic tendency to acquire novel dispositions that is extremely strong
in well encephalized human beings.44
The previous two sections have introduced to both the interplay between internal
and external representations and to some basic semiotic aspects of abductive reasoning: the following sections will take advantage of this background. I will describe
how the interplay of signs, objects, and interpretants is working in important aspects of abductive reasoning. Of course model-based cognition acquires its peculiar
creative relevance when embedded in abductive processes. I will show some examples of model-based inferences. It is well known the importance Peirce ascribed
to diagrammatic thinking (a kind of iconic thinking), as shown by his discovery of
the powerful system of predicate logic based on diagrams or “existential graphs”.
As I have already stressed, Peirce considers inferential any cognitive activity whatever, not only conscious abstract thought; he also includes perceptual knowledge
and subconscious cognitive activity. For instance in subconscious mental activities
visual representations play an immediate role [Queiroz and Merrell, 2005].
3.6
3.6.1
Constructing Meaning through Mimetic and Creative
External Objects
Constructing Meaning through Manipulative Abduction
Manipulative abduction occurs when many external things, usually inert from the
semiotic point of view, can be transformed into what in the first chapter I have
called, in the case of scientific reasoning, “epistemic mediators” (see also [Magnani, 2001b]) that give rise to new signs, new chances for interpretants, and new
interpretations.
We can cognitively account for this process of externalization45 taking advantage
of the concept of manipulative abduction (cf. chapter one section 1.6 and Figure
1.6.2). It happens when we are thinking through doing and not only, in a pragmatic
sense, about doing. It happens, for instance, when we are creating geometry constructing and manipulating an external suitably realized icon like a triangle looking
for new meaningful features of it, like in the case given by Kant in the “Transcendental Doctrine of Method” (cf. [Magnani, 2001c], and the following subsection). It
44
45
The idea of morality as “habit” – originated through the long negotiation between instinctual
impulses and the inescapable pressure of cultural practices – is also supported by James Q. Wilson in a strict Darwinian framework: “I am not trying to discover ‘facts’ that will prove ‘values’;
I am endeavoring to uncover the evolutionary, developmental, and cultural origins of our moral
habits and our moral sense.” He also argues for a biological counterpart that would facilitate the
formation of these habits. He continues “But in discovering these origins, I suspect we will encounter uniformities; and by revealing uniformities, I think that we can better appreciate what is
general, non-arbitrary, and emotionally compelling about human nature” [Wilson, 1993, p. 26].
I have illustrated above in this chapter a significant contribution to the comprehension of this
process in terms of the so–called “disembodiment of the mind”.
3.6 Constructing Meaning through Mimetic and Creative External Objects
175
refers to an extra–theoretical behavior that aims at creating communicable accounts
of new experiences to integrate them into previously existing systems of experimental and linguistic (semantic) practices. [Gooding, 1990] refers to this kind of concrete manipulative reasoning when he illustrates the role in science of the so-called
“construals” that embody tacit inferences in procedures that are often apparatus and
machine based. I have described them in chapter one, section 1.6.2.
It is difficult to establish a list of invariant behaviors that are able to describe
manipulative abduction in science.46 Even if abduction operates, like Peirce says,
according to the aesthetic process of musement: “a certain agreeable occupation
of the mind” [Peirce, 1992-1998, II, p. 436] which must follow “the very law of
liberty” [Peirce, 1931-1958, 6.458], as I have already illustrated above, the expert
manipulation of objects in a highly semiotically constrained experimental environment certainly implies the application of old and new templates of behavior that
exhibit some regularities.47 The activity of building construals is highly conjectural
and not necessarily or immediately explanatory: these templates are hypotheses of
behavior (creative or already cognitively present in the scientist’s mind-body system, and sometimes already applied) that abductively enable a kind of epistemic
“doing”. Hence, some templates of action and manipulation can be selected in the
set of the ones available and pre-stored, others have to be created for the first time
to perform the most interesting creative cognitive accomplishments of manipulative
abduction.
3.6.2
Manipulating Meanings through External Semiotic
Anchors
If the structures of the environment play such an important role in shaping our semiotic representations and, hence, our cognitive processes, we can expect that physical
manipulations of the environment receive a cognitive relevance.
Several authors have pointed out the role that physical actions can have at a cognitive level. In this sense Kirsh and Maglio [1994] distinguish actions into two categories, namely pragmatic actions and epistemic actions. Pragmatic actions are the
actions that an agent performs in the environment in order to bring itself physically
closer to a goal. In this case the action modifies the environment so that the latter
acquires a configuration that helps the agent to reach a goal which is understood as
physical, that is, as a desired state of affairs. Epistemic actions are the actions that
an agent performs in a semiotic environment in order to discharge the mind of a
cognitive load or to extract information that is hidden or that would be very hard to
obtain only by internal computation.
46
47
A list is provided in chapter one, section 1.6.2.
It is simple to explain why abduction works according to musement. This is the general attitude
we adopt when we are wondering about the beauty and the harmony of universes and their
connections [Peirce, 1992-1998, II, p. 436]. I think that beauty plays a kind of exciting emotional
role in abductive reasoning, very similar to the one played by anomalies and surprise. Cf. also
[Maddalena, 2005, p. 247].
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3 Semiotic Brains and Artificial Minds
In this subsection I want to focus specifically on the relationship that can exist
between manipulations of the environment and representations. In particular, I want
to examine whether external manipulations can be considered as means to construct
external representations.
If a manipulative action performed upon the environment is devoted to create a
configuration of signs that carries relevant information, that action will well be able
to be considered as a cognitive semiotic process and the configuration of elements it
creates will well be able to be considered an external representation. In this case, we
can really speak of an embodied cognitive process in which an action constructs an
external representation by means of manipulation. We define cognitive manipulating
as any manipulation of the environment devoted to construct external configurations
that can count as representations.
An example of cognitive manipulating is the diagrammatic demonstration illustrated in Figure 3.5, taken from the field of elementary geometry. In this case a
simple manipulation of the triangle in Figure 3.5(a) gives rise to an external configuration – Figure 3.5(b) – that carries relevant semiotic information about the internal
angles of a triangle “anchoring” new meanings.
Fig. 3.5 Diagrammatic demonstration that the sum of the internal angles of any triangle is
180. (a) Triangle. (b) Diagrammatic manipulation/construction.
The entire process through which an agent arrives at a physical action that can
count as cognitive manipulating can be understood by means of the concept of manipulative abduction. In this perspective manipulative abduction is a specific case
of cognitive manipulating in which an agent, when faced with an external situation
from which it is hard or impossible to extract new meaningful features of an object, selects or creates an action that structures the environment in such a way that
it gives new information which would be otherwise unavailable and which is used
specifically to infer explanatory hypotheses.
In this way the semiotic result is achieved on external representations used in
lieu of the internal ones. Here action plays an epistemic and not merely performatory role, for example relevant to abductive reasoning. The process also illustrates a synthesis between a constructive procedure of motor origin (the putting the
new segment end to end parallel to one side in the externally represented given
3.6 Constructing Meaning through Mimetic and Creative External Objects
177
triangle), followed by a sensory procedure, “visual” (calculation of the sizes of the
now clearly – externally – “seen” angles).48
It is important to note that in this manipulative and “multimodal”49 abductive
case abduction and induction play a role similar to the one described in the area of
logic programming: abductive reasoning extends the intension of known individuals
(because abducible properties are rendered true for these individuals, for example
by providing new situated “samples”, as “anchors” which offer chances for further
knowledge), without having a genuine generalization impact on the observables (it
does not increase their extension). Abductively building new situated results through
manipulation of the external diagram is in this case central to make possible an “induction” able to generate new general knowledge, not reachable through abduction
(on the variety of the roles played by induction in its interaction with abduction cf.
above the considerations I have illustrated at p. 14 and p. 30).
3.6.3
Geometrical Construction Is a Kind of Manipulatxive
Abduction
Let’s quote Peirce’s passage about mathematical constructions. Peirce says that
mathematical and geometrical reasoning “[. . . ] consists in constructing a diagram
according to a general precept, in observing certain relations between parts of that
diagram not explicitly required by the precept, showing that these relations will hold
for all such diagrams, and in formulating this conclusion in general terms. All valid
necessary reasoning is in fact thus diagrammatic” [Peirce, 1931-1958, 1.54]. This
passage clearly refers to a situation like the one I have illustrated in the previous
subsection. This kind of reasoning is also called by Peirce “theorematic” and it is
a kind of “deduction” necessary to derive significant theorems (Necessary Deduction]: “[. . . ] is one which, having represented the conditions of the conclusion in
a diagram, performs an ingenious experiment upon the diagram, and by observation of the diagram, so modified, ascertains the truth of the conclusion” [Peirce,
1931-1958, 2.267]. The experiment is performed with the help of “[. . . ] imagination upon the image of the premiss in order from the result of such experiment to
make corollarial deductions to the truth of the conclusion” [Peirce, 1976, IV, p. 38].
48
49
“The essential step in the construction of the Euclidean space, has been the possibility of the
division of a motor field; and here we come up against an evident physiological impossibility. Greek geometry resolved this problem of the division of a segment into equal segments
by the discovery of Thales’ Theorem: equidistant parallel lines cut two secants in proportional
segments” [Thom, 1980, p. 134]. Furthermore, following Thom, I think this ancient Greek geometry example already represents the quintessence of the scientific approach, that is “[. . . ]
replacing a non-local operation (for example, taking the intersection of two lines in a plane) by
a verbal description the formal analysis of which became the demonstration that it was virtually autonomous, that is, able to be rendered independent of the non-local intuitive approaches
which described it” [Thom, 1980, p. 135]. The use of literary symbols, which are empty of
sense, together with the axiomatic approach realizes the localization of the non-local intuition
of the plane (and of space).
Both propositional and model-based aspects are at play. On the concept of multimodal abduction
cf. this book, chapter four, section 4.1.
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3 Semiotic Brains and Artificial Minds
The “corollarial” reasoning is mechanical (Peirce thinks it can be performed by a
“logical machine”) and not creative, “A Corollarial Deduction is one which represents the condition of the conclusion in a diagram and finds from the observation
of this diagram, as it is, the truth of the conclusion” [Peirce, 1931-1958, 2.267] (cf.
also [Hoffmann, 1999]).
In summary, the point of theorematic reasoning is the transformation of the problem by establishing an unnoticed point of view to get interesting – and possibly new
– insights. The demonstrations of “new” theorems in mathematics are examples of
theorematic deduction.
Not dissimilarly Kant says that in geometrical construction of external diagrams
“[. . . ] I must not restrict my attention to what I am actually thinking in my concept
of a triangle (this is nothing more than the mere definition); I must pass beyond it to
properties which are not contained in this concept, but yet belong to it” [Kant, 1929,
A718-B746, p. 580].
Theorematic deduction can be easily interpreted in terms of manipulative abduction. We have seen that manipulative abduction is a kind of abduction, mainly
model-based, that exploits external models endowed with delegated (and often
implicit) cognitive and semiotic roles and attributes:
1. the model (diagram) is external and the strategy that organizes the manipulations is unknown a priori;
2. the result achieved is new (if we, for instance, refer to the constructions of
the first creators of geometry), and adds properties not contained before in the
concept (the Kantian to “pass beyond” or “advance beyond” the given concept
[Kant, 1929, A154-B193/194, p. 192]).50
Iconicity in theorematic reasoning is central. Peirce, analogously to Kant,
maintains that “[. . . ] philosophical reasoning is reasoning with words; while theorematic reasoning, or mathematical reasoning is reasoning with specially constructed schemata” [Peirce, 1931-1958, 4.233]; moreover, he uses diagrammatic
and schematic as synonyms, thus relating his considerations to the Kantian tradition
where schemata mediate between intellect and phenomena.51 The following is the
famous related passage in the Critique of Pure Reason (“Transcendental Doctrine
of Method”):
Suppose a philosopher be given the concept of a triangle and he be left to find out, in
his own way, what relation the sum of its angles bears to a right angle. He has nothing
but the concept of a figure enclosed by three straight lines, and possessing three angles.
However long he meditates on this concept, he will never produce anything new. He
can analyse and clarify the concept of a straight line or of an angle or of the number
three, but he can never arrive at any properties not already contained in these concepts.
50
51
Of course in the case we are using diagrams to demonstrate already known theorems (for instance in didactic settings), the strategy of manipulations is not necessary unknown and the
result is not new, like in the Peircean case of corollarial deduction.
Schematism, a fruit of the imagination is, according to Kant, “[. . . ] an art concealed in the
depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us
to discover, and to have open to our gaze” [Kant, 1929, A141-B181, p. 183].
3.6 Constructing Meaning through Mimetic and Creative External Objects
179
Now let the geometrician take up these questions. He at once begins by constructing a
triangle. Since he knows that the sum of two right angles is exactly equal to the sum of
all the adjacent angles which can be constructed from a single point on a straight line,
he prolongs one side of his triangle and obtains two adjacent angles, which together
are equal to two right angles. He then divides the external angle by drawing a line
parallel to the opposite side of the triangle, and observes that he has thus obtained
an external adjacent angle which is equal to an internal angle – and so on.52 In this
fashion, through a chain of inferences guided throughout by intuition, he arrives at a
fully evident and universally valid solution of the problem [Kant, 1929, A716-B744,
pp. 578-579].
We can depict the situation of the philosopher described by Kant at the beginning
of the previous passage taking advantage of some ideas coming from the catastrophe theory (cf. also this book, chapter eight). As a human being who is not able to
produce anything new relating to the angles of the triangle, the philosopher experiences a feeling of frustration (just like the Kölher’s monkey which cannot keep the
banana out of reach). The bad affective experience “deforms” the organism’s regulatory structure by complicating it and the cognitive process stops altogether. The
geometer instead “at once constructs the triangle”, that is, he makes an external representation of a triangle and acts on it with suitable manipulations. Thom thinks that
this action is triggered by a “sleeping phase” generated by possible previous frustrations which then change the cognitive status of the geometer’s available and correct
internal idea of triangle (like the philosopher, he “has nothing but the concept of a
figure enclosed by three straight lines, and possessing three angles”, but his action
is triggered by a sleeping phase). Here the idea of the triangle is no longer the occasion for “meditation”, “analysis” and “clarification” of the “concepts” at play, like
in the case of the “philosopher”. Here the inner concept of triangle – symbolized
as insufficient – is amplified and transformed thanks to the sleeping phase (a kind
of Kantian imagination active through schematization) in a prosthetic triangle to be
put outside, in some external support. The instrument (here an external diagram)
becomes the extension of an organ:
What is strictly speaking the end [. . . ] [in our case, to find the sum of the internal
angles of a triangle] must be set aside in order to concentrate on the means of getting
there. Thus the problem arises, a sort of vague notion altogether suggested by the state
of privation. [. . . ] As a science, heuristics does not exist. There is only one possible
explanation: the affective trauma of privation leads to a folding of the regulation figure.
But if it is to be stabilized, there must be some exterior form to hold on to. So this
anchorage problem remains whole and the above considerations provide no answer as
to why the folding is stabilized in certain animals or certain human beings whilst in
others (the majority of cases, needless to say!) it fails [Thom, 1988, pp. 63–64].53
52
53
It is Euclid’s Proposition XXXII, Book I, cf. above Figure 3.5.
A full analysis of the Kölher’s chimpanzee getting hold of a stick to knock a banana hanging out
of reach in terms of the mathematical models of the perception and the capture catastrophes is
given in [Thom, 1988, pp. 62–64]. On the role of emotions, for example frustration, in scientific
discovery cf. [Thagard, 2002b].
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As we have already said, for Peirce the whole mathematics consists in building diagrams that are “[. . . ] (continuous in geometry and arrays of repeated signs/letters in
algebra) according to general precepts and then [in] observing in the parts of these
diagrams relations not explicitly required in the precepts” [Peirce, 1931-1958, 1.54].
Peirce contends that this diagrammatic nature is not clear if we only consider syllogistic reasoning “which may be produced by a machine” but becomes extremely
clear in the case of the “logic of relatives, where any premise whatever will yield an
endless series of conclusions, and attention has to be directed to the particular kind
of conclusion desired” [Peirce, 1987, pp. 11–23].
In ordinary geometrical proofs auxiliary constructions are present in terms of
“conveniently chosen” figures and diagrams where strategic moves are important
aspects of deduction. The system of reasoning exhibits a dual character: deductive
and “hypothetical”. Also in other – for example logical – deductive frameworks
there is room for strategic moves which play a fundamental role in the generations of proofs. These strategic moves correspond to particular forms of abductive
reasoning.
We know that the kind of reasoned inference that is involved in creative abduction
goes beyond the mere relationship that there is between premises and conclusions
in valid deductions, where the truth of the premises guarantees the truth of the conclusions, but also beyond the relationship that there is in probabilistic reasoning,
which renders the conclusion just more or less probable. On the contrary, we have
to see creative abduction as formed by the application of heuristic procedures that
involve all kinds of good and bad inferential actions, and not only the mechanical
application of rules. It is only by means of these heuristic procedures that the acquisition of new truths is guaranteed. Also Peirce’s mature view illustrated above on
creative abduction as a kind of inference seems to stress the strategic component of
reasoning.
Many researchers in the field of philosophy, logic, and cognitive science have
maintained that deductive reasoning also consists in the employment of logical
rules in a heuristic manner, even maintaining the truth preserving character: the application of the rules is organized in a way that is able to recommend a particular
course of actions instead of another one. Moreover, very often the heuristic procedures of deductive reasoning are performed by means of model-based abductive
steps where iconicity is central.
We have seen that the most common example of manipulative creative abduction
is the usual experience people have of solving problems in geometry in a modelbased way trying to devise proofs using diagrams and illustrations: of course the
attribute of creativity we give to abduction in this case does not mean that it has
never been performed before by anyone or that it is original in the history of some
knowledge (they actually are cases of Peircean corollarial deduction).54
54
We have to say that model-based abductions – which for example exploit iconicity – also operate
in deductive reasoning. On the role of strategies and heuristics in deductive proofs cf. chapter
seven, section 7.3.2.
3.6 Constructing Meaning through Mimetic and Creative External Objects
3.6.3.1
181
Theoric Reasoning and Creativity
I think the previous considerations concerning manipulative abduction also hold for
Peircean theorematic reasoning. Let us quote again the important Peirce’s passage
about theorematic reasoning:
A Necessary Deduction is a method of producing Dicent Symbols55 by the study of a
diagram. It is either Corollarial or Theorematic. A Corollarial Deduction is one which
represents the conditions of the conclusion in a diagram and finds from the observation
of this diagram, as it is, the truth of the conclusion. A Theorematic Deduction is one
which, having represented the conditions of the conclusion in a diagram, performs an
ingenious experiment upon the diagram, and by the observation of the diagram, so
modified, ascertains the truth of the conclusion [Peirce, 1931-1958, 2.267].
As I have already indicated Peirce further distinguished a “corollarial” and a “theoric” part within “theorematic reasoning”, and connected theoric aspects to abduction [Hoffmann, 1999, p. 293]: “Thêoric reasoning [. . . ] is very plainly allied
to” what is normally called abduction [Peirce, 1966, 754, ISP, p. 8]. Indeed theoric reasoning is considered a kind of creative diagrammatic reasoning: following
[Hoffmann, 2003, p. 167] we can say that it
[. . . ] is based on just the same idea, which is the idea of “the transformation of the
problem, – or its statement,– due to viewing it from another point of view” [Peirce,
1966, 1907, 318; CSP, p. 68; ISP, p. 225]. Peirce takes the term “theoric” from the
(theory) which he translates as ‘the power of looking at facts from a novel
Greek
point of view’ [Peirce, 1966, 1907, 318; CSP, p. 50; ISP, p. 42]. For Peirce, the most
important discoveries in mathematics are also based on reaching new perspectives, as
he shows in his 1907 manuscript about “Pragmatism” with the example of the proof of
the “ten points theorem”.
In a passage of the manuscripts not contained in the microfilm edition, quoted by
[Hoffmann, 2003, p. 293],56 Peirce clearly states his own surprise at seeing retroduction (that is abduction) at work in a non empirical science, like mathematics,
where new results are reached through an abductive reasoning that strangely leads
to indisputable achievements.
Further study, however, leads me to lop off/discard a corollarial part from/of the Theorematic Deductions, which follows that which originates a new point of view. I will
call this part of the theorematic procedure, thêoric reasoning. It is very plainly allied to
retroduction, from which it only differs, as far as I now see, in that it is “indisputable”
[Peirce, 1966, 754; ISP, p. 8].
I think Peirce is referring here to the creative and non-explanatory side of what I
have called manipulative abduction. Indeed he also said he “[. . . ] would regard the
great hypotheses of pure mathematics [. . . ] as coming to us through retroduction
55
56
A dicent symbol (such as a proposition or a description) is a sign which may be interpreted to
refer to an actually existing object.
Already indicated by [Levy, 1997, p. 106] and [Levy, 1997, p. 482].
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3 Semiotic Brains and Artificial Minds
from considering what for want of a better word I may call the facts of mathematics” [Peirce, 1966, 754; ISP, p. 3]. I wholeheartedly agree with Peirce’s following
observation, written about a century before the new perspective on mathematical
reasoning offered by Lakatos’s work [1976]: “It has long been a puzzle how it could
be that, on the one hand, mathematics is purely deductive in nature, and draws its
conclusions apodictically, while in the other hand, it presents as rich and apparently
unending a series of surprising discoveries as any observational science” [Peirce,
1931-1958, 1885, 3.363].
Of course, as already stressed, we have to remember this abductive aspect of
mathematical reasoning can be performed both in creative [theorematic] (to find
new theorems and mathematical hypotheses) and non creative [corollarial] (merely
“selective”) ways, for example in the case that we are using diagrams to demonstrate already known theorems (for instance in didactic settings), where selecting
the strategy of manipulations is among chances not necessarily unknown and where
the result is not new. With respect to abduction in empirical science abduction in
mathematics aims at hypothesizing ideal objects, which later we can then possibly
insert into a deductive apodictic and truth preserving framework.57
The epistemological situation of this geometrical example is similar to the one I
have illustrated in the last sections of chapter two, concerning the analysis in terms
of abduction of the non-Euclidean discovery:
1. the inferential process is a kind of manipulative and model-based abduction
(visual), first of all endowed with an explanatory character: the abduced mirror diagrams of the triangle furnishes a visual explanation/description of our
internal representation of it;
2. at the same time the external image, and the construction based on it offer the
chance of a further multimodal and distributed abductive step (based on both
internal and external representations, and on both visual and sentential aspects)
mainly non-explanatory and instrumental. This further abductive process makes
possible to derive the new “indisputable” result/theorem of the sum of the internal angles of a triangle.
Finally, the example of diagrams in geometry furnishes a semiotic and epistemological example of the nature of the cognitive interplay between internal neuronal
representations (and embodied “cognitive” kinesthetic and motor abilities) and external representations I have illustrated above: also for Peirce, more than a century
before the new ideas derived from the field of distributed cognition, the two aspects
are intertwined in the pragmatic and semiotic view, going beyond the rigidity of the
Kantian approach in terms of schematism. Diagrams are icons that take material and
semiotic form in an external environment endowed with
57
In a recent analysis of further aspects of the relationship between abduction and the inference
to the best explanation, [Minnameier, 2004, p. 85] contends theorematic deduction should be
basically considered an inverse deduction, that is “[. . . ] an inference not from the premises of
ordinary deduction (which Peirce terms ‘corollarial’) to the conclusion, but from the (prospective) conclusion to the premises of the deductive argument from which the conclusion follows”.
I am inclined to think this interpretation underestimates the role played by the creative side
(theoric) in theorematic reasoning, and its manipulative character.
3.6 Constructing Meaning through Mimetic and Creative External Objects
183
- constraints depending on the specific cognitive delegation performed by human
beings and
- the particular intrinsic constraints of the materiality at play.58
Concrete manipulations on them can be done for instance to get new data and cognitive information and/or to simplify the problem at issue (cf. the epistemic templates
illustrated above in subsection 3.6.1).
3.6.4
The Semiosis of Re-embodiment and Its Sensorimotor
Nature
Some interesting semiotic aspects of the above illustrated process can be nicely
analyzed. Imagine that a suitable fixed internal record exists – deriving from the
cognitive exploitation of the previous suitable interplay with external structures –
at the level of neural activation and that for instance it embeds an abstract concept
endowed with all its features, for example the concept of triangle. Now, the human
agent, via neural mechanisms and bodily actions, can “re-embody” that concept by
making an external perceivable sign, for instance available to the attention of other
human or animal senses and brains. For instance that human agent can use what in
semiotics is called a symbol (with its conventional character: ABC, for example), but
also an icon of relations (a suitable diagram of a triangle), or a hybrid representation
that will take advantage of both. In Peircean terms:
A representation of an idea is nothing but a sign that calls up another idea. When one
mind desires to communicate an idea to another, he embodies his idea by making an
outward perceptible image which directly calls up a like idea; and another mind perceiving that image gets a like idea. Two persons may agree upon a conventional sign
which shall call up to them an idea it would not call up to anybody else. But in framing
the convention they must have resorted to the primitive diagrammatic method of embodying the idea in an outward form, a picture. Remembering what likeness consists
in, namely, in the natural attraction of ideas apart from habitual outward associations,
I call those signs which stand for their likeness to them icons.
Accordingly, I say that the only way of directly communicating an idea is by mean
of an icon; and every indirect method of communicating an idea must depend for its
establishment upon the use of an icon [Peirce, 1966, 787, 26–28].
We have to note that for Peirce an idea “[. . . ] is not properly a conception, because a
conception is not an idea at all, but a habit. But the repeated occurrence of a general
idea and the experience of its utility, results in the formation or strengthening of that
habit which is the conception” [Peirce, 1931-1958, 7.498].
Habits, as beliefs and vehicles of cognition and at the same time anticipation of
future chances for action, are usually considered bodily states in so far as they are,
according to Peirce, comparable to “dispositions” [Peirce, 1931-1958, 5.440]. In the
58
An admirable analysis of the constraints intrinsic to the external material exploited by the ancient Greek mathematicians (especially geometricians) is given in [Netz, 1999]. The book also
illustrates the most important semiotic tools at work in ancient Greek mathematical reasoning.
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light of the cognitive interplay internal/external I have described above it is better
to interpret them as forms of interaction with the suitable circumstances involved in
the related action, as [Määttänen, 2009] stresses. In this perspective perception and
action are strictly intertwined simply as different degrees of interaction with the environment: in action “our modification of other things is more prominent that their
reaction on us” as compared to perception “where their effect on us is overwhelmingly greater than our effect on them” [Peirce, 1931-1958, 1.324].
Of course what is external to the body is not necessarily external to the process
realizing cognition and basically resorts to “sensorimotor” representations that are
created or re-activated (if already formed and stable) during the interaction with
the physical world.59 Nevertheless, very often a considerable part of the cognitive
process occurs outside, thanks to the suitable materiality endowed with contingent
cognitive delegations. It is in this sense that the possible establishment of a habit is in
itself also the institution of new meanings. As maintained by Peirce, acquired habits
are in themselves meanings, being the result of interactions with the environment
they are not literally only in the head but also intertwined with motor action: they are
embodied. “Sensory inputs [we could add: that are abductively matched to a suitable
habit] are associated not only with each other but also, and more importantly, with
neural mechanisms controlling overt motor action” [Määttänen, 1997; Määttänen,
2009].
Peirce pays much attention to interactional play when dealing with consciousness
and “Secondness”:
We are continually bumping up against hard fact. We expect one thing, or passively
take it for granted, having the image of it in our minds, but experience then forces
that idea into the background, and compels us to think quite differently. You get this
kind of consciousness in some approach to purity when you put your shoulder against
a door and try to force it open. You have a sense of resistance and at the same time
a sense of effort. There can be no resistance without effort; there can be no effort
without resistance. They are only two ways of describing the same experience. It is a
double consciousness. We become aware of ourselves in becoming aware of the notself. The waking state is a consciousness of reaction and, as consciousness itself is
two-sided, it has two varieties: namely, action, where our modification of other things
59
[Noë, 2005; Noë, 2006] and other researchers like K. O’Regan [O’Regan and Noë, 2001] and
S. Hurley propose a sensorimotor theory of perception that challenges its merely traditional
representational character: perceptual experience – and so visual system – is fundamentally
structured (even if not caused) by our sensorimotor competence, which allows us to access the
world and to act. In the first case [Fusaroli, 2007; Fusaroli and Vandi, 2009] contend that the
traditional concept of “representation” can be either rejected or it can acquire a new operational
status. In this case, perception is taken as direct access to the world and representations do not
play any role; the world would serve as its own representation and as an external memory, as
is similarly contended by researchers in the field of active vision (cf. above section 3.4.1); in
the latter case – action – it is the “body” of the human being or of the animal that governs
the entire cognitive process of externalization/re-embodiment and that furnishes the suitable
final “meaning” and interpretation. On the sensorimotor theory of perception as contrasted to
the explanation of perception as inner encoding cf. the deep and rich considerations given by
[Clark, 2008, chapters seven and eight]: Clark eloquently label these approaches “strongly”
sensorimotor models of perception (SSM).
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185
is more prominent than their reaction to us, and perception, where their effect on us
is overwhelmingly greater than our effect on them. This notion, of being what other
things make us, is such a prominent part of our life that we also conceive other things to
exist by virtue of their reactions against each other. The idea of other, of not, becomes
central to our thinking. To this element I give the name of Secondness [Peirce, 19311958, 1.324].
The process of re-embodiment concerns the formation of internal “mental” representations (as mere brain states) which are also strictly intertwined with motor
aspects, at both the neural and the somatic level. From this perspective the world
is experienced as giving various opportunities to carry out “habitual” actions, that
is it provides what Gibson calls affordances: habits of action abductively “reveal”
affordances.60
This is the correct sense in which we can say that cognition is “embodied”, as
“the sharing of neural mechanisms between sensorimotor processes and higherlevel cognitive processes”: many, if not all, higher-level cognitive processes seem
body-based in the sense that “they make use of (partial) emulations or simulations
of sensorimotor processes through the reactivation of neural circuitry that is also
active in bodily perception and action” [Svensson and Ziemke, 2004, p. 1309], as
already stressed by the theory of autopoiesis (self-organization) put forward by
Maturana and Varela [Maturana and Varela, 1980; Varela et al., 1991]. The traditional distinction between perception and action as well as between sensorimotor
and cognitive processes has to be given up: the same neural structures that are at the
basis of actions and/or perception would also be exploited in the performance of various cognitive tasks. Empirical data have suggested that perceptual and motor areas
of the brain can be covertly activated either separately or in sequence, for example
there are similarities between the neural structures activated during preparation and
execution of an action and those employed in its mental simulation through what
is called motor imagery, as well as in the case of perception and visual imagery (it
is easy to suppose that in both cases the same representational formats are at play,
so this does not need to resort to the computer metaphor of internal symbol manipulation). Simulating an action involves some simulator [Barsalou et al., 2003;
Decety, 1996; Decety and Grèzes, 2006; Frith and Dolan, 1996; Hesslow, 2002;
Jeannerod, 2001] (or emulator [Grush, 2004a; Grush, 2007]) devices that abductively anticipate the perceptual feedback that would have occurred in the case of the
executed action.61
Research on neurons located in the rostral part of the inferior premotor cortex
(area F5) has demonstrated that they discharge and respond to goal directed actions
such as grasping, holding, or tearing that have the same meaning. They are interpreted as internal representations of action, rather than motor or movement commands. Some of those neurons, which are called canonical neurons, discharge both
60
61
A full treatment of the concept of affordance in its relationship with abduction is given in chapter
six.
[Pickering and Garrod, 2006] further stress that in the case of language, comprehenders use
prediction and imitation to construct an “emulator” using the production system, and combine
predictions with the input dynamically.
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during the action they code and when an object affords that action, so that it can
be said they express affordances coding for example the graspability of things from
both the perceptual and the action perspectives; consequently they account for a basic link between an agent and its environment. Internally reactivated perceptions and
actions are also at play 1) in the case of various inner planning and problem solving
performances [Dagher et al., 1999; Hesslow, 2002], and (2) in social cognition (especially emotive states based on social stimuli), where simulation of “bodily states”
occurs: they are not conscious mediating knowledge structures, but they affect higher
cognition [Barsalou et al., 2003]. F5 also contains the well-known “mirror neurons”
that become activated both when performing a specific action and when observing
the same goal-directed hand (or mouth) movements of an experimenter.62 They provide a clear example of sensorimotor brain parts performing a resonance task devoted to both performing and understanding actions.
It is well-known that for Peirce every picture is an icon and thus every diagram,
even if it lacks a sensuous similarity with the object, but just exhibits an analogy
between the relations of the part of it and of the object:
All iconic signs, like diagrams, rarely function as pure icons: symbolic aspects are
often at stake and background knowledge of such conventions is necessary to obtain
the desired information. Particularly deserving of notice are icons in which the likeness
is aided by conventional rules. Thus, an algebraic formula is an icon, rendered such by
the rules of commutation, association, and distribution of the symbols; that it might
as well, or better, be regarded as a compound conventional sign. It may seem at first
glance that it is an arbitrary classification to call an algebraic expression an icon. But
it is not so. For a great distinguishing property of the icon is that by direct observation
of it other truths concerning its object can de discovered than those which suffice to
determine its construction. Thus, by means of two photographs a map can be drawn,
etc. Given a conventional or other general sign of an object, to deduce any other truth
than which it explicitly signifies, it is necessary, in all cases, to replace that sign by an
icon. This capacity of revealing unexpected truth is precisely that wherein the utility of
algebraic formulae consists, so that the icon in character is the prevailing one [Peirce,
1966, 787, CSP 26–28].
Stressing the role of iconic dimensions of semiosis63 in the meantime celebrates
the virtues of analogy, as a kind of “association by resemblance”, as contrasted to
“association by contiguity”.
[Stenning, 2000] provides an indepth philosophical and cognitive analysis of diagrammatic reasoning which further clarifies the Peircean observation above about
the fact that algebraic formulas can be considered icons. He acknowledges that homomorphism – which resorts to “likeness” – between diagrams and their referents
is what distinguishes diagrammatic semantics from sentential semantics. From a
Peircean perspective languages are fundamentally symbolic and have indexical aspects, and diagrams – which are of course iconic – also contain symbolic elements
such as words, often indexically related to their reference like labels by spatial
62
63
On the role of mirror neurons in social cognition cf. chapter four, section 4.3.2.
We have to remember that in this perspective any proposition is a diagram as well, because it
represents a certain relation of symbols and indices.
3.6 Constructing Meaning through Mimetic and Creative External Objects
187
deixis. Stenning proposes a new distinction that is intertwined with the Peircean one
but avoids some of its problems: we have to distinguish between direct interpretation
(for diagrammatic semantics) and indirect interpretation (for sentential semantics).
In this last case the interpretation is indirect because between representation and
the referenced world an abstract syntax based on concatenation is interposed: “The
interpretation is indirect because the significance between two elements being spatially [in written language] or temporally [in spoken language] concatenated cannot
be assessed without knowing what abstract syntactic relation holds between them”
[Stenning, 2000, p. 136].
Some two-dimensional representation systems, like semantic networks and conceptual graphs, are close to language systems because they have a semantics that
interposes an abstract syntax. For example Peirce clearly stated that syntactic relations in a language with an abstract syntax could be iconic, like in the case of
algebraic relations that represent transitivity iconically (cf. the quotation above).
Some interesting differences between sentential and diagrammatic reasoning
have to be pointed out. [Shin, 2002] has demonstrated that Peircean existential
graphs (that lack connectives) can have multiple equivalents in sentential calculi
with connectives, just like the fact that two sentences are translations of the same
existential graph demonstrates they are logically equivalent. Moreover, sentential
graphs are written from left to right while existential graphs do not have this rigid
layout. Sentential representation systems use sentences discursively (when a conclusion is drawn from earlier sentences, it is rewritten on a new line of results), but
diagrammatic systems are often used and represented agglomeratively (in diagrams
all the icons are automatically related to each other by all the interpreted spatial relations and if a new assumption is made, it is represented in the particular existential
graph at play). The inferences in the diagram are made by modifying the “individual” existential graph, in this way giving rise to a derivation. In this last case history
is erased (history in sentential representation systems is very much needed because
it guarantees the legitimacy of later inferences). [Of course the derivations can be
expressed by drawing diagrams in a sequence or as a tree]. In the case of Euler diagrams they have to be used in an agglomerative mode that preserves history but they
do not present inferences because of the lack of diagram combinations.
The interplay between indirect interpretation (discursive use) and direct interpretation (agglomerative use) can help exceed their relative limits, as is clearly seen in
the case of some geometrical diagrammatic proof, that appears neither useless nor
adequate. Proof without words can be justified in a static diagram unaccompanied
by words and can be directly interpreted and agglomeratively used as in the case of
the diagrammatic proof contained in a single diagram of the Pythagoras theorem.
But what about the statement of the theorem?
If we do not know what the Pythagoras’ theorem is, we are unlikely to find it in this
diagram. Even if we know that it is about triangles, there are still many triangles to
choose from in the figure and no indication which is the topic of the theorem. To even
state Pythagoras’ theorem requires a representation system that can provide only part
of the truth about right angled triangles. In particular, a representation system that can
represent the square of the hypotenuse without representing the rest (especially the
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sum of squares on the other two sides) and v.v.; and can represent the equality of areas between these two entities. Only indirectly interpreted systems with their syntactic
articulation can do this. On the other hand, proof without words can supply a kind of
insight into proof which sentential proof finds it hard to match. Proof-without words
can be sequentialised, after a fashion, by providing a kind of “comic-strip” animation
of a sequence of constructions. This however raises problems about which inferences
and constructions are to count as “formal” [. . . ] It is intriguing that an interaction between diagrams and language appears to have been what gave rise to the first invention
of Greek geometry [Stenning, 2000, pp. 147–148] .64
[Clark, 2006, p. 371] has recently stressed the cognitive role in mathematics of “tokening” numerical expressions in some way, as symbol strings of our own public
language so that human arithmetic thinking is de facto hybrid, made up of a combination of this tokening and the activation of some basic biological/neurological
resources.65
Human beings delegate cognitive features to external representations through
semiotic attributions because for example in many problem solving situations the
internal computation would be impossible or it would involve a very great effort
because of human mind’s limited capacity. First a kind of “alienation” is performed,
second a recapitulation is accomplished at the neuronal level by re-representing internally that which was “discovered” outside. Consequently only later on do we internally perform cognitive operations on the structure of data that synaptic patterns
have “picked up” in an analogical way from the environment. We can maintain that
internal representations used in cognitive processes like many events of meaning
creation have a deeper origin in the experience lived in the semiotic environment.
[Hutchins, 2005, p. 1575] further clarifies this process of recapitulation: “[. . . ] when
a material structure becomes very familiar, it may be possible to imagine the material structure when it is not present in the environment. It is even possible to imagine
systematic transformations applied to such a representation. This happened historically with the development of mathematical and logical symbol systems in our own
cultural tradition”.
As we will see in chapter six, in this interplay of re-embodiment diagrams “afford” some actions as being possible and the embodied result can be considered as
the establishment of a habit, in a Peircean sense, not only a theoretical result but
also a kind of “know how”: “We imagine cases, place mental diagrams before our
mind’s eye, and multiply these cases, until a habit is formed of expecting what always turns out the case, which has been seen to be the result in all the diagrams.
To appeal to such a habit is a very different thing from appealing to any immediate
instinct of rationality. That the process of forming a habit of reasoning by the use of
64
65
On the interplay between spatial convention of order preference and various kinds of formal
knowledge cf. [Landy and Goldstone, 2007b; Landy and Goldstone, 2007a]. This perspective
further challenges the conception that human reasoning with formal systems exploits only the
formal properties of symbolic notations: people also use other regularities, formal, visual, diagrammatic, rule-based, and statistical.
On the role of external symbols and natural language in mathematical discovery and reasoning
cf. also [Dehaene, 1997; Dehaene et al., 1999].
3.6 Constructing Meaning through Mimetic and Creative External Objects
189
diagrams is often performed there is no room for doubt” [Peirce, 1931-1958, 2.170].
D. Landy and R. L. Goldstone
I already illustrated in section 3.4 that I think there are two kinds of artifacts that
play the role of external objects (representations) active in this process of externalization of the mind: creative and mimetic. Mimetic external representations mirror
concepts and problems that are already represented in the brain and need to be enhanced, solved, further complicated, etc. so they sometimes can creatively give rise
to new concepts and meanings.
Following my perspective it is at this point evident that the “mind” transcends the
boundary of the individual and includes parts of that individual’s environment. It is
in this sense that the mind is constitutively semiotic and artificial.
3.6.5
On-line and Off-line Intelligence Intertwined: The Problem
of Language and of Inner Rehearsal
I have said above in subsection 3.6.2 that the entire process through which an agent
arrives at a physical action – that counts as a more or less creative cognitive manipulating – can be understood by means of the concept of manipulative abduction.
In this case the agent, when faced with an external situation from which it is for
example hard or impossible to extract new meaningful cognitive features of a concept, selects or creates an action that structures a mimetic representation referring
to the concept in the environment in such a way that it can give information, which
would be otherwise unavailable and which is used specifically to infer hypotheses.
Moreover, as subsequently illustrated in the previous subsection, I have stressed the
fact that in this interplay first a kind of “alienation” is performed, and second a recapitulation is accomplished at the neuronal level by re-representing internally that
which was “discovered” outside. [Dartnall, 2005, p. 136] says that in this case the
“world leaks into the mind”.
Only later on the agent internally performs cognitive operations on the structure of data that synaptic patterns have “picked up” in an analogical way from the
mimetic representation stored in the environment. I have already said that it is possible to conclude that internal representations exploited in cognitive processes like
many events of meaning creation have a deep origin in the experience lived in the
semiotic environment.66
Following Clark’s perspective on language as an external tool [Clark, 1997]
Wheeler qualifies the double process above speaking of on-line – like in the case
of manipulative abduction – and off-line thinking (also called inner rehearsal). Language is inner: “[. . . ] just so long as there are private thought processes which are
66
The process can be accounted for in terms of the emulation theory which in such a way nicely
complements the extended mind thesis: “If something counts as cognitive when it is performed
in the head, it should also count as cognitive when it is performed in the world (mind leaks into
the world). Also, if a process gives us an empirical discovery when it is performed in the world,
it will also give us an empirical discovery when it is performed in the head (the world leaks into
the mind)” [Dartnall, 2004, p. 402].
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formulated in language” [Wheeler, 2004, p. 699] in these processes no languagespecific computational device is used, but just “[. . . ] the brain’s basic modes of representation and computation” [Clark, 1997, p. 198]. A true situation of distributed
cognition is occurring in the case of on-line thinking, like in our case of manipulative abduction and in other less expert and less creative cases, where the resources
are not merely inner (neural) and embodied, but hybridly intertwined with the environment: in this case we come face to face with an abductive/adaptive process
produced in the dynamical inner/outer coupling where internal elements are “directly causally locked onto the contributing external elements” [Wheeler, 2004, p.
705].
It is extremely important to note that both sides of the process contribute to the
result: both intrinsic inner and outer constraints. For example in the case of language
learning and rehearsed recapitulation, external signs and symbols are needed, but so
too are the “productive internal capacities” to contribute to its aspects of infinite
productivity and systematicity that perform the language-like combinatorial syntax.67 Through re-embodiment I have illustrated above that the inner aspect (inner
rehearsal, when for instance we make an arithmetical addition internally projecting
the arithmetical written standard method on our “visual buffer”, or when conversing
with ourselves) can run alone and disentangle itself from the perception-action cycle
typical of on-line thinking, by means of mere pattern-completion neural resources
amenable to connectionist modelling (cf. above section 3.4). In this case inner representations, like for example perceptually-based visual, auditory, kinesthetic, motor,
etc. imageries, fruit of a suitable past training of neural networks due to previous
on-line processes, can furnish the necessary internal surrogate structures.
The origin of these inner representational structures can be accounted for by remembering how Brooks once fundamentally observed that at the root of the more
basic forms of cognition it can be hypothesized that the “world serves as its own
best model” [Brooks, 1991, p. 145]. [Thomas, 1999] says than rather than storing
inner analogues from the external world, human brains generate them by running
their perceptual abilities off-line. [Logan, 2006, p. 150] – following [Donald, 2001]
– also speculates that “[. . . ] as a starting point it was assumed that before the advent of speech hominid thought processes as inherited from our earliest ancestors
were percept-based”: mimetic culture, before the emergence of verbal language,
would have had a perceptual basis. The human-like ancestors, to defend themselves
from predators and to increase their food supply acquired tool making, control of
fire, group foraging and coordinated hunting techniques, giving rise to a complex
social organization which became too great to be handled merely through perceptbased thought. Beyond mere perceptual-based culture,68 verbal language emerged
to deal with the new information overload [Logan, 2000] caused by the richness and
67
68
On this problem cf. below subsection 3.6.7.
The so called preverbal proto-languages [Logan, 2006, p. 157] of hominid mimetic culture
– percept-based – are considered by [Donald, 1991] as related to 1) manual praxic articulation
(tool-using); 2) socio-emotional organization and interaction; 3) preverbal mimetic communication (hand signals, mime, gestures and suitably related vocal tones to express various meanings
as prosodic verbalizations).
3.6 Constructing Meaning through Mimetic and Creative External Objects
191
challenges of the new social organization, furnishing at the same time the medium
which made the mutual emergence of concept-based thought and new ways of managing things that are remote in both time and space possible.
Moreover, verbal language and its proper essential generativity would have
emerged from a form of protolanguage [Bickerton, 1990] consisting of a limited
verbal lexicon without syntax: [Logan, 2006, p. 158] usefully notes that this kind
of language probably constituted a further step with respect to the proto-language
(here with a hyphen, a language possibly endowed with a “through doing” protosemantic and protosyntax) – for example in tool-making and tool-using. In this way
tools acquired the status of protosemantic elements – as intended by Donald (cf. the
previous footnote) and furnished a kind of preadaptation for the generative grammar
of spoken language, which probably arose 50-100 thousand years ago: “Many of the
cognitive features usually identified exclusively with language were already present
in mimesis: for instance, intentional communication, recursion, and differentiation
of reference” [Donald, 1991, p. 200].69 Of course the mind came into being thanks
to verbal language and hence conceptual thought: “Syntactilized verbal language
extended the effectiveness of human brain and created the mind. Language is a tool
[. . . ]. The human mind is the verbal extension of the brain, a bifurcation of the brain
which vestigially retains the perceptual features of the hominid brain while at the
same time becoming capable of abstract conceptual thought” [Logan, 2006, p. 162]:
a kind of process made up, to use a metaphor, with the help of a software and not a
hardware stratagem.70
I have noted that [Dartnall, 2005, p. 136] further contends that humans can perform operations in their heads that they would normally have performed in the
world and consequently they can also make empirical discoveries in an internal
way through the off-line deployment of their sensory abilities.71 The inner operations are analogues of the inner/outer operations and there are no epistemological
differences in the two cases; Dartnall usefully provides a further clarification which
is epistemologically obvious but sometimes disregarded: “When we scan inner images we employ perceptual mechanisms that we normally employ in processing information about the world. This normal ‘employment’, however, takes place in our
heads, not in the world. We perform operations in our heads on things in the world
(frogs and foxes) and perform the same operations on things in our heads (images
of frogs and foxes). This is weaker than internalism which says that we perform
69
70
71
Unlike Donald, who sees speech as emerging from mimetic communication, [Deacon, 1995]
contends that speech would have coevolved with it.
It has to be recalled that, contrarily to the hypothesis above, Chomsky contended that humans
possess a hardwired generative grammar which permits the quick and universal acquisition of
speech by young children.
[Weiskopf, 2008] usefully stresses that different mechanisms are at work when humans interact
with the environment than when they use their natural, biological cognitive resources, so that
we cannot speak of the same process being carried in the two different systems. A defense of the
extended cognition hypothesis against several recent criticisms is provided by [Chemero and
Silberstein, 2008]: they argue that extended cognition hypothesis does not derive from armchair
theorizing and it neither disregards the results of neural sciences, nor minimizes the importance
of the brain in the production of cognition.
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operations in our heads that we normally perform in the world” [Dartnall, 2005,
p. 140]. I would emphasize that this observation also suggests that “recapitulating”
inner rehearsal capacities and endowments “in turn” can of course suitably enter
further on-line processes – abductively anticipating and emulating [Grush, 2004a;
Grush, 2007] various external aspects already internalized – to mirror new external
representations and to favor subsequent cognitive manipulations and results.72
Finally, in the case of language Clark sees off-line thinking (like in the case of
silently speaking to ourselves) as a – necessary – fundamental psychological ability
that allows human beings to think “about” their own thoughts (second-order thinking), because he contends that only the capability to formulate thoughts in words
renders a thought a stable object for evaluation and treatment. I agree with Wheeler
who criticizes this conviction: language would not be the “only” route to this kind of
second-order process, because many non-linguistic animals could also, in principle,
present this capability through the use of other inner states (i.e. model-based representations).73 Language would not be the “ultimate artifact”, like Clark contends,
because the same kind of intimate interlocking (almost invisible) with language that
we see in human beings as users is also present with other cognitive tools: the example below of geometrical reasoning in subsection 3.6.3 is impressive, even if of
course these kind of model-based skills seem less diffuse than the linguistic ones.74
It is worth quoting Clark’s general summary of the ways in which body and
world share the problem solving “load” with the biological brain, so that the mind
can be properly considered as “extended”. They are deeply illustrated in the first
four chapters of the recent [Clark, 2008, p. 81], and all conform to the Principle of
Ecological Assembly (PEA) I have quoted in section 1.6 of chapter one, devoted to
the concept of manipulative abduction:
• The complex interplay between morphology and control and the value of “ecological control systems” in which goals are not achieved by micro managing every
detail of the desired action or response but by making the most of robust, reliable
sources of relevant order in the bodily or worldly environment of the controller.
• The use of “deictic pointers” and active sensing routines that retrieve information
from worldly sources just in time for problem-solving use and the possible role of
whole sensorimotor cycles in the construction of phenomenal experience.
72
73
74
On the abductive role of anticipations in the so-called emulation and simulation theories cf.
[Barsalou et al., 2003; Decety, 1996; Frith and Dolan, 1996; Grush, 2004a; Hesslow, 2002;
Jeannerod, 2001], cf. also chapter four of this book, section 4.7.4.
On animal cognition and animal abductive capabilities cf. chapter five.
Wheeler also presents the ultimateness of other tools/artifacts, different from language, taking advantage of some well-known Heideggerian ideas [Heidegger, 1926], even if it is highly
questionable whether Heidegger considers language as a tool or just as a constitutive precondition of meaningful experience: “[. . . ] Heidegger observes, not only are the hammer, nails,
and work-bench in this way not part of the engaged carpenter’s phenomenal world, neither, in
a sense, is the carpenter! The carpenter becomes absorbed in his activity in such a way that he
has no awareness of himself as a subject over and against a world of objects. So, in the domain
of smooth and uninterrupted skilled tool-use there are, phenomenologically speaking, no subjects and no objects; there is only the experience of the ongoing task (e.g., hammering) [. . . ]
there’s nothing special about language when compared with more familiar tools and artifacts”
[Wheeler, 2004, p. 701].
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• The use of open perceptual channels as a means of stabilizing an ongoing organismenvironment relation rather than as transducers leading to internal recapitulations
of the external scene.
• Our propensity to incorporate bodily and tool-based extensions and substitute
sensory strategies deep into our problem-solving routines.
• The use of material symbols to augment our mental powers by adding problemsimplifying structure to our external and internal environments.
• The repeated and nested use of space, environmental structuring, and epistemic
actions in online problem solving.
• The potential role of nonbiological media as support for an agents dispositional
beliefs.
3.6.6
External Diagrammatization and Iconic Brain Coevolution
Following our previous considerations it would seem that diagrams can be fruitfully
seen from a semiotic perspective as external representations expressed through icons
and symbols, aimed at simply “mimicking” various humans’ internal images. However, we have seen that they can also play the role of creative representations human
beings externalize and manipulate not just to mirror the internal ways of thinking of
human agents but to find room for concepts and new ways of inferring which cannot
– at a certain time – be found internally “in the mind”.
In summary, we can say that
- diagrams as external iconic (often enriched by symbols) representations are
formed by external materials that either mimic (through reification) concepts and
problems already internally present in the brain or creatively express concepts
and problems that do not have a semiotic “natural home” in the brain;
- subsequent internalized diagrammatic representations are internal
re-projections, a kind of recapitulations (learning), in terms of neural patterns of
activation in the brain (“thoughts”, in Peircean sense), of external diagrammatic
representations. In some simple cases complex diagrammatic transformations –
can be “internally” manipulated like external objects and can further originate
new internal reconstructed representations through the neural activity of transformation and integration.
I have already stressed that this process explains – from a cognitive point of view –
why human agents seem to perform both computations of a connectionist type such
as the ones involving representations as
- (I Level) patterns of neural activation that arise as the result of the interaction
(also presemiotic) between body and environment (and suitably shaped by the
evolution and the individual history): pattern completion or image recognition,
and computations that use representations as
- (II Level) derived combinatorial syntax and semantics dynamically shaped by
the various artificial external representations and reasoning devices found or constructed in the semiotic environment (for example iconic representations); they
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are – more or less completely – neurologically represented contingently as patterns of neural activations that “sometimes” tend to become stabilized meaning
structures and to fix and so to permanently belong to the I Level above.
It is in this sense we can say the “System of Diagrammatization”, in Peircean words,
allows for a self-controlled process of thought in the fixation of originally vague
beliefs: as a system of learning, it is a process that leads from “absolutely undefined
and unlimited possibility” [Peirce, 1931-1958, 6.217] to a fixation of belief and “by
means of which any course of thought can be represented with exactitude” [Peirce,
1931-1958, 4.530]. Moreover, it is a system which could also improve other areas of
science, beyond mathematics, like logic, it “[. . . ] greatly facilitates the solution of
problems of Logic. [. . . ] If logicians would only embrace this method, we should no
longer see attempts to base their science on the fragile foundations of metaphysics
or a psychology not based on logical theory” [Peirce, 1931-1958, 4.571].
As already stressed the I Level originates those sensations (they constitute a kind
of “face” we think the world has), that provide room for the II Level to reflect the
structure of the environment, and, most important, that can follow the computations suggested by the iconic external structures available. It is clear that in this case
we can conclude that the growth of the brain and especially the synaptic and dendritic growth are profoundly determined by the environment. Consequently we can
hypothesize a form of coevolution between what we can call the iconic brain and
the development of the external diagrammatic systems. Brains build iconic signs as
diagrams in the external environment learning from them new meanings through interpretation (both at the spatial and sentential level) after having manipulated them.
When the fixation is reached – imagine for instance the example above, that fixes
the sum of the internal angles of the triangle, cf. above subsection 3.6.2 – the pattern
of neural activation no longer needs a direct stimulus from the external spatial representation in the environment for its construction and can activate a “final logical
interpretant”, in Peircean terms. It can be neurologically viewed as a fixed internal record of an external structure (a fixed belief in Peircean terms) that can exist
also in the absence of such external structure. The pattern of neural activation that
constitutes the I Level Representation has kept record of the experience that generated it and, thus, carries the II Level Representation associated to it, even if in a
different form, the form of semiotic memory and not the form of the vivid sensorial
experience for example of the triangular construction drawn externally, over there,
for instance in a blackboard. Now, the human agent, via neural mechanisms, can
retrieve that II Level Representation and use it as an internal representation (and
can use it to construct new internal representations less complicated than the ones
previously available and stored in memory).
At this point we can easily understand the particular mimetic and creative role
played by external diagrammatic representations in mathematics:
1. some concepts, meanings, and “ways of [geometrical] inferring” performed by
the biological human agents appear hidden and more or less tacit and can be
rendered explicit by building external diagrammatic mimetic models and structures; later on the agent will be able to pick up and use what was suggested
3.6 Constructing Meaning through Mimetic and Creative External Objects
195
by the constraints and features intrinsic and immanent to their external semiotic materiality and the relative established conventionality: artificial languages,
proofs, new figures, examples, etc.;
2. some concepts, meanings, and “new ways of inferring” can be discovered only
through a problem solving process occurring in a distributed interplay between
brains and external representations. I have called this process externalization
(or disembodiment) of the mind: the representations are mediators of results
obtained and allow human beings
(a) to re-represent in their brains new concepts, meanings, and reasoning devices picked up outside, externally, previously absent at the internal level
and thus impossible: first, a kind of alienation is performed, second, a recapitulation is accomplished at the neuronal level by re-representing internally
that which has been “discovered” outside. We perform cognitive geometric
operations on the structure of data that synaptic patterns have “picked up”
in an analogical way from the explicit diagrammatic representations in the
environment;
(b) to re-represent in their brains portions of concepts, meanings, and reasoning devices which, insofar as explicit, can facilitate inferences that previously
involved a very great effort because of human brain’s limited capacity. In this
case the thinking performance is not completely processed internally but in a
hybrid interplay between internal (both tacit and explicit) and external iconic
representations. In some cases this interaction is between the internal level
and a computational tool which in turn can exploit iconic/geometrical representations to perform inferences (cf. above subsection 3.6.1).
An evolved mind is unlikely to have a natural home for complicated concepts like
the ones geometry introduced, as such concepts do not exist in a definite way in
the natural (not artificially manipulated) world: so whereas evolved minds could
construct spatial frameworks and perform some simple spatial inferences in a more
or less tacit way by exploiting modules shaped by natural selection, how could one
think exploiting explicit complicated geometrical concepts without having picked
them up outside, after having produced them?
Let me repeat that a mind consisting of different separated implicit templates
of thinking and modes of inferences exemplified in various exemplars expressed
through natural language cannot come up with certain mathematical and geometrical entities without the help of the external representations. The only way is to
extend the mind into the material world, exploiting paper, blackboards, symbols,
artificial languages, and other various semiotic tools, to provide semiotic anchors75
for finding ways of inferring that have no natural home within the mind, that is for
finding ways of inferring and concepts that take us beyond those that natural selection and previous cultural training could enable us to possess at a certain moment.
Hence, we can hypothesize – for example – that many valid spatial reasoning
habits which in human agents are performed internally have a deep origin in the
75
[Enfield, 2005; Callagher, 2005] point out the role of the body itself as and “anchoring” of cognitive processes, for instance in the case of human gestures linked to the expression of meanings.
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past experience lived in the interplay with iconic systems at first represented in the
environment. As I have just illustrated other recorded thinking habits only partially
occur internally because they are hybridized with the exploitation of already available or suitably constructed external diagrammatic artifacts.
3.6.7
Delegated and Intrinsic Constraints in External Agents and
the Role of Anchors in Conceptual Blending
We have said that through the cognitive interplay with external representations the
human agent is able to pick up and use what suggested by the constraints and features intrinsic to their external materiality and to their relative established conventionality: artificial languages, proofs, examples, etc. Let us consider the example
above (section 3.6.2) of the sum of the internal angles of a triangle. At the beginning the human agent – that is an interpretant in Peircean sense – embodies a sign in
the external world that is in this case an icon endowed with “intentional” delegated
cognitive conventional and public features – meanings – that resort to some already
known properties of the Euclidean geometry: a certain language and a certain notation, the definition of a triangle, the properties of parallel lines that also hold in
case of new elements and “auxiliary” constructions obtained through manipulation,
etc. Then she looks, through diagram manipulations, for possible necessary consequences that occur over there, in the diagram/icon and that obey both
- the conventional delegated properties and
- the properties intrinsic to the materiality of the model.
This external model becomes a kind of autonomous cognitive agent offered to new
interpretants of the problem/object in question. In its presence the competent reasoner is induced to trace series of interpretants in some directions and not in others,
because the features of the external materiality at play dispose movement along certain paths and not others. They confront us both as a cluster of constraints and as
a possibility. The model can be picked up later and acknowledged by the human
agent through fixation of a new neural configuration – a new “thought” (in the case
the new result concerning the sum of the internal angles).
In a recent article [Hutchins, 2005], taking advantage of various amazing and
very interesting examples ranging from everyday to scientific cases, further analyzes
the role of constraints through the association of conceptual structure and material
structure in what he calls “conceptual blending” as a key cognitive strategy. First
of all it is noted that in the external representations embodied in material artifacts –
which form a “blended” space – some aspects can be manipulated and other parts
remain stable.76 Empirical results have shown the relevance of stability, portability,
76
This perspective on conceptual blending and integration is further developed by [Fauconnier
and Turner, 2003; Fauconnier, 2005]. It is especially expanded the analysis of “running the
blend”, seen as the cause of the formation of additional emergent structures, in some cases
concerning mathematics and natural language, and of the requirement for simplicity in these
processes.
3.6 Constructing Meaning through Mimetic and Creative External Objects
197
and simplicity of representations in facilitating reasoning and their role as anchors
for thoughts and at the same time as sources of new inferences and results. Hutchins
describes many cases, for example the role of a “line” for people queuing at the
theater creates a spatial memory for the order of arrival of clients: the blend – which
originates the queue – consists of the mixture of the line and of the directional
ordering. Like Brooks said: “the world is its own best model” [Brooks, 1991]. From
the perspective of traditional representationalism we can consider the two inputs
to the blend a mental (neural) conceptual structure on the one hand and a mental
representation (neural) of the material structure on the other. Hutchins prefers to
adopt a different view and avoids giving a separate mental representation of the
material structure as an input space:
Another alternative is to say that the physical objects themselves are input to the conceptual blending process. This is what I intend when I speak of “material anchors”
for conceptual blends. What is at stake here is the boundary of the conceptual blending process. Shall the conceptual blending process be an entirely conceptual process
that operates on (“real space” as delivered to the process in the form of) the output of
perceptual processes, or shall the conceptual blending process include the perceptual
processes and therefore include bodily interaction with the physical world. [. . . ] First
there is the selectivity of perception that produces a filtered conceptual representation
of the physical world. Second, there is selective projection in the process by which the
prior conceptualization of the world (the “real space” representation) is blended with
the other conceptual input. Is there any evidence that these are two separate processes?
It seems preferable to assume that the selective attention to, and projection of, structure from the material world to the blended space is the perceptual process. That is,
that selective perception is a conceptual process [Hutchins, 2005, p. 1559–1561] .
The main “emergent” property of the blend is the stabilization of representations
of the conceptual relationships at stake (sequential relations among persons in the
queue), thus enabling further inferential chances and providing full “cultural” models (habits, in Peircean terms). In summary, the material anchor does not have a
cognitive value merely because of its intrinsic quality, but because of the way it
is used: “If conceptual elements are mapped onto a material pattern in such a way
that the perceived relationships among the material elements are taken as proxies
(consciously or unconsciously) for relationships among conceptual elements, then
the material pattern is acting as a material anchor. The conceptual relationships that
are mapped into material structure range from the minimum case of individuation
(this element is distinguishable from all others) to extremely complex systems of
relationships (the scales on a sliderule, for example)” [Hutchins, 2005, p. 1562].77
The distinction above between delegated and intrinsic and immanent properties
is also clear if we adopt the Peircean semiotic perspective. Peirce – speaking about
77
[Fauconnier and Turner, 2003] illustrate the clock face, other gauges, and the method of loci
taking advantage of Hutchins’ idea of conceptual blending. They also extend the analysis to
graves, headstones, dead people, money, and spoken and also written language. In the case
of language, Hutchins says, the contribution of the material aspects, like a written word, just
furnishes a minimal criterium of individuation unlike in the case of larger linguistic units such
as grammatical forms.
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the case of syllogistic logic, and not of geometry or algebra – deals with this problem by making an important distinction between what is going on in the brain of
the logical human agent and the autonomous power of the chosen external system
of representation or diagrammatization [Hoffmann, 2003]. The presence of this “autonomous power” explains why I attribute to the external system of representation
a status of cognitive agency similar to the one of a human person, even if of course
lacking aspects like direct intention and responsibility. Any diagram, Peirce says,
makes use
[. . . ] of a particular system of symbols – a perfectly regular and very limited kind of
language. It may be a part of a logician’s duty to show how ordinary ways of speaking
and of thinking are to be translated into that symbolism of formal logic; but it is no
part of syllogistic itself. Logical principles of inference are merely rules for the illative transformation of the symbols of the particular system employed. If the system is
essentially changed, they will be quite different [Peirce, 1931-1958, 2.599].
Of course the argumentation above also holds for our case of iconic geometric representation. This distinction integrates the one I have introduced above in the two
levels of representations, and in some sense blurs it by showing how the hybrid
character of the system composed by the two levels themselves, where the whole
package of sensorial and kinesthetic/motor abilities are involved.
The construction of the diagram also depends on those delegated semiotic properties that are embedded in what Peirce calls “precept” as he says in the passage
we have already quoted above and not only on the constraints expressed by the
materiality of the model itself.78 Semiotic delegation is made possible by humans’
instinctual nature plus cultural inheritances and individual training as they can perform cognitive inner actions able to form various “precepts” that can interact with
the material objects. These actions, that occur internally, are contrasted with the actions that instead are immediately related to the world external to the body: “Human
instinct is no whit less miraculous than that of a bird, the beaver, or the ant. Only,
instead of being directed to bodily motions, such as singing and flying, or to the construction of dwelling, or to the organization of communities, its theater is the plastic
inner world, and its products are the marvelous conceptions of which the greatest
are the ideas of number, time and space” [Peirce, 1966, 318]. In terms of traditional
philosophical concepts, it is an activity that relates to the “imagining” of what might
be in “fantasy”. I must stress that, in this perspective, this inner activity is experience and action in itself and no less experience and action than that performed in
the external world.79
Pickering depicts the role of some externalities (representations, artifacts, tools,
etc.) in terms of a kind of non-human agency that interactively stabilizes with human
agency in a dialectic of resistance and accommodation [Pickering, 1995, p. 17 and p.
78
79
It is worth noting that this process is obviously completely related to the Peircean idea of pragmatism [Hoffmann, 2004], that he simply considers “the experimental method”, which is the
procedure of all science.
On the Peircean emphasis on diagrammatic reasoning as a case of distributed cognition cf.
[Skagestad, 1993].
3.6 Constructing Meaning through Mimetic and Creative External Objects
199
22]. The two agencies, for example in scientific reasoning, originate a co-production
of cognition the results of which cannot be presented and identified in advance: the
outcome of the co-production is intrinsically “unpredictable”. Latour’s notions of
the de-humanizing effect of technologies are based on the so-called “actor network
theory”,80 which also stresses the semiotic role of externalities like the so-called non
human agents. The actor network theory basically maintains that we should think
of science, technology, and society as a field of human and non-human (material)
agency. Human and non-human agents are associated with one another in networks,
and they evolve together within these networks. Because the two aspects are equally
important, neither can be reduced to the other: “An actor network is simultaneously
an actor whose activity is networking heterogeneous elements and a network that
is able to redefine and transform what is it made of [. . . ]. The actor network is
reducible neither to an actor alone nor to a network” [Callon, 1997, p. 93].
The whole process can be seen as a kind of experiment and, at the same time, an
operation of thought. Peirce M. J. Pickering and S. Garrod is still of help: “There is
not reason why ‘thought’ [. . . ] should be taken in that narrow sense in which silence
and darkness are favorable to thought. It should rather be understood as covering
all rational life, so that an experiment shall be an operation of thought” [Peirce,
1931-1958, 5.420]. In this sense thought can be conceived of as a semiotic process
occurring in the publicly observable domain of natural processes (including human
actions) as in the publicly inaccessible realm of someone’s individual consciousness
[Colapietro, 2005, p. 416]. In this perspective the interplay between internal and
external representation is a kind of experiment like “[. . . ] conversation in which
the topic being discussed is, by various contrivances, afforded by the opportunity
to speak back, to object to the ways it is being spoken about” (ibid.). The object
investigated becomes – through semiotic cognitive delegations – an interlocutor and
the process transforms apparently “mute, objects, brute things” [Backhtin, 1982, p.
351] in a critical source.81
The operation on a diagram has reduced complexity enabling concentration on
essential relations and has revealed new data. Moreover, through manipulations of
the diagram new perspectives are offered to the observation, or interesting anomalies
with respect the internal expectations are discovered. In the case of mathematicians,
Peirce maintains, the diagram “[. . . ] puts before him an icon by the observation
of which he detects relations between parts of the diagram other than those which
were used in its construction” [Peirce, 1976, III, p. 749]: “unnoticed and hidden relations among the parts” are discovered [Peirce, 1931-1958, 3.363]. This activity is
80
81
This theory has been proposed by Callon, Latour himself, and Law [Callon, 1994; Callon, 1997;
Latour, 1987; Latour, 1988; Callon and Latour, 1992; Law, 1993].
Colapietro further observes that to make this dialogue possible at least three presuppositions are
necessary: “We must suppose that reality can be other than our representation of it. We must also
suppose that human experimenters are rational subjects whose unique individuality is largely of
a privative character (individuals, so far as they are anything apart from others, and apart from
what they and the others with whom their lives are so intimately and inescapably bound up,
are mere negations [Peirce, 1931-1958, 5.317]. Finally, we must suppose that human beings are
autonomous agents who can exercise an indeterminable measure of effective control over their
future conduct” [Colapietro, 2005, p. 416].
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a kind of “thinking through doing”: “In geometry, subsidiary lines are drawn. In algebra permissible transformations are made. Thereupon, the faculty of observation
is called into play. [. . . ] Theorematic reasoning invariably depends upon experimentation with individual schemata” [Peirce, 1931-1958, 4.233].
We have said that firstly the human agent embodies structured signs in the external world that is in this geometrical case an icon endowed with “intentional”
delegated cognitive conventional and public features – meanings – that resort to
some already known properties of the Euclidean geometry: these features can be
considered a kind of immanent rationality and regularity [Hoffmann, 2004] that establishes a disciplinary field to envisage conclusions. The system remains relative
to the chosen conventional framework. These features are real as long as there is
no serious doubt in their adequacy: “The ‘real,’ for Peirce, is part of an evolutionary
process and while ‘pragmatic belief’ and unconscious habits might be doubted from
a scientific point a view, such a science might also formulate serious doubts in its
own representational systems” [Hoffmann, 2004, p. 295].
Paavola, Hakkarainen, and Sintonen [Paavola et al., 2006] consider the interplay
between internal and external aspects of abductive reasoning in the framework of
the interrogative model of “explanation-seeking why-questions” and in the light of
the perspective of distributed cognition. They emphasize interaction with the “environment” and show the importance of the heuristic strategies and of their trialogic
nature (inquirer and fellow inquirers, object of inquiry, mediating artifacts and processes), also taking advantage of Davidson’s ideas [Davidson, 2001] – as already
stressed by Wirth [1999; 2005] – concerning triangulation.82
Let us imagine we choose a different representational system still exploiting material and external diagrams. Through the manipulation of the new symbols and
diagrams we expect very different conclusions. An example is the one of the nonEuclidean discoveries. In Euclidean geometry, by adopting the postulate of parallels
we necessarily arrive to the ineluctable conclusion that the sum of internal angles of
a triangle is 180◦, but this does not occur in the case of the non-Euclidean geometry
where a different selected representational system – that still uses Euclidean icons
– determines quite different possibilities of constructions, and thus different results
from iconic experimenting.83
82
83
Cf. also Arrighi and Ferrario’s [2008] study on mutual understanding that emphasizes the role
in abductive reasoning of the collaborative processes involved in interaction with other speakers
and with the entities of the environment; they explicitly refer to my approach called “manipulative framework” and to the “strategic framework” described by Paavola and his collaborators.
The fact that science is inherently seen as a social process is emphasized by [Addis and Gooding,
2008], who argue that abduction does not work in isolation from other inference mechanisms
and use game theory to relate the abductive system to actions that produce new information. To
suitably model this process an interesting computational model is proposed in order to display
various aspects of collective belief-revision leading to consensus-formation.
I have illustrated this problem in detail in [Magnani, 2002a]. Sections 2.9 and 2.11 of chapter two of this book illustrated an example of this process of cognitive delegation to external
diagrams just taking advantage of the discovery of non-Euclidean geometry.
3.7 Mimetic Minds as Semiotic Minds
3.7
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Mimetic Minds as Semiotic Minds
I contend that there are external representations that are representations of other
external representations. In some cases they carry new scientific knowledge. To
make an example, Hilbert’s Grundlagen der Geometrie is a “formal” representation of the geometrical problem solving through diagrams: in Hilbertian systems
solutions of problems become proofs of theorems in terms of an axiomatic model.
In turn a calculator is able to re-represent (through an artifact) (and to perform)
those geometrical proofs with diagrams already performed by human beings with
pencil and paper. In this case we have representations that mimic particular cognitive performances that we usually attribute to our minds (cf. the first sections of
this chapter).
We have seen that our brains delegate cognitive (and epistemic) roles to externalities and then tend to “adopt” and recapitulate what they have checked occurring
outside, over there, after having manipulated – often with creative results – the external invented structured model. A simple example: it is relatively neurologically
easy to perform an addition of numbers by depicting in our mind – thanks to that
brain device that is called visual buffer – the images of that addition thought as it
occurs concretely, with paper and pencil, taking advantage of external materials. We
have said that mind representations are also over there, in the environment, where
mind has objectified itself in various semiotic structures that mimic and enhance its
internal representations.
Turing adds a new structure to this list of external objectified devices: an abstract
tool, the (Universal) Logical Computing Machine (LCM), endowed with powerful
mimetic properties. We have concluded the subsection 3.4.1 remarking that the creative “mind” is in itself extended and, so to say, both internal and external: the mind
is semiotic because transcends the boundary of the individual and includes parts
of that individual’s environment, and thus constitutively artificial. Turing’s LCM,
which is an externalized device, is able to mimic human cognitive operations that
occur in that interplay between the internal mind and the external one. Indeed Turing already in 1950 maintains that, taking advantage of the existence of the LCM,
“Digital computers [. . . ] can be constructed, and indeed have been constructed, and
[. . . ] they can in fact mimic the actions of a human computer very closely” [Turing,
1950, p. 435].
In the light of my perspective both (Universal) Logical Computing Machine
(LCM) (the theoretical artifact) and (Universal) Practical Computing Machine
(PCM) (the practical artifact) are mimetic minds because they are able to mimic
the mind in a kind of universal way (wonderfully continuing the activity of disembodiment of minds and of semiotic delegations to the external materiality our
ancestors rudimentary started). LCM and PCM are able to re-represent and perform
in a very powerful way plenty of cognitive skills of human beings. Universal Turing
Machines are discrete-state machines, DSM, “with a Laplacian behavior” [Longo,
2002; Lassègue, 1998; Lassègue, 1999]: “[. . . ] it is always possible to predict all
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future states”) and they are equivalent to all formalisms for computability (what
is thinkable is calculable and mechanizable), and because universal they are able
to simulate – that is to mimic – any human cognitive function, that is what is
usually called mind. A natural consequence of this perspective is that Universal
Turing machines do not represent (against classical AI and modern cognitivist computationalism) a “knowledge” of the mind and of human intelligence. Turing is
perfectly aware of the fact that brain is not a DSM, but as he says, a “continuous” system, where instead a mathematical modeling can guarantee a satisfactory
scientific intelligibility (cf. his studies on non-Laplacian mathematical models of
morphogenesis).
We have seen that our brains delegate meaningful semiotic (and of course cognitive and epistemic) roles to externalities and then tend to “adopt” what they have
checked occurring outside, over there, in the external invented structured and model.
And a large part of meaning formation takes advantage of the exploitation of external representations and mediators. Our view about the disembodiment of mind
certainly involves that the Mind/Body dualist view is less credible as well as Cartesian computationalism. Also the view that mind is computational independently of
the physical (functionalism) is jeopardized. In my perspective on human cognition
in terms of mimetic minds we no longer need Descartes dualism: we only have
semiotic brains that make up large, integrated, material cognitive systems like for
example LCMs and PCMs. These are new independent semiotic agencies that constitute real artificial minds aiming at “universally” imitating human cognition. In
this perspective what we usually call mind simply consists in the union of both the
changing neural configurations of brains together with those large, integrated, and
material cognitive systems the brains themselves are continuously building in an
infinite semiotic process.
Minds are material like brains, in so far as they take advantage of intertwined
internal and external semiotic processes. It seems to me at this point we can better
and more deeply understand Peirce’s semiotic motto “man is an external sign” in
the passage we have completely quoted above in subsection 3.5.1: “[. . . ] as the fact
that every thought is a sign, taken in conjunction with the fact that life is a train
of thoughts, proves that man is a sign; so, that every thought is an external sign,
proves that man is an external sign” [Peirce, 1931-1958, 5.324]. The only problem
seems “how meat knows”: we can reverse the Cartesian motto and say “sum ergo
cogito”.
We have seen that our brains delegate meaningful cognitive (and epistemic) roles
to externalities and then tend to “adopt” what they have checked occurring outside, over there, in the external invented structures and models. And a large part
of meaning formation takes advantage of the exploitation of external representations and mediators. We have said that PCMs can be considered mimetic minds
(they are ideal “practical” – in Turing’s sense – agents): what is in turn the cognitive status of “logical agents” from the point of view of their demonstrative aspect? I will treat this important problem in chapter seven, where various aspects
3.8 “Symbols” as Memory Mediators. Maximizing Abducibility
203
concerning logical systems as ideal externalizations in demonstrative frameworks
will be illustrated.
3.8
“Symbols” as Memory Mediators. Maximizing Abducibility
through Psychic Energy Mediators
We have seen in the previous sections that recent research in the area of distributed
cognition acknowledges the distinction between internal and external
representations. To illustrate this process I have taken advantage of some paleoanthropological results on the birth of material culture, that provide an evolutionary
perspective on the origin of intelligent behaviors, and of Turing’s ideas about the
passage from what he called unorganized brains to organized, mature, ones. Unorganized brains (in Turing’s sense) organize themselves through semiotic activity that
is reified in the external environment and then re-projected and reinterpreted through
new configurations of neural networks and chemical processes. In the following sections, also considering some psychoanalytic insights, I will describe the centrality to
semiotic cognitive information processes of disembodiment of mind from the point
of view of cognitive interplay between internal and external representations. Humans continuously delegate and distribute cognitive functions to the environment to
lessen their limits. They build models, representations, and other various mediating
structures, that are thought to be good for thinking. In building various mediating
structures and designing activities, such as models or representations, humans alter
the environment and thus create those cognitive niches I will describe in chapter six.
What is the role of this environment modification in psychoanalysis? In the following sections I will illustrate some fundamental aspects of the interplay above in the
light of Jungian observations about the cognitive and therapeutic role of what we
can call external energy mediators.
3.8.1
Mythologization of External “Observations”
Let us consider this interplay between internal and external representations taking
advantage of some stimulating speculations made by Jung. Jung says “Psychic existence can be recognized only by the presence of contents that are capable of consciousness. We can therefore speak of an unconscious only insofar as we are able
to demonstrate its contents. The contents of the personal unconscious are chiefly
feeling-toned complexes: they constitute the personal and private side of psychic
life. The contents of the collective unconscious, on the other hand, are known as
archetypes” [Jung, 1968a, pp. 3-5]. Usually the contents of the collective unconscious have not yet been submitted to conscious elaboration and so they are an “immediate datum of psychic experience”. They are “altered” by becoming conscious
and by being perceived: the archetype, “a hypothetical and irrepresentable model”,
“takes its color from the individual consciousness in which it happens to appear”
(ibid., p. 5).
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In the case of the primitive human beings unconscious psyche “[. . . ] has an imperative need – or rather [. . . ] an irresistible urge – to assimilate all outer sense
experience to inner, psychic events. It is not enough for the primitive to see the sun
rise and set; this external observation must at the same time be a psychic happening:
the sun in its course must represent the fate of a god or hero who, in the last analysis, dwell nowhere except in the soul of man” (ibid, p. 6).84 This process leads to a
consciousness that in those primitive creatures is largely undifferentiated so we can
guess that what we call “external” representations may not be seen by those individuals as external in the same way that we see them: it is only our perspective that
sees that kind of consciousness as formed through the intervention of “externalities”
(arrived at through “outer sense experience”, Jung says).
In the light of the interplay I have illustrated in the previous sections of this
chapter we can say that rough external representations (Jung says “observations”),
merely arrived at through the senses, are rapidly “internalized” and become “mythologized”. “Summer and winter, the phases of the moon, the rainy season, and so
forth, are in no sense allegories” of those primary observations, because they become “symbolic expressions of the inner” and “become accessible to man’s consciousness by way of projection, that is mirrored in the events of nature” (ibid., p.
6). Let us reiterate that of course the “subjectivity” – so to speak – of the primitives
is so large and extended that those external seen events, the – “primary observations” – which are suitably mythologized, are not “thought” of as “external”, in the
way we modern humans think. Of course in the case of the primitives those events
that “we” clearly see as “external” are on the whole events of their large undifferentiated psyche (“a suffocating atmosphere of egocentric subjectivity”, in Junghian
terms), which of course does not allow a net distinction between inner and outer. It
has to be noted that also in healthy modern humans who trust astrology some hesitation in discriminating between inner and outer events is present: the effects of that
“partécipation mystique” already described by Lévi-Bruhl are still significantly in
operation [Lévi-Bruhl, 1923].
This Junghian remark about the hesitation in discriminating between inner and
outer events is confirmed in the framework of the catastrophe theory. Thom sees
astrology as an intermediate level between magic, where narrative cognition that
makes the world intelligible is controlled by the will of man (the “magician”), and
science, where “[. . . ] control is determined by the internal generativity of formal
language describing external situations, a generativity over which man has no hold,
once the initial conditions are laid down” [Thom, 1988, p. 33] (cf. also this book,
chapter eight, subsection 8.5.2). Astrology depicts human situations as supposedly
84
It is interesting to note that also René Thom recognizes this fact in the framework of his mathematical catastrophe theory: “Men (as well as prehominids) were early incited by group living
to build up some representation of the behavior of their kind, a representation, in particular, of
the paths of their affective regulation. As a result, any external entity thought of as being individuated tends, by empathy, to be imagined after the manner of a living being” [Thom, 1988, p.
16].
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ruled by the mathematically determined course of the heavenly bodies, “a belief for
which geocentrism was no doubts largely responsible” [Thom, 1988, p. 33].85
For the primitive “[. . . ] knowledge of nature is essentially the language and outer
dress of an unconscious psychic process. But the very fact that this process is unconscious gives us the reason why man has thought of everything except the psyche in
his attempts to explain myths” (ibid, pp. 6-7).86 Indeed “[. . . ] anyone who descends
into the unconscious gets into a suffocating atmosphere of egocentric subjectivity,
and in this blind alley is exposed to the attack of all the ferocious beasts which the
caverns of the psychic underworld are supposed to harbor” (ibid., p. 20).
Reflecting upon the processes of mind externalization and disembodiment and
subsequent re-internalization Jung of course speaks of projection: “The projection
is so fundamental that it has taken several thousand years of civilization to detach it
in some measure from the outer object” (ibid., p. 6). Once formed – and in presence
of an established, significant and more or less stable separation between the self
and the external world – the internalized representations (mythologized) can be reexternalized (“projected”) so giving rise to new “external representations” that go
85
On the basis of these considerations Thom also further details that Lévi-Bruhl’s classic notion of
participation, (the possibility that two spatially separate beings can constitute the same being),
and the notions associated with “magic”, cannot actually be thought of as “pre-logic”:
For example a sorcerer may be at one and the same time a man sleeping in a hut and a
tiger hunting in the jungle some distance away [. . . ] if the tiger is wounded by hunters
in the jungle, then the man-sorcerer in his hut, will reveal a wound in the homologous
place on his body. A belief of this kind justifies the statement that the man-sorcerer, and
the tiger have their “local somatic maps” identified, in spite of the fact that these maps
relate to beings separated by several kilometres. From this viewpoint, it can be said
that the act of magic is characterized essentially by an “action at a distance” which can
be interpreted as a modification of the usual topology of space-time. In other words,
the linking up between local maps which define usual space will not be fixed, but could
be modified at the pleasure or the will of certain men (magicians or sorcerers) thanks
to the use of specific procedures (magical rites, sacrifices, etc.). Further, the topology
of the space will cease to be the same for all, given that the perceptual experiences of
an observer can themselves be affected by magical action [Thom, 1980, p. 132].
86
The somatic local maps, predominant in primitives and animals, emanate from the individual as
forms of control of the external world and identification of one’s own body relating to the need
to acknowledge the presence of local morphological accidents of which many have a “pregnant” character (cf. also chapter eight of this book, section 8.3): “This conception of a flexible
and individual space-time, which will cease to be a universal frame valid for all men, clearly
conflicts head on with the basic postulate of all modern science that there exists a universal
space-time valid and isomorphic for all. It is without doubt this essential difference that LéviBruhl had wished to signify in speaking of “pre-logical mentality” – unhappy words, for logic
has in principle, nothing to do with the representation of space” [Thom, 1980, p. 133]. Further
details on the cognitive problem of spatial frameworks are illustrated in the following chapter,
subsection 4.7.
“He simply didn’t know that the psyche contains all the images that have ever given rise to
myths, and that our unconscious is an acting and suffering subject with an inner drama which
primitive man rediscovers, by means of analogy, in the processes of nature both great and small”
(ibid., p. 7).
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beyond the previous ones, and that can mimic what is already internal. Through this
process the externalities at play acquire new mental/psychic contents.
Recent research on “identity” processes in individual human beings have stressed
the role of the non-human environment, for example in the case of plants, animals,
wind, and water. Let us consider the case of trees. Jung sees the tree as participating
in the processes of the formation of the psyche in so far as it constitutes an archetype
in the collective unconscious. Darwinians sometimes speak of an innate emotional
affiliation of humans with other living organisms so that their preferences would
have been shaped over millennia through interactions with features of the environment helpful to the survival of the species in its early development (for example
they offer prospect in predation and refuge). The so-called phenomenological approaches rely on various metaphors: roots, trunk, and canopy mirror the infernal,
earthy, and heavenly domains, flowers, fruits, and colors supply subsidiary arguments for human identity – in this respect trees certainly offer more than grass, the
most universal and successful of plants. Gibsonian ecological psychologists emphasize that trees are the source for humans of multiple innate affordances87 that provide various action possibilities (climbing, hide, and seek), the possibility of making
artifacts (rope swing, tree forts), and of satisfying human needs (shelter, food, fuel,
and medicine) [Sommer, 2003].88 Finally, ecopsychologists maintain that beyond
the individual self there is an ecological self that is “nurtured through the contact
with the natural environment” [Sommer, 2003, p. 191] (from this perspective trees
are important for city residents because they provide contact with natural rhythms,
life forms, seasonal markers, and the gentle motion and sound of rustling leaves).
Moreover, through anthropomorphic interpretation (for example in children) an
external object such as a tree or a squirrel is perceived as being similar to oneself
and humanlike in certain respects, where the identity of both the object and the
observer is reached [Gebhard et al., 2003]. This interpretation also includes moral
aspects, such as freedom and an affectionate and caring nature, which are attributed
in an isomorphic way to organisms or natural objects making it possible to grant
greater independence and environmental moral value to them [Kahn, 2003]. In turn,
in the case of physiomorphism, human experience can be interpreted in terms of
nonhuman nature or natural objects. Both anthropomorphism and physiomorphism
can start a never ending, cyclic process of mirrors:
Thus we may draw upon experiences with natural objects to understand ourselves
(physiomorphysm), but in turn our representations of these natural objects will have
arisen by interpreting them in terms of ourselves and our personal experience (anthropomorphism). [. . . ] But attaching subjective meaning to an object, the object and
the self become mentally intertwined and a unique relationship between the two is
87
88
The concept of affordance is illustrated below in chapter six of this book.
In this last case, in modern humans, the satisfaction of needs occurs through the mediation
of sophisticated cultural schemes (such as in the exploitation of trees to counter pollution, to
protect privacy and limit noise and to shape the person-home-neighbourhood interplay on which
survival of the individual depends).
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207
established. It is perhaps in this manner that external objects contribute to the formation of personal identity (cit., pp. 104-105).89
I have contended above that there are two basic kinds of external representations
active in this process of externalization of the mind: creative and mimetic. Mimetic
external representations mirror concepts, emotional tones, and other structures that
are already present or re-presented in the brain and need to be enhanced, solved or
further complicated, etc., in order for them to sometimes give rise to new concepts,
meanings, etc. I quoted above the Junghian passage stating that “Psychic existence
can be recognized only by the presence of contents that are capable of consciousness”: now it is clear that consciousness is basically made of suitably internalized
sensory data.
In sum, a “differentiated” psyche is a hybrid product of the interplay between
internal and external sensory representations. Conversely, external representations
are continuously re-built through the delegation of psychic contents, like, for example, in the case of the ancient religious images such as the Trinity or the mystery of
the Virgin birth. These representations are placed and “produced” over there, outside, hybridized with and within material supports90 from the external environment,
autonomized with respect to their human origin but more or less available,91 they
can suitably be “picked up” by human beings and re-represented in their brains.
They are picked up to favor extension and “consolidation of consciousness” and “to
keep back the dangers of unconscious”, the “peril of the souls”’ given the fact that
“mankind always stands on the brink of actions it performs itself but does not control. The whole world wants peace and the whole world prepares for war” (ibid. p.
23). They are also picked up through imitation and sometimes to contrast individuation processes. “[. . . ] the more beautiful, the more sublime, the more comprehensive
the image that has evolved and been handed down by tradition, the further removed
it is from individual experience. We can just feel our way into it and sense something of it, but the original experience is lost, [the images] have stiffened into mere
objects of belief” (ibid., p. 7). In these externalized images that became symbols
of dogmatic archetypical ideas – “collective unconscious has been channelled [. . . ]
and flows along like a well-controlled stream in the symbolism of creed and ritual”
(ibid., p. 12).
I have said that for Jung consciousness is basically made of suitably internalized external “observations”: in sum, psyche is a hybrid product of the interplay
between internal and external representations. Conversely, once representations are
89
90
91
In this perspective perceiving an object as humanlike can be related to the problem of its possible
moral worth (thus activating a kind of micro morality at the personal level) and, consequently,
for example in the case of animals or trees, it can lead to the more extended awareness of the
need for their protection and preservation (a “biocentric” perspective that expresses a kind of
transpersonal macromorality): killing plants can be seen as analogous to killing humans [Rest
et al., 1999]. Human bodily and mental characters play, through anthropomorphism, the role of
moral mediators [Magnani, 2007d], that can permit nature to be moralized, at least at the level
of micromorality.
On the re-externalization in artifacts cf. the following section.
Jung says that “[. . . ] archetypal images are so packed with meaning in themselves that people
never think of asking what they really do mean” (ibid., p. 13).
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internalized, we have them at our private disposal for re-building external representations through delegation (projections) of their psychic contents. First, this process presents the growth in complexity of the psyche where archetypes manifest
themselves through their capacity to – unconsciously – organize images and ideas;
later on archetypes, thanks to the above external/internal interplay, “by assimilating
ideational material whose provenance in the phenomenal world is not to be contested, they become visible and psychic” [Jung, 1972b, p. 128].
From the perspective of the individual psyche Jung’s remark is central and clearly
stated. Acknowledging the importance of the above hybrid interplay he says that the
word “projection” is not really appropriate, and the role of the senses is fundamental
“[. . . ] for nothing has been cast out of the psyche; rather, the psyche has attained its
present complexity by a series of acts of introjections. Its complexity has increased
in proportion to the despiritualization of nature” [Jung, 1968a, p. 25]. Even more
clearly, Jung points out the relevance of the hybridization processes: “The organization of these particles [of light] produces a picture of the phenomenal world which
depends essentially upon the constitution of the apperceiving psyche on the one
hand, and upon that of the light medium on the other” [Jung, 1972b, p. 125].
I have already said that we can hypothesize a form of coevolution between the
structural complexity of the psyche and that of the cognitively delegated cognitive
external systems. Brains build external representations in the environment learning new meanings from them through interpretation (both at the model-based and
sentential level), after having manipulated them through motor actions.92 When the
internal fixation of a new meaning is reached through internalization – like in the
above example, concerning the formation of a new religious icon, that for example
fixes the character of a suitable rite – the pattern of neural activation no longer needs
a direct stimulus from the external representation in the environment for its construction. In this last case the new meaning can be neurologically viewed as a fixed
internal record of an external structure (a fixed belief in Peircean terms) that can
also exist in the absence of such external structure. In the examples I will illustrate
in the following sections it will be clear how, for instance, a mimetic representation
(for example embedded in an artifact) can become creative by giving rise to new
meanings and ideas in the hybrid interplay between psyche and suitable cognitively
delegated environments.
3.8.2
Cognitive/Affective Delegations to Artifacts
In chapter one I have introduced the concept of sentential, model-based, and manipulative abduction mainly at the level of logical and scientific reasoning. Manipulative abduction is also important in explaining how Jung conceives of “hypothesis”
generation and creativity in human beings. We now have a good conceptual tool at
92
Representations and inferences can be sentential (based on natural language), model-based (that
is sensory-related, formed for example by visualizations, analogies, thought experiments, etc.)
or hybrid (a mixture of the two aspects above together with various manipulations of the world)
[Magnani, 2001b].
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209
our disposal which can shed light on Jung’s considerations illustrated in “On Psychic Energy”. The manipulation of external mediators (and of the related external
representations) is active at the level of scientific discovery but it can be viewed as
a general more or less creative way of producing/extending cognition, in the widest
sense of the term, also involving emotional, affective, attentional, doxastic, and other
aspects. Jung acknowledges this fact: “The apperceiving consciousness has proved
capable of a high degree of development, and constructs instruments with the help
of which our range of seeing and hearing has been extended by many octaves. Consequently the postulated reality of the phenomenal world as well as the subjective
world of consciousness has undergone an unparalleled expansion” [Jung, 1972b, p.
228].
Furthermore, the creative construction of artifacts as cognitive/affective mediators can be seen in the framework of the “psychic energy” flow: the secret of cultural
development is the mobility and disposability of psychic energy [Jung, 1967], that
appears – as a true “life-process” – in phenomena like “instincts, wishing, willing,
affect, attention capacity to work”, sexuality, morality, etc.93 This “psychic energy
flow” is at the core of the various possible processes of progression and regression
as adaptations to the environment and to the inner world, as key tools able to satisfy
the demand of individuation.94 Psychic energy and its capacity to be extended to
the external world is appropriately compared by Jung to the fundamental primitive
idea of mana, in its capacity to externalize and delegate meanings, and potentially
consume everything.
In this perspective “values” can be considered quantitative estimates of energy
that people can attribute to external things in various ways. For example, in the
case of ethics, the recent tradition of moral philosophy classifies things that are
endowed with values attributed by humans as endowed with “intrinsic values”, a
mechanism which I have illustrated in detail in a recent book on morality in our
technological world [Magnani, 2007d]. These evaluations are of course attributed
by consciousness, but also by the unconscious [Jung, 1972c, p. 10].
Once externalized and stabilized, values are available to be picked up. From this
perspective the constellations of psychic elements grouped around feeling toned
contents (complexes) are related to both inner experience (intertwined with innate
aspects of an individual’s character and dispositions) and suitably sensory external
environment representations picked up when available (ibid, p. 11). These constellations centrally relate to both conscious and unconscious value quantities (affective
intensities). Moral and other values (sexual, esthetic, rational, etc.) externalized in
artifacts, icons, etc. normally belong to an established collective framework, shared
by a relatively stable group of human beings: of course “repression” or “displacement of affect” can give rise to false estimates so that “subjective evaluation is
93
94
It has to be noted that this mobility and disposability of energy is granted by the fact that Jung
contends that man, more than other animals, “possesses a relative surplus of energy that is
capable of application apart from the natural flow” [Jung, 1972a, p. 47].
In “civilized man” psychic energy is strongly canalized in that rationalism of consciousness,
“otherwise so useful to him”, but which in turn can become a possible obstacle to the “frictionless transformations of energy” [Jung, 1972a, p. 25].
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therefore completely out of the question in estimating unconscious value intensities” (ibid. p. 10), in turn giving rise to various disequilibria.
3.8.3
Artifacts as Memory Mediators
An example of psychic energy delegation presented by Jung, that clearly expresses
human culture as a “transformer of energy”95 is the one related to an artifact build
by the Wachandi of Australia:
They dig a hole in the ground, oval in shape and set about with bushes so that it looks
like a woman’s genitals. Then they dance round this hole, holding their spears in front
of them in imitation of an erect penis. As they dance round, they thrust their spears into
the hole, shouting “Pulli nira, pulli nira, wataka!” (non fossa, non fossa, sed cunnus!).
During the ceremony none of the participants is allowed to look at a woman [Jung,
1972a, p. 43].
It is a process of semiotic delegation of meanings to an external natural object – the
ground, which applies energy for special purposes through the building of a mimetic
artifact: an “analogue of the object of instinct”, Jung says [1972a, p. 42]. The artifact
is an analogue of female genitals, an “object of natural instinct”, that through the reiterated dance, in turn mimicking the sexual act, suggests that the hole is in reality
a vulva. This artifact makes possible and promotes the related inferential cognitive
processes of the rite. Once the representations at play are externalized (representations which are psychic values, from the Junghian psychoanalytic perspective), they
can be picked up in a sensory way (and so learnt) by other individuals not previously involved in its construction. They can in turn manipulate and reinternalize the
meanings semiotically embedded in the artifact:
The mind then busies itself with the earth, and in turn is affected by it, so that there
is the possibility and even a probability that man will give it his attention, which is
the psychological prerequisite for cultivation. Agriculture did in fact arise, though not
exclusively, from the formation of sexual analogies [Jung, 1972a, p. 43].
Artifacts are produced by individuals and/or small groups and left over there, in the
environment, perceivable, sharable, and more or less available. It is in this sense
that we can classify an artifactual mediator of this psychoanalytic type as a memory
mediator (as a kind of “memory store”, in Leyton’s sense),96 which mediates and
95
96
Animals also make artifacts, and Jung is aware of this fact when he acknowledges the role
of what he calls “natural culture”: “When the beaver fells trees and dams up a river, this is a
performance conditioned by its differentiation. Its differentiation is a product of what one might
call ‘natural culture’, which functions as a transformer of energy” [Jung, 1972a, p. 42].
[Leyton, 1999; Leyton, 2001] introduces this concept in a very interesting new geometry
where forms are no longer memoryless as in classical approaches such as the Euclidean and
the Kleinian one, in terms of groups of transformations. From this mathematical perspective
artifacts, in so far as they are expressed through icons, visual and other non linguistic configurations, are “memory stores” in themselves [Leyton, 2006]. Of course in our case memory has to
be intended in an extended Junghian sense, going beyond the explicit, linguistic, or model-based
aspects which are the main focus of the recent tradition of cognitive science: specific implicit
structures are also at play.
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211
makes available the story of its origin and the actions related to it, which can be
learnt and/or re-activated when needed.97
Let us come back to the artifact above. Primitive minds are not a “natural home”
(cf. above, sections 3.3.3 and 3.6.6) for thinking on agriculture: together with the
cognitive externalization and the artifact – and the subsequent recapitulations – certain actions can be triggered, actions that otherwise would have been impossible
with only the help of the simple available “internal” resources. The whole process
actualizes an example of that manipulative abduction I have described above. When
created for the first time it is a creative social process, however, when meanings are
subsequently picked up through the process involving the symbolic genital artifact
and suitably reproduced, it is no longer creative, at least from the collective point
of view, but it can still be creative from the perspective of individuals’ new cognitive achievements and learning. It is possible to infer (abduce) from the artifacts the
events and meanings that generated them, and thus the clear and reliable cognitive
hypotheses which can in turn trigger related motor responses. They yield information about the past, being equivalent to the story they have undergone. In terms of
Gibsonian [Gibson, 1979] affordances we can say that artifacts as memory mediators – as reliable “external anchors” – afford the subject in terms of energy stimuli
transduced by sensorial systems, so maximing abducibility (they maximize “recoverability” in Leyton’s sense – cf. the following subsection) and actively providing
humans with new, often unexpected, opportunities for both “psychic” and “motor”
actions.
3.8.3.1
Speech as an Artifact and Hybrid Mediators
Speech can also be seen as an external artifactual tool in so far as it consists in the
outward flow of thoughts formulated for communication [Jung, 1967]. I have illustrated in sections 3.4.2 and 3.6.5 that speech/language is able to “scaffold” thoughts
that are externalized and open to the interplay of communication. Through this artifactual interplay new meanings can arise usually shaped by (and embedded in)
suitable narratives. Often speech (and related narrative) is hybridized with suitable
manipulations of other external iconic aspects, such as drawings and various representations contained in suitable material artifacts. For example, in the interplay of
the communicative environment which characterizes the psychoanalytic therapeutic
setting – speech (together with the help of the other “tools” described above) grants
“explanations” of patient’s events (internal, external – and “externalized” –, hybrid),
also thanks to the mediating empathic endowments of the analyst.
97
It is interesting to note that [Turner, 2005] identifies a range of “affordances” offered by a variety
of mediating artifacts including the life stories of recovering alcoholics in AA meeting (affording rehabilitation), patients’ charts in a hospital setting (affording access to a patient’s medical
history), poker chips (affording gambling) and “sexy” clothing (affording gender stereotyping)
[Cole, 1996]. In this perspective mediating artifacts embody their own “developmental histories” which is a reflection of their use. I will illustrate in details the relationships between
abduction and affordances in chapter six.
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In “The Transcendent Function” Jung says that “visual types” will be more inclined to look for inner images and further analyze their externalization in material
supports. “Audio-verbal types” hear inner words and will note these down in writing. Again, others will directly use “hands” (or, more rarely, bodily movements) to
spontaneously build artifacts (for instance “plastic materials”) of various kinds to try
to give “expression to the contents of the unconscious” [Jung, 1972c, pp. 83–84]:
Often it is necessary to clarify a vague content by giving it a visible form. This can be
done by drawing, painting, or modeling. Often the hands know how to solve the riddle
with which the intellect has wrestled in vain [Jung, 1972c, pp. 83–86].
3.8.4
3.8.4.1
Artifacts as Symbols That Maximize Abducibility
Symbols as Memory Mediators
I have contended that a primitive mind is unlikely to have a natural home for complicated concepts like those of agriculture, because such concepts do not exist in a definite way in the natural (not artificially manipulated) world. Jung says that in these
cases we aim at doing something that “exceeds our powers” [Jung, 1972a, p. 45]:
humans always resorted to “external” magical formalities and religious ceremonies,
which can release deep emotion and cognitive forces. In other words, whereas primitive minds could construct knowledge about human and animal genitals and reproduction, and perform some trivial inferences about them in a more or less tacit way
by exploiting modules shaped by natural selection, how could they think of exploiting more explicit, sophisticated concepts involving agriculture? It is necessary to
“disembody” the mind, and after having built an artifact through the hybrid internal/external interplay, to pick the new meanings up, once they are available over
there, like the Wachandi did with the help of the hole in the ground.
A primitive mind consisting in different separated implicit templates of thinking
and modes of inferences exemplified in various exemplars – for example expressed
through natural language – and merely shaped by natural selection, cannot come up
with certain agricultural entities without the help of external representations. The
only way is to extend the mind into the material/artifactual world, exploiting the
ground, tools and bodily movements which are suitably enriched through cognitive
delegations, to provide semiotic anchors for finding ways of inferring that have no
natural home within the mind, that is for finding ways of thinking that take humans
beyond those that natural selection and cultural training could enable us to possess
at a certain moment.
The activity of delegation to external objects of cognitive values through the construction of artifacts is certainly semiotic in itself (and of course a diversion of libido/psychic energy, in Junghian terms), the result is the emergence of new intrinsic
meanings, expressed by what Jung calls a symbol. It is to be recalled that artifacts
are the fruit of the hybridization of both internal and external constraints. First of all
this result expresses the “quality” of the cognitive aspects – in our example above
– delegated by Whacandi’s “minds” to the external materiality, which gives birth to
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213
the hybrid interplay. Second, it expresses the particular cognitive “reactions” triggered in other individuals by the materiality at hand (that specific ground, the tools,
the shapes made possible by the specific bodies of the dancers, etc.).
Jung also nicely stresses the protoepistemic role that can be played by magical
artifactual externalizations in creative reasoning, and he is aware that these magical
externalizations constitute the ancestors of the scientific artifacts, like those – mainly
explicit – I have described in my book [Magnani, 2001c] concerning the discovery
of new geometrical properties through external diagrams: Jung says “Through a sustained playful interest in the object, a man may make all sorts of discoveries about
it which would otherwise have escaped him. [. . . ] Not for nothing is magic called
the ‘mother of science”’ [Jung, 1972a, p. 46]. Alchemy, which always provided external symbolism related to “flows of energy”, furnishes plenty of examples, which
support this conviction.98
Progressively, what possible meaning that can be seen and learnt through the Whacandi artifact and the related rite can become completely internalized and fixed so that
referral to this externality – and learning from it – is no longer needed. Once internalized, the knowledge and the templates of action are already available at the brain level
of suitably trained neural networks with their electrical and chemical pathways. When
fixed and internalized they provide an immediate and ready “disposable energy”: for
example “We no longer need magical dances to make us ‘strong’ for whatever we
want to do, at least not in ordinary cases” [Jung, 1972a, p. 45].
The semiotic process of externalization leads to the formation of a new meaning,
which, as I have already said, Jung calls a symbol:99 “The Wachandi’s hole in the
earth is not a sign for the genitals of a woman, but a symbol that stands for the idea
of the earth woman who is to be made fruitful” [Jung, 1972a, p. 45]. The artifact is a
symbol, formed in the hybrid interplay between internal and external semiotic representations, and furnishes a “working potential in relation to the psyche” [Jung,
1972a, p. 46]. Another example is given by “[. . . ] those South American rockdrawings which consist of furrows deeply engraved in the hard stone. They were
made by the Indians playfully retracting the furrow again and again with stones,
over hundreds of years. The content of the drawings is difficult to interpret, but the
activity bound up with them is incomparably more significant” (ibid.).
3.8.4.2
Abducibility Maximization through Symbols
Through artifacts, the natural niche is transformed in a “cognitive niche”100 by human consciousness and unconscious: symbols are provided as “libido analogues”
98
99
100
Scientific historians have clearly illustrated the importance of Newton’s early research on
alchemy in the origin of classical Newtonian physics and of the concept of action-at-the-distance
[Dobbs, 1983], cf. chapter two of this book, section 2.3.
The Junghian concept of a symbol is a little different from the one used in semiotics: it is of
course richer in psychoanalytic value. However, it has to be noted that also for Peirce’s semiotics
a symbol is just a kind of iconic sign, which is conventional and fixed, like the ones used in
mathematics and logic, unlike generic signs, that are generally arbitrary and flexible.
Cognitive niches are fully described in chapter six, subsection 6.1.3.
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that convert energy “ad infinitum” [Jung, 1972a, pp. 49–50], and thus cognition and
culture. It is clear that symbols are artifacts that exhibit a maximization of abducibility ([Leyton, 1999; Leyton, 2001] speaks of the“maximization of recoverability”)
regarding past history, that is, of all the events that originate them: they are collective, stable, more or less available and sharable, related to both unconscious and
conscious dimensions, firm anchors for thinking and for triggering action, which
escape the fleeting nature of internal subjective representations.
The maximization of recoverability of symbols clearly explains their abductive
force in the analytic treatment. Symbolic artifacts made by individuals under treatment are obviously connected to the objective (already) externalized ones – which
are certainly more or less conscious and explicit in individuals – but are clearly provided (created) through the long history of humanity. Individuals’ symbols share
their archetypal primordial origin with these. Through suitable manipulations of
their external iconic character, together with the help of the externalization of speech
and affective signs in the communicative mediating environment of the therapeutic
setting, the constructed symbols can grant “explanations” of various psychic events
(based on internal, external, and hybrid representations). These explanations can
emerge thanks to the fact that symbols are memory mediators and, moreover, maximize abducibility (recoverability) of their past history, that is of all the psychic
events that originate them. Of course the explanations found convert psychic energy
flows (information, both cognitive and affective) by themselves and so activate and
further reshape the processes of progression and regression, which the fundamental therapeutical exigency of Junghian “individuation” requires. Symbols maximize
abducibility because they maximize recoverability, they mean “the best possible
expression” of something not yet grasped by consciousness.
Re-stating Jung’s views in the light of abduction and distributed cognition and
taking advantage of Leyton’s ideas has offered the new perspective concerning external artifactual symbols as abducibility maximizers: a new notion I consider both
provocative and promising. Some external symbols of the right sort are optimal for
the storage of semiotic meanings and their participation in thinking, like in the case
of psychoanalytic setting. However, an artifact (or any machine) is optimal only
against a set of assumptions about what alternatives are possible. I think this issue
is worth to be further studied, both from cognitive and ethical point of view.
These “symbols” go beyond the already considerable abducibility/recoverability
force of various semiotic (for instance iconic) externalizations related to more basic survival needs – also present in many animals – (like caches of food, hunting
landmarks, etc.) that are more constrained, if compared to symbols, in their capacity to trigger actions by promptly recovering various information and skills. These
last externalizations, often plastically shaped by learning and not a simple fruit of
instinctual endowments, are more or less widespread in the human and non-human
animals’ collectives, but they are normally merely behavior oriented to the direct
satisfaction of basic instincts, and thus they do not involve the broad cognitive role
of symbols (in a Junghian sense). These artifacts basically play the role of strong
cognitive remodeling of the human and animal niches and at the same time present
a regulative function of higher cognitive skills.
3.8 “Symbols” as Memory Mediators. Maximizing Abducibility
215
To make a simple example, the huge success of some symbols of this kind,
for instance the religious ones, can be certainly explained in terms of their capacity to maximize abducibility in a very extended domain of human “minds”, even
if endowed with various degrees of cognitive skills. They trigger good hypotheses/thoughts, but the “user” of those symbols available over there in the close environment is in general very passive. I guess the concept of “moral mediator” I have
introduced in my book [Magnani, 2007d] can be exploited to the aim of clarifying
the use of kinds of maximizing symbols especially in general social and collective
situation where moral issues are at stake. Of course, a similar role is played by
the epistemic mediators I have illustrated in chapters one and three, that maximize
abducibility in smaller collectives, like the scientific ones: successful manipulative
abduction reaches relevant hypotheses the agent – here active and interactive – has
exploited suitable artifacts, external representations and cognitive delegations and a
smart manipulations of them.
It may not be superfluous, at this point, to say a few words about the frequently
heard objection that the constructive method is simply “suggestion”. The method
is based, rather, on evaluating the symbol (i.e. dream-image or fantasy) not merely
semiotically, as a sign for elementary instinctual processes, but symbolically in the
true sense, the word “symbol” being taken to mean the best possible expression for
a complex fact not yet clearly apprehended by consciousness [Jung, 1972c, p. 75].
We can clearly acknowledge the fact that the inferential process described in the
passage above is in itself an explanatory abduction, because the problem, in front of
the available data which constitute the “unconscious material” [Jung, 1972c, p. 77],
is that of creating or selecting the suitable symbol, among the several available, and
then appropriately managing it, with the help of the construction of explanatory narratives, with the aim of correctly reverting the psychic energy of both the analysed
and the analyst.
The Junghian focus on symbolic artifacts called mandala, made by patients, not
merely based on the tradition of religious ones, but free creations determined by
certain archetypical ideas unknown to their creators, is related to the problem of
“seeing” for example stages of individuation, where step by step patients “give a
mind to that part of the personality which has remained behind” [Jung, 1968c, p.
350]. They are presented as “ideograms” of unconscious contents. In this case the
hybrid character of the process is at stake, where the (relative) autonomous role
of the external materiality is patent: “[. . . ] one can paint very complicated pictures
without having the least idea of their real meaning. While painting them, the picture
seems to develop out of itself and often in opposition to one’s conscious intentions”
[Jung, 1968c, p. 352]. They function as “magical” meanings related to the collective
unconscious, like “icons, whose possible efficacy was never consciously felt by the
patient” [Jung, 1968b, p. 361].
For Jung “the making of a religion” is a primary interest of the primitive mind
and strongly relates to the production of symbols, which “enable man to set up a
spiritual counterpole to its primitive instinctual nature” [Jung, 1972a, p. 59], like
already Vico clearly stated. For Vico, the most “savage, wild, and monstrous men”
did not lack a “notion of God,” for a man of that sort, who has “fallen into despair
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3 Semiotic Brains and Artificial Minds
of all the succours of nature, desires something superior to save him” [Vico, 1968,
339, p. 100]. This desire led those “monstrous men” to invent the idea of God as a
protective and salvific agent outside themselves; this shift engendered the first rough
concept of an external world, one with distinctions and choices and thus established
conditions for the possibility of free will. In the mythical story, the idea of God
supplies the first instance of “elbow room” for free will illustrated by [Dennett,
1984]: through God, men can “hold in check the motions impressed on the mind101
by the body” and become “wise” and “civil.”
According to Vico, it is God that gives men the “conatus” of consciousness and
free will:
[. . . ] these first men, who later became the princes of the gentile nations, must have
done their thinking under the strong impulsion of violent passions, as beasts do. We
must therefore proceed from a vulgar metaphysics, such as we shall find the theology
of the poets to have been, and seek by its aid that frightful thought of some divinity
which imposed form and measure on the bestial passions of these lost men and thus
transformed them into human passions. From this thought must have sprung the conatus proper to the human will, to hold in check the motions impressed on the mind by
the body, so as either to quiet them altogether, as becomes the wise man, or at least
to direct them to better use, as becomes the civil man. This control over the motion of
their bodies is certainly an effect of the freedom of human choice, and thus of free will,
which is the home and seat of all the virtues, and among the others of justice. When
informed by justice, the will is the fount of all that is just and of all the laws dictated
by justice. But to impute conatus to bodies is as much as to impute to them freedom to
regulate their motions, whereas all bodies are by nature necessary agents (ibid., 340,
p. 101.)
Free will, then, leads to “family”: “Moral virtue began, as it must, from conatus.
For the giants, enchanted under the mountains by the frightful religion of the thunderbolts, learned to check their bestial habits of wandering wild through the great
forests of the earth, and acquired the contrary custom of remaining hidden and settled in their fields. [. . . ] And hence came Jove’s title of stayer or establisher. With
this conatus, the virtue of the spirit began likewise to show itself to them, restraining
their bestial lust from finding satisfaction in the sight of heaven, of which they had
a mortal terror” (ibid., 504, p. 171.) “The new direction took the form of forcibly
seizing their women, who were naturally shy and unruly, dragging them into their
caves, and, in order to have intercourse with them, keeping them there as perpetual
lifelong companions” (ibid., 1098, p. 420.).
101
Indeed “That is, the human mind does not understand anything of which it has had no previous
impression [. . . ] from the senses” (ibid., 363, p. 110). “And human nature, so far as it is like that
of animals, carries with it this property, that senses are its sole way of knowing things” (ibid.,
374, p. 116). Again, humans “in their robust ignorance” know things “by virtue of a wholly
corporeal imagination” (ibid., 376, p. 117). Aristotle had already contended that “nihil est in
intellectu quod prius non fuerit in sensu.”
3.8 “Symbols” as Memory Mediators. Maximizing Abducibility
217
Summary
The main thesis of this chapter is that the externalization/disembodiment of mind
is a significant cognitive perspective able to unveil some basic features of creative
abductive thinking and its cognitive and computational problems. Its fruitfulness in
explaining the semiotic interplay between internal and external levels of cognition is
evident and was traced back to some seminal thoughts Turing provided about what
he called the transition from “unorganized” to “organized” brains. I maintained that
various aspects of creative meaning formation could take advantage of the research
on this interplay: for instance study of external mediators can provide a better understanding of the processes of explanation and discovery in science and in some
areas of artificial intelligence related to mechanizing discovery processes.102
From the paleoanthropological perspective we have learnt that an evolved mind
is unlikely to have a natural home for new concepts and meanings, as such concepts
and meanings do not exist in the artificial and natural world as it is already known.
Analogously, from this perspective, we have seen how the cognitive referral to the
central role of the relation between meaningful behavior and dynamical interactions
with the environment becomes critical to the problem of modeling up-to-date artificial systems devoted to performing creative and explanatory tasks: I contend that the
epistemological role of those artifacts, such as computers, which I called “mimetic
minds”, can be further studied, taking advantage of research on hypercomputation.
The imminent construction of new types of universal “abstract” and “practical” machines will constitute important and interesting new “mimetic minds” externalized
and available over there, in the environment, as sources of the mechanisms underlying the emergence of new meaning processes. They will provide new tools for
creating meaning in classical areas like analogical, visual, and spatial inferences,
both in science and everyday situations, thereby extending the epistemological and
psychological theory.
Finally, the externalization/disembodiment of mind is a significant cognitive
perspective able to unveil some aspects of creative meaning formation central to
psychoanalytic research and therapy. I have highlighted some Junghian analysis regarding the role of certain external artifacts where the mobility and disposability
of psychic energy are seen as the secret of cultural development both at the collective and individual level. I have contended that symbols, in a psychoanalytic sense,
are artifacts/tools that maximize abducibility, because they maximize the recoverability of something hidden, not yet grasped by consciousness. The new concept
of maximization of abducibility promises to stimulate further research about the
relationships between abduction and external mediators.
102
On recent achievements in the area of machine discovery simulations of model-based creative
tasks cf. [Magnani et al., 2002a]. Cf. also section 2.7 of chapter two.
Chapter 4
Neuro-multimodal Abduction
Pre-wired Brains, Embodiment, Neurospaces
In chapter three I have illustrated the main features of the so-called disembodiment of mind from the point of view of the cognitive interplay between internal and
external representations, where the problem of the continuous interaction between
on-line and off-line intelligence can be properly addressed. I consider this interplay
critical in analyzing the relation between meaningful semiotic internal resources
and devices and their dynamical contact with the externalized semiotic materiality
already embedded in the artificialized environment. Hence, minds are “extended”
and artificial in themselves. It is from this distributed perspective that I will further
stress how abduction is essentially multimodal, in that both data and hypotheses can
have a full range of verbal and sensory representations, involving words, sights, images, smells, etc., but also kinesthetic experiences and other feelings such as pain,
and thus all sensory modalities. The presence of kinesthetic aspects plainly demonstrates that abductive reasoning is basically manipulative. Again, both linguistic and
non linguistic signs have an intrinsic semiotic life, as particular configurations of
neural networks and chemical distributions (and in terms of their transformations)
at the level of human brains, and as somatic expressions. However they can also
be delegated to many external objects and devices, for example written texts, diagrams, artifacts, etc. We can also see, in this regard, how unconscious factors take
part in the abductive procedure, which consequently acquires the character of a kind
of “thinking through doing”.
Hence, abductive cognition is occurring in a “distributed” framework and in a
hybrid way, that is, in the interplay between internal and external signs. First of all
we can say that all representations are brain structures and that abduction certainly
is a neural process in terms of transformations of neural representations. We can
reconceptualize abduction neurologically as a process in which one neural structure
representing the explanatory (or non-explanatory and instrumental) target generates
another neural structure that constitutes a hypothesis. Some fMRI studies on problem solving where the insight involved is more or less creative and accompanied
by Aha! experience and on non-insight based problem solving interestingly show
the different brain areas involved and the role played by emotional aspects. The
neuro-multimodal perspective also clearly demonstrates how the classical view of
L. Magnani: Abductive Cognition, COSMOS 3, pp. 219–264.
c Springer-Verlag Berlin Heidelberg 2009
springerlink.com
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4 Neuro-multimodal Abduction
abduction based on logic (from the classical Peircean syllogistic model to the more
recent non-standard deductive models) only captures limited properties of this cognitive process (fallacious vs. non-classical truth-value preservation, stabilization in
axiomatic theories of standard modalities of inferring, etc.). Indeed, from the neuromultimodal perspective even propositions “are” internal neural structures consisting
of neural connections and spiking behaviors. Of course, I repeat, propositions and
other semiotic aggregates, according to this externalist view, can also be represented
in external supports, where they have to obey the proper constraints of the materiality at play.
Furthermore, cognitive abductive performances are to a large extent neurally
hardwired: “mind” results from the rigid execution of the DNA program. When
based on merely pre-wired genetic endowments, however, this execution interacts
with the world and the phenotype is basically a creation of both genotype and environment. Thus, organisms are equipped with various ontogenetic mechanisms that
permit them to acquire information and better adapt to the environment. For instance, the immune system in vertebrates and brain-based learning in animals and
humans, which are mechanisms characterized by plasticity. I also describe how
some well-known research on neurons, which in primates and humans react to observation of actions, raises interesting questions concerning the so-called “embodied
cognition” and is able to shed light on the role of abduction in guessing intentions,
in mentation and metamentation, in affective attunement and in other emotional and
empathic appraisals.
The main body of the chapter illustrates that “abduction” is central to understanding some features of action and decision making. Abduction prompts action
and plays a key role in decision making. Peirce teaches that the neurological perspective, depicted in this chapter, also increases knowledge about the distinction
between thought and motor action, seeing both aspects as fruit of brain activity.
We can say that thought possesses an essential “motoric” component reflected in
brain action but not in actual movement. On the basis of this analysis I can further
illustrate some problems related to the role of abduction in decision-making, both
in deliberate and unconscious cases, and its relationship with both hardwired and
trained emotions. I also contend that ethical deliberation, as a form of practical reasoning, shares many aspects with hypothetical explanatory reasoning (selection and
creation of hypothesis, inference to the best explanation) as it is described by abductive reasoning in science. Of course in the moral case we have reasons that support
conclusions instead of explanations that account for data, like in epistemological
settings. To support this perspective, I propose a novel analysis of the “logical structure of reasons”, which supports the thesis that we can look to scientific thinking and
problem solving for models of practical reasoning. The distinction between “internal” and “external” reasons, originally proposed by Searle, is fundamental: internal
reasons are based on a desire or on an intention, whereas external reasons are, for
instance, based on external obligations and duties which we can possibly recognize
as such. Some of these external reasons can be grounded in epistemic mediators
of various types. Finally, it is important to illustrate why it is difficult to “deductively” grasp practical reasoning, at least when we are aided only by classical logic;
4.1 Multimodal Abduction
221
complications arise from the intrinsic multiplicity of possible reasons and from the
fact that in practical reasoning we can often hold two or more inconsistent reasons
at the same time.
The third and last part of the chapter, on “Spatial Frameworks, Anticipation,
and Geometry”, fulfils the exigence of presenting how abduction is at the basis of
mammalian cognitive systems representing the location of objects within the spatial
framework. Various aspects of this fundamental abductive activity are illustrated:
1. the concepts of spatial egocentric and allocentric mapping and its plasticity,
2. the role of the hippocampus in performing internal subsequent representations
such as abductive hypotheses of space,
3. the discovery of a neuronal spatial map in the medial dorsocaudal entorhinal
cortex, anchored by external landmarks, which constitutes the basic spatial input
exploited by the hippocampus to construct more specific and context-dependent
spatial firing in its place cells.
Related to the cognitive problem of spatiality and of the genesis of space is the
description of the abductive role of the Abschattungen (adumbrations), as they are
described in the framework of the philosophical tradition of phenomenology. The
adumbrations naturally lead to the analysis of the so-called “anticipations”, which
share various features with visual and manipulative abduction, such as the way that
they are conjectural and nonmonotonic, which means that incorrect anticipations
have to be replaced by more plausible ones. The problem of anticipation is further
complicated in the framework of the so-called emulation theory, which contends
that emulation circuits are able “to hypothesize” any forward mapping from control signals to the anticipated – and so abduced – consequences of executing the
control command. They “mimic” the body and its interaction with the environment
enhancing motor control through sensorimotor abductive hypotheticals, and nicely
explain the emergence of implicit and explicit agency. The abductive character of
the concept of anticipation will be further reworked in chapter eight (subsection
8.2.1) linking it to the concept of attractor of the dynamical system theory.
4.1
Multimodal Abduction
As I have already stressed, Peirce considers inferential any cognitive activity whatever, not only conscious abstract thought; he also includes perceptual knowledge
and subconscious cognitive activity. For instance in subconscious mental activities
visual representations play an immediate role.1 Many commentators criticized this
Peircean ambiguity in treating abduction at the same time as inference and perception. It is important to clarify this problem, because perception and imagery are
kinds of that model-based cognition which we are exploiting to explain abduction:
I contend that we can render consistent the two views [Magnani, 2006c], beyond
Peirce, but perhaps also within the Peircean texts, partially taking advantage of the
1
Cf. [Queiroz and Merrell, 2005].
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4 Neuro-multimodal Abduction
concept of multimodal abduction, which depicts hybrid aspects of abductive reasoning. [Thagard, 2005; Thagard, 2007] observes, that abductive inference can be visual
as well as verbal, and consequently acknowledges the sentential, model-based, and
manipulative nature of abduction I have illustrated above. Moreover, both data and
hypotheses can be visually represented:
For example, when I see a scratch along the side of my car, I can generate the mental
image of a grocery cart sliding into the car and producing the scratch. In this case both
the target (the scratch) and the hypothesis (the collision) are visually represented. [. . . ]
It is an interesting question whether hypotheses can be represented using all sensory
modalities. For vision the answer is obvious, as images and diagrams can clearly be
used to represent events and structures that have causal effects.
Indeed hypotheses can be also represented using other sensory modalities:
I may recoil because something I touch feels slimy, or jump because of a loud noise,
or frown because of a rotten smell, or gag because something tastes too salty. Hence
in explaining my own behavior my mental image of the full range of examples of
sensory experiences may have causal significance. Applying such explanations of the
behavior of others requires projecting onto them the possession of sensory experiences
that I think are like the ones that I have in similar situations. [. . . ] Empathy works the
same way, when I explain people’s behavior in a particular situation by inferring that
they are having the same kind of emotional experience that I have in similar situations
[Thagard, 2007].
Thagard illustrates the case in which a colleague with a recently rejected
manuscript is frowning: other colleagues can empathize by remembering how annoyed they felt in the same circumstances, projecting a mental image onto the colleague that is a non-verbal representation able to explain the frown. Of course a
verbal explanation can be added, but this just complements the empathetic one. It is
in this sense that Thagard concludes that abduction can be fully multimodal, in that
both data and hypotheses can have a full range of verbal and sensory representations.
Thagard also insists on the fact that Peirce noticed that abduction often begins
with puzzlement, but philosophers rarely acknowledged the emotional character of
this moment: so not only is emotion an abduction itself, like Peirce maintains, but it
is at the starting point of most abductive processes, no less than at the end, when a
kind of positive emotional satisfaction is experienced by humans.
4.2
Neuroabduction: Internal and External Semiotic Carriers
Some basic aspects of this constitutive hybrid nature of multimodal abduction – involving words, sights, images, smells, etc. but also kinesthetic experiences and other
feelings such as pain, and thus all sensorimotor modalities, clearly show the usefulness of accounting for all this semiotic activity from a neurological perspective. A
neural structure can be seen as a set of neurons, connections, and spiking behaviors,
and their interplay, and the behavior of neurons as patterns of activation, like maintained by the connectionist tradition, also endowed with an important exchange of
4.2 Neuroabduction: Internal and External Semiotic Carriers
223
chemical information. In this perspective it is clear we can say all representations
are brain structures and abduction is a neural process in terms of transformations
of neural representations. Thagard concludes: “Hence we can reconceptualize abduction neurologically as a process in which one neural structure representing the
explanatory target generates another neural structure that constitutes a hypothesis”
[Thagard, 2007].2
As I have already said, it is important to note that, in both humans and other
vertebrates, neurons fire and provide electrical inputs to other neurons suitably connected by excitatory and inhibitory links, as illustrated in the connectionist neuralnetwork models of brain. However, the direct effects of real neurons on each other
are chemical rather than electrical, in that various molecules (“neurotransmitters”,
with excitatory and inhibitory effects) are emitted from one neuron and then passed
to another neuron, where they trigger chemical reactions that generate the electrical functions of the stimulated neuron. Neural network are Turing-complete, that is
they can compute any function that a Turing machine can, but of course they are
also directly – physically – responsible for the organisms’ cognitive capabilities.
The chemical messengers also include hormones and other molecules, and this
neurochemistry is certainly central: it involves the action of the so-called “neuromodulators”, which can also travel to parts of the body such as the adrenal glands,
which in turn release other hormones that travel back to the brain and influence
2
Recent research depict the localization in human brain of different abductive performances that
emphasize some aspects of this multimodality at least from the neurological point of view.
[Jung-Beeman et al., 2004; Bowden and Jung-Beeman, 2003] have provided a neurological
study on insight accompanied by Aha! experience in various problem solving abductive settings
in their relationships with unconscious processing. The research depicts the different cognitive
and neural processes that lead to insight vs. non insight solutions. There is different hemispheric
involvement in subjects that solve verbal problems (recognizing distant or novel semantic –
or associative – relations, extracting themes, comprehending indirect language such as jokes,
metaphors and unconnected discourse, forming coherent memories for stories). fMRI data reveal increased activity in the right hemisphere (RH) anterior superior gyrus (aSTG) for insight
relative to non insight solutions. The same area is involved during the initial effort; usually people cannot report the processing that enabled them to restructure the problem and to overcome
the impasse. Scalp EEG recordings revealed a sudden burst of high-frequency (gamma-band)
neural activity in the same area beginning 0, 3s prior to insight solutions. This right anterior
temporal area is associated with making connections across distantly related information during comprehension. Of course all problem solving relies on a largely shared cortical network,
but the sudden flash occurs when the agents exploit distinct neural and cognitive processes that
allow them to abductively envisage connections that previously eluded them. The researchers
also detected an insight effect in small clusters in or near bilateral amygdala or parahippocampal
gyrus, that is plausible if memory interacts with insight solutions differently from how it interacts with noninsight solutions. The authors are not arguing that the left hemisphere (LH) solves
noninsight problems, or that the LH is conscious and the RH unconscious: it actually seems that
people make conscious decisions and reach explicit results influenced by partially independent
activation in each hemisphere of a population of many thousands of neurons, without the need
of an executive “homunculus or grandmother cell” [Bowden and Jung-Beeman, 2003, p. 736].
This population is divided among the two hemispheres which work through distant mechanisms
(LH → semantic coding, RH → coarse novel semantic coding). Other cortical areas such as
the prefrontal cortes and the anterior cingulate (AC) may also be involved in this process of
providing insight and noninsight solutions.
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the firing of the appropriate neurons. Of course we can agree with Thagard on the
fact that these neurochemical mechanisms can further clarify deep aspects of cognition, like emotions, problem solving, and decision-making, which can only be
completely understood with difficulty through the traditional connectionist neuralnetwork models. Hence, most synapses are chemical, neurotransmitter pathways
that “[. . . ] provide the brain with a kind of organization that is useful to accomplish
different functions. [. . . ] Neurotransmitters provide a course kind of wiring diagram, organizing general connections between areas of the brain that need to work
together to produce appropriate reactions to different situations” [Thagard, 2002a]
in a more flexible way.
Emotions can be easily thought of within this framework, they are neural structures that involve complicated interactions among sensory processes linking bodily
and various other cognitive processes distributed in many brain areas. Let us see
an example that comes form the area of scientific reasoning. In Thagard’s terms
introduced above, first of all a target meaningful assembly of possibly anomalous
data (made available through the sensory processes), is internally emotionally transformed and marked as disturbing or puzzling. Through further synaptic connections
it is coordinated to the spiking behavior of the emotional structures: in this way
emotion furnishes immediate abductive appraisals of the bodily states, and provides
a kind of “explanation” of them. Of course a marked emotional state can be coordinated to neural structures which in turn express other abductive verbal or sensory
reactions, to which a further emotional experience of satisfaction or pleasure can
in turn be associated. Also every unconscious activity of cognition can be reinterpreted in the meaningful terms of neural transformations, the study of which seems
ultimately most approachable through new techniques and experimentation.
The neuro-multimodal perspective shows, resorting to basic biological levels,
how the classical perspective of abduction based on logic (from the classical
Peircean syllogistic model to the more recent non-standard deductive models – cf.
[Magnani, 2007a]) only captures limited properties of this cognitive process (fallacious or truth-value preservation, stabilization in axiomatic theories of standard
modalities of inferring, etc.). Indeed, in the neuro-multimodal perspective propositions too “are” internal neural structures consisting of neural connections and
spiking behaviors. Consequently, beliefs and desires, that traditional philosophy interpreted as propositional attitudes, can be usefully seen as brain structures, and
moreover, in this extended framework the concept of inference can be reinterpreted
to encompass non-verbal representations from all sensory modalities and their hybrid combination, going beyond its merely logical meaning in terms of arguments
on sentences.
Of course propositions, and other semiotic aggregates, can also be represented in
external supports, where they have to obey the proper constraints of the materiality
at play. In the previous chapter I have already illustrated that in the case of humans
and other organisms, it is only through the interplay between internal and external
representations that the many kinds of cognitive processes can work. Furthermore,
an interplay between sentential/symbolic and model-based aspects is often at work
in important cognitive processes as in the creative abductive ones. For example,
4.2 Neuroabduction: Internal and External Semiotic Carriers
225
when mathematicians mentally represent suitably composed or discovered sets of
equations or symbolic structures to solve a problem, taking advantage of the mental
recapitulations of visual images already eventually represented externally. Donald
says
[. . . ] they cannot evaluate what they have done until they break the circle of symbols
and relate them to other mental structures, usually visual images, that reside outside
the equations themselves. Driven by a deeper intuition and a need for closure or differentiation, they evaluate the new symbolic expression and modify it out of necessity.
The success of a truly new symbolic expression can therefore be judged only by part of
the mind that intuits the successful clarification of its own inner state [Donald, 2001,
p. 278].
Signs are everywhere in our human artificialized world, on blackboards, in books,
on videos, as propositions, icons, symbols, configurations, diagrams, etc. But many
kinds of signs are also expressed at the neural level. This means that semiotic
minds/brains are not self-sufficient neural devices, like eyes, but the hybrid product of the brain-culture symbiosis [Donald, 2001, p. 202]. The most efficient move
for individual human brains has been to become part of this external semiotic materiality – thus they can far exceed their capacity of coping with or remembering it
– and enable themselves to evolve with it, tracking what is over there and fulfilling
various degrees of need.
In this endeavor human beings always contribute to the modification of that external semiotic materiality, and in some cases favor its enhancement and creative
change. The baby is already encapsulated in a world of model-based signs that operate at a pre-linguistic level, but very soon she can take advantage of subsequent
encapsulation into a whole semiotic culture (also including language), mediated
by parents, family, tribal customs or institutions, etc., that takes further control of
his/her cognitive development.3
Starting from the “virtual” reality established at the evolutionary birth of human
language, through the construction of an oral-mythic culture and scientific theories, right up until modern technological artifacts, which ideally continue the material culture of the hominids, human beings have always endowed themselves with
powerful external devices able to overcome their brain biological limitations. These
prostheses have enabled them to also build narratives that in turn have allowed the
undertaking of big projects. In particular technological advances have provided external devices and artifacts, like computers, “specifically” designed to help us reason, remember, mime various internal representations and internally re-represent
the previously externally stored representations. These are truly formidable devices,
3
It is well-known that Vygotsky already focused the attention to this interplay between external
and internal representations (and the process of re-internalization) in his pioneering studies on
children’s language acquisition (Outside/Inside principle) [Vygotsky, 1978; Vygotsky, 1986].
The developmental rule is that brain first represents external action and only later reconstructs
it so that it will occur internally. On the problem of the so-called affective attunement in human
infants cf. chapter five, subsection 5.7.3, on some suggestions coming from Thom’s catastrophe
theory on how natural syntactical language is seen in attunement of infants to mother’s language
cf. chapter eight, subsections 8.4.1 and 8.5.1.
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4 Neuro-multimodal Abduction
which I have called in the previous chapter “mimetic minds” (section 3.7, cf. also
[Magnani, 2006c]). At the same time these tools have produced the possibility to
aggregate externalized thoughts in various ways, taking advantage of the external
constraints of the electronic materiality at hand, of course different from the neural
one available through brains.
Donald contends that this process is also manifest when we analyze the role
played by memory media in the functioning of the human conscious mind: “The
biological memory records, known as engrams, differ from the external symbols, or
exograms, in most of their computational properties. [. . . ] The conscious mind is
thus sandwiched between two systems of representation, one stored inside the head
and the other outside. [. . . ] In this case, the conscious mind receives simultaneous
displays from both working memory and the external memory field. Both displays
remain distinct in the nervous system” [Donald, 2001, pp. 309–311].
4.3
4.3.1
Pre-wired Brains and Embodiment
The Pre-wired Brain
Cognitive performances are to a large extent neurally pre-specified. Research in genetics shows substantial evidence for genetic pre-wiring of a great deal of brain
structure in both human and non-human animals. Important gene expression patterns of the brain occur before experience-dependent input. Hence, the brain is prewired even if not with total specificity, and with a great degree of chance involved.4
Ramus says:
Indeed whether a neurone will grow dendrites or produce a particular molecular cue
at a given time depends on the expression of particular genes, which itself depends on
many internal factors like which other genes the neurone currently expresses, as well
as external factors like which molecules surround it and in what concentration (which
can in particular specify the neurones’ position within the brain and within its neural
structure) [Ramus, 2006, p. 255].
[Baum, 2006, p. 336] observes, taking advantage of a computational metaphor, that
“[. . . ] mind results from the execution of the DNA program. But [. . . ] this execution proceeds in interaction with the world. Culture is in a sense part of the working
memory, the data space, used by this execution. [. . . ] Evolution naturally discovers
programs that interact with the environment to learn”. [Marcus, 2004, p. 84] adds
that “[. . . ] the same genes that are used to adjust synapses based on internal instruction can be reused by external instruction”. It is in this perspective that we can easily
4
The term “wired” can be easily misunderstood. Generally speaking, I accept the distinction
between cognitive aspects that are “hardwired” and those which are simply “pre-wired”. By the
former term I refer to those aspects of cognition which are fixed in advance and not modifiable.
Conversely, the latter term refers to those abilities that are built-in prior the experience, but that
are modifiable in later individual development and through the process of attunement to relevant
environmental cues: the importance of development, and its relation with plasticity, is clearly
captured thanks to the above distinction. Not all aspects of cognition are pre-determined by
genes and hardwired components. Cf. also [Barrett and Kurzban, 2006].
4.3 Pre-wired Brains and Embodiment
227
understand why some authors consider a revolution in evolutionary biology “[. . . ]
to actually admit what geneticists and evolutionists have claimed all along without
seeing: the phenotype is a creature of both genotype and environment. It is the mediator of all genetic and environmental influence, in both development and, as the
object of selection, evolution” [West-Eberhard, 2003, p. 525].
Of course many neuroanatomical modules need considerable input from the external world (already at the level of utero biochemical factors), fine tuning, and
experience-driven maintenance to get their – restructured – functional adult abilities, and also to preserve the structure itself. In this sense pre-wiring does not
imply hardwiring, but the so-called “brain plasticity” endowments have limits and
genome-directed constraints.5 All environmental experience has to pass through the
rigid features of sensory receptors imposed by the neural structure (especially in
sub-cortical and sensory areas), and it is only in this way that it can be seen as the
“execution” of a genetic program that codes for proteins: not everything is learnable.6 In the framework of genetic influences on brain processes concepts like innateness, domain-specificity, and evolutionary selection, which are rather vague,
could be reshaped in a more neurogenetical satisfactory scientific way, for instance
taking advantage of research between genes and brain development, and its anomalies and cognitive dysfunctions.
Organisms are equipped with various ontogenetic mechanisms that permit them
to acquire information and thus better adapt to the environment: for instance, the
immune system in vertebrates and brain-based learning in animals and humans.
Plasticity characterizes these mechanisms, which, West-Eberhard says, “mimic” selection: “Learning itself can be fine-tuned under selection and then can mimic selection to create, and rapidly spread, novel adaptive traits” [West-Eberhard, 2003,
p. 337].7 The role of these mechanisms is to provide organisms with supplementary
devices to acquire information and thus afford various environmental contingencies
that are not – and cannot be – specified at the genetic level [Odling-Smee et al.,
2003, p. 255]. A genetically specified initial set of behaviors is elaborated through
experience of a relevant environment. These ontogenetic mechanisms are therefore
a sort of on-board system allowing flexibility and plasticity of response to an everchanging environment, which are at the core of the notion of cognition that is at the
basis of our treatment [Godfrey-Smith, 2002].8
5
6
7
8
On the so-called brain “cross-modal” plasticity, which deals with changes and reorganization
of cortical functions in an individual brain in front of sensory deprivation cf. [Bavelier and
Neville, 2002].
Genetic control also operates throughout life and has on-line effects (for instance on coding of
neurotransmitters, their receptors and other molecules involved in neurotransmission pathways)
[Ramus, 2006, p. 258].
On Edelman’s neural Darwinism, which sees neurons as populations submitted to “loosely”
Darwinian effects, cf. subsection 6.1.4, chapter six.
Godfrey-Smith defines cognition as the capacity of coping with a range of possible behavioral
options with different consequences for the organism’s chance to survive. This definition allows
him to embrace a broader notion of cognition which extends it to many animal and plant behaviors. I will discuss this thesis in chapter six, subsection 6.4.4 and in chapter eight 8.5.1, devoted
to the interplay between abduction and affordances.
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4 Neuro-multimodal Abduction
In the case of human beings and other mammals, bigger brains allow the storage
of information which could not be pre-defined by genes [Aunger, 2002, pp. 182–
193]. Flexibility and plasticity of response to an ever-changing environment are
connected to the necessity of having other means for acquiring information, more
readily and quickly than the genetic one. I posit that niche construction plays a fundamental role to in meeting this requirement. Plasticity and flexibility depend on
niche construction as far as various organisms may alter local selective pressure via
niche construction itself, and thus increase their chances of survival. More specifically, cognitive niches are crucial in developing ever more sophisticated forms of
flexibility, because they constitute an additional source of information favoring behavior and development control. In this case, epigenesis is therefore augmented,
and, at a genetic level, it is favored by genes regulating epigenetic openness [Sinha,
2006]. Epigenetic openness is closely related phenotypic plasticity [Godfrey-Smith,
2002]; the flexible response of living organisms (humans in particular) leans on sensitivity to environmental clues, and this process of attunement to relevant aspects of
the environment cannot be separated from niche construction (cf. subsection 6.1.3,
chapter six, on the interesting concept of cognitive niche).9
What are the consequences of the scientific results I have previously illustrated on
the concept of abduction? We have to observe that of course all the abductive performances I have illustrated have neural correlates. Recent research in neurology has
especially increased knowledge about cognitive skills in various organisms, mainly
dealing with perception and motor control in non-human animals, and some important new scientific perspectives could be useful to further detail certain aspects –
especially non-verbal – of abductive thinking which have already been emphasized
in philosophical, logical and psychological investigations. In the following subsection I will describe how some well known research on neurons, which in primates
and humans react to observation of actions, raise interesting questions concerning
the so-called “embodied cognition”.
4.3.2
Embodiment and Intentionality
Neurons in area F5 in the monkey ventral premotor cortex do not code elementary motions but goal-related actions [Rizzolatti et al., 1988]. A subclass of them
– the very famous mirror neurons – fire both when a monkey observes an action
performed by another individual and when it executes the same or a similar action,
like grasping, tearing, holding or manipulating objects. A subset of mirror neurons
9
The relationships between developmental plasticity and evolution are described in [WestEberhard, 2003]. For an illustration of the recent controversies and conceptual confusions about
phenotypic plasticity and genetic assimilation cf. [Pigliucci et al., 2006, p. 2366]: the authors
contend that phenotypic plasticity is not a threat to Modern Synthesis but an expansion of it, it
is (in part) a developmental process, not an evolutionary one. “As such, it can be the target of
natural selection (an evolutionary mechanism, though of course not the only one), and yields
– under certain conditions – the evolutionary outcome of genetic assimilation or phenotypic
accommodation. Once one recognizes the clear hierarchical distinctions among these concepts,
most fears about an imminent overthrow of the Modern Synthesis should dissipate.”
4.3 Pre-wired Brains and Embodiment
229
respond not only when the monkey executes or observes an action but also when it
hears that same action is performed by another agent. Neither the sight of the other
agent alone nor the sight of the object alone are sufficient to fire the mirror neurons’
response, as in the case of mimicking actions without a target object. Another subset
of mirror neurons can generalize and react in the presence of various, similar actions
and not only in the presence of a specific one, so they present a kind of inductive
hypothesizing pre-wired character. There is also evidence in favor of their existence
in humans.
The discovery of mirror neurons has given rise to speculation on various aspects
of social cognition such as intentions, action, empathy, mind-reading, emergence of
language, and the discussion has also included the problem of affective attunement
that I have cited in the previous subsection. What it is important to note is that in
the experiments on mirror neurons the interaction between agents, and the object
of the action is independent of the self-other distinction. [Gallese, 2006] contends
that the interaction would instead be “we-centric”, and would also underpin the
understanding of others as rudimentary and implicit “intentional” agents.
I am inclined to partially follow [Tummolini et al., 2006], in saying that mirror
neurons do not underpin a “representation” of the other agent, neither taking advantage of a self-representation nor of a representation in terms of a “we-agent”. Indeed,
frankly, I do not think the interaction can be considered “we-centric”: how is it possible to conjecture a “we” if not in terms of an already hypostatized “me” and “you”?
The problem is that there is neither the we-centric situation nor the self/other one, at
least, not as they are understood in our ordinary folk psychology. The observed interaction in primates cannot say anything about the self/non-self distinction, it seems
to be basically agentless. It can simply affect changes and transformations in the individual’s behavior that we (as researchers) see. Moreover, if representations are at
play, they are representations in a Picwickian sense, like the ones I will describe in
the following chapter of this book, acting in many cases of animal behavior, that is,
they are simply perceptual-, motor-, and behavior-directed and not mentalistic.
I have said that many researchers on mirror neurons hypothesize that the interaction at play would also underpin, in the case of children, the understanding of
others as rudimentary and implicit “intentional” agents. Of course in the absence
of the standard agentive and objective units it is difficult to hypothesize a kind of
(implicit) intention attribution in the perspective of the standard psychological sense
of the concept. Rather, in infants, only something similar to the case of some animals can be hypothesized where visual and motor “representations” carry perceptual
representations among external events, so that actions are understood as motor processes that lead to certain outcomes, that is, like “self-propelled beings that make
things happen” [Tummolini et al., 2006, p. 106]. Of course this framework involves
a kind of intentionality that cannot be described as fully psychological. In such
a way, through the equivalence between actions perceived and actions performed,
animals and infants can abductively form preferential hypotheses in terms of “intentions”, which explain some perceptual events linking different motor schemata.
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4 Neuro-multimodal Abduction
These hypotheses enable the organisms to predict the consequences of the actions
perceived.10
It has also been contended that the process leading to the abduction of subsequent self-correcting “hypotheses” that in turn lead to affective attunement,11 which
is formed through the interplay of facial imitation (cf. [Meltzoff and Brooks, 2001])
is also at play and underpinned by mirror neurons. In affective attunement, the coordinated process of exchange of a full range of somatosensory perceptual information
(visual, auditory, and tactile) can be seen in this light. A process in which the slow
formation of a kind of “selfness”, can be hypothesized, suitably accompanied by the
first social feeling of an identity of “being-like-you” [Gallese, 2006].
This embodied and subpersonal way of “understanding” and feeling events is
present also in adult humans. In this case it is either implicit, isolated, and basically unconscious, or accompanied by that effect of mentalization that leads to the
interpretation of beings like full intentional agents, showing a movement from the
attribution of a kind of external – “in the world” – intentionality to the agent-oriented
intentionality of folk psychology. The shift is from “goals as relational structures in
the world to goals as intentional relations between agents and the world” (ibid.), in
terms of belief/desire and intentions mental/brain states. In this last case it is obvious
to note that full representational mechanisms are needed, for example propositional
ones, which go far beyond the basic visual and motor framework, and involve other
regions of the brain, embracing the sensorimotor ones. I agree with [Gallese, 2006]
that this distinction between “behavior readers”, like non-human primates and other
animals on the one hand and “mind readers”, like humans on the other, does not have
to be taken as a sharp distinction depicting a strong discontinuity, where the role of
propositional attitudes in the formation of the self-other distinction is overstated.12
In the experiments on primates it can be clearly seen how information (modelbased, visual or auditory), conveyed through perception from the outside, is stored
through mirror neurons and coupled with them, and made available to enable suitable actions and new behaviors (i. e., appropriate to the ecological situation at
stake). Mirror neurons are simulators of the planned action, used to predict its consequences and thus achieve a better control of the action itself: information is picked
up outside and through their neural visual and motor processing, it is so to speak
“socially” re-externalized in the action performed, which of course is endowed
10
11
12
On the distinction between desires, beliefs, and intentions and on the various skillful abductive
metarepresentational processes that are at play in human intention attribution – where intentions
are intended as private or joint (in groups of people, the so-called “we-intentions”) mental states
of an agent – cf. the issues described in Malle, Moses, and Baldwin [2001]. The inferential
process – based on both the observed behavior and external information (multi-sensory: visualkinesthetic, auditory, etc.) and including other cues in the immediate context – involves an expert
“explanatory” selective abduction that has to discriminate among a very large range of possible
intentions that are consistent with a given action.
Cf. chapter five of this book, subsection 5.7.3 and chapter eight, subsection 8.5.1.
An analysis of the problem of embodiment in neuroscience, in traditional cognitive science
and in some aspects of phenomenology is given in [Gallese, 2005]. Recent research suggests
that both the understanding of intentionality in others – engagement in intentional exchanges,
and understanding how the mind of others has been affected by the communicative act, is also
present in people that lack language, such as deaf non signers [Donald, 2001, p. 144].
4.3 Pre-wired Brains and Embodiment
231
with a visual dynamic structure made available over there, in the environment, for
other watchers and listeners, in a cycle of further possible repetitions and modifications/enhancements.13 The representations carried out are of course not propositional and so they cannot carry “understanding” in the current meaning of the term.
They can activate cognition exactly in the sense of the term we will encounter, in the
following chapter, in the case of nonlinguistic animals. Of course it is perfectly plausible to guess that these representations ground (the neuroscientists say “scaffold”)
further development of more explicit abductive intentional attribution and agentive
understanding, even at the conscious level.
The entire process of non-declarative and non-conceptual embodied simulation
implied by the same brain areas of mirror neurons seen in non-human primates
and infants can be seen, as many authors do, like a grounding embodied process
– both from the ontogenetic and the phylogenetic perspective – of full maturation
in adult human beings. [Iacoboni, 2003] demonstrates how intention can be understood through imitation, a perspective that sheds light on the formation of complex
social cognitive skills like intentions themselves, planned actions, empathy, mindreading, and the emergence of language. The embodied and prereflexive effect carried out by the sensorimotor system also seems to be particularly important in bodily
recognition and emotion sharing (for instance, the experience of painful sensations).
It is also supposed to be the foundation of empathy because the embodied process of pretension is both a-centered and, at the same time, the basis of self-other
distinction.
The objectual “self” that is being formed through mirror neurons becomes the
“pseudoself” that is being circumscribed.14 Both emotions and empathy can acquire
various levels of awareness and meta-awareness through the more complicated intervention of larger brain areas in human adults, which enact possible new ways of
abductive emotional and empathic appraisals. Finally, it has to be remembered that
also spatial mapping plays an important role in the formation of the self-subject-asobject and consequently of its distinction from other objects (and possible agents)
(cf. below section 4.7).
Further insight on the problem of mentation, metamentation and the reflexive
mind is illustrated by [Bogdan, 2003], who also takes into account an evolutionary
perspective. Bogdan contends that, given the fact that the pressures on (and opportunities for) planning and problem solving are much greater in the precultural social
brain (genetically fixed) than in the mere manipulative “mechanical domain”, at
the origin of mentation there would be the re-use of patterns tracked by interpretation in the social domain (thus not the ones merely derived from physical skills
operating in the mechanical domains) already seen in primates: they slowly become
objects of mental rehearsal. I sum, social life (rather than physical work) and asocial
agency directed to conspecifics (rather than mechanical agency directed at the physical world) would be the main forces behind the evolution of primate mentation.
13
14
On mirror neurons as a clear example of sensorimotor brain structure cf. chapter three, section
3.6.4.
Research on imitation deficit in autism seems to confirm the presence of dysfunctions in mirror
motor-sensory areas of children affected by that disease [Oberman et al., 2005].
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4 Neuro-multimodal Abduction
Interpretation and mental rehearsal – thinking about thoughts – with the obvious
function of imagining nonactual situations, would be in turn crucial to the evolution of propositional attitudes and of explicit metathoughts, that are at the heart of
metamentation, thinking about representations of agency and intentionality.
4.4
Actions vs. Thoughts?
Adult and normal human brain circuitry compute the operations of human intelligence and cognition through hierarchical structures, embedded sequences and
hash coding. Naturalistically considered, these are physical and biological events
in-the-world that embody the semiotic life of human and many non-human animals. From this neurological perspective an interesting conclusion on our traditional
dichotomous view of organisms’ actions and thoughts can be derived.
Let us show a fragment of brain neurocomputational mechanisms, as illustrated
by Granger in a recent article [2006], which illustrates brain circuitry at work at the
level of striatal cortex. “It results that two separated pathways from cortex through
matrisomes involve different subpopulations of cells: (1) MSN1 neurons project to
GPi [pallidum, pars interna] → thalamus → cortex; (2) MSN2 neurons insert an
extra step: GPe [pallidum, pars externa] → GPi → thalamus → cortex. MSN and
GP projections are inhibitory (GABAergic), such that cortical excitatory activation
of MSN1 s causes inhibition in GPi cells, which otherwise inhibit thalamus and brainstem regions. Hence MSN1 cells disinhibit, or enhance, cortical and brainstem activity. In contrast, the extra inhibitory link intercalated in the MSN2 pathway causes
MSN2 s to decrease the activity of cortex and brainstem neurons. These two pathways
through MSN1 and MSN2 cells are thus called go and stop paths, for their opposing
effect on their ultimate cortical and motor targets” [Granger, 2006, pp. 16-17].
Coordinated operation over time can yield a sophisticated combination of activated “go” and withheld “stop” motor responses (for example to stand or walk), or
correspondingly complex thought (cortical responses). The cortex → striosome path
triggers a kind of evaluation signal, provisionally settled in default values, corresponding to an expected experiential (sensory) reward for the given action, which, if
the reward is not present, can lead to modifications which in turn trigger through other
complicated paths other new possible actions and thoughts. Of course thoughts can
in turn “mediate” further actions. At the level of the thalamocortical system, “core”
circuit cells that respond to a particular input pattern, in turn elicit activation patterns which involve an effect of “clustering”, and so of abductive generalization by
preventing fine distinction between the members of the cluster. Through subsequent
“samples” across time, refinements that activate subclustering are originated. The
process is then directed to a learning process that generates the synaptic weights that
can be assimilated to those “representations” we know through cognitive science.15
I think this example can imply two important theoretical considerations. First,
both brain events, motor and thought responses, are material/biological processes
15
For details on the role of other brain circuits cf. [Granger, 2006, pp. 19-24].
4.4 Actions vs. Thoughts?
233
of the organism, the first originating action at the phenomenal level of the individual, the second originating thought, which we hypothesize in its physico/chemical
aspects. In both cases, so to speak, the organisms “act”. Second, both “processes”
are subsequently modified by calculation based on the experiential outcomes, so
that the action or thought chosen can be revised like in the epistemological schema
of the abductive process I have illustrated in chapter one.16 In this neural naturalistic perspective the quasi-ontological dichotomy between actions and thoughts,
even if justified at a different, not neural, epistemological level – typical of the received philosophical and cognitive tradition – vanishes: obviously, both actions and
thoughts are, so to speak, “actions” of the organisms, both phenomenal and not
phenomenal levels are “performed” in the organism’s body. This conclusion is also
acknowledged by Edelman who, in the perspective of its neural Darwinism, quotes
Peirce:
Peirce pointed out that sensations are immediately present to us as long as they last.
He noted that other elements of of conscious life, for example, thoughts, are actions
having a beginning, middle, and end covering some portion of past or future. This fits
our proposal that thought has an essential motoric component reflected in brain action
but not in actual movement.17 [. . . ] This view of thought as being essentially motoric
is consistent with the known interactions of the frontal and parietal cortex with basal
ganglia, the subcortical regions involved in motor programs [Edelman, 2006, p. 123
and p. 168, footnote 3].
4.4.1
Decision Making and Action
Rational and deliberate decisions made by an agent are basically mediated by a
conscious processing of high-level cognitive functions like the sentential ones (for
example natural language) and various model-based ways of reasoning, but can also
be intertwined with “thinking through doing” and action-based cognition, all able
to carry an adequate amount of suitable knowledge. This kind of decision making
has to be distinguished from that in which thoughts or cognitive actions enter the
cognitive process without self-awareness, even if it has to be said that many decision
making processes are the fruit of a hybrid blending between conscious and unconscious cognitive aspects [Piller, 2000; Thagard, 2001].18 In rational and deliberate
16
17
18
Cf. also [Magnani, 2001b].
Thom further stresses that spoken a word is at the stage of emission an “action” in the literal
sense of a “muscular motor field (a chreod in Waddington’s sense) affecting the muscles of
the thorax, the glottis, the vocal chords and the mouth” [Thom, 1980, p. 236]. On Thom’s
catastrophe theory and abduction cf. chapter eight of this book.
The analysis of the concept of affordance [Gibson, 1979] also provides an alternative account of
the role of the environment and of external – also artifactual – objects and devices, as the source
of action possibilities (constraints for allowable actions). Artifactual cognitive objects and devices extend, modify, or substitute “natural” affordances actively providing humans and many
animals with new opportunities for action [Norman, 1988]. Neuropsychological and physiological evidence on how simple visual information affords and potentiates action – and the highly
integrated nature of visual and motor representations – is described in [Tucker and Ellis, 2006;
Knoblich and Flach, 2001; Derbyshire et al., 2006]. For further details on the interplay between
affordances, actions, and decisions [Magnani and Bardone, 2008] and this book, chapter six.
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4 Neuro-multimodal Abduction
decision making strategies (strategic principles)19 are at work [Brogaard, 1999], as
already stressed by the supporters of the general theory of games. These strategic principles always mediate between a given situation and a continuous range of
future possibilities or choices that are described and provided by suitable pieces of
hypothetical and generalized knowledge about events and processes (and “possible”
events and processes).
Of course decision processes in humans constitutively occur in the presence of
incomplete information and knowledge, like Peirce pointed out: “[. . . ] the sum of
all that will be known up at any time, however advanced, into the future, has a ratio
less than any assignable ratio to all that may be known at a time still more advanced”
[Peirce, 1931-1958, 5.330]. As I have already illustrated in chapter two (subsection
2.1) – where the abduction as an ignorance preserving kind of cognition is stressed
– abduction plays a key role in decision making processes: one of the central aims
of abduction is to recommend a course of action, in fact abduction usually provides
previously unavailable more or less reliable hypothetical knowledge able to explain
data which in themselves are considered inadequate to trigger a decision for action
(indeed the abductive hypotheses describe what will happen, if an action is carried
out). Nevertheless, even after having extracted new knowledge through abduction,
the best rational and deliberate decision is never reached like it would be in the
ideal situation where all the possible required knowledge is available: the best performance resorts to a simple activity of “maximization”, where the presence of the
available information and the smart use of strategic principles are the tools that make
humans able to pursue this target.
I have said in the previous subsection that, both brain events, – motor and thought
[inner] responses – are material/biological processes of the organism, the first originating action at the phenomenal level of the individual, the second originating
thought, which we can only hypothesize. In both cases, so to speak, the organisms
“act”. Both “processes” are subsequently modified by calculation based on the experiential outcomes, so that the action or thought chosen can be revised as in my
epistemological schema of the abductive process. From this neurological perspective the traditional dichotomous view between organism’s actions and organism’s
thoughts can be weakened.20
From this perspective abduction recommends decisions
1. which leads to a course of immediate motor actions,
• that, for instance by acquiring new information with respect to future interrogation and control, further trigger internal thoughts “while” modifying
the environment (thinking through doing). Peirce provides the example of a
cook making an apple pie for her master: “Throughout her whole proceedings she pursues an idea or dream without any particular thisness or thatness
19
20
I will describe in more detail the status of strategies in abductive reasoning in chapter seven,
subsection 7.3.2.2.
Cf. Edelman’s remarkable words about this issue, I have already quoted above, where : “essential
motoric” aspect of thought is emphasized [Edelman, 2006, p. 123 and p. 168, footnote 3].
4.4 Actions vs. Thoughts?
235
– or, as we say, hecceity – to it, but this dream she wishes to realize in connection with an object of experience, which as such does possess hecceity;
and since she has to act, and action only related to this and that, she has
to be perpetually making random selection, that is, taking whatever comes
handiest” [Peirce, 1931-1958, 1.341] (I think this case is related to the role
of manipulative abduction in my epistemological schema),
or
• that are more defined and not immediate, less random, and more pragmatical
and less intertwined with a continuous interplay with subsequent “thoughts”;
in this case action derives from a classical planning determined by inner
established thoughts/hypotheses.
but abduction also recommends decisions/actions
2. (as mere thoughts), which – internally – lead to a further course of thinking detached from any immediate motor action to reach new hypothetical knowledge
(of course, later on, open to make recommendations on further motor action).
4.4.2
Decision and Emotion
In the previous section I have said that rational and deliberate decision is basically
mediated by a conscious processing of high-level cognitive functions like the sentential ones (for example natural language) and various model-based ways of reasoning, but it can also be intertwined with “thinking through doing”. Emotion, an
important model-based aspect of cognition, plays a pivotal role in decision making:
emotions speed up the process and lead directly to actions. However using them to
make choices is usually considered irrational because of their disadvantages: in the
throes of strong feeling, we may be blind to some options, overlook critical information, or, when participating in a group charged with making a collective decision,
fail to engage or connect with others who do not share our emotional state [Thagard,
2001, 356–357].
I think it is important to understand, however, that emotions are not inherently irrational. For example, they can be useful tools in moral decision making if they are
successfully intertwined with learned cultural behaviors so that they become “intelligent emotions.” Emotions can be developed, and Picard points out, “Adult emotional intelligence consists of the abilities to recognize, express, and have emotions,
coupled with the ability to regulate these emotions, harness them for constructive
purposes, and skillfully handle the emotions of others.”21 There is ongoing debate
about the use of the expression “emotional intelligence”: while the word intelligence implies something innate, many aspects typical of emotional intelligence are
actually skills that can be learned.22
21
22
[Picard, 1994, p. 49], cf. also [Nussbaum, 2001].
On the neurological and cognitive role of emotions, cf. [Damasio, 1994; Damasio, 1999]. A
cognitive theory of moral emotions in terms of “coherence” is illustrated in [Thagard, 2000;
Thagard, 2001]. For recent work on emotional intelligence, see [Ben-Ze’ev, 2000], [Matthews
et al., 2002] and [Moore and Oaksford, 2002].
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Antonio Damasio differentiates conscious “feeling” from unconscious “emotion”
(of course, only conscious individuals “feel”) [Damasio, 1999]: the genesis of emotions also relates to an individual animal’s need to respond with its whole body –
to run away from danger, for example, or to care for offspring. Emotions can communicate information about a situation and trigger a response even in absence of
consciousness; in turn, this holistic response seems to have influenced the evolutionary formation of self and consciousness.23
Happiness, sadness, fear, anger, disgust, and surprise all can be viewed as judgments about a person’s general state; a man who unexpectedly comes across a tiger
on the loose, for example, would be understandably afraid because the large carnivore threatens his instinct to stay alive. In fact, all emotions are connected to goal
accomplishment:24 people become angry when they are thwarted, for instance, and
feel pleased when they are successful. In this sense, emotion is a abductive summary
appraisal of a problem-solving situation. Moreover, it provides cognitive “focalization” of the situation and readies us for action. On the contrary, we can consider
emotions just as physiological reactions rather than cognitive judgments. Damasio
refers to the signals that the body sends to the brain as somatic markers. Neuroscience taught us that emotions depend on interaction between bodily signals and
cognitive appraisal. That is, they involve “both” judgments about how the current
situation is affecting our goals and neurological assessment of our body’s reaction
to that situation.
Emotions are represented in the brain, but they cannot be represented like concepts because this conceals their links to a judgment that involves abductive processes, physiology, and feeling. We can imagine emotions as patterns of activation
across many neurons in many brain areas, including those sites involved in cognitive
judgments, like the prefrontal cortex, as well as those that receive input from bodily
states, like the amygdala. Put another way, emotion activates neurons in different
areas of the brain, areas that may have either inferential or sensory functions (cf.
[Wagar and Thagard, 2004].).
We have already pointed out that emotions play an important role in decision
making (a striking example is given by the case of moral deliberations). Damasio hypothesizes that in some cases of brain damage to the ventromedial, bottom-middle,
or prefrontal cortex areas, people loose the ability to make effective decisions because they cannot discern the future consequences of their actions, especially in
social contexts. That part of the brain provides connections between areas of the
cortex involved in judgment and areas involved in emotion and memory, the amygdala and hippocampus.
23
24
[Modell, 2003]. On consciousness, conscious will, and free will, cf. my book [Magnani, 2007d],
chapter three, section “Critical Links: Consciousness, Free Will, and Knowledge in the Hybrid
Human.”
On the role and nature of goals cf. [Thagard and Millgram, 2001]. The paper illustrates a theory
(in terms of deliberative coherence) and a computational model of decision making that sees it
not only as a process of choosing actions but also of evaluating goals.
4.4 Actions vs. Thoughts?
237
Computer simulations of decision making have made it clear that we need more
neurologically “realistic” models involving the role of emotions.25 The GAGE neurocomputational program [Wagar and Thagard, 2004] aims at filling this gap. It
models the above cognitive situation, which is due to a brain lesion, using groups
of computational spiking neurons corresponding to each of the crucial brain areas
involved: 1) vetromedial frontal cortex, 2) amygdala, 3) nucleus accumbens (a region strongly associated with rewards). So GAGE is capable of taking into account
both cognitive aspects of judgment and appraisal performed by the ventromedial
prefrontal cortex and physiological input mediated by the amygdala.26
Feelings serve as decisional inferences only if they are intertwined with learned
cultural behaviors and therefore become “intelligent emotions” or, as some ethicists
say, “appropriate” emotions.27 Hume was wrong to view emotions as separate from
intellect, says Johnson [1956], who maintains that the two dimensions are actually
blended. I do not think we need to blend rational and emotional aspects; emotions
are clearly distinguishable, even though we may be tempted to lump them together
with purely cognitive functions because they can function in decision-making under
certain conditions – that is, when they are not just raw products of evolution but
are, instead, shaped further by knowledge and information. In this sense a decision
lead by certain trained emotions, even if not fully deliberate and conscious, must not
be considered as instinct-based. This decision derives from feelings built in a past
history of conscious cognitive choices which have been able to reshape emotions
giving rise to certain sophisticated feelings. Consider the example of a husband and
his positive emotional attitude toward his marriage – it can be hypothesized that his
strong commitment to his wife relates to his understanding of marriage, which in
his case is stable and well formed, even if tacit and unreflective.
I have already pointed out that I agree wholeheartedly with Peirce that all thinking is in signs and that these signs take many forms – icons, indices, or symbols
and so on, as we mentioned before. If all inference is, in fact, a form of sign activity – as Peirce contends – and we use the word sign to include feelings, images,
conceptions, and other representations, then we must include unconscious thought
among the model-based ways of moral thinking. Indeed, it is not only conscious abstract thought that we can consider inferential: we can characterize many cognitive
activities that way.
Martha Nussbaum has emphasized the cognitive value of emotions and further clarified their moral role; in her work she improves and updates the Greek
Stoic view, which holds that emotions are evaluative judgments that ascribe great
importance to certain things and persons outside a person’s own control. In this perspective, such things then have the power to determine human flourishing
25
26
27
They of course will still lack the possibility of “feeling” emotions: indeed they will not have
bodily inputs.
Some meta-ethicists call moral intuitionism the view of emotions as central in justifying moral
beliefs [Sinnott-Armstrong, 1996]. [Ben-Ze’ev, 2000] maintains that optimal moral behavior is
that which combines emotions and intellectual reasoning, a complex integration that requires
the so-called “emotional intelligence”.
Cf. [Thomson, 1999, pp. 148-149]. In this case [Oatley, 1992] speaks of “learned spontaneity.”
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(eudaimonia).28 Put another way, through emotions, people acknowledge that external things/persons they do not fully control are very important for their own flourishing. Emotions are always seen as involving thought of an “intentional” object
combined with thought of that object’s salience, value, and importance in the framework of what Nussbaum calls the “cognitive-evaluative” view. This perspective
contrasts with the “adversary view” that considers emotions mere “non-reasoning
movements” that would derive “bodily” from an animal part of our nature rather
than “mentally” from a specifically human part. Unlike the Stoic approach, it is
difficult to see emotions as judgments in this view, and it would seem hard “to account for their urgency and heat given the facts that thoughts/judgments are usually
imagined as detached and calm” [Nussbaum, 2001, p. 27]: emotions are fundamentally seen as irrational and a bad guide to action in general and to moral action in
particular.
In the “cognitive-evaluative” perspective, it is very easy to think of emotions
more broadly in a way that goes beyond the Stoic starting point; consider, for example, the cognitive role of emotions in animals and the evaluative appraisal they
perform in moral life. Of particular interest is the role that elements of culture –
social norms, for example – play in shaping certain feelings like compassion that
I refer to above as “trained emotions”: “Human deliberative sociability also affects
the range of emotions of which humans are capable, [. . . ]” [Nussbaum, 2001, p.
148] just as individual history influences the perception of that effect and cognitively embeds emotions in a complex of personal narratives. In this last sense, to
acknowledge the influence that social constructions have on emotions is to see that
emotions consist of elements we have not ourselves constructed.
Finally, I must note that Michael Gazzaniga, citing James Q. Wilson’s prediction,
provides a brain-based account of moral reasoning centered in the areas of emotion.
It has been found that brain regions normally involved in emotional processing may
be activated by one type of moral judgment but not another. In this sense, when
someone is willing to act on a moral belief, it is because the emotional side of her
brain was activated as she checked the moral question at hand. If, on the other hand,
she decides not to act, the emotional part of the brain does not become active.29
28
29
Greek eudaimonistic ethical theories are concerned with human flourishing: eudaimonia is taken
to include everything to which a person attributes intrinsic value. Nussbaum retains this spelling,
rather than using the English word “eudaemonistic,” because she wants to refer to the ancient
Greek concept and avoid more recent connotations associated with the idea, “namely, the view
that the supreme good is happiness or pleasure” [Nussbaum, 2001, p. 31].
[Gazzaniga, 2005]. Other studies exploiting neuroimaging have dealt with the neuroanatomy
and neuroorganization of emotion, social cognition, and other neural processes related to moral
judgment in normal adults and in adults who exhibit aberrant moral behavior [Greene and
Haidt, 2002]. [Moll et al., 2002; Moll et al., 2005] have established that moral emotions differ
from basic emotions in that they are interpersonal: the neural correlates that are more interested
in moral appraisal appear to be the orbital and medial sectors of the prefrontal cortex and the
superior sulcus region, which are also critical regions for social behavior and perception.
4.5 The Agent-Based and Abductive Structure of Reasons in Moral Deliberation
4.5
239
The Agent-Based and Abductive Structure of Reasons in
Moral Deliberation
This section illustrates in detail that “abduction”, that is the reasoning to hypotheses,
is central to the problem of “inferring reasons” in decision making, as a fundamental kind of practical reasoning. Moral deliberation will be our example. We have
seen that in abduction we usually base our guessing of hypotheses on incomplete
information, and so we are facing nonmonotonic inferences: we reach defeasible
conclusions from limited information, and these conclusions are always withdrawable.30 It is in this sense that both explanatory and instrumental abductive reasoning
constitutes a possible useful model of practical reasoning: ethical deliberations are
always adopted on the basis of incomplete information and on the basis of the selection of particular abduced hypotheses which play the role of reasons. Hence,
ethical deliberation shares some aspects with hypothetical explanatory reasoning as
it is typically illustrated by abductive reasoning in scientific settings. To support this
perspective on the “logical structure of reasons” we will provide an analysis based
on the distinction between “internal” and “external” reasons and on the difficulties
in “deductively” grasping practical reasoning, at least with the only help of classical
logic.
In a previous work [Magnani, 2007d, chapters six and seven] devoted to introduce
the methodological problems of ethical deliberation, I contend, following Rachels,
that morality is the effort to guide one’s conduct by reasons, that is, to do what there
are the best reasons for doing while giving equal weight to the interests of each
individual who will be affected by one’s conduct. “The logical structure of reasons”
is the title of chapter four in Searle’s book Rationality in Action [2001]. I plan to
use Searle’s conceptual framework to better understand what exactly are “reasons”
in the specific case of ethics. Whereas Searle deals with rational decision making,
many of his conclusions appear to be appropriate for ethical cases, too.
By criticizing the classical model of rational decision making (which always requires the presence of a desire as the condition for triggering a decision), Searle
establishes the fundamental distinction between internal and external reasons for
action: those that are internal might be based on a desire or on an intention, for instance, while external reasons might be grounded in external obligations and duties.
When I pay my bill at the restaurant, I am not doing so to satisfy an internal desire,
so this action does not arise from internal motivations; instead, it is the result of my
recognition of an external obligation to pay the restaurant for the meal it has provided. Analogously, if an agent cites a reason for a past action, it must have been the
reason that the agent “acted on”. Finally, reasons can be for future action, and this is
particularly true in ethics where they do not always trigger an action – in this case,
however, they must still be able to motivate an action: they are reasons an agent can
“act on”.
Searle’s anti-classical emphasis on “external reasons” does not have to appear
strange: in [2007d] I have often stressed the fact that human beings not only
30
For further specifications cf. chapter one, section 1.3 and chapter two, section 2.1, where the
fallacious character of abduction is described.
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4 Neuro-multimodal Abduction
delegate cognitive roles but also and moral worth to external objects that consequently acquire the status of deontic moral structures. This also occurs when we
articulate ideas in verbal statements – promises, commitments, duties, and obligations, for example – that then exist “over there”, in the external world. Imagine the
deontic role that concrete buildings (like for instance the ones whose shapes restrict
routes people can follow) or abstract institutions (for example, some modern constitutions usually compel us to consider equality of citizens as important) can play
in depicting duties and commitments we can (or have to) respect. Human beings are
bound to behave in certain ways as spouses, tax payers, teachers, workers, drivers,
and so on. All these external factors can become – Searle says – reasons/motivators
for prior intentions and intentions-in-action of human beings.
Many things around us are human made, artificial – not only concrete objects
like a hammer or a PC, but also human organizations, institutions, and societies.
Economic life, laws, corporations, states, and school structures, for example, can
also fall into that category. We have also projected many intrinsic values on things
like flags, justice rituals, or ecological systems, and as a result, these external objects
have acquired a kind of autonomous automatism “over there” that conditions us and
distributes roles, duties, moral engagements – that is, it supplies potential “external
reasons”. Non-human things (as well as so-to-say “non-things” like future human
beings and animals, etc.) become moral clients as well as human beings, so that
current ethics must pay attention not only to relationships between human beings,
but also to those between human and non-human entities.
Moreover, we can observe how external things we usually consider to be morally
inert can be transformed into those moral mediators which express the idea of
a distributed morality. For example, we can use animals to highlight new, previously unseen moral features of other living objects, as we can do with the earth
or with (non natural) cultural objects; we can also use external “tools” like writing, narratives, others persons’ information, rituals, and various kinds of institutions to morally reconfigure social orders. Hence, not all moral tools are inside the
head along with the emotions we experience or the abstract principles we refer to;
many are over there, even if they have not yet been identified and represented internally, distributed in external objects and structures which function as ethical devices
available for acknowledgment by every human agent. These delegations to external
structures – thus transformed in moral mediators – encourage or direct ethical commitments, and, they favor the predictability in human behavior that is the foundation
for conscious will, free will, freedom, and of the ownership of our own destinies: if
we cannot anticipate other human beings’ intentions and values, we cannot ascertain which actions will lead us to our goals, and authoring our own lives becomes
impossible.
Let us return to the role played by reasons in ethical reasoning. Intentional states
with a propositional content have typical conditions of satisfaction and directions of
fit.
1. First, mental and linguistic entities have directions of fit: for example, a belief
has a mind-to-world direction of fit. For example, if I believe it is raining, my
belief is satisfied if and only if it is raining “[. . . ] because it is the responsibility
4.5 The Agent-Based and Abductive Structure of Reasons in Moral Deliberation
241
of the belief to match an independently existing reality, and it will succeed or
fail depending or whether or not the content of the belief in the mind actually
does fit the reality of the world” [Searle, 2001, p. 37]. On the other hand, a
desire (or an order, promise, or intention) has a world-to-mind direction of fit:
“[. . . ] if my belief is false, I can fix it up by changing the belief, but I do not in
that way make things right if my desire is not satisfied by changing the desire.
To fix things up, the world has to change to match the content of the desire”
[Searle, 2001, p. 38].
2. Second, other objects (not mental and not linguistic) also have a direction of fit
similar to the ones of beliefs. A map, for example, which may be accurate or not,
has a map-to-world direction of fit, whereas the blueprints for a house have a
world-to-blueprint direction of fit because they can be followed or not followed
[Searle, 2001, p. 39]. Needs, obligations, requirements, and duties are not in a
strict sense linguistic entities, but they have propositional contents and directions of fit similar to the ones of desires, intentions, orders, commitments, and
promises that have a world-to-mind, world-to-language direction of fit. Indeed,
an obligation is satisfied if and only if the world changes to match the content
of the obligation: if I owe money to a friend, the obligation will be discharged
only when the world changes in the sense that I have repaid the money.
When for example we apply the moral principle of the wrongness of discriminating
against the handicapped to the a specific moral case (for example the recent famous
case of Baby Jane Doe [Rachels, 1999] where the parents had to decide (and so they
had to choose/infer the right “reason”) in favor or against a fundamental surgical operation), we resort to a kind of “external” reason that we have to “internalize” – that
is, recognize as a reason worth considering for a possible deliberation. If we instead
exploit strong personal feelings like pity and compassion to guide our reasoning, we
would decide for or against the operation based on a completely “internal” reason.
We have to note, of course, that external reasons are always observer-relative. It is
only human intentionality that furnishes meaning to a particular configuration of
things in the external moral or non-moral world. The objective fact that, say, I have
an increased white blood cell level acquires a direction of fit that is a direction for
action only if related to a human being’s interpretation (for example only “in the
light” of a diagnosed disease, that same fact can trigger the decision for a therapy).
Searle also discusses the so-called collective intentionality that enables people to
create common institutions such as those involving money, property, marriage, government, and language itself, an intentionality that gives rise to new sets of “conditions of satisfaction”, duties, and commitments. In our perspective we say these
external structures have acquired a kind of delegated intentionality because they
have become moral mediators, they have acquired a kind of moral “direction”, as I
have illustrated in [Magnani, 2007d, chapter six]. In those cases, when we have to
deal with a moral problem through moral mediators, evaluating reasons of any kind
immediately involves manipulating non-human externalities in natural or artificial
environments by applying old and new behavior templates that exhibit some uniformities. This moral process is still hypothetical (abductive): these templates are
embodied hypotheses of moral behavior (either pre-stored or newly created in the
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4 Neuro-multimodal Abduction
mind-body system) that, when appropriately employed, make possible what can be
called a moral “doing” (cf. also [Magnani, 2006e]).
I contend that external moral mediators are a powerful source of information and
knowledge; they redistribute moral effort by managing objects and information in
new ways that transcend the limits and the poverty of the moral options immediately
represented or found internally (for example exploiting resources in terms of merely
internal/mental moral principles, utilitarian envisaging, and model-based moral
reasoning – emotions, for example).
It follows from the previous discussion that many entities can play the role of deontic moral structures. This fact can lead to a re-examination of the concept of duty.
In this perspective duties can be also grounded on trained emotional habits, visual
imagery, embodied ways of manipulating the world, exploitation of moral mediators
– as we have just seen, endowed with a sufficient ethical worth in a collective.
4.5.1
The Ontology of Reasons
What are these “reasons” that, following Searle, are the basis of rational actions and
the basis of moral action? A reason answers the question “Why?” with a “Because”;
it can be a statement, like a moral principle, as in the answer to “Why should we
perform surgery on a handicapped baby?”: “Because of the wrongness of discriminating against the handicapped”. In reality, reasons are “expressed” by the
statements-explanations in so far as they are facts in the world (the fact that it is
raining is the reason I am carrying an umbrella). They are also represented by
propositional intentional states such as desires (my desire to stay dry is the reason I am carrying the umbrella), and, finally, by propositionally structured entities
such as obligations, commitments, needs, and requirements, like in the case of our
moral “principle” of “the wrongness of discriminating against the handicapped”.
Usually good reasons explain and usually explanations give reasons. Searle also
distinguishes between reasons that justify my action and thus explain why it was the
right action to perform, and the reasons that explain why in fact I did it.
1. First of all, in rational decision making, when we must provide a reason for an
intentional state, we have to make an intelligent selection from a range of reasons that exist either internally or externally – in the latter case, we must take the
external reason, recognize it as good, and internalize it. With respect to our ideal
of an ethical deliberation sustained by “reasons”, we can affirm that it is not unusual for the “deliberator” to have limited knowledge and inferential expertise
at his or her disposal. For instance, she may simply not have important pieces
of information about the moral problem she has to manage, or she may possess only a rudimentary ability to compare reasons and ascertain data. Ethical
reasoning is so abductive and defeasible: because it is impossible to obtain all
information about any given ethical situation, every instance of moral reasoning
occurs without benefit of full knowledge, so we must remember that any reason can be rendered irrelevant or inappropriate by new information. Generally
4.5 The Agent-Based and Abductive Structure of Reasons in Moral Deliberation
243
speaking, as illustrated above, these reasons can take three different forms: external facts in the world, such as empirical data; internal intentional states such
as beliefs, desires, or emotions; and entities in the external world like duties,
obligations, and commitments with the direction of fit upward (world-to-mind).
External facts must be internalized and “believed”, while external entities must
be internalized and adopted (“recognized”) as good and worth of consideration.
The same happens in the case of rational moral deliberation.
2. Second, we must remember that maintaining a flexible, open mind is particularly important when we lack the ethical knowledge necessary to confront new
or extreme concrete situations.
When evaluating an ethical case, we have at hand all the elements of rational moral
decision making: the problem we face, the “reasons”, and the agents involved. Every
reason, Searle says, contributes to a “total reason” that is ultimately a composite of
every good reason that has been considered – beliefs, desires, obligations, or facts,
for example. As already observed, first, “rationality” requires the agent to recognize
the facts at hand (I have to believe that it is raining) and the obligations undertaken
(I have to adopt the principle of the sanctity of human life) without denying them
(which would be obviously irrational) [Searle, 2001, p. 115]. Second, reasons can
be more than one, indeed I need at least one motivator, but in some cases there are
many, and these reasons often conflict with one another; it then becomes necessary
to appraise their relative weights in order to arrive at the prior intention and the
intention-in-action.
In abductive reasoning, this kind of appraisal is linked to evaluating various inferred explanatory, non-explanatory, and instrumental hypotheses/reasons, and, of
course, it varies depending on the concrete cognitive and/or epistemological situation. In the section 1.3 of chapter one, we have illustrated that epistemologically
using abduction as an inference to the best explanation simply requires evaluating
competing hypotheses (that express competing “reasons” in the ethical case). The
best [total] reason would be the one that creates prior intention and intention-inaction.
What criteria can we adopt to choose the reason(s) that will become the motivator(s)? Thagard [2000] has proposed a framework in terms of coherence, in which
ethical deliberation is seen as involving conflicting reasons (deductive, explanatory,
deliberative, analogical) that can be appraised by testing their relative “coherence”.
This “coherence view” is terrifically interesting because it reveals multidimensional
character of ethical deliberations. The criteria for choosing the most coherent “reason/motivator” represent a possible abstract cognitive reconstruction of an ideal of
“rationality” in moral decision making, but they can also describe the behavior of
real human beings. Human beings usually take into account just a fraction of the
possible knowledge when performing ethical judgments. For example, when making judgments, it is common for utilitarians to employ only what Thagard calls
“deliberative” coherence or for Kantians to privilege principles over consequences.
Psychological resources are limited for any agent, so it is difficult to mentally process all levels of ethical knowledge simultaneously in an attempt to calculate and
maximize the overall coherence of the competing moral options. The “coherence”
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model accounts for these “real” cases of human moral reasoning by showing they fit
only “local areas” of the coherence framework: in general, real human beings come
to immediate conclusions through one moral aspect (for instance, the “consequentialist” one) and disregard the possible change in coherence weight that could result
from considering other levels (for instance, the “Kantian” one).
Searle interprets rationality in decisions naturalistically: “Rationality is a biological phenomenon. Rationality in action is that feature which enables organisms, with
brains big and complex enough to have conscious selves, to coordinate their intentional contents, so as to produce better actions than would be produced by random
behavior, instinct, tropism, or acting on impulse” [Searle, 2001, p. 142]. I agree, but
I would add that rationality is a product of a hybrid organism. This notion obviously
derives from the fact that even the external tools and models we use in decision
making – an externalized obligation, a computational aid, and even Thagard’s “coherence” model described above – are products of biological human beings, but at
the same time these tools constitutively affect human beings, who are, as we already
know, highly “hybridized”.31
4.5.2
Abduction in Practical Agent-Based Reasoning
Searle considers “bizarre”, and I strongly agree with him – that feature of our intellectual tradition, according to which true statements that describe how things are
in the world can never imply a statement about how they ought to be: in reality,
to make a simple example, to say something is true is already to say you ought to
believe it, that is other things being equal, you ought not to deny it. Also, logical
consequence can be easily mapped to the commitments of belief. Given the fact that
logical inferences preserve truth, “The notion of a valid inference is such that, if p
can be validly inferred from q, then anyone who asserts p ought not deny q, that
anyone who is committed to p ought to recognize its commitment to q” (ibid., p.
148.). This means that normativity is more widespread than expected.
Certainly, theoretical reasoning can be seen as a kind of practical reasoning where
deciding what beliefs to accept or reject is a special case of deciding what to do.
The reason it is difficult to “deductively” grasp practical reasoning is related to
the intrinsic multiplicity of possible reasons and to the fact that we can hold two
or more inconsistent reasons at the same time.32 The following example illustrates
how practical contexts are refractory to logical modeling. Given the fact that we
31
32
Further details on coherence, truth, and the development of scientific knowledge are illustrated
in [Thagard, 2006]. Searle [2001] calls the means and ways of performing an action (for instance
to fulfill an obligation) “effectors” and “constitutors”. An obligation to another person is an
example. I know I own you some money: “I can drive to your house” and “give you the money”
– effector and constitutor.
Searle “reluctantly” declares that it is impossible to construct a formal logic of practical reasoning “adequate to the facts of the philosophical psychology” [Searle, 2001, p. 250]. I think that
many types of non-standard logic (deontic, nonmonotonic, dynamic, ampliative, adaptive, etc.)
reveal interesting aspects of practical reasoning by addressing the problem of defeasibility of
reasons and of their selection and evaluation.
4.6 Picking Up Information
245
consider it a duty to do p and that I also feel committed not to do p, we cannot infer
that I am committed to do (p and not p). I am a physician committed to not killing a
patient in a coma, but at the same time my compassion for the patient commits me
to the opposite duty. This does not mean that I want to preserve the life of the patient
and, at the same time, I want to kill him – that would lead to an inconsistent moral
duty. All this represents an unwelcome consequence of the fact that commitment to
a duty is not closed under conjunction [Searle, 2001, p. 250].
In practical reasoning, we are always faced with desires, obligations, duties, commitments, needs, and requirements, etc., that are at odds with one another. Moreover,
even if I consider it a duty to do p and I believe that (if p then q), I am not committed to do q as a duty: I can be committed to killing a patient in a coma and at the
same time believe this act will cause pain for his friends, but I am not committed
to causing this pain. Modus ponens does not work for duty/belief mixture [Searle,
2001, pp. 254–255].
The examples above illustrate the difficulties that arise when classical logic meets
practical reasoning. They further stress the importance we attribute to abductive
explanatory inferences in agent-based practical settings, where creating, selecting,
and appraising hypotheses are central functions.
4.6
Picking Up Information
We have seen that it is difficult to hypothesize internal cognitive states in nonlinguistic organisms.33 The approach in terms of the so-called active perception, that
minimizes the role of representations, can help us overcome this impasse. From this
perspective we can first of all say, at least in the case of human beings, that abduction is a complex process that works through imagination: for example, it suggests
a new direction in reasoning by shaping new ways for explaining (cf. the templates
mentioned above). Imagination should not, however, be confused with intuition.
Peirce describes abduction as a dynamic modeling process that fluctuates between
states of doubt and states of belief. To assuage doubt and account for anomalies,
the agent gathers information that relates to the “problem,” to the agent’s evolving
understanding of the situation, and to its changing requirements. When I use the
word “imagination” here, I am referring to this process of knowledge gathering and
shaping, a process that Kant considered invisible to us and yet which leads us to see
things we would not otherwise have seen: it is “a blind but indispensable function
of the soul, without which we should have no knowledge whatsoever” [Kant, 1929,
A78-B103,p. 112]. For example scientific creativity, it is pretty obvious, involves
seeing the world in a particular new way: scientific understanding permits us to see
some aspects of reality in a particular way and creativity relates to this capacity to
shed new light.
We can further analyze this process using the active perception approach
[Aloimonos et al., 1988; Ballard, 1991], a theory developed in the area of
33
The whole problem of animal abduction and of the so-called mindless cognition will be treated
in the following chapter.
246
4 Neuro-multimodal Abduction
computer vision [Thomas, 1999]. This approach seeks to understand cognitive systems in terms of their environmental situatedness: instead of being used to build a
comprehensive inner model of its surroundings, the agent’s perceptual capacities are
seen as simply used to obtain “whatever” specific pieces of information are necessary for its behavior in the world. The agent constantly “adjusts” its vantage point,
updating and refining its procedures, in order to uncover a piece of information. This
resorts to the need to specify how to efficiently examine and explore and to “interpret” an object of a certain type. It is a process of attentive and controlled perceptual
exploration through which the agent is able to collect the necessary information: a
purposeful examination is carried out, actively picking up information rather than
passively transducing (cf. [Gibson, 1979]).
As suggested for instance by Lederman and Klatzky, this view of perception may
be applied to all sense modes: for example, it can be easily extended to the haptic
mode [1990]. Mere passive touch, in fact, tells us little, but by actively exploring an
object with our hands we can find out a great deal. Our hands incorporate not only
sensory transducers, but also specific groups of muscles and musculature which,
under central control, move in appropriate ways: lifting something tells us about its
weight, running fingers around the contours provides shape information, rubbing it
reveals for instance texture, as already stressed by Peirce in the quotation I reported
above, when dealing with the hypothesizing activity of what I call manipulative
abduction [Peirce, 1931-1958, 5.221].34
Nigel Thomas suggests we think of the fingers together with the neural structures
that control them so that we can consider the afferent signals they generate as a sort
of knowledge-gathering (perceptual) instrument: a complex of physiological structures capable of active testing for some environmental property [Thomas, 1999].
The study of manipulative abduction that I outlined above can benefit from this
approach. For example, the analysis of particular epistemic mediators (optical diagrams) in non-standard analysis, I have illustrated in chapter one (section 1.7), and
their function in grasping and teaching abstract and difficult mathematical concepts
stresses the activity on picking up described above. In this case the external models
(mathematical diagrams) do not give all available knowledge about a mathematical
object, but compel the agent to engage in a continual epistemic dialogue between
the diagrams themselves and her internal knowledge either to enhance personal understanding of existing information or to facilitate the creation of new knowledge.
As I have already noted in chapter two (section 2.8) human beings and other animals make frequent use of perceptual reasoning and kinesthetic abilities. Usually
the “computations” these tasks require are not fully conscious. Mathematical cognition uses verbal explanations, but it also involves nonlinguistic notational devices
34
A kind of inner touch can be very significant in human brains and so furnish a kind of “imagery”
that drives thoughts: the famous case is Helen Keller, who became deaf and blind at the age of
eighteen months, and so, lacking normal auditory and visual channels, did not meet the standard
requirement for acquiring language. Later on, with the help of Annie Sullivan, she was able to
learn language and an adult personality mainly exploiting haptic modes. This extraordinary
story tells us that her brain plastically employed an anatomical path usually not at work in
normal linguistic communication, which uses very different neural patterns (cf. [Donald, 2001,
pp. 232-250] ).
4.7 Spatial Frameworks, Anticipation, and Geometry
247
and models that require our perceptive and kinesthetic capacities. In chapter two I
have illustrated how geometrical constructions are a prototypical case of this kind of
extra-linguistic system that functions in a model-based, manipulative, and abductive
way.
4.7
4.7.1
Spatial Frameworks, Anticipation, and Geometry
Abduction and Neurospaces
Many parts of the mammalian cognitive system represent the location of objects
within the spatial framework. The egocentric ones are spaces where the objects are
located in a framework that is referenced to a sensory receptor or body surface, e.g.
retinal axes of the visual cortex, head-centered axes of the partial cortex. In many
vertebrates these spaces are formed by taking advantage of the available cues in
natural environment and/or of the artificially made cues and landmarks suitably externalized in the material environment by the individual or group in question. The
cues become part of the internal representation through the perceptual system so furnishing the basic data which make the abductive formation of the spatial mapping
possible. Of course these sources, even if reliable, often are not easily accessible.35
Another spatial framework, called allocentric, is instead referenced to the environment and so not centered on the organism.36
Research in neuroscience has stressed the pre-wired role of the hippocampus,
a paradigmatic example of archicortex, in building a prereflexive allocentric spatial framework in mammals. Many empirical investigations and mathematical and
computational models of this mechanism have been provided in the last decades
[O’Keefe, 1999]. Hippocampus receives input from the “[. . . ] entorhinal cortex and
the septum. The entorhinal cortex in turn receives inputs directly or indirectly from
many neocortical areas and is believed to be the major conduit of sensory information into the hippocampus. In contrast, the septum gets its input primarily from
the hypothalamus and brainstem, and is thought to convey information about actual or intended movements and about the animal’s bodily states and needs” (ibid.,
pp. 53-54). Models of hippocampus functions have been recently studied to detect
the effects, for example of lesions, on the dentate gyrus and CA3. It has resulted
35
36
More information on the exploitation of spatial external representations is detailed in [Freska,
2000, pp. 1126-1127] ).
More details on the high plasticity in animal spatial egocentric and allocentric mapping, also
focusing the attention on switching between different mappings depending on the local situation, is provided by [Roberts, 2001]. The role of external representations, as “spatial products”,
in human cognition, is illustrated in [Liben, 2001; Tversky, 2001; Tversky et al., 2006]. On
the role in chicks’ spatial orientation of non-geometrical information given by landmarks and
of geometrical information given by the shape of the enclosure cf. [Vallortigara et al., 2005;
Chiesa et al., 2006], who also stress the role in these tasks of the spatial logics of a dual brain.
The research also aims at suggesting that the reliance on the use of geometric information of the
spatial scale of the environment is not an exclusive endowment of humans: animals do (implicit)
geometry (also in the case of fish [Sovrano et al., 2005]).
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4 Neuro-multimodal Abduction
that both lesions strongly reduce the efficacy of the exploration associated with displayed objects and affect detection of spatial novelty (cf. [Lee et al., 2005], and
[Hasselmo, 2005]). Finally, the role of the hippocampus seems involved not only in
the representation of the environment but also in the building of the primitive cognitive pre-conditions for the representation of the subject-as-object and the further
related various levels of consciousness.
In the process of hippocampal abductive formation of spatial mapping it is important to stress the complicated interplay between internal and external sensory
representations (visual, acoustic, and proprioceptive), together with the fact that dynamical motor aspects, which also involve manipulations of objects, are central and
basically independent of human language [Freska, 2000]. In the case of rats, as the
animal moves around a known environment the hippocampal mapping system continuously updates various parameters through a comparison between the (suitable,
decoupled) internal navigation representations (a kind of spatial imagination), and
actual representations derived from the sensory input. Internal subsequent representations are abductive hypotheses of space (Husserl would say, anticipations, cf.
subsection 4.7.4). Given the fact I have often remarked that various cognitive biological agents must reason on the basis of incomplete or uncertain information,
an appraisal of the necessary implications of spatial relations and actions is only
slowly and progressively reached through a cycle of continuous updating of spatial
mappings.
The process occurs in such a way that deviations from the expected sensory data
provide an internal signal for exploration to the aim of abductively re-constructing
and modifying the spatial representation of the environment. The internal signals
for exploration are also driven by a motivational system activated for instance by
hunger and by food in a particular location. Of course the neural, settled “representation” obtained can be reliably re-used when exploring the same niche: spatial relations can be replicated by superimposing them upon the sensory data at hand and
thus implicitly filling in missing relations not explicitly available. Even the wellknown three-dimensionality of space can be accounted for by the pre-wired brain
limitations on the representational properties.
[O’Keefe, 1999] contends that the results on hippocampal spatial mapping in
vertebrates would furnish a kind of naturalistic confirmation of the Kantian philosophical concept of spatial “pure intuition”. Furthermore, it can be hypothesized that
the historical perplexities of philosophers and geometricians over the centuries regarding the famous Euclidean fifth postulate,37 can be finally explained considering
the intrinsic neural features of the mammalian hippocampal mapping system. The
perplexities were mainly due to the fact that the postulate appeals to infinity, and
so to properties that cannot be verified by the experience accumulated through human perception. Studies on the hippocampus show that the abductive formation of
a directional system – which projects a set of parallel lines, which never meet, upon
the given environment – is intrinsic and allows the organism to compute a direction
37
Cf. my book [Magnani, 2001c] and chapter two of this book, sections 2.9 and 2.11.
4.7 Spatial Frameworks, Anticipation, and Geometry
249
based on cue distribution, and this direction is independent of location within the
environment [O’Keefe, 1999, pp. 59–62].38
A further consequence of this neural perspective concerns the hypothesis that the
strong development of temporal and prefrontal neocortices has been driven in part
by the existence of the hippocampal map. Indeed, the formation of the self-other
distinction (and thus the idea of “agent”) and the related formation of the image of
a self-referenced body are probably related to the development of the frontal cortex which is in turn based on the spatial schemes furnished by the hippocampal
map. The progressive acknowledgement of the pregnant fact that there is nothing
in the mapped spatial framework corresponding to an entity in the location of the
place where the organism actually is, possibly leads to “filling” the empty site with
an object marker. Later on other complicated cognitive abilities would intervene to
support a self-referenced image, also based on the recognition that agents are certainly objects that can change location in spatial mapping without external influence.
It would be thanks to this nonlinguistic background that, finally, in humans, the abductive formation of the higher awareness of the self can be implemented, typical of
the mentalized idea of a free and intentional agent. In conclusion, it is plausible to
affirm that a spatio-temporal packet of sensory stimuli, which maintains its integrity
as the organism moves or as it itself moves through a succession of sites within the
map, can be the precondition for more articulated and more or less conscious ideas
of “subject” and “object”.39
Moser’s research group has recently provided some of the most groundbreaking
insights so far concerning the computation of spatial location and spatial memory in
rat brains [Fyhn et al., 2004], by discovering a neuronal spatial map in the medial
dorsocaudal entorhinal cortex. The key unit of the map is the “grid cell”, which is
activated whenever the position of the animal coincides with any of the vertex of
a regular grid of equilateral triangles spanning the surface of the environment. The
“geometrical” map is anchored by external landmarks, but persists in their absence,
suggesting that grid cells may be part of a generalized, path-integration-based map
of the spatial environment. The grid cells constantly update the mammal’s sense of
its location, even in absence of the external sensory input, so providing a constant
and very general abductive appraisal of the situation at hand: indeed “The firing pattern – which is similar regardless of whether the rat is in a familiar, well-lit room
or in a strange location that is pitch-dark – must be a pure cognitive construct. Although grid cell firing patterns are updated and calibrated by sensory input from the
vestibular, visual and other sensory systems, they do not depend on external sensory
cues” [Knierim, 2007, p. 48]. Grid cells seem to constitute the basic spatial input that
is exploited by the hippocampus to construct more specific and context-dependent
spatial firing in its place cells. Place cells merely fire when a mammal occupies a
single, particular location but each grid cell – which projects a latticework of perfect
38
39
It seems the components of the mapping system require a large number of hippocampal identical harmonic oscillators, which are in variable ways intrinsic endowments of many living
organisms.
On the role of the auditory systems in spatial cognition of vertebrates cf. [de Cheveigné, 2006]
and this book, chapter five, section 5.5.2.
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4 Neuro-multimodal Abduction
equilateral triangles across the environment, the corners of which are sensible to the
rat’s presence – will fire when it is any one of the many locations that are arranged
in a stunningly uniform hexagonal grid (as if the cell were related to a number of
alarm tiles spaced at specific, regular distances). Because the grids projected by the
brain’s grid cells overlap, the grid cell system fires whenever the rat moves, thus
updating the animal’s location [Knierim, 2007, pp. 44–45].
4.7.2
Adumbrations: Perceptions and Kinesthetic Sensations
Intertwined
Also the philosophical tradition of phenomenology fully recognizes the protogeometrical role of kinesthetic data in the generation of the so-called “idealities” (and
of geometrical idealities). The objective space we usually subjectively experience
has to be put in brackets by means of the transcendental reduction, so that pure lived
experiences can be examined without the compromising intervention of any psychological perspective, any “doxa”. By means of this transcendental reduction, we
will be able to recognize perception as a structured “intentional constitution” of the
external objects,40 established by the rule-governed activity of consciousness (similarly, we will see that space and geometrical idealities, like the Euclidean ones, are
“constituted” objective properties of these transcendental objects).
The modality of appearing in perception is already markedly structured: it is not
that of concrete material things immediately given, but it is mediated by sensible
schemata constituted in the temporal continual mutation of adumbrations. So at the
level of “presentational perception” of pure lived experiences, only partial aspects
(adumbrations [Abschattungen]) of the objects are provided. Therefore, an activity
of unification of the different adumbrations to establish they belong to a particular
and single object (noema) it is further needed.41
The analysis of the generation of idealities (and geometrical idealities) is constructed in a very thoughtful philosophical scenario. The noematic appearances are
the objects as they are intuitively and immediately given (by direct acquaintance)
in the constituting multiplicity of the so-called adumbrations, endowed with a morphological character. The noematic meaning consists of a syntactically structured
categorical content associated with judgment. Its ideality is logical. The noema consists of the object as deriving from a constitutive rule or synthetic unity of the appearances, in the transcendental sense [Petitot, 1999]. To further use the complex
Husserlian philosophical terminology, we can say: hyletic data (that is immediate given data) are vivified by an intentional synthesis (a noetic apprehension) that
transforms them into noematic appearances that adumbrate objects, etc.
40
41
A recent article [Overgaard and Grünbaum, 2007] deals with the relationship between perceptual intentionality, agency, and bodily movement and acknowledges the abductive role of
adumbrations. In the remaining part of this section I will try to clarify their meaning.
On the role of adumbrations in the genesis of ideal space and on their abductive and nonmonotonic character cf. below section 4.7.4.
4.7 Spatial Frameworks, Anticipation, and Geometry
4.7.3
251
The Genesis of Space
As illustrated by Husserl in Ding und Raum [1907] [Husserl, 1973] the geometrical
concepts of point, line, surface, plane, figure, size, etc., used in eidetic descriptions
are not spatial “in the thing-like sense”: rather, in this case, we deal with the problem
of the generation of the objective space itself. Husserl observes: it is “senseless” to
believe that “the visual field is [. . . ] in any way a surface on objective space” (§48, p.
166), that is, to act “as if the oculomotor field were located, as a surface, in the space
of things” (§67, p. 236).42 What about the phenomenological genesis of geometrical
global three-dimensional space?
We have to start dealing with the problem of the treatment of adumbrations. The
adumbrative aspects of things are part of the visual field. To manage them a first
requirement is related to the need of gluing different fillings-in of the visual field to
construct the temporal continuum of perceptive adumbrations in a global space: the
visual field is considered not translation-invariant, because the images situated at its
periphery are less differentiated than those situated at its center (and so resolution is
weaker at the periphery than at the center), as subsequently proved by the pyramidal
algorithms in neurophysiology of vision research.
Perceptual intentionality basically depends on the ability to realize kinesthetic situations and sequences. In order for the subject to have visual sensations of the world,
he/she must be able not only to possess kinesthetic sensations but also to freely initiate kinesthetic sequences: this involves a bodily sense of agency and awareness on
the part of the doer [Overgaard and Grünbaum, 2007, p. 20]. The kinesthetic control
of perception is related to the problem of generating the objective notion of threedimensional space, that is, to the phenomenological constitution of a “thing”,43 as a
single body unified through the multiplicity of its appearances. The “meaning identity” of a thing is of course related to the continuous flow of adumbrations: given the
fact that the incompleteness of adumbrations implies their synthetic consideration in
a temporal way, the synthesis in this case, kinetic, involves eyes, body, and objects.
Visual sensations are not sufficient to constitute objective spatiality. Kinesthetic
sensations44 (relative to the movements of the perceiver’s own body)45 are required.
Petitot continues:
Besides their “objectivizing” function, kinesthetic sensations share a “subjectivizing”
function that lets the lived body appear as a proprioceptive embodiment of pure experiences, and the adumbrations as subjective events. [. . . ] There exists an obvious
42
43
44
45
Moreover, Husserl thinks that space is endowed with a double function: it is able to constitute
a phenomenal extension at the level of sensible data and also it furnishes an intentional moment. Petitot says: “Space possesses, therefore, a noetic face (format of passive synthesis) and
a noematic one (pure intuition in Kant’s sense)” [Petitot, 1999, p. 336].
Cf. also [Husserl, 1931, §40, p. 129] [originally published in 1913].
Husserl uses the terms “kinestetic sensations” and “kinesthetic sequences” to denote the subjective awareness of position and movement in order to distinguish it from the position and
movement of perceived objects in space. On some results of neuroscience that corroborate and
improve several phenomenological intuitions cf. [Pachoud, 1999, pp. 211–216] and [Barbaras,
1999; Petit, 1999].
The ego itself is only constituted thanks to the capabilities of movement and action.
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4 Neuro-multimodal Abduction
equivalence between a situation where the eyes move and the objects in the visual
field remain at rest, and the reciprocal situation where the eyes remain at rest and the
objects move. But this trivial aspect of the relativity principle is by no means phenomenologically trivial, at least if one does not confuse what is constituting and what
is constituted. Relativity presupposes an already constituted space. At the preempirical constituting level, one must be able to discriminate the two equivalent situations.
The kinesthetic control paths are essential for achieving such a task [Petitot, 1999, pp.
354–355].
Multidimensional and hierarchically organized, the space of kinesthetic controls includes several degrees of freedom for movements of eyes, head, and body. Kinesthetic controls are kinds of spatial gluing operators. They are able to compose, in
the case of visual field, different partial aspects – identifying them as belonging
to the same object, (cf. Figure 4.1), that is constituting an ideal and transcendent
“object”. They are realized in the pure consciousness and are characterized by an
intentionality that demands a temporal lapse of time.
With the help of very complex eidetic descriptions,46 that further develop the
operations we sketched, Husserl is able to explain the constitution of the objective
parametrized time and of space. Discussing the intertwined role played by the kinesthetic systems composed by eyes, head, and body (that is not restricting himself to
the oculomotor kinesthetic level), and binocular vision and stereopsis, Husserl is
able to account for the formation of objective three-dimensional space and of the
three-dimensional things inside it. He stresses that stereopsis derives from the fact
that the two binocular images are not identical, so their differences are “intentionally” deciphered by the visual system as depth values47 thereby the third dimension
is constituted.
Of course, when the three-dimensional space (still inexact) is generated (by
means of two-dimensional gluing and stereopsis) it is possible to invert the phenomenological order: the visual field is so viewed as a portion of surface in R3 ,
and the objective constituted space comes first, instead of the objects as they are
intuitively and immediately given by direct acquaintance. So the space is in this
case an objective datum informing the cognitive agent about the external world
where she can find objects from the point of view of their referentiality and denotation. The kinesthetic system “makes the oculomotor field (eventually enlarged
to infinity) the mere projection of a three spatial thingness” [Husserl, 1973, section 63, p. 227]. Adumbrations now also appear to be consequences of the objective
46
47
Husserl considered it impossible to give a scientific account (for instance mathematical, neurobiological, or in terms of dynamical systems) of operations and events at the level of descriptive
eidetics and of morphological essences in perception. The so-called naturalized phenomenology tries to fill this gap [Petitot et al., 1999]. For instance Petitot demonstrates that there exists
“[. . . ] a geometrical descriptive eidetics able to assume for perception the constitutive tasks of
transcendental phenomenology and to mathematize the correlations between the kinetic noetic
synthesis and the noematic morphological Abschattungen” [Petitot, 1999, p. 371]; the mathematical apparatus he exploits is partially derived from Thom’s theory of catastrophes [Thom,
1975] I will reconsider in chapter eight of this book.
This point of view is confirmed by recent research on stereopsis [Ninio, 1989].
4.7 Spatial Frameworks, Anticipation, and Geometry
253
Fig. 4.1 Scanning square S with corners a, b, c, d. To each position p corresponds a token
Dp of the visual field D centered on p (focalization on p). The neighboring Dp overlap.
c
(From [Petitot et al., 1999], 1999
by the Board of Trustees of the Leland Stanford Junior
University, Stanford University Press, Stanford, reprinted by permission).
three-dimensional space, as continuous transformations of two-dimensional images
as if the body were embedded in the space R3 .48
4.7.4
Anticipations as Abductions
Of course adumbrations, the substrate of gluing operations that give rise to the twodimensional space, are multiple and infinite, and there is a potential co-givenness
of some of them (those potentially related to single objects). They are incomplete
and partial so for the complete givenness of an object a temporal process is necessary. Anticipations are the operations necessary to manage adunbrations that have
to be performed by objective transcendence. Adumbrations, not only intuitively presented, can be also represented at the level of imagination (on the role of imagination
cf. the following section).
Just because incomplete, anticipations correspond to a kind of non-intuitive intentional expectation. When we see a spherical form from one perspective (as an
adumbration), we will assume that it is effectively a sphere, but it could be also a
hemisphere (an example already employed by Locke).
Anticipations share with visual and manipulative abduction (cf. chapter one, this
book) various features: they are highly conjectural and nonmonotonic, so wrong anticipations have to be replaced by other plausible ones. Moreover, they constitute an
activity of “generate and test” as a kind of action-based cognition: the finding of adumbrations involves kinesthetic controls, sometimes in turn involving manipulations
of objects; but the activity of testing anticipations also implies kinesthetic controls
48
The role of adumbrations in objectifying entities can be hypothesized in many cases of nonlinguistic animal cognition dealing with the problem of reification and the formation of a kind of
“concept”, cf. chapter five of this book, section 5.5. In human adults objects are further individuated and reidentified by using both spatial aspects, such as place and trajectory information
and static-property information (in this last case exploiting what was gained through previous
adumbration activity); adults use this property information to explain and predict appearances
and disappareances: “If the same large, distinctive white rabbit appears in the box and later on
in the hat, I assume it’s the same rabbit” [Gopnik and Meltzoff, 1997].
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4 Neuro-multimodal Abduction
and manipulations. Finally, not all the anticipations are informationally equivalent
and work like attractors for privileged individuations of objects. In this sense the
whole activity is toward “the best anticipation”, the one that can display the object
in an optimal way. Prototypical adumbrations work like structural-stable systems, in
the sense that they can “vary inside some limits” without altering the apprehension
of the object.
Like in the case of selective abduction, anticipations are able to select possible
paths for constituting objects, actualizing them among the many that remain completely tacit. Like in the case of creative abduction, they can construct new ways
of aggregating adumbrations, by delineating the constitution of new objects/things.
In this case they originate interesting “attractors” that give rise to new “conceptual”
generalizations.
Some of the wonderful, philosophical Husserlian speculations are being further
developed scientifically from the neurological and cognitive perspective in current
cognitive science research. [Grush, 2004a; Grush, 2007] has built an emulation theory based on control theory where forward models as emulators (shared by humans
and many other animals) are used to illustrate, in the case of humans, various cognitive processes like perception, imagery, reasoning, and language.49 He contends that
simulation circuits are able to hypothesize forward mapping from control signals to
the anticipated – and so abduced – consequences of executing the control command.
In other words, they mimic the body and its interaction with the environment, enhancing motor control through sensorimotor abductive hypotheticals: “For example,
in goal-directed hand movements the brain has to plan parts of the movement before it starts. To achieve a smooth and accurate movement proprioceptive/kinesthetic
(and sometimes visual) feedback is necessary, but sensory feedback per se is too
slow to affect control appropriately [Desmurget and Grafton, 2002]. The “solution”
is an emulator/forward model that can predict the sensory feedback resulting from
executing a particular motor command” [Svensson and Ziemke, 2004, p. 1310].
The control theory framework is also useful to describe the emergence of implicit
and explicit agency [Grush, 2007]. The humans’ understanding of themselves as explicit agents is accomplished through an interplay between the standard egocentric
point of view and the so-called “simulated alter-egocentric” point of view, which represents the agent itself as an entity in the environment. In sum two emulators work in
tandem when an agent has to conceive its own actions as objective: the first is egocentric and it maintains the egocentric representation of the environment, the second is
alter-egocentric and it recalls knowledge of the agent’s own action as an entity in the
environment. The organism coordinates the two fundamental emulators simultaneously, representing the egocentric environment and at the same time representing the
first representation of the scene from the alter-egocentric point of view. This perspective leads to a new and interesting reinterpretation of mirror neurons, I agree with:
If this is correct, then mirror neurons are, in a sense, not mirror neurons at all. They
have one precise function: to fire when there is a representation of another agent
49
This approach is related to the so-called “simulation theory” (cf. chapter three, subsection
3.6.3.1) which does not posit anything corresponding to an emulator.
4.7 Spatial Frameworks, Anticipation, and Geometry
255
performing some action. Such a representation occurs when the monkey observes another animal perform the action. In that case the representation is a straight-forward
perceptual representation. However, when the monkey is itself performing an action a
representation of “another” agent performing an action is also maintained in its cognitive system. In this case, this representation is a mock perceptual representation, the
situation as perceived by an alter-ego. In fact this alter-ego perceives the monkey itself
as another agent. The mirror neurons are the crucial link between the agent’s implicit
representation of itself and its capacity to represent itself explicitly and objectively as
an agent [Grush, 2007, pp. 65–66].
Given the fact that motor imagery can be seen as the off-line driving force of the
emulator via efference copies, it is noteworthy that the emulation theory can be
usefully extended to account for visual imagery as the off-line operator behind an
emulator of the motor-visual loop. In these systems a kind of amodal spatial imagery can be hypothesized: “Modal imagery [. . . ] is imagery based on the operation
of an emulator of the sensory system itself, whereas amodal imagery is based on
the operation of an emulator of the organism and its environment: something like
arrangements of solid objects and surfaces in egocentric space. I show how the two
forms of emulation can work in tandem” [Grush, 2004a, p. 386]. It is important to
note that amodal imagery is neither sentential nor pictorial because the amodal environment space/objects emulators are closely tied to the organism’s sensorimotor
engagement with the environment.
A discussion of amodal emulators, considered puzzling because they seem entirely independent of any sensory “tags”, is provided by [Sathian, 2004], who
proposes clearer interpretation of them as multi-modal emulators, systems which
receive inputs from more than one sensory modality and are able to coordinate their
transformation and integration. Amodal systems, following Sathian, would be better
illustrated as conceptual and linguistic rather than as perceptual or as the substrate
for either imagery or sensorimotor emulation. However, amodal emulators also refer to cases, like those mentioned by Grush “where an object cannot currently be
sensed by any sensory modality (because it is behind an occluder, is silent and odorless, etc.) yet it is represented as being at a location. I think it is safe to say that our
representation of our own behavioral (egocentric) space allows for this, and it is not
clear how a multisensory system, in which tags for specific modalities were always
present, could accomplish this” [Grush, 2004b, p. 434]. Coherent with the Kantian
idea of “pure intuition”, I would say!50
4.7.5
The Genesis of Geometrical Idealities
What about the genesis of Euclidean geometry? Husserl declares:
Geometry and the sciences most closely related to it [the prescientific world] have
to do with space-time and the shapes, figures, also shapes of motion, alterations of
50
On Grush’s approach cf. the detailed discussion illustrated in [Clark, 2008, chapter seven] in the
framework of the theory of the extended mind; a treatment of current cognitive theories, such
as the sensorimotor theory of perception, which implicitly furnish a scientific account of the
phenomenological concept of anticipation, is given in chapter eight of the same book.
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deformation, etc., that are possible within space-time, particularly as measurable magnitudes. It is now clear that even if we know almost nothing about the historical surrounding world of the first geometers, this much is certain as an invariant, essential
structure: that it was a world of “things” (including the human beings themselves as
subjects of this world); that all things necessarily had to have a bodily character. [. . . ]
What is also clear [. . . ] is that these pure bodies had spatiotemporal shapes and “material” qualities (color, warmth, weight, hardness, etc.) related to them. Further it is clear
that in the life of practical needs certain particularizations of shape stood out and that a
technical praxis always aimed at the production of particular preferred shapes and the
improvement of them according to certain directions of gradualness [Husserl, 1978,
pp. 177–178, originally published in 1939].
4.7.5.1
Prescientific World
At the origins of geometry, as the science of what is absolutely objective, there is
a prescientific world,51 where first of all geometrical protoidealities are produced:
it is a world of things/bodies endowed with spatial shapes, shapes of motion and
deformations, material qualities, and “disposed of according to an inexact space and
time” [Derrida, 1978, p. 122]; by practical needs some of these shapes are perceived,
restored and perfected (rigid lines and surfaces). These pregeometrical things of the
prescientific world present a merely morphological character (for instance they are
more or less smooth surfaces). This pregeometrical, sensible world, is fundamentally a world of interactions with external things/bodies and of manipulations of
them.
4.7.5.2
Imagination
An act of imagination leads to pure morphological types (like roundness, under
which the geometrical ideality of the “circle” will be constructed), that still are of
a sensible order (that is they are not yet geometrical idealities, emancipated from
any sensible/imaginative intuitiveness): they are a kind of pure but sensible ideality. Husserlian imagination is different from Kant’s52 in that it realizes a kind
of “method of variation”53 of shapes [Husserl, 1978, p. 178] that produces the
51
52
53
Of course we do not have to confuse the prescientific world with the more elementary prepredicative world of appearances and primordial and immediately given experiences. The prescientific world is already characterized by predications, values, empirical manipulations and
techniques of measurement.
“According to Kant, geometry is not imaginary because it is grounded on the universal form
of pure sensibility, on the ideality of sensible space. But according to Husserl, on the contrary,
geometrical ideality is not imaginary because it is uprooted from all sensible ground in general.
[. . . ] Husserl remains then nearer to Descartes than to Kant. It is true for the latter, as has been
sufficiently emphasized, that the concept of sensibility is no longer derived from a ‘sensualist’
definition. We could not say this is always the case for Descartes or Husserl” [Derrida, 1978,
pp. 124-125, footnote 140].
Cf. below subsection 4.7.5.5, “Diagram Constructions as Epistemic Mediators”.
4.7 Spatial Frameworks, Anticipation, and Geometry
257
essential form. As clearly stated in the Crisis: “fantasy can transform sensible shapes
only into other sensible shapes” [Husserl, 1970, §9a, p. 25] [1954] uprooting morphological pregeometrical idealities from pure sensible reality. Imagination operates
on empirical ways of measurement too (for instance in surveying, design for buildings – for instance altars, pathways) that can be considered a further step in the
direction of pure geometrical idealities: “the rough estimate of magnitudes is transformed into the measurement of magnitudes by counting the equal. [. . . ] Measuring
belongs to every culture” [Husserl, 1978, p. 178]:
The art of measuring discovers practically the possibility of picking out as standard
measures certain empirical basic shapes, concretely fixed on empirical rigid bodies
which are in fact generally available; and by means of the relations which obtain (or
can be discovered) between these and other body-shapes it determines the latter intersubjectively and in practice univocally – at first within narrow spheres (as in the art of
surveying land), then in new spheres where shape is involved [Husserl, 1970, §9a, p.
28].
The philosopher (candidate geometer), “proceeding from the practical, finite, surrounding world (of the room, the city, the landscape, etc.), and temporally the world
of periodical occurences: day, month, etc.” (ibid.) can create geometry by means of
idealizations (“limit-shapes emerge toward which the particular series of perfecting
tend”, [Husserl, 1970, §9a, p. 26]) and the abductive anticipatory structure of intentionality, beyond every sensible and factual level. A horizon of “open infinity” is disclosed. Geometry definitely presents itself like a completely created eidetic science.
The whole activity is attributed to the “ancients”, governed by the Platonic doctrine
of ideas; moreover, Husserl notes exact concepts of geometry have the character of
Ideas in the Kantian sense.
4.7.5.3
Orality, Writing, Historicity
First orality, then language and writing are the ways for exposing and making public the generated ideal objectivities: this means those objectivities are constitutively
historical, so that historicity coincides with the openness of the infinite task of developing geometrical idealities. Ideal objects are traditional objects, and so they
possess historicity as one of their multiple eidetic components: they are “sedimentations of a truth meaning”.
Sedimentation describes the cumulative character of human experience: not every “abiding possession” of mine is traceable to a self-evidence of my own. Those
derived from social context are the sedimentations of someone else’s experience
that, of course, either I can repeat, given the suitable circumstances, or I can taken
for granted; every sedimentation produces a traditionalization. So geometrical idealities: “If each geometer tried seriously to repeat all the mental processes on which
the work of its predecessors was based, he would have no time of energy left for
advancing the discipline [. . . ] In a vast and cumulative enterprise like geometry,
especially in its more advanced stages, it would be counterproductive for such an
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4 Neuro-multimodal Abduction
ideal to be realized” [Carr, 1981, p. 252]. In case the tradition were interrupted, the
entire process of traditionalization could be started up again.
It is clear that the characterization of history is in this case totally philosophical,
and related to the phenomenological explanation of the birth of geometry. Every
effort to find the “origins” of geometry is unavoidably noetic, a kind of “reduction”, endowed with noetic characters: “We can also say that history is from the
start nothing other than the vital movement of the coexistence and the interweaving
of original formations and sedimentations of meaning” [Husserl, 1978, p. 174]. Of
course this does not mean that an historical approach founded on facts is forbidden.
Nevertheless “historicism is mistaken in principle”:
In any case, we can now recognize from all this that historicism, which wishes to clarify the historical and epistemological essence of mathematics from the standpoint of
the magical circumstances or other manners of apperception of a time-bound civilization, is mistaken in principle. For romantic spirits the mythical-magical elements of
the historical and prehistorical aspects of mathematics may be particularly attractive;
but to cling to this merely historically factual aspect of mathematics is precisely to lose
oneself to a sort of romanticism and to overlook the genuine problem. The internalhistorical problem, the epistemological problem. Also, one’s gaze obviously cannot
then become free to recognize that facticities of every type, including those involved
in the historicist objection, have a root in the essential structure of what is generally human, through which a teleological reason running throughout all historicity announces
itself [Husserl, 1978, p. 180].
Husserl contends that “facticities of every type [. . . ] have a root in the essential
structure of what is generally human”, and that “human surrounding world is the
same today and always” (ibid.). Of course this does not hold when we consider
the possible evolutionary character of this surrounding world. A similar kind of
possibility was advanced by Helmholtz and Poincaré, when they hypothesized the
famous “fantastic worlds” in which there are beings educated in an environment
quite different from ours [Poincaré, 1902, pp. 64–68]. Their different “experience”
will lead these beings to classify phenomena in a different way than we would,
that is a non-Euclidean way, because it is more convenient, even though the same
phenomena could be described in a Euclidean way. In fact, Poincaré says that
these worlds can be described “without forsaking the use of ordinary geometrical
language” [Poincaré, 1902, p. 71].
4.7.5.4
Axiomatics
Finally, definitional expressions and self-evident axioms are created, [Husserl, 1978,
p. 170] and so the classical axiomatic structure of Euclidean geometry, with the
realization of “the highly impressive idea of a systematically deductive theory”
[Husserl, 1970, §8, p. 21], where deduction is able to derive, potentially, and from a
finite number of concepts and propositions, all the forms that exist in space.
4.7 Spatial Frameworks, Anticipation, and Geometry
4.7.5.5
259
Diagram Constructions as Epistemic Mediators
With the institution of geometrical idealities the road to the mathematization of
nature, where “nature itself is idealized under the guidance of the new mathematics”
[Husserl, 1970, §9, p. 23] is opened: geometry is constantly and practically applied
to the world of sense experience, also as a means for technology.54 The limit-shapes
are acquired as tools that can be used and applied habitually. Geometry “becomes in
a certain respect a general method of knowing the real” [Husserl, 1970, §9b, p. 33]:
Like all cultural acquisitions which arise out of human accomplishment, they remain objectively knowable and available without requiring that the formulation of
their meaning be repeatedly and explicitly renewed. On the basis of sensible embodiment, e.g., in speech and writing, they are simply apperceptively grasped and
dealt with in our operations. Sensible “models” function in a similar way, including
especially the drawings on paper which are constantly used during work, printed
drawings in textbooks for those who learn by reading, and the like. [. . . ] Serving in
the methodical praxis of mathematicians, in this form of long-understood acquisitions, are significations which are. So to speak, sedimented in their embodiments.
And thus they make mental manipulation possible in the geometrical world of the
ideal objects [Husserl, 1970, §9a, pp. 26–27].
Geometrical constructions (that Husserl calls, in the passage above, “models”),
used in education, are sedimented in their embodiments. In chapter one I have called
these kinds of external cognitive objects epistemic mediators. In this perspective
geometrical constructions are sedimented epistemic mediators.
We have to notice that these mediators are also important for abductively discovering new geometrical theorems and properties. Following the Husserlian phenomenological point of view, this is due to the fact that they are analogous to the
sensible intuitable shapes that were at the origins of geometry, as I have already illustrated. To increase geometrical knowledge it is possible to use these models, that
are “sensible”
[. . . ] according to universal operations which can be carried out with them, to construct
not only more and more shapes which, because of the method which produces them,
are intersubjectively and univocally determined. For in the end the possibility emerges
of producing constructively and univocally, through an a priori, all-encompassing systematic method, all possible conceivable ideal shapes [Husserl, 1970, §9a, p. 27].
The horizon of constructions offers a collection of epistemic mediators that are able
to perform creative geometrical developments according to abductive manipulations
guided by “universal operations”. It is by means of constructions, again, like in Kant,
that the “exactness” of new geometrical idealities is attained and, moreover:
This occurs not only in particular cases, according to an everywhere similar method
which, operating on sensible intuitable shapes chosen at random, could carry out idealizations everywhere and originally create, in objective and univocal determinateness,
the pure idealities which correspond to them (ibid.).
54
A very simple example is given by the fact it is used to improve methods of measurement
increasing the approximation of geometrical tools to the geometrical ideals.
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4 Neuro-multimodal Abduction
The operations performed by constructions are analogous to the ones Husserl illustrates in the case of the so-called eidetic variation (or method of variation) and consist in trying out various objects that instantiate some essences to see whether they
also instantiate others. For instance, using an “empirical example” of an ideal geometrical object, we can find properties of the objects not yet discovered. [Føllesdal,
1999, p. 190] describes another case: Bolzano constructed an example of a continuous function which is not differentiable; Weierstrass thirty years later constructed
another more complex non differentiable function – two ways of adding new properties to the ideal concept of function by means of empirical, tangible examples.
Consequently, eidetic variation re-echo that “passing beyond” we already explained
when Kant examined geometrical constructions and manipulations of a concrete
triangle:
For I must not restrict my attention to what I am actually thinking in my concept of
a triangle (this is nothing more than the mere definition); I must pass beyond it to
properties which are not contained in this concept, but yet belong to it [Kant, 1929,
A718-B746, p. 580].
Like in Kant, in Husserl the role of imagination is still central, together with the acknowledgment of importance of the constraints imposed by the external materiality
cognitively exploited (cf. previous chapter, subsection 3.6.7):
[. . . ] in actual drawing and modelling he [the geometer] is restricted, in fancy he has
a perfect freedom in the arbitrary recasting of the figures he has imagined [. . . ]. The
drawings therefore follow normally after the constructions of fancy and the pure eidetic thought built upon these as a basis, and serve chiefly to fix stages in the process
already previously gone through, thereby making it easier to bring it back to consciousness again [Husserl, 1931, §70, pp. 199-200].
The imagination has to be devoted to look for a “perfect clearness” but also has to
be enriched by the systematic exploitation of the “best observations” in primordial
intuition.
4.7.5.6
Geometry Model of Phenomenology
Like in the case of Kant, in Husserl too geometry can be considered a model of
philosophy. This is explicitly stated in Ideas I: “[. . . ] the position for the phenomenologist [. . . ] is essentially the same [as the geometer]” (ibid.). There are infinite
essential forms of the phenomenological kind and the phenomenologist can make a
limited use of the primordial order of givenness. Only the main types of primordial
data are at his disposal. Consequently he has to operate with the help of “fancy”:
“But naturally not for all possible special forms, just as little as the geometer depends on drawings and models for the infinite variety of his corporeal types” (ibid.).
This relationship between the two eidetic activities and the role of imagination
leads us to say that the “element which makes up the life of phenomenology as of all
eidetical science is ‘fiction’ ” (Husserl says in the footnote “A sentence which should
be particularly appropriate as a quotation for bringing ridicule from the naturalistic
side on the eidetic way of knowledge!” – cit., §70, p. 201).
4.8 Non-conceptual and Spatial Abilities
4.8
261
Non-conceptual and Spatial Abilities
The importance of abductive manipulative skills can also be understood by considering the recent tradition of cognitive research in dynamical systems. The importance
and the validity of this tradition is controversial in the cognitive science community,
yet – as I will better illustrate in chapter eight of this book – I think it can provide many interesting suggestions to further develop the abductive cognitive aspects
of external and bodily epistemic mediators. It is well-known that cognitive science
has been dominated by the approach that considers cognition as an operation of a
special mental computer, situated in the brain.55 Sensory organs discharge representations of the state of the environment to the mental computer. The system processes
a specification of appropriate thought, reasoning or actions. In the last case it is the
body which carries out the action. Representations are considered like static structures of symbols, and cognitive procedures are sequential transformations from one
structure to the next.
Following the cognitive approach suggested by research in dynamical systems,
we immediately learn that cognitive processes and their context have to be considered as unfolding “continuously and simultaneously in real time” [van Gelder
and Port, 1995; van Gelder, 1999]. This approach [Clark, 1997] tries to explain
how a cognitive system can generate its own change, displaying its self-organizing
character. Hence, a cognitive system is not a computer, but a dynamical system, a
whole system including the nervous system, body (with its movements, feelings, and
emotions), and environment: every cognitive process takes place in real biological
hardware and this embeddedness, and the various “interactions” involved, become
its central aspect.
Many studies in the area are related to the way infants acquire simple body skills
and actions, showing how thought is embodied: thought grows from actions and
from control of the body, as already guessed and partially described by [Piaget,
1952] and [Piaget and Inhelder, 1956], who illustrated the role of sensorimotor period of here-and-now bodily existence. For example we have a felt embodied understanding of bilateral geometrical symmetry that can be considered one of the basic
experiential levels from which the highest levels of human art and language are developed. Experiments show that exploration of the environment and control of body
in children is the fundamental step that favors the cognitive constructions of hidden embodied templates and patterns of kinematic skills but also of speech abilities:
“[. . . ] what infants sense and what they feel in their ordinary looking and moving
are teaching their brain about their bodies and about their worlds” [Thelen, 1995].
When explained in dynamic terms [Saltzman, 1995], the activity of perceptual
motor category formation can be easily seen as highly abductive and foundational
for all cognitive development. Of course, interactions between the body and the environment are not the only form of cognitive mediation with the world. It is obvious
that social communication too (and of course manipulations of the conditions of
possibility of this communication) provides rich information to many of our senses.
55
It is the so-called CRUM (Computational-Representational Understanding of Mind) illustrated
and criticized by [Thagard, 1996].
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4 Neuro-multimodal Abduction
Other research that involves the problem of embodiment comes from the field of
robotics [Chrisley, 1995], where the study of human cognition emphasizes the role
of acts in real-time and real-space environments, going beyond the computer/brain
model to expand the analogy to the robot/body. Robotic computation can help to
learn how embeddedness and embodiment of non-conceptual abilities in an intentional system can be delineated and understood (cf. also [Dorigo and Colombetti,
1998]).
A very interesting kind of formation of non-conceptual hidden templates, patterns, and skills, is illustrated by the generation of spatial abilities in children,
adults, non-human mammals and birds. This investigation also challenges some
certainties of the propositional view of the mind. Non-conceptual spatial patterns
are abductively formed in cognitive situations that are highly integrated with external objects, environment, and body movements [Foreman and Gillett, 1997].
Many cognitive cases are studied using traditional experimentation in psychology
and ethology, but also taking advantage of a neurobehavioral approach: 1. egocentric
ways of encoding space in comparison to the allocentric ones, capable of guaranteeing navigational spatial skills, 2. spatial mapping in people, 3. homing behavior of
various mammals and birds [Bovet, 1997; Papi, 1992], 4. use of landmarks and/or
gestures in orientation and perceptual localization (to reach external objects) [Bloch
and Morange, 1997], 5. several ways – landmark, route, and survey based – of children’s way finding [Blades, 1997], 6. people navigating in large scale environments
[Gärling et al., 1997], 7. spatial abilities in mechanical reasoning [Hegarty and
Kozhevnikov, 2000].
Many of these cognitive behaviors and attitudes are related in various ways to
the exploitation of formation of geometrical shapes and frameworks. For example
in the orienting and reaching behavior, distant objects are generally viewed as parts
of a spatial situation and are treated by reference to a spatial frame often endowed
with geometrical characters. Different spatial frameworks with various geometrical
features are present at the level of exploration, as a sensorimotor activity, organized along a body-centred referent, entailing the position of the sensory receptors,
the direction of the displacement, and gravitational forces (the so-called “personal”
spaces), and at the level of more abstract representations, such as cognitive maps,
that are independent of the subject’s actual position.
Finally, it is interesting to note that in mammalian species the sensorimotor activity of exploration is displayed in the presence of novel and/or unexpected events
and situations. This kind of investigatory behavior seems to be part of a general
process of knowledge. Also environment and interactive “punishments” in cases of
non-human animals and robots spatial explorations can be cognitively seen as playing the role of contradicting some expected outcomes and as an important step that
encourages and supports the emergence of more or less stable spatial templates.56
We can guess that some abduced patterns and templates acquired and formed during exploration constitute intermediate steps between body-centred non-conceptual
abilities and further representational and more general and abstract frameworks in
56
On recent research concerning the neural correlated of this process cf. above section 4.7.
4.8 Non-conceptual and Spatial Abilities
263
humans as well, like for example cognitive maps and diagrams and geometrical
knowledge and generalizations. It can be reasonably hypothesized that during exploration, feedback arising from the trajectory itself (vestibular, muscular, and other
information) is matched with the ever-changing visual scenes of the environment.
This matching would inform the subject that it is moving in a stable environment
whose properties are invariant whatever their perceptual appearance [Thinus-Blanc
et al., 1997].
Summary
I have contended in this chapter that abduction is essentially multimodal, in that
both data and hypotheses can have a full range of verbal and sensory representations, involving words, sights, images, smells, etc., but also kinesthetic and motor
experiences and other feelings such as pain. Using a methodological approach to rethink abduction in mere neurological terms is a particularly useful exercise. It shows
that both linguistic and non linguistic signs have an internal semiotic life as particular configurations of neural networks and chemical distributions (and in terms of
their transformations) at the level of human brains, and as somatic expressions, not
disregarding the fact they can also be delegated to many external objects and devices. The revaluation of neural and multimodal aspects of abduction is compelling,
given the fact that abductive cognition is occurring in a “distributed” framework
and in a hybrid way, that is, in the interplay between internal and external signs I
have described in the previous chapter. It also shows how the classical perspective
on abduction based on logic captures important but limited properties of this cognitive process, basically ignoring the instinctual, model-based and embodied aspects.
These last features can only be accounted for if we acknowledge that abductive
performances are to a considerable extent neurally hardwired and embodied, resulting from the rigid execution of the DNA program. Of course organisms are also
equipped with various ontogenetic mechanisms that – made possible by pre-wired
genetic endowments – permit them to plastically acquire and produce information
and knowledge and thus better adapt to the environment (for example by forming
logical templates of reasoning). If we aim at shedding light on the role of abduction
in guessing intentions, in mentation and metamentation, in affective attunement and
in other emotional and empathic appraisals, going beyond logical models is mandatory and cognitive processes allowed by both hardwired and pre-wired aspects have
to be considered.
Finally, I would like to reiterate the importance of the sections devoted to the
distinction between thought and motor action, seeing both aspects as fruit of brain
activity. This approach highlights the role of internal and external “reasons” in ethical deliberation, as a form of practical reasoning, which shares many aspects with
hypothetical reasoning as it is described by abductive reasoning. In this case abduction nicely accounts for the choice of internal and external “reasons” in decision
making processes. I also believe it can help us to overcome some sterile consequences of the old-fashioned assumptions that prohibit arrival at an “ought” from
an “is” in the tradition of moral philosophy.
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4 Neuro-multimodal Abduction
I have concluded the chapter showing how abduction also deserves full attention
when performed in mammalian cognitive systems representing the location of objects within the spatial framework. I believe spatial cognition does not have to be
merely considered in neurological, biological and psychological terms. We need not
fear the synthesis of scientific results with philosophical intuitions, such as those
provided by the phenomenological tradition in terms of adumbrations and anticipations. The consideration of these philosophical results in turn acquires further clarification in the framework of the description of agency due to the so-called emulation
theory. This framework presents emulation circuits as abductive devices able to hypothesize a forward mapping from control signals to the anticipated consequences
of executing the control command.
Chapter 5
Animal Abduction
From Mindless Organisms to Artifactual Mediators
The first two sections of this chapter are strictly related to some seminal Peircean
philosophical considerations concerning abduction, perception, inference, and instinct which I consider are still important to current cognitive research. Peircean
analysis helps us to better grasp how model-based, sentential and manipulative aspects of abduction have to be seen as intertwined. Moreover, Peircean emphasis on
the role of instincts in abduction provides a perfect philosophical introduction to the
problem of animal hypothetical cognition in the remaining part of the chapter.
1. First, Peirce explains to us that perceptions are abductions, and thus that they
are hypothetical and withdrawable. Moreover, given the fact that judgments in
perception are fallible but indubitable abductions, we are not in any psychological condition to conceive that they are false, as they are unconscious habits
of inference. Unconscious cognition legitimately enters the abductive processes
(and not only in the case of some aspects of perception, as we will see). The
same happens in the case of emotions, which provide a quick – even if often highly unreliable – abductive appraisal/explanation of given data, which is
usually anomalous or inconsistent.
2. Second, Peirce contends that perception is the fruit of an abductive “semiotic”
activity that is inferential in itself. The philosophical reason is simple, Peirce
stated that all thinking is in signs, and signs can be icons, indices, or symbols.
The concept of sign includes “feeling, image, conception, and other representation”: inference is in turn a form of sign activity, that is, the word inference is
not exhausted by its logical aspects and refers to the effect of various sensorial
activities.
3. Third, iconicity hybridates logicality: the sentential aspects of symbolic disciplines like logic or algebra coexist with model-based features – iconic. Sentential features like symbols and conventional rules1 are intertwined with the
spatial configuration, like in the case of “compound conventional signs”. What
I have called sentential abduction is in reality far from being strongly separated
1
Written natural languages are intertwined with iconic aspects too.
L. Magnani: Abductive Cognition, COSMOS 3, pp. 265–316.
c Springer-Verlag Berlin Heidelberg 2009
springerlink.com
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5 Animal Abduction
by model-based aspects: iconicity is always present in human reasoning, even
if often hidden and implicit.
It is from this perspective that [sentential] syllogism and [model-based] perception
are seen as rigorously intertwined. Consequently, there is no sharp contrast between
the idea of abduction (both creative and selective) as perception and the idea of
abduction as something that pertains to logic. Both aspects are inferential in themselves and fruit of sign activity. Taking the Peircean philosophical path we return
to observations made in the previous chapter: abduction is basically multimodal in
that both data and hypotheses can have a full range of verbal and sensory representations, involving words, sights, images, smells, etc. but also kinesthetic and motor
experiences and feelings such as pain, and thus all sensory modalities.
As I argue in the second section of the chapter, the Peircean architectural view
of abduction is completed and further enhanced by his consideration of the role of
instincts seen as “inherited habits, or in a more accurate language, inherited dispositions” [Peirce, 1931-1958, 2.170]:
1. Peirce says abduction even takes place when a new born chick picks up the
right sort of corn. This is another example of what could be called spontaneous
abduction – analogous to the case of some unconscious/embodied abductive
processes in humans;
2. not only hypothesis generation has to be considered as a largely instinctual endowment of human beings, a fact which can be justified thanks either to:
a. the idealistic notion of synechism, according to which everything is continuous and the future is in some measure continuous with the past, and where
mind and matter are not entirely distinct. Just as it is – analogously – for
instinct and inference. The human mind would have developed under the
same metaphysical laws that govern the universe leading us to hypothesize
that the mind has a tendency to find true hypotheses concerning the universe. Peirce thinks that thought is not necessarily connected with the brain
and in fact it appears in the work of bees, crystals and throughout the purely
physical world;
or to
b. the naturalistic view, which involves at least two aspects: evolutionary/
adaptive and perceptual. The capacity to guess correct hypotheses can be
seen as instinctive and enrooted in our evolution and from this perspective
abduction is undoubtedly a property of naturally evolving organisms;
3. nature “fecundates” – in Peircean words – the mind because it is through its
disembodiment and extension in nature that in turn nature affects the mind. If
we argue a conception of mind as extended (cf. chapter three of this book), it is
simple to consider its instinctual part as shaped by evolution through the constraints found in nature itself. It is in this sense that the mind’s guesses – both
instinctual and reasoned (in this last case shaped through the coevolution between nature and cognitive niches) – can be classified as plausible hypotheses
5 Animal Abduction
267
about nature/the external world. The mind grows together with the representational delegations to the external world that mind itself has made throughout the
history of culture by constructing so-called cognitive niches.
At this point an obvious conclusion can be derived. The idea that there would be
another sharp conflict (present in Peirce’s texts too) between views of abduction
(and of practical reasoning) in terms of heuristic strategies and in terms of instinct
(insight, perception), appears old-fashioned. The two aspects simply coexist at the
level of the real organic agent, it all depends on the cognitive/semiotic perspective
we adopt: either
1. we can see an organic agent as a practical agent that mainly takes advantage
of its implicit endowments in terms of guessing right, hardwired by evolution,
where of course instinct or hardwired programs are central,
or
2. we can see it as the user of explicit and more or less abstract semiotic devices
(language, logic, visualizations, etc.) internally stored and/or externally available – hybrid – which realize heuristic plastic strategies that in some organisms
are “conscious”. These strategies, used for guessing right, exploit various and
contextual relevance and plausibility criteria built up during cultural evolution
and made available in cognitive niches, where they can potentially be taught
and learnt.
I can conclude that instinct vs. inference represents a conflict we can overcome
simply by observing that the work of abduction is partly explicable as a biological
phenomenon and partly as a more or less “logical” operation related to “plastic”
cognitive endowments of all organisms. I entirely agree with Peirce: a guess in science and the appearance of a new hypothesis is also a biological phenomenon and as
such it is related to instinct, in the sense that we can compare it to a chance variation
in biological evolution (even if of course the evolution of scientific guesses does not
conform to the pattern of biological evolution). An abduced hypothesis introduces a
change (and an opportunity) in the semiotic processes to advance new perspectives
in the coevolution of the organism and the environment.
The resulting idea that abduction is partly explicable as a biological instinctual
phenomenon and partly as a more or less “logical” operation related to “plastic”
cognitive endowments of all organisms naturally leads to the remaining sections
(starting from section 5.3) of this key chapter. Many animals – traditionally considered “mindless” organisms – make up a series of signs and are engaged in making, manifesting or reacting to a series of signs.2 Through this semiotic activity –
which is considerably model-based – they are at the same time engaged in “being cognitive agents” and therefore in thinking intelligently. An important effect of
this semiotic activity is a continuous process of “hypothesis generation” that can be
seen at the level of both instinctual behavior, as a kind of “hardwired” cognition,
2
For a recent survey on the current research on the origin, evolution, dynamics, and learning
of signaling systems, in humans and other animals, both from an individual and a “network”
perspective, cf. [Skyrms, 2008].
268
5 Animal Abduction
and representation-oriented behavior, where nonlinguistic pseudothoughts drive a
plastic model-based cognitive role.
This activity is at the root of a variety of human and non-human abductive performances, which I analyze in the light of the concept of affordance. Another important character of the model-based cognitive activity above is the externalization
of artifacts that play the role of mediators in animal languageless reflexive thinking. That is, the interplay between internal and external representations exhibits a
new cognitive perspective on the mechanisms underlying the semiotic emergence of
abductive processes in important areas of model-based thinking of mindless organisms. To illustrate this process I will take advantage of the case of affect attunement
which exhibits an impressive case of model-based communication. Again, a considerable part of abductive cognition occurs through an activity consisting in a kind
of reification in the external environment followed by re-projection and reinterpretation through new configurations of neural networks and their chemical processes.
Analysis of the central problems of abduction and hypothesis generation helps to
address the problems of other related topics in model-based animal cognition, like
pseudological and reflexive thinking, the role of pseudoexplanatory guesses in plastic cognition, the role of reification and beliefs and the problem of the relationship
between abduction and perception and rationality and instincts.
5.1
5.1.1
Iconicity and Logicality in Reasoning
Perception vs. Inference
We should remember, as Peirce noted and I already stressed in chapter one (cf.
section 1.5), that abduction plays a role even in relatively simple visual phenomena. What I have called visual abduction [Magnani et al., 1994; Magnani, 1996],
a special form of non verbal abduction – a kind of model-based cognition – occurs when hypotheses are instantly derived from a stored series of previous similar
experiences. It covers a mental procedure that falls into the category called “perception”. Peirce considers perception a fast and uncontrolled knowledge-production
process. Perception is a kind of vehicle for the instantaneous retrieval of knowledge
that was previously assembled in our mind through inferential processes: “[. . . ] a
fully accepted, simple, and interesting inference tends to obliterate all recognition
of the uninteresting and complex premises from which it was derived” [Peirce,
1931-1958, 7.37]. Perception is abductive in itself: “Abductive inference shades
into perceptual judgment without any sharp line of demarcation between them”
[Peirce, 1992-1998, p. 224]. In chapter one I have called this kind of image-based
hypothesis formation visual (or iconic) abduction (cf. also [Magnani et al., 1994;
Magnani, 1996]). It plays an important cognitive role in both everyday reasoning
and science, where it is well known it can provide epistemically substantial shortcuts to dramatic new discoveries.
If perceptions are abductions they are basically withdrawable, just like the scientific hypotheses abductively found. They are “hypotheses” about data we can accept
5.1 Iconicity and Logicality in Reasoning
269
(sometimes this happens spontaneously) or carefully evaluate. Moreover, the fact
they are, as we will see in the following subsection, inferences, in the Peircean
sense, and of course withdrawable, does not mean they are controlled (deliberate),
like in the case of explicit inferences, for example in logic and other types of rational
or fully conscious human reasoning. Perception involves semiosis and is abductive,
and it is able to correct itself when it falls into error, and consequently it can be
censured. However, we have to carefully analyze the proper character of this kind of
controllability, following Peirce’s considerations on the so-called “perceptual judgment” (“The seven systems of metaphysics”, 1903):
Where then in the process of cognition does the possibility of controlling it begin?
Certainly not before the percept is formed. Even after the percept is formed there is an
operation, which seems to me to be quite uncontrollable. It is that of judging what it
is that the person perceives. A judgment is an act of formation of a mental proposition
combined with an adoption of it or act of assent to it. A percept on the other hand is
an image or moving picture or other exhibition. The perceptual judgment, that is, the
first judgment of a person as to what is before his senses, bears no more resemblance
to the percept than the figure [cf. figure 5.1] I am going to draw is like a man.
I do not see that it is possible to exercise any control over that operation or to subject it
to criticism. If we can criticize it at all, as far as I can see, that criticism would be limited to performing it again and seeing whether with closer attention we get the same
result. But when we so perform it again, paying now closer attention, the percept is
presumably not such it was before. I do not see what other means we have of knowing
whether it is the same as it was before or not, except by comparing the former perceptual judgment to the later one. I would utterly distrust any other method of ascertaining
what the character of the percept was. Consequently, until I am better advised, I shall
consider the perceptual judgment to be utterly beyond control [Peirce, 1992-1998, II,
p. 191].
c
Fig. 5.1 In [Peirce, 1992-1998, II, p. 191].1998
Indiana University Press, reprinted by
permission.
In summary, judgments in perception are fallible but indubitable abductions – we
are not in any condition to psychologically conceive that they are false, as they are
unconscious habits of inference.
Nevertheless, percept and perceptual judgment are not unrelated to abduction
because they are not entirely free
270
5 Animal Abduction
[. . . ] from any character that is proper to interpretations [. . . ]. The fact is that it is
not necessary to go beyond ordinary observations of common life to find a variety
of widely different ways in which perception is interpretative. The whole series of
hypnotic phenomena, of which so many fall within the realm of ordinary everyday
observation, – such as waking up at the hour we wish to wake much nearer than our
waking selves could guess it, – involve the fact that we perceive what we are adjusted
for interpreting though it be far less perceptible that any express effort could enable
us to perceive [. . . ]. It is a marvel to me that the clock in my study strikes every half
an hour in the most audible manner, and yet I never hear it [. . . ]. Some politicians
think it is a clever thing to convey an idea which they carefully abstain from stating in
words. The result is that a reporter is ready to swear quite sincerely that a politician
said something to him which the politician was most careful not to say. It is plainly
nothing but the extremest case of Abductive Judgment [Peirce, 1992-1998, II, p. 229].
The fact that perception functions as a kind of “abstractive observation” [Peirce,
1992-1998, II, p. 206], so that “perceptual judgments contain general elements”
[Peirce, 1992-1998, II, p. 227] relates it to the expressive power of icons. It is analogous to what is occurring in mathematics when the reasoner “sees” – through the
manipulations and constructions on an external single diagram (icon) – that some
properties are not merely single but of a general nature: perception functions as
“an abstractive observation”.3 Peirce eloquently says that it is “[. . . ] a very extraordinary nature of Diagrams that they show – as literally as Percept shows the
Perceptual Judgment to be true, – that a consequence does follow, and more marvelously yet, that it would follow under all varieties of circumstances accompanying
the premises” [Peirce, 1976, pp. 317-318].4
One more example that supports this interpretative nature is given by the fact that
the perception of tone arises from the activity of the mind only after having noted the
rapidity of the vibrations of the sound waves, but the possibility of individuating a
tone happens only after having heard several of the sound impulses and after having
judged their frequency. Consequently the sensation of pitch is made possible by
previous experiences and cognitions stored in memory, so that one oscillation of the
air would not produce a tone.
For Peirce all knowing is inferring and inferring is not instantaneous, it happens
in a process that needs an activity of comparisons involving many kinds of patterns
in a more or less considerable lapse of time. We have already seen in chapter one that
all sensations or perceptions participate in the nature of a unifying hypothesis, that
is, in abduction, in the case of emotions too: for example the various sounds made
by the musical instruments of the orchestra strike upon the ear, and cause a peculiar
musical emotion, completely distinct from the sounds themselves. Emotion is in this
case considered by Peirce the same thing as a hypothetic inference, an abduction.
The analogy between abduction and emotion is strong in Peircean writings and
Peirce was impressed by the elicitation of an emotion by a complex cognition.
3
4
I have illustrated this important cognitive and epistemological issue in chapter two, sections 2.9
and 2.11, and in chapter three, subsection 3.6.3.
Cf. [Turrisi, 1990]. Other considerations on abduction and perception are given in [Tiercelin,
2005].
5.1 Iconicity and Logicality in Reasoning
271
Emotion detects a kind of inconsistency among a set of beliefs, so what beliefs
to abandon has to be determined in producing an explanation that resolves the inconsistency. Peirce said emotions are simple predicates that are elicited by complex
predicates like in the case of the anxiety that is triggered by the thought that someone has died. In this sense emotions resort to a wonderful example of model-based
reasoning, where a signal is sent to the rest of the brain if a certain event occurs.
Peirce would have agreed with the current view that in humans, emotions – that can
be hardwired or learned through long experience with other human beings and certain situations – are typically non-intentional abductive signals to themselves that
“[. . . ] allow humans, who have slender computational resources, to choose among
multiple goals, and to act – despite their limited and often incorrect knowledge, and
despite their limited physical powers” [Oatley and Johnson-Laird, 2002, p. 171].
They can sometimes provide the first indication of an inconsistency, like in the
case of anxiety when a loved-one’s lateness for an appointment exceeds a certain
time but also in high-level cognitive settings such as scientific reasoning. They are
also useful to enter mental models of other individuals and tell you about their
suitability for possible agreements in the future:
One woman, for instance, waited for a new colleague in one restaurant, while he sat
for over an hour in a different located restaurant in the same chain waiting for her. The
fact that he had “stood her up”, she said, would be at the back of her mind the next
time she had dealings with him. Indeed, it was, even though she stated in her diary that
his explanation was convincing. He waited longer than she had in the restaurant, and
he was the one who had to phone to find out what had gone wrong. She knew he had
been no more in fault than her. Nonetheless the emotion of distrust provided a new
kind of forward consistency for her in her relations with this man. This evaluation was
compelling even though she held explicit beliefs that were inconsistent with it. The
emotion overruled the propositional inconsistency [Oatley and Johnson-Laird, 2002,
p. 176].
Of course abductive results can also cause emotions, for example depression can
be the sign of the invalidity of certain previously abduced hypotheses coupled with
some basic aspects of a certain individual’s life.
5.1.2
5.1.2.1
Iconicity Hybridates Logicality
Is Perception an Inference?
Let us consider some basic philosophical aspects related to this problem of perception. In the following passage, which Peirce decided to skip in his last of the seven
Harvard Lectures (14 May 1903), perception is clearly considered a kind of abduction: “A mass of facts is before us. We go through them. We examine them. We find
them a confused snarl, an impenetrable jungle. We are unable to hold them in our
minds. [. . . ] But suddenly, while we are poring over our digest of the facts and are
endeavoring to set them into order, it occurs to us that if we were to assume something to be true that we do not know to be true, these facts would arrange themselves
272
5 Animal Abduction
luminously. That is abduction [. . . ]”.5 This passage seems to classify abduction as
emerging in “perceiving” facts and experiences, and not only in the conclusions of
an “inference” [Hoffmann, 1999, pp. 279-280]. In this sense perceptual and inferential views would be contrasted and a kind of inconsistency would arise, like many of
the researchers on Peirce contend. It is well-known that in Peirce the inferential side
is first of all expressed and denoted by the syllogistic framework.6 Following this
point of view the genesis of an – abductive – perceptual judgment would have to be
located at the level of the premises of the famous Peircean syllogistic schema that
depicts abduction as the fallacy of the affirming the consequent. Moreover, it would
be at the level of this perceptual side, and not at the level of the logico-sentential one
that the proper creative virtues of abduction are disclosed. The explaining solution
would emerge in perceiving facts and experience and not in the conclusion of the
logical inference (“the initial conceiving of a novel hypothesis is not the product of
an inferential transition” [Kapitan, 1997, p. 2]).7
I further think that the two – often considered contrasting – views more simply
and coherently can coexist, beyond Peirce,8 but also in the perspective of the orthodoxy of Peircean texts: the prevailing Peircean semiotic conception of inference as
a form of sign activity, where the word sign includes “feeling, image, conception,
and other representation” offers the solution to this potential conflict.9 In this perspective the meaning of the word inference is not exhausted by its “logical” aspects
but is referred to the effect of various sensorial activities. One more reason that supports my contention is that for Peirce the sentential aspects of symbolic disciplines
like logic or algebra coexist with model-based features – iconic. Sentential features
like symbols and conventional rules are intertwined with the spatial configuration;
in Peirce’s terms:
The truth, however, appears to be that all deductive reasoning, even simple syllogism,
involves an element of observation; namely, deduction consists in constructing an icon
or diagram the relations of whose parts shall present a complete analogy with those of
the parts of the object of reasoning, of experimenting upon this image in the imagination and of observing the result so as to discover unnoticed and hidden relations among
the parts [Peirce, 1931-1958, 3.363] .
5
6
7
8
9
Cf. “Pragmatism as the logic of abduction”, in [Peirce, 1992-1998, pp. 227-241] , the quotation
is from footnote 12, pp. 531-532.
Cf. section 1.4, chapter one, this book.
It has to be said that some authors (for example [Hoffmann, 1999, p. 280]) contend that, in
order to explain abduction as the process of forming an explanatory hypothesis within Peirce’s
concept of “logic”, it is necessary to see both sides as coming together.
It is well-known that in later writings Peirce seems more inclined to see abduction as both
insight and inference.
[Anderson, 1987, p. 45] maintains that “Peirce quite explicitly states that abduction is both an
insight and an inference. This is a fact to be explained, not to be explained away”. Anderson
nicely solves this problem by referring to Peirce’s complicated theory of the three fundamental
categories, Firstness, Secondness, and Thirdness: abduction, as a form of reasoning is essentially
a third, but it also occurs at the level of Firstness “as a sensuous form of reasoning” (p. 56 ff.).
5.1 Iconicity and Logicality in Reasoning
273
In another passage, which refers to the “conventional” character of algebraic formulas as icons, the idea is even clearer and takes advantage of the introduction of the
idea of the “compound conventional sign”:10
Particularly deserving of notice are icons in which the likeness is aided by conventional
rules. Thus, an algebraic formula is an icon, rendered such by the rules of commutation,
association, and distribution of the symbols; that it might as well, or better, be regarded
as a compound conventional sign [Peirce, 1966, pp. 787 and pp. frm-e6-28 CSP].
It seems for Peirce that iconicity of reasoning, and consequently of abduction are
fundamental, like it is clearly stressed in the following passage: “I said, Abduction,
or the suggestion of an explanatory theory, is inference through an Icon” [Peirce,
1986, p. 276]. Moreover, induction and deduction are inferences “through an Index”
and “through a Symbol” (ibid.).
To conclude, it would seem that there is not an inferential aspect of abduction, characterized by the syllogistic model, separated from (or contrasted with) the
perceptual one, which would be “creative” instead, like many authors contend.11
I consider the two aspects consistent, and both are perfectly understandable in the
framework of Peircean philosophy and semiotics.12
A further evidence of the fact that the two aspects of abduction are intertwined
derives from the study of children’s early word acquisition [Roberts, 2004]. Children form knowledge and expectations about the symbolic functioning of a particular word in routine events where model-based perceptual and manipulative aspects
of reasoning are predominant and furnish suitable constraints: they generate abductions that help to acquire the content-related symbolic functioning, going beyond
what was already experienced. These abduced hypotheses are “practical”, about
knowing how to use a word to direct attention in a certain way. These hypotheses
need not be verbalized by the children, who only later on acquire a more theoretical status through a systematization of their knowledge. It is at this level that they
are expressed verbally and concern causal frameworks rather than specific causal
mechanisms – for instance of natural kind terms.
To deepen the particular “inferential” status of abduction we have illustrated
above further problems regarding the relationship between sentential and modelbased aspects of abduction have to be analyzed.
10
11
12
Cf. subsection 3.6.4, chapter one of this book. [Stjernfelt, 2007] provides a full analysis of the
role of icons and diagrams in Peircean philosophical and semiotic approach, also taking into
account the Husserlian tradition of phenomenology.
For example [Kapitan, 1997; Hoffmann, 1999].
On the contrary, some authors (for example [Hoffmann, 1999; Hoffmann, 2004; Paavola,
2004]), as [Frankfurt, 1958, p. 594] synthesized, find a central paradox in “[. . . ] that Peirce
holds both that hypotheses are the products of a wonderful imaginative faculty in man and that
they are product of a certain sort of logical inference”. Furthermore, some commentators seem
to maintain that “creative” aspects of abduction would exclusively belong to the perceptual side.
274
5 Animal Abduction
5.1.2.2
Syllogism vs. Perception
The following is a frequently quoted passage by Peirce on perception and abduction related to the passage on “perceptual judgment” that I reported above at the
beginning of this section:
Looking out of my window this lovely spring morning I see an azalea in full bloom.
No no! I do not see that; though that is the only way I can describe what I see. That
is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence,
fact, but only an image, which I make intelligible in part by means of a statement of
fact. This statement is abstract; but what I see is concrete. I perform and abduction
when I so much as express in a sentence anything I see. The truth is that the whole
fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined
by induction. Not the smallest advance can be made in knowledge beyond the stage of
vacant staring, without making an abduction in every step.13
The classical interpretation of this passage stresses the existence of a vicious circle
[Hoffmann, 1999, p. 283] on the one hand, we learn that the creativity of abduction
is based on the genesis of perceptual judgments. On the other hand, it is now said
that any perceptual judgment is in itself the result of an abduction. Or, as Peirce
says, “[. . . ] our first premises, the perceptual judgments, are to be regarded as an
extreme case of abductive inference, from which they differ in being absolutely
beyond criticism” [Peirce, 1931-1958, 5.181].
Surely it can be maintained that for Peirce perception on the whole is more precisely the act of subsuming sense data or “percepts” under concepts or ideas to give
rise to perceptual judgments: we have just said that he in turn analyzed this act of
subsuming as an abductive inference depicted in syllogistic terms
(P1) A well-recognized kind of object, M, has for its ordinary predicates P[1], P[2],
P[3], etc.
(P2) The suggesting object, S, has these predicates P[1], P[2], P[3], etc.
(C) Hence, S is of the kind M [Peirce, 1931-1958, 8.64].
In this abductive inference – which actually is merely selective – the creative act
“would” take place in the second premise: if we distinguish in abduction an inferential part and a perceptual one – cf. the previous subsection – (that is the genesis
of a perceptual judgment), and if we understand according to Peirce the arising of
a perceptual judgment for itself as an abductive inference, then in explaining the
possibility of abduction we get an infinite regress:
On its side, the perceptive judgment is the result of a process, although of a process not
sufficiently conscious to be controlled, or, to state it more truly, not controllable and
therefore not fully conscious. If we were to subject this subconscious process to logical
analysis, we should find that it terminated in what that analysis would represent as an
abductive inference, resting on the result of a similar process which a similar logical
13
Cf. the article “The proper treatment of hypotheses: a preliminary chapter, toward and examination of Hume’s argument against miracles, in its logic and in its history” [1901] (in [Peirce,
1966, p. 692]).
5.1 Iconicity and Logicality in Reasoning
275
analysis would represent to be terminated by a similar abductive inference and so on ad
infinitum. This analysis would be precisely analogous to which the sophism of Achilles
and the Tortoise applied to the chase of the Tortoise by Achilles, and it would fail to
represent the real process for the same reason. Namely, just as Achilles does not have
to make the series of distinct endeavors which he is represented as making, so this
process of forming the perceptual judgment, because it is sub-conscious and so not
amenable to logical criticism, does not have to make separate acts of inference, but
performs its act in one continuous process [Peirce, 1931-1958, 5.181].
This recursiveness, and the related vicious circle, even if stressed by many commentators, does not seem to me really important. I think we can give a simpler explanation of this conflict between the inferential and perceptual side of abduction by
recalling once again the Peircean semiotic conception of inference as a form of sign
activity, where the word sign includes “feeling, image, conception, and other representation”. It is interesting to note that recent research on non-deductive reasoning
stresses the presence of Gestalt phenomena not only in the realm of perception but
also in the realm of logical inference [Pizzi, 2006].14
5.1.2.3
Explicit, Uncontrolled, and Unconscious Inferences in Multimodal
Abduction
As I have maintained in the previous subsections, I think that two contrasting views
of abduction such as inference and perception can coherently coexist: I have already contended that the prevailing Peircean semiotic conception of inference as a
form of sign activity offers the solution to the conflict. We also said that for Peirce
the sentential aspects of logic, even if central, coexist with model-based features –
iconic. Abduction can be performed by words, symbols, and logical inferences, but
also by internal processes that treat external sensuous input/signs through a merely
unconscious mechanisms which give rise to abductive actions and reactions, like in
the case of the humble Peircean chicken (cf. below subsection 5.2.1) or of human
emotions and other various implicit ways of thinking. In these last cases sentential
aspects do not play any role.
We can say, following Thagard [2005; 2007] that abduction is fundamentally
performed in a multimodal way:15 for example, we consciously perform a perceptual judgment about the azalea, and in this case also concepts, ideas and statements
certainly play a central abductive role, but – Peirce says, they are only part of the
whole process: “what I perceived is not proposition, sentence, fact, but only image,
14
15
The exploitation of this analogy is fruitful: from the perspective of logic a Gestalt effect can be
seen as the derivability of incompatible indifferent conclusions on the basis of the same background information, such as it occurs in counterfactual and ampliative – inductive and abductive
– reasoning. It can be concluded that beyond the structural analogies between counterfactual,
inductive, and abductive reasoning there is a net of unequivocal logical relations between the
various forms of conditionals expressing contextually different applications of the considered
schema of argument. A kind of general theory of rational inference in which counterfactual,
inductive and abductive conditionals can be treated as special cases of what we could call a
rational conditional.
On the concept of multimodal abduction see chapter four, section 4.1, in this book.
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5 Animal Abduction
which I made intelligible in part by means of a statement of fact”.16 It is in this way
that perceptions acquire “meanings”: they nevertheless remain “hypotheses” about
data we can accept (sometimes this happens spontaneously) or carefully submit to
criticism. It is in this sense that the visual model of perception does not work in
isolation from other modes of perception or from other persons or sources of experience [Gooding, 1996]. As I have already illustrated in the first subsection of
this chapter perceptions are withdrawable “inferences”, even if not controlled (deliberate), like we control explicit inferences for example in logic and other types of
rational human “reasoning” and argumentation.
Being creative is not a peculiarity of perceptual/visual abduction, like – as I
have already said – some commentators seem to maintain [Kapitan, 1997]. Moreover, perception and cognition alike are inherently inferential. If awareness, whether
propositional or perceptual, is semiotic, then all awareness involves the interpretation of signs, and all such interpretation is inferential: semiosis not only involves the
interpretation of linguistic signs, but also the interpretation of non-linguistic signs.
Abduction of course embraces much of these semiotic performances.
Both linguistic and non linguistic signs
1. have an internal semiotic life, as particular configurations of neural networks
and chemical distributions (and in terms of their transformations) at the level of
human brains, and as somatic expressions,
2. but can also be delegated to many external objects and devices, for example
written texts, diagrams, artifacts, etc.
In this “distributed” framework those central forms of abductive cognition that occur
in a hybrid way, that is in the interplay between internal and external signs, are of
special interest, as I have illustrated in chapter three.
5.2
5.2.1
Instinct vs. Heuristic Strategies
The Peircean Abductive Chicken and Animal Hypothetical
Cognition
An example of instinctual (and putatively “unconscious”) abduction is given by the
case of animal embodied kinesthetic/motor abilities, capable of leading to some appropriate cognitive behavior; Peirce says abduction even takes place when a new
born chick picks up the right sort of corn. This is another example, so to say,
of spontaneous abduction – analogous to the case of some unconscious/embodied
abductive processes in humans:
When a chicken first emerges from the shell, it does not try fifty random ways of appeasing its hunger, but within five minutes is picking up food, choosing as it picks, and
16
Cf. “The proper treatment of hypotheses: a preliminary chapter, toward an examination of
Hume’s argument against miracles, in its logic and in its history” (1901) (in [Peirce, 1966,
p. 692]).
5.2 Instinct vs. Heuristic Strategies
277
picking what it aims to pick. That is not reasoning, because it is not done deliberately;
but in every respect but that, it is just like abductive inference.17
What happens when the abductive reasoning in science is strongly related to extratheoretical actions and manipulations of “external” objects? When abduction is
“action-based” on external models? When thinking is “through doing”, as illustrated
in the simple case above18 of distinguishing the simple textures of cloth by feeling?
To answer these questions I have delineated the features of what I have called manipulative abduction (cf. above chapter one and [Magnani, 2001b, chapter three])
by showing how we can find in scientific and everyday reasoning methods of constructivity based on external models and actions, where external things, usually inert
from the semiotic point of view, acquire central cognitive status.
5.2.2
Instinct-Based Abduction
Stressing the role of iconic dimensions of semiosis in the meantime celebrates the
virtues of analogy, as a kind of “association by resemblance”, as opposed to “association by contiguity”:
That combination almost instantly flashed out into vividness. Now it cannot be contiguity; for the combination is altogether a new idea. It never occurred to me before; and
consequently cannot be subject to any acquired habit. It must be, as it appears to be,
its analogy, or resemblance in form, to the nodus of my problem which brings it into
vividness. Now what can that be but pure fundamental association by resemblance?
[Peirce, 1931-1958, 7.498].
Hypothesis selection is a largely instinctual endowment19 of human beings which
Peirce thinks is given by God or related to a kind of Galilean “lume naturale”: “It
is a primary hypothesis underlying all abduction that the human mind is akin to the
truth in the sense that in a finite number of guesses it will light upon the correct
hypothesis” [Peirce, 1931-1958, 7.220]. Again, the example of the innate ideas of
“every little chicken” is of help to describe this human instinctual endowment:
How was it that man was ever led to entertain that true theory? You cannot say that
it happened by chance, because the possible theories, if not strictly innumerable, at
any rate exceed a trillion – or the third power of a million; and therefore the chances
are too overwhelmingly against the single true theory in the twenty or thirty thousand
years during which man has been a thinking animal, ever having come into any man’s
head. Besides, you cannot seriously think that every little chicken, that is hatched, has
17
18
19
Cf. the article “The proper treatment of hypotheses: a preliminary chapter, toward and examination of Hume’s argument against miracles, in its logic and in its history” [1901] (in [Peirce,
1966, p. 692]).
Cf. section 1.6.2, chapter one of this book.
Instinct is of course in part conscious: it is “always partially controlled by the deliberate exercise
of imagination and reflection” [Peirce, 1931-1958, 7.381].
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5 Animal Abduction
to rummage through all possible theories until it lights upon the good idea of picking
up something and eating it. On the contrary, you think the chicken has an innate idea of
doing this; that is to say, that it can think of this, but has no faculty of thinking anything
else. The chicken you say pecks by instinct. But if you are going to think every poor
chicken endowed with an innate tendency toward a positive truth, why should you
think that to man alone this gift is denied? [Peirce, 1931-1958, 5.591].
Paavola [2005] illustrates various Peircean ways of understanding the nature of instinct: naturalistic (for getting food and for reproducing), theistic (also related to the
concept of agapastic evolution, the idea that the law of love is operative in the cosmos [Peirce, 1992-1998, I, pp. 352-371]), and idealistic. The last case is related to
the so-called synechism, according to which everything is continuous and the future
will be in some measure continuous with the past, mind and matter are not entirely
distinct, and so it is – analogously – for instinct and inference [Santaella, 2005, p.
191].20 The human mind would have been developed under those metaphysical laws
that govern the universe so that we can consequently hypothesize that the mind has
a tendency to find true hypotheses concerning the universe.
The naturalistic view of instinct involves at least two aspects: evolutionary/
adaptive and perceptual – as a “certain insight” [Peirce, 1931-1958, 5.173]: the
instinctual insight that leads to a hypothesis is considered by Peirce to be of “the
same general class of operations to which Perceptive Judgments belong (ibid.) (cf.
above section 5.1). Hence, Peirce considers the capacity to guess correct hypotheses
as instinctive and enrooted in our evolution and from this perspective abduction is
surely a property of naturally evolving organisms:
If you carefully consider with an unbiased mind all the circumstances of the early
history of science and all the other facts bearing on the question [. . . ] I am quite sure
that you must be brought to acknowledge that man’s mind has a natural adaptation
to imagining correct theories of some kind, and in particular to correct theories about
forces, without some glimmer of which he could not form social ties and consequently
could not reproduce his kind [Peirce, 1931-1958, 5.591].
5.2.3
Mind and Matter Intertwined
Peirce says “Thought is not necessarily connected with brain. It appears in the work
of bees, of crystals, and throughout the purely physical world; and one can no more
deny that it is really there, than that the colours, the shapes, etc., of objects are really
there” [Peirce, 1931-1958, 4.551]. It is vital to explain the meaning of this important
statement.
First of all it has to be noted that instincts themselves can undergo modifications through evolution: they are “inherited habits, or in a more accurate language,
inherited dispositions” [Peirce, 1931-1958, 2.170]. Elsewhere Peirce seems to maintain that instinct is not really relevant in scientific reasoning but that it is typical of
20
I think some of the ideas of the traditional synechism can be usefully deepened in the framework
of current research on the so-called multiple realizability thesis, which admits that mind can be
“realized” in several material supports, cf. [Shapiro, 2004; Baum, 2006].
5.2 Instinct vs. Heuristic Strategies
279
just “the reasoning of practical men about every day affairs”. So as to say, we can
perform instinctive abduction (that is not controlled, not “reasoned”) in practical
reasoning, but this is not typical of scientific thinking:
These two [practical and scientific reasoning] would be shown to be governed by
somewhat different principles, inasmuch as the practical reasoning is forced to reach
some definite conclusion promptly, while science can wait a century or five centuries,
if need be, before coming to any conclusion at all. Another cause which acts still more
strongly to differentiate the methodeutic of theoretical and practical reasoning is that
the latter can be regulated by instinct acting in its natural way, while theory of how one
should reason depends upon one’s ultimate purpose and is modified with every modification of ethics. Theory is thus at a special disadvantage here; but instinct within its
proper domain is generally far keener, and surer, and above all swifter, than any deduction from theory can be. Besides, logical instinct has, at all events, to be employed in
applying the theory. On the other hand, the ultimate purpose of pure science, as such,
is perfectly definite and simple; the theory of purely scientific reasoning can be worked
out with mathematical certainty; and the application of the theory does not require the
logical instinct to be strained beyond its natural function. On the other hand, if we
attempt to apply natural logical instinct to purely scientific questions of any difficulty,
it not only becomes uncertain, but if it is heeded, the voice of instinct itself is that
objective considerations should be the decisive ones.21
I think that the considerations above do not mean, like some commentators seem
to maintain [Rescher, 1995; Hoffmann, 1999; Paavola, 2005], that instinct – as a
kind of mysterious, not analyzed, guessing power – “does not” operate at the level
of conscious inferences like for example in the case of scientific reasoning. I think
a better interpretation is the following that I am proposing here: certainly instinct,
which I consider a simple and not a mysterious endowment of human beings, is at
the basis of both “practical” and scientific reasoning, in turn instinct shows the obvious origin of both in natural evolution. If every kind of cognitive activity is rooted
in a hybrid interplay with external sources and representations, which exhibit their
specific constraints and features, as I have illustrated in the previous chapters and as
would Peirce certainly agree, it does not appear surprising that “[. . . ] the instincts
conducive to assimilation of food, and the instincts conducive to reproduction, must
have involved from the beginning certain tendencies to think truly about physics,
on the one hand, and about psychics, on the other. It is somehow more than a mere
figure of speech to say that nature fecundates the mind of man with ideas which,
when those ideas grow up, will resemble their father, Nature” [Peirce, 1931-1958,
5.591]. Hence, from an evolutionary perspective instincts are rooted in humans in
this interplay between internal and external aspects and so it is obvious to see that
externalities (“Nature”) “fecundate” the mind.
Beyond the multifarious and sometimes contrasting Peircean intellectual strategies and steps in illustrating concepts like inference, abduction, perception and
21
Cf. Arisbe Website, http://members.door.net/arisbe/. The passage comes from MS L75 Logic,
regarded as semeiotic (The Carnegie application of 1902).
280
5 Animal Abduction
instinct, which of course are of great interest for the historians of philosophy,22 the
perspective I have illustrated seems to me to be able to clearly focus on some central
recent cognitive issues which I contend also implicitly underlie Peircean thoughts:
nature fecundates the mind because it is through a disembodiment and extension of
the mind in nature that in turn nature affects the mind. If we contend a conception
of mind as “extended”, it is simple to grasp its instinctual part as shaped by evolution through the constraints found in nature itself. It is in this sense that the mind’s
guesses – both instinctual and reasoned – can be classified as plausible hypotheses about nature/the external world because the mind grows up together with the
representational delegations to the external world that has made itself throughout
the history of culture by constructing the so-called cognitive niches.23 In this strict
perspective hypotheses are not merely made by pure unnatural chance.24
Peirce says, in the framework of his synechism that “[. . . ] the reaction between
mind and matter would be of not essential different kind from the action between
parts of mind that are in continuous union” [Peirce, 1931-1958, 6.277]. This is
clearly seen if we notice that “[. . . ] habit is by no means a mental fact. Empirically, we find that some plants take habits. The stream of water that wears a bed for
itself is forming an habit” [Peirce, 1931-1958, 5.492]. Finally, here the passage we
already quoted at the beginning of this subsection, clearly establishing Peirce’s concerns about the mind: “Thought is not necessarily connected with brain. It appears
in the work of bees, of crystals, and throughout the purely physical world; and one
can no more deny that it is really there, than that the colours, the shapes, etc., of
objects are really there” [Peirce, 1931-1958, 4.551].
To conclude, instinct vs. inference represents a conflict we can overcome simply by observing that the work of abduction is partly explicable as an instinctual
biological phenomenon and partly as a “logical” operation related to “plastic” cognitive endowments of all organisms. I entirely agree with Peirce: a guess in science,
the appearance of a new hypothesis, is also25 a biological phenomenon and so it
is related to instinct: in the sense that we can compare it to a chance variation in
biological evolution [Peirce, 1931-1958, 7.38], even if of course the evolution of
scientific guesses does not conform to the pattern of biological evolution [Colapietro, 2005, p. 427]. An abduced hypothesis introduces a change (and a chance) in the
semiotic processes to advance new perspectives in the co-evolution of the organism
and the environment: it is in this way that they find a continuous mutual variation.
The organism modifies its character in order to reach better fitness; however, the
environment (already artificially – culturally – modified, i.e. a cognitive niche), is
equally continuously changing and very sensitive to every modification.
22
23
24
25
For example, in the latest writings at the beginning of XIX century Peirce more clearly stresses
the instinctual nature of abduction and at the same time its inferential nature [Paavola, 2005, p.
150]. On the various approaches regarding perception in Peircean text cf. [Tiercelin, 2005].
The concept of cognitive niche is illustrated in detail in chapter six of this book.
This is not a view that conflicts with the idea of God’s creation of human instinct: it is instead
meant on this basis, that we can add the theistic hypothesis, if desired.
Of course this conclusion does not mean that artifacts like computers do not or cannot perform
abductions.
5.2 Instinct vs. Heuristic Strategies
5.2.4
281
Peircean Chickens, Human Agents, Logical Agents
It is certainly true that Peirce is also convinced that there is a gap between logic and
scientific reasoning on one side and practical reasoning on the other (he also rejects
the possibility of a practical logic and consequently of a logic of abductive reasoning
in practical contexts): “In everyday business reasoning is tolerably successful but I
am inclined to think that it is done as well without the aid of theory as with it”
[Peirce, 2005, p. 109]. “My proposition is that logic, in the strict sense of the term,
has nothing to do with how you think [. . . ]. Logic in the narrower sense is that
science which concerns itself primarily with distinguishing reasonings into good
and bad reasonings, and with distinguishing probable reasonings into strong and
weak reasonings. Secondarily, logic concerns itself with all that it must study in
order to draw those distinctions about reasoning, and with nothing else” (ibid., p.
143). We have illustrated that the role of instinct at the level of human unconscious
reasoning is obvious, this kind of cognition has been wired by the evolution (like
also happens in the case of some animals, for example the Peircean chicken above),
and in some organisms cannot be even partially accessed by consciousness.
However, today we have at our disposal many logics of abduction: [Gabbay
and Woods, 2005] contend that these logics are just formal and somewhat idealized
descriptions of an abductive agent. A real human agent (the every day “business reasoner”) can be considered a kind of biological realization of a nonmonotonic paraconsistent base logic and surely the strategies provided by classical logic and some
strictly related non standard logics form a very small part of individual cognitive
skills, given the fact that human agents are not in general dedicated to error avoidance like “classical” logical agents [Magnani, 2007a].26 The fact that human beings
are error prone does not have to be considered as something bad from the evolutionary point of view, like Quine contends [1969]: for example, hasty generalizations
(and many other fallacies) are bad ways of reasoning but can be the best means for
survival (or at least for reaching good aims) in particular contexts [Woods, 2004;
Magnani and Belli, 2006].
Questions of relevance and plausibility regarding the activity of guessing hypotheses (in an inductive or abductive way) are embedded at the level of the implicit
reasoning performances of the practical agent. It will be at the level of the formal
model, as an idealized description of what an abductive/inductive agent does, that
for example questions of economy, relevance and plausibility, in so far as they are
heuristics strategies, will be explicitly described.27
In summary, from a semiotic point of view, the idea that there is a conflict (or
a potential conflict) (present in Peirce’s texts too) between views of abduction –
and of practical reasoning – in terms of heuristic strategies or in terms of instinct
(insight, perception) [Hoffmann, 1999; Paavola, 2004; Paavola, 2005], appears
26
27
Cf. also chapter seven of this book.
On the role of strategies, plausibility, and economy of research and their relationships with
Peircean Grammar, Critic, and Methodeutic cf. [Paavola, 2004]. A detailed and in-depth description of these difficult aspects of philosophical and semiotic issues of Peirce’s approach is
given in [Kruijff, 2005].
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5 Animal Abduction
old-fashioned. The two aspects simply coexist at the level of the real organic agent,
it depends on the cognitive/semiotic perspective we adopt:
1. we can see it as a practical agent that mainly takes advantage of its implicit
endowments in terms of guessing right, wired by evolution, where of course
instinct or hardwired programs are central, or
2. we can see it as the user of explicit and more or less abstract semiotic devices
internally stored or externally available – or hybrid – where heuristic plastic
strategies (in some organism they are “conscious”) exploiting relevance and
plausibility criteria – various and contextual – for guessing hypotheses are exploited.
What is still important to note is that these heuristic strategies and reasoning devices
are determined and created at the level of individuals and through the interplay
of both the internal and the external agency already endowed with those cognitive
delegated representations and tools occurring in the continuous semiotic activity of
“disembodiment of mind” that I have illustrated in chapter three. This interplay of
course occurs both at the contextual level of learning in the individual history and
at the level of the evolutionary effects. The efficiency of these strategies in terms of
“naturalistic” – and so instinctual – characters is just guaranteed by this interplay.
In the first case the role of instinct is clear in the sense that the cognitive skills
have been wired thanks to the evolutionary interplay between organic agents and
their environments. In the second case the role of instinct is still at stake, but in so
far as it is at the origins of the historical process of formation of heuristic strategies, and thus of reasoning devices, there is the same interplay between organism
and environment, internal and external representations, but in terms of explicit tools
sedimented in historical practices and learnt – and possibly improved – by the individuals. Sedimented heuristics are context-dependent, to make an example, scientists, in their various fields, make use of many heuristic strategies that are explicitly
stated, learnt, and enhanced. These reasoning processes, even if far from being considered merely instinctual, still serve what Peirce calls “the probable perpetuation”
[Peirce, 1992-1998, II, pp. 464 f.] of the race.
For example, when we model abduction through a computational logic-based
system, the fundamental operation is to search, which expresses the heuristic strategies [Thagard, 1996]. As I have already illustrated in chapter one (section 1.4),
when there is a problem to solve, we usually face several possibilities (hypotheses)
and we have to select the suitable one (selective abduction). Accomplishing the assigned task requires that we have to search through the whole space of potential solutions to find the desired one. In this situation we have to rely on heuristics, that are
rules of thumb expressed in sentential terms. The well-known concept of heuristic
search, which is at the basis of many computational systems based on propositional
rules, can perform this kind of sentential abduction (selective). We have pointed out
that other computational tools can be used to this aim, like neural and probabilistic networks, and frames-like representations also able to imitate both sentential,
5.3 Mindless Organisms and Cognition
283
model-based, and hybrid ways of reasoning of real human agents, but less appropriate to model the traditional concept of heuristic strategy.28
5.3
Mindless Organisms and Cognition
I have illustrated in the first two sections of this chapter some seminal Peircean
philosophical considerations concerning abduction, perception, inference, and instinct. I think they are of strong philosophical importance in current cognitive research. Peircean analysis helps us to better grasp how model-based, sentential and
manipulative aspects of abduction have to be seen as intertwined. Moreover, they
show how we can exploit the concept of abduction, as a basic kind of human cognition, not only as a conceptual tool helpful in delineating the first principles of a new
theory of science, but also in the unification of interdisciplinary perspectives, which
would otherwise remain fragmented and dispersed, and thus devoid of the necessary
philosophical analysis.
The present chapter aims at illustrating how Peircean emphasis on the role of instincts in abduction provides a deep philosophical framework which in turn supplies
an anticipatory and integrated introduction to the problem of animal hypothetical
cognition. In a sense, the results of recent research on animal cognition present a
confirmation of the epistemological utility of the theory of abductive cognition I
am presenting in this book, a theory which also delineates an “ideal” framework
very useful for the interdisciplinary dialogue, where the role of abstract and general
concepts is central.
Philosophy itself has for a long time disregarded the ways of thinking and knowing of animals, traditionally considered “mindless” organisms. Peircean insight regarding the role of abduction in animals was a good starting point, but only more
recent results in the fields of cognitive science and ethology about animals, and
of developmental psychology and cognitive archeology about humans and infants,
have provided the actual intellectual awareness of the importance of the comparative
studies.
Sometimes philosophy has anthropocentrically condemned itself to partial results when reflecting upon human cognition because it lacked in appreciation of the
more “animal-like” aspects of thinking and feeling, which are certainly in operation
and are greatly important in human behavior. Also in ethical inquiry a better understanding of animal cognition could in turn increase knowledge about some hidden
aspects of human behavior, which I think still tend to evade any ethical account and
awareness. Scientists too often disregard the ethical concern.
In the recent [Magnani, 2007d] I maintain that people have to learn to be “respected as things”, sometimes, are. Various kinds of “things”, and among them
work of arts, institutions, symbols, and of course animals, are now endowed with
intrinsic moral worth. Animals are certainly morally respected in many ways in our
technological societies, but certain knowledge about them has been disregarded. It
28
A more detailed description of the role of heuristic and strategies in abductive (and deductive)
reasoning is illustrated in subsection 7.3.2.2 of chapter seven of this book.
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5 Animal Abduction
is still difficult to acknowledge respect for their cognitive skills and endowments.
Would our having more knowledge about animals happen to coincide with having
more knowledge about humans and infants, and be linked to the suppression of constitutive “anthropomorphism” in treating and studying them that we have inherited
through tradition? Consequently, would not novel and unexpected achievements in
this field be a fresh chance to grant new “values” to humans and discover new knowledge regarding their cognitive features? (cf. also [Gruen, 2002]). Darwin already
noted that studying cognitive capacities in humans but also in non-human animals
“[. . . ] possesses, also, some independent interest, as an attempt to see how far the
study of the lower animals throws light on one of the highest psychical faculties of
man” – the moral sense [Darwin, 1981].
Among scientists it is of course Darwin [1985] who first clearly captured the idea
of an “inner life” (the “world of perception” included) in some humble earthworms
[Crist, 2002]. A kind of mental life can be hypothesized in many organisms: Darwin
wanted “to learn how far the worms acted consciously and how much mental power
they displayed” [Darwin, 1985, p. 3]. He found levels of “mind ” where it was not
presumed to exist. It can be said that this new idea, which bridges the gap between
humans and other animals, in some sense furnishes a partial scientific support to
that metaphysical synechism claimed by Peirce contending that matter and mind
are intertwined and in some sense indistinguishable.29
5.3.1
Worm Intelligence, Abductive Chickens, Instincts
Let us consider the behavior of very simple creatures. Earthworms plug the opening
of their burrow with leaves and petioles: Darwin recognized that behavior as being
too regular to be random and at the same time too variable to be merely instinctive.
He concluded that, even if the worms were innately inclined to construct protective
basket structures, they also had a capacity to “judge” based on their tactile sense
and showed “some degree of intelligence” [Darwin, 1985, p. 91]. Instinct alone
would not explain how worms actually handle leaves to be put into the burrow. This
behavior seemed more similar to their “having acquired the habit” [Darwin, 1985,
p. 68]. Crist says: “Darwin realized that ‘worm intelligence’ would be an oxymoron
for skeptics and even from a commonsense viewpoint ‘This will strike everyone as
very improbable’ he wrote [Darwin, 1985, p. 98]. [. . . ] He noted that little is known
about the nervous system of ‘lower animals’, implying they might possess more
cognitive potential than generally assumed” [Crist, 2002, p. 5].
It is important to note that Darwin also paid great attention to those external
structures built by worms and engineered for utility, comfort, and security. I will
describe later on in this chapter the cognitive role of artifacts in both human and
non-human animals. Artifacts can be illustrated as cognitive mediators [Magnani,
2001b] which are the building blocks that bring into existence what it is now called
29
The recent discovery of the cognitive roles (basically in the case of learning and memory) played
by spinal cord further supports this conviction that mind is extended and distributed and that it
can also be – so to say – “brainless” [Grau, 2002].
5.3 Mindless Organisms and Cognition
285
a “cognitive niche”: 30 Darwin maintains that “We thus see that burrows are not mere
excavations, but may rather be compared with tunnels lined with cement” [Darwin,
1985, p. 112]. Like humans, worms build external artifacts endowed with precise
roles and functions, which strongly affect their lives in various ways, and of course
their opportunity to “know” the environment.
I have said their behavior cannot be accounted for in merely instinctual terms.
Indeed, the “variability” of their behavior is for example illustrated by the precautionary capacity of worms to exploit pine needles by bending over pointed ends:
“Had this not effectually been done, the sharp points could have prevented the retreat of the worms into their burrows; and these structures would have resembled
traps armed with converging points of wire rendering the ingress of an animal easy
and its egress difficult or impossible” [Darwin, 1985, p. 112]. Cognitive plasticity is
clearly demonstrated by the fact that Darwin detected that pine was not a native tree!
If we cannot say that worms are aware like we are (consciousness is unlikely even
among non-human vertebrates), certainly we can acknowledge in this case a form
of material, interactive, and embodied, manifestation of awareness in the world.
Recent research has also demonstrated the existence of developmental plasticity
in plants [Novoplansky, 2002]. For example developing tissues and organs “inform”
the plant about their states and respond according to the signals and substrates they
receive. The plant adjusts structurally and physiologically to its own development
and to the habitat it happens to be in (for example a plasticity of organs in the
relations between neighboring plants can be developed) Mackey, J. M. L. [Sachs,
2002; Grime and Mackey, 2002].
In the following sections I am interested in further improving knowledge on abduction and model-based thinking. By way of introduction let me quote again the
interesting Peircean passage again about hypothesis selection and chickens, which
touches on both ideas, showing a kind of completely language-free, model-based
abduction:
How was it that man was ever led to entertain that true theory? You cannot say that
it happened by chance, because the possible theories, if not strictly innumerable, at
any rate exceed a trillion – or the third power of a million; and therefore the chances
are too overwhelmingly against the single true theory in the twenty or thirty thousand
years during which man has been a thinking animal, ever having come into any man’s
head. Besides, you cannot seriously think that every little chicken, that is hatched, has
to rummage through all possible theories until it lights upon the good idea of picking
up something and eating it. On the contrary, you think the chicken has an innate idea of
doing this; that is to say, that it can think of this, but has no faculty of thinking anything
else. The chicken you say pecks by instinct. But if you are going to think every poor
chicken endowed with an innate tendency toward a positive truth, why should you
think that to man alone this gift is denied? [Peirce, 1931-1958, 5.591].
and again, even more clearly, in another related passage we have already quoted
above
30
A concept introduced by Tooby and DeVore [1987] and later on reused by Pinker [1997; 2003].
I will illustrate it in the following chapter.
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5 Animal Abduction
When a chicken first emerges from the shell, it does not try fifty random ways of appeasing its hunger, but within five minutes is picking up food, choosing as it picks, and
picking what it aims to pick. That is not reasoning, because it is not done deliberately;
but in every respect but that, it is just like abductive inference. 31
From this Peircean perspective hypothesis generation is a largely instinctual and
nonlinguistic endowment of human beings and, of course, also of animals. It is
clear that for Peirce abduction is rooted in the instinct and that many basically
instinctual-rooted cognitive performances, like emotions, provide examples of abduction available to both human and non-human animals. Also cognitive archeology
[Mithen, 1996; Donald, 2001] acknowledges that it was not language that made
cognition possible: rather it rendered possible the integration in social environments
of preexistent, separated, domain-specific modules in prelinguistic hominids, like
complex motor skills learnt by imitation or created independently for the first time
[Bermúdez, 2003]. This integration made the emergence of tool making possible
through the process of “disembodiment of mind” that I illustrated in in chapter three
of this book. Integration also seeks out established policies, rituals, and complicated forms of social cognition, which are related to the other forms of prevalently
nonlinguistic cognitive behaviors.
5.3.2
Nonlinguistic Representational States
It can be hypothesized that some language-free, more or less stable, representational states that are merely model-based32 are present in animals, early hominids,
and human infants. Of course tropistic and classically conditioned schemes can be
accounted for without reference to these kind of model-based “representations”,
because in these cases the response is invariant once the creature in question has
registered the relevant stimuli.
The problem of attributing to those beings strictly nonlinguistic model-based
inner “thoughts”, beliefs, and desires, and thus suitable ways of representing the
world, and of comparing them to language-oriented mixed (both model-based and
sentential) representations, typical of modern adult humans, appears to be fundamental to comprehending the status of animal presumptive abductive performances.
Of course this issue recalls the traditional epistemological Kuhnian question of
the incommensurability of meaning [Kuhn, 1962]. In this case it refers to the possibility of comparing cognitive attitudes in different biological species, which express
potentially incomparable meanings. Such problems already arose when dealing with
the interpretation of primitive culture. If we admit, together with some ethologists,
31
32
Cf. the article “The proper treatment of hypotheses: a preliminary chapter, toward and examination of Hume’s argument against miracles, in its logic and in its history” [1901] [Peirce, 1966,
p. 692].
They do not have to be taken like for example visual and spatial imagery or other internal
model-based states typical of modern adult humans, but more like action-related representations
and thus intrinsically intertwined with perception and kinesthetic/motor abilities. Saidel [2002]
interestingly studies the role of these kinds of representations in rats.
5.4 Animal Abduction
287
animal behaviorists, and developmental psychologists, that in nonlinguistic organisms there are some intermediate representations, it is still difficult to make an analogy with those found in adult humans. The anthropologists who carried out the first
structured research on human primitive cultures and languages already stressed this
point, because it is difficult to circumstantiate thoughts that can hold in beings but
only manifest themselves in superficial and external conducts (cf. Quine [1960]).
A similar puzzling incommensurability already arises when we deal with the different sensorial modalities of certain species and their ways of being and of feeling
to be in the world. We cannot put ourselves in the living situation of a dolphin, which
lives and feels by using echolocations, or of our cat, which “sees” differently, and it
is difficult to put forward scientific hypotheses on these features using human-biased
language, perceptive capacities, and cognitive representations. The problem of the
existence of “representation states” is deeply epistemological: the analogous situation in science concerns for example the status of the so-called theoretical terms,
like quarks or electrons, which are not directly observable but still “real”, reliable,
and consistent when meaningfully legitimated/justified by their epistemological
unavoidability in suitable scientific research programs [Lakatos, 1970].
I have already said that commitment to research on animal cognition is rare in human beings. Unfortunately, even when interested in animal cognition, human adult
researchers, victims of an uncontrolled, “biocentric” anthropomorphic attitude, always risk attributing to animals (and of course infants) their own concepts and thus
misunderstanding their specific cognitive skills [Rivas and Burghardt, 2002].
5.4
5.4.1
Animal Abduction
“Wired Cognition” and Pseudothoughts
Nature writes programs for cognitive behavior in many ways. In certain cases these
programs draw on cognitive functions and sometimes they do not. In the latter case
the fact that we describe the behavioral effect as “cognitive” is just a metaphor. This
is a case of instinctual behavior, which we should more properly name “hardwired
cognition”.
Peirce spoke – already over a century ago – of a wide semiotic perspective, which
taught us that a human internal representational medium is not necessarily structured
like a language. I plan to develop and broaden this perspective. Of course this conviction strongly diverges from that maintained by the intellectual traditions which
resort to the insight provided by the modern Fregean logical perspective, in which
thoughts are just considered the “senses of sentences”. Recent views on cognition
are still influenced by this logical perspective, and further stress the importance of
an isomorphism between thoughts and language sentences (cf. for example Fodor’s
theory [1987]).
Bermúdez clearly explains how this perspective also affected the so-called minimalist view on animal cognition (also called deflationary view) [Bermúdez, 2003, p.
27]. We can describe nonlinguistic creatures as thinkers and capable of goal-directed
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5 Animal Abduction
actions, but we need to avoid assigning to them the type of thinking common to linguistic creatures, for example in terms of belief-desire psychology: “Nonlinguistic
thinking does not involve propositional attitudes – and, a fortiori, psychological
explanation at the nonlinguistic level is not a variant of belief-desire psychology”
(ibid.). Belief-desire framework should only be related to linguistic creatures. Instead, the problem for the researcher on animal cognition would be to detect how a
kind of what we can call “general belief” is formed, rather than concentrating on its
content, as we would in the light of human linguistic tools.
Many forms of thinking, such as imagistic, empathetic, trial and error, and analogical reasoning, and cognitive activities performed through complex bodily skills,
appear to be basically model-based and manipulative. They are usually described in
terms of living beings that adjust themselves to the environment rather than in terms
of beings that acquire information from the environment. In this sense these kinds
of thinking would produce responses that do not seem to involve sentential aspects
but rather merely “non-inferential” ways of cognition. If we adopt the semiotic perspective above, which does not reduce the term “inference” to its sentential level,
but which includes the whole arena of sign activity – in the light of Peircean tradition – these kinds of thinking promptly appear full, inferential forms of thought.
Let me recall that Peirce stated that all thinking is in signs, and signs can be icons,
indices, or symbols, and, moreover, all inference is a form of sign activity, where the
word sign includes “feeling, image, conception, and other representation” [Peirce,
1931-1958, 5.283].
From this perspective human and the most part of non-human animals possess
what I have called semiotic brains (cf. chapter three of this book and [Magnani,
2007c]), which make up a series of signs and which are engaged in making or manifesting or reacting to a series of signs: through this semiotic activity they are at
the same time occasionally engaged in “being cognitive agents” (like in the case of
human beings) or at least in thinking intelligently.33
From a perspective similar to the one I have followed, where a broad concept of
cognition is adopted, [Godfrey-Smith, 2002] contends that all the mechanisms that
enable organisms to coordinate their behavior with complex environmental conditions by tracking and dealing with them34 involve some degree of intelligence
“so there is no opposition between intelligence and what is often referred to as
‘instinct”’. From this perspective abductive endowments – that are also complex
– range across a multiple set of adaptive and maladaptive skills, from instincts to
high-level cognitive functions. They are “sets of capacities” that regard perception,
internal representations, memory, learning, decision-making and of course actions.
They shade into each other and shade off into non-cognitive parts of the biological
organisms. From this angle an idea of “continuity” is adopted with regards to cognition, even if cognition is expressed in various ways, often presenting opposite and
33
34
Research in biosemiotics has provided new knowledge about the semiotic aspect of cognition in
various organisms; cf. the first issue of the journal Biosemiotics, 2008, and the recent collection
[Barbieri, 2008].
The environment is complex is so far as it is heterogeneous and problematic but also in so far
as it provides suitable opportunities – that is “affordances”, cf. chapter six, this book.
5.4 Animal Abduction
289
incommensurable characteristics. Examples of cases where broad animal capacities
are shared with humans typically express this idea of continuity of cognition. These
shared capacities can be seen in the evolution of associative learning, in the development – beyond the immediate effect of conditioning – of very complicated and
variegated forms of spatial memory and of cognitive spatial maps (which can be
inner and/or taking advantage of suitable outer natural or artifactual landmarks),35
and in social intelligence.
From this point of view a low-level variety of cognition and intelligence exists
and it helps in meeting the challenges of complex environments and if so, it is selectively favored.36 It would be better to use only the term cognition, given the fact
the term intelligence has strong connotations in common usage, where it is strictly
related to humans and expresses complicated endowments like consciousness and
planning skills. Cognition in a broader sense is “discovered and rediscovered by evolution many times”, and exists at various levels starting from those which can also be
classified as proto-cognitive and which are still embedded in higher-level organisms,
such as in many vertebrates and in humans themselves. This is evident in the case of
endocrine and immune systems. Godfrey-Smith’s main thesis is that the function of
cognition is to enable the agent to deal with environmental complexity, even if, “In
some cases it is hard to distinguish cognition from other control systems in the body,
and hard to distinguish behavior from such things as growth, development and the
regulation of metabolism” (ibid.). Organisms exploit or consume information, that
is semiotic systems consume semiotic resources in the complex environment, including those resources that they and other organisms have themselves previously
embedded in it (one of the reasons why the environment is complex is because it is
suitably complicated by – and dependant on – the various cognitive niches which
all organisms build in it.)37
For example, spatial imaging and analogies based on perceiving similarities –
fundamentally context-dependent and circumstantiated – are ways of thinking in
which the “sign activity” is of a nonlinguistic sort, and it is founded on various
kinds of implicit naı̈ve physical, biological, psychological, social, etc., forms of intelligibility. In scientific experimentation on prelinguistic infants a common result is
the detection of completely language-free working ontologies, which only later on,
during cognitive development, will become intertwined with the effect of language
and other “symbolic” ways of thinking.38
With the aim of describing the kinds of representations which would be at
work in these nonlinguistic cognitive processes Dummett [1993] proposes the
term protothought. I would prefer to use the term pseudothought, to minimize the
35
36
37
38
Cf. chapter four, section 4.7.1.
The “lowest” level would be represented by cases of flexibility of behavior or control of development through the fixed response to an environmental cue – in the absence of proper inner
processing, but where the response is not directly driven by the physical properties of the cue
but is instead characterized by a kind of arbitrariness.
On the role of organisms in building “cognitive niches” see chapter six in this book.
[Godfrey-Smith, 2002] also stresses the fact that internal representations do not have to be
intended as necessarily requiring language.
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5 Animal Abduction
hierarchical effect that – ethnocentrically – already affected some aspects of the
seminal work on primitives of an author like Lévi-Bruhl, who introduced the concept of “pre-logical” primitive mentality [1923]. An example of the function of
model-based pseudothoughts can be hypothesized in the perception of space in the
case of both human and non-human animals. The perceived space is not necessarily three-dimensional and merely involves the apprehension of movement changes,
and the rough properties of material objects. Dummett illustrates the case of the car
driver and of the canoeist:
A car driver or canoeist may have to estimate the speed and direction of oncoming
cars and boats and their probable trajectory, consider what avoiding action to take, and
so on: it is natural to say that he is highly concentrated in thought. But the vehicle
of such thoughts is certainly not language: it would be said, I think, to consist in visual imagination superimposed on the visual perceived scene. It is not just that these
thoughts are not in fact framed in words: it is that they do not have the structure of
verbally expressed thoughts. But they deserve the name of “protothoughts” because
while it would be ponderous to speak of truth or falsity in application to them, they
are intrinsically connected with the possibility of their being mistaken: judgment, in a
non-technical sense, is just what the driver and the canoeist need to exercise [Dummett,
1993, p. 122].
5.4.2
Plastic Cognition in Organisms’ Pseudoexplanatory
Guesses
To better understand what the study of nonlinguistic creatures teaches us about
model-based and manipulative abduction (and go beyond Peirce’s insights on chickens’ “hardwired” abductive abilities), it is necessary to acknowledge the fact that it
is difficult to attribute many of their thinking performances to innate releasing processes, trial and error or to a mere reinforcement learning, which do not involve
complicated and more stable internal representations.
Fleeting and evanescent (not merely reflex-based) pseudorepresentations are
needed to account for many animal “communication” performances even at the level
of the calls of “the humble and much-maligned chicken”, like Evans says:
We conclude that chicken calls produce effects by evoking representations of a class
of eliciting events [food, predators, and presence of the appropriate receiver]. This
finding should contribute to resolution of the debate about the meaning of referential
signals. We can now confidently reject reflexive models, those that postulate only behavioral referents, and those that view referential signals as imperative. The humble
and much maligned chicken thus has a remarkably sophisticated system. Its calls denote at least three classes of external objects. They are not involuntary exclamations,
but are produced under particular social circumstances [Evans, 2002a, p. 321].
In sum, in nonlinguistics animals, a higher degree of abductive abilities has to be
acknowledged: chicken form separate representations faced with different events
5.4 Animal Abduction
291
and they are affected by prior experience (of food, for example). They are mainly
due to internally developed plastic capacities to react to the environment, and can be
thought of as the fruit of learning. In general this plasticity is often accompanied by
the suitable reification of external artificial “pseudorepresentations” (for example
landmarks, alarm calls, urine-marks and roars, etc.) which artificially modify the
environment, and/or by the referral to externalities already endowed with delegated
cognitive values, made by the animals themselves or provided by humans.
The following is an example of not merely reflex-based cognition and it is fruit
of plasticity: a mouse in a research lab perceives not simply the lever but the fact
that the action on it affords the chance of having food; the mouse “desires” the goal
(food) and consequently acts in the appropriate way. Some authors contend this is
not the fruit of innate and instinctual mechanisms, merely a trial and error routine,
or brute reinforcement learning able to provide the correct (and direct) abductive
appraisal of the given environmental situation. Instead it can be better described as
the fruit of learnt and flexible thinking devices, which are not merely fixed and stimulus driven but also involve “thought”.39 “Pseudothought” – I have already said – is
a better term to use, resorting to the formation of internal structured representations
and various – possibly new – links between them. The mouse also takes advantage
in its environment of an external device, the lever, which the humans have endowed
with a fundamental predominant cognitive value, which can afford the animal: the
mouse is able to cognitively pick up this externality, and to embody it in internal,
useful representations.
Another example of plastic cognition comes from the animal activity of reshaping
the environment through its mapping by means of seed caches:
Consider, for example, a bird returning to a stored cache of seeds. It is known from both
ethological studies and laboratory experiments that species such as chickadees and
marsh tits are capable of hiding extraordinary number of seeds in a range of different
hiding places and then retrieving them after considerable periods of time have elapsed
([Sherry, 1988], quoted in [Bermúdez, 2003, p. 48]).
It is also likely to hypothesize that this behavior is governed by the combination
of a motivational state (a general desire for food) and a memory of the particular
location, and how to get to it.40 The possibility of performing such behavior is based
on structured internal pseudorepresentations originating from the previous interplay
between internal and external signs suitably picked up from the environment in a
step-by-step procedure.
To summarize, in these cases we are no longer observing the simple situation of
the Peircean, picking chicken, which “[. . . ] has an innate idea of doing this; that
is to say, that it can think of this, but has no faculty of thinking anything else”.
39
40
On this problem cf. also the following subsection about the distinction between classical and
instrumental conditioning. In chapter eight, section 8.4, an analogous case is analyzed in the
framework of Pavlovian conditioning: in this perspective the emergence of the relationship between the food and its index, the lever, coincides with the emergence of what we can call a
“semiotic” activity.
Of course the use of concepts like “desire”, deriving from the “folk-psychology” lexicon, has to
be considered merely metaphorical.
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5 Animal Abduction
This “cognitive” behavior is the one already described by the minimalist contention
that there is no need to specify any kind of internal content. It is minimally – here
and now and immediately related to action – goal-directed, mechanistic, and not
“psychological” in any sense, even in a metaphorical one, as we use the term in the
case of animals [Bermúdez, 2003, p. 49].
On the contrary, the birds in the example above have at their disposal flexible
ways of reacting to events and evidence, which are explainable only in terms of a
kind of thinking “something else”, to use the Peircean words, beyond mere – so
say – “mechanistic” (hardwired) responses. They can choose between alternative
behaviors founding their choice on the basis of evidence available to be picked up.
The activity is “abductive” in itself: it can be selective, when the pseudoexplanatory
guess, on which the subsequent action is based, is selected among those already
internally available, but it can also be creative, because the animal can form and
excogitate for the first time a particular pseudoexplanation of the situation at hand
and then creatively act on the basis of it. The tamarins quickly learn to select the best
hypothesis about the tool – taking into account the different tools on offer – that has
to be used to obtain the most food in “varied” situations. To avoid “psychological”
descriptions, animal abductive cognitive reaction at this level can be seen as an
emergent property of the whole organism, and not, in an anthropocentric way, as a
small set of specialized skills like we usually see them in the case of humans. By
the way, if we adopt this perspective it is also easier to think that some organisms
can learn and memorize even without the brain.41
As I will illustrate in subsection 5.4.4, animals occupy different environmental
niches that “directly” afford their possibility to act, like Gibson’s original theory
teaches, but this is only one of the ways the organism exploits its surroundings to
be suitably attuned to the environment. When behaviors are more complicated other
factors are at stake. For example, animals can act on a goal that they cannot perceive
– the predator that waits for the prey for example – so the organism’s appraisal of
the situation includes factors that cannot be immediately perceived,
Well-known dishabituation experiments have shown how infants use modelbased high-level physical principles to relate to the environment. They look longer
at the facts that they find surprising, showing what expectations they have; animals
like dolphins respond to structured complex gestural signs in ways that can hardly
be accounted for in terms of the Gibsonian original notion of immediate affordance.
A similar situation can be seen in the case of monkeys that perform complicated
technical manipulations of objects, and in birds that build artifacts to house beings
that have not yet been born. The problem here is that organisms can dynamically abductively “extract” or “create” – and further stabilize – affordances not previously
available, taking advantage not only of their instinctual capacities but also of the
plastic cognitive ones (cf. below subsection 5.4.4).
41
It is interesting to note that recent neurobiological research has shown that neural systems within
the spinal cord in rats are quite a bit smarter than most researchers have assumed, they can, for
example, learn from experience [Grau, 2002]. Cf. also footnote 29, p. 284.
5.4 Animal Abduction
5.4.3
293
Artifacts and Classical and Instrumental Conditioning
Other evidence supports the assumption about the relevance of nonlinguistic modelbased thinking beyond the mere reflex-based level. The birth of what is called material culture in hominids, I will quote in the following subsection, and the use of
artifacts as external cognitive mediators in animals, reflect a kind of instrumental
thought that cannot be expressed in terms of the minimalist conception. The instrumental properties are framed by exploiting artificially made material cognitive tools
that mediate and so enhance perception, body kinesthetic skills, and a full-range of
new cognitive opportunities. Through artifacts more courses of action can be selected, where – so to say – “sensitivity” to the consequences is higher. In this case
actions cannot be accounted for solely in terms of the mere perceptual level.42
The difference has to be acknowledged between sensitivity to consequences,
which is merely due to innate mechanisms and/or classical conditioning (where
behavior is simply modified in an adaptive way on the basis of failures and successes), and the more sophisticated sensitivity performed through some doxastic/representational intermediate states:
In classical conditioning, a neutral stimulus (e. g., the sound of a bell) is followed by
an unconditioned stimulus (e. g., the presentation of food) that elicits a reaction (e.
g., salivation). The outcome of classical conditioning is that the conditioned response
(the salivation) comes to be given to the conditioned stimulus (the sound of the bell)
in the absence of the unconditioned stimulus. In instrumental operant conditioning the
presentation of the reinforcing stimulus is contingent on the animal making a particular behavioral response (such as a pecking lever). If the behavioral response does
not occur, the reinforcing stimulus is withheld. Classical conditioning behavior is not
outcome-sensitive in any interesting sense, since it is not the behavior that is reinforced
[Bermúdez, 2003, p. 167].
It is evident that instrumental conditioning is also important in (and intertwined
with) tool and artifact construction where for example the ability to plan ahead
(modifying plans and reacting to contingencies, such as unexpected flaws in the
material and miss-hits) is central.
5.4.4
Affordances and Abduction
Gibson’s eco-cognitive concept of “affordance” [Gibson, 1979] and Brunswik’s interplay between proximal and distal environment also deal with the problem of the
so-called model-based pseudothoughts, which concern any kind of thinking far from
the cognitive features granted by human language.43 These kinds of cognitive tools
typical of infants and of many animals (and still operating in human adults in various forms of more or less unexpressed thinking) are hypothesized to express the
42
43
This sensitivity is already present in birds like ravens [Heinrich, 2002].
A detailed illustration of the relationships between affordances and abduction is given in
[Magnani and Bardone, 2008] and in the following chapter of this book.
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5 Animal Abduction
organic beings’ implicit skills to act in a perceived environment as a distal environment ordered in terms of the possibilities to afford the action in response to local
changes.
Different actions will be suitable to different ways of apprehending aspects of the
external world. The objectification of the world made possible by language and other
highly abstract organizing cognitive techniques (like mathematics) is not needed. An
affordance is a resource or chance that the environment presents to the “specific” organism, such as the availability of water or of finding recovery and concealment. Of
course the same part of the environment offers different affordances to different
organisms. The concept can be also extended to artificial environments built by humans, my cat affords her actions in the kitchen of my house differently than me,
for example I do not find affordable to easily jump through the window or on the
table! I simply cannot imagine the number of things that my cat Sheena is possibly
“aware” of (and her way of being aware) in a precise moment, such as the taste of
the last mouse she caught and the type of memory she has of her last encounter with
a lizard:44 “Only a small part of the network within which mouseness is nested for
us extends into the cat’s world” [Beers, 1997, p. 203]. It is possible to imagine – but
this is just science fiction – that we can “afford” the world like a dolphin only artificializing us by using prosthetic instruments and tools like sonar, fruit of modern
scientific knowledge.
It can be hypothesized that in many organisms the perceptual world is the only
possible model of itself and in this case they can be accounted for in terms of a
merely reflex-based notions: no other internal more or less stable representations are
available. In the case of affordance in the sensitive organisms described above the
coupling with the environment is more flexible because it is important in coupling
with the niche to determine what environmental dynamics are currently the most
relevant, among the several ones that afford and that are available. An individual
that is looking for its prey and at the same time for a mate (which both immediately
afford it without any ambiguity) is contemporarily in front of two different affordances and has to abductively select the most suitable one weighting them. Both
affordances and the more or less plastic processes of their selection in specific situations can be stabilized, but both can also be modified, increased, and substituted
with new ones. In many animals, still at the higher level on not-merely reflex-based
cognitive abilities, no representational internal states need be hypothesized [Tirassa
et al., 1998].
The etheromorphism of affordances is also important: bats use echolocation, and
have a kind of sensory capacity that exceeds that of any man-made systems; dolphins can for example detect, dig out, and feed on fish and small eels buried up to
44
The point of view of Gibson has been taken into account by several people in the computational
community, for example by Brooks in robotics [1991]. “Vision is not delivering a high level
representation of the world, instead it cooperates with motor controls enabling survival behavior
in the environment. [. . . ] While it is very sensible that the main goal of vision in humans is to
contribute to moving and acting with objects in the word, it is highly improbable that a set
of actions can be identified as the output of vision. Otherwise, vision must include all sort of
computations contributing to the acting behavior in that set: it is like saying that vision should
cover more or less the whole brain activity” [Domenella and Plebe, 2005, pp. 369–370].
5.4 Animal Abduction
295
45 cm beneath the sandy seabed and are able to detect the size, structure, shape,
and material composition of distant objects.45 They can also discriminate among
aluminum, copper, and brass circular targets, and among circles, squares, and triangular targets covered with neoprene [Roitblat, 2002]. These amazing cognitive
performances in dolphins are processed through complex computations that transform one dimensional waves (and multiple echoes), arriving at each of their two
ears, into representations of objects and their features in the organism’s niche. The
process is “multimodal” because dolphins also interface with their world using visual and other auditory signals, vocal and behavioral mimicry, and representational
capabilities. It even seems that significant degrees of self-awareness are at work,
unique to nonhuman animals [Herman, 2002]. I have already said that it is easy to
imagine that we could afford the world in a similar way only by hybridizing ourselves using artificial instruments and tools like sonar: the fruit of modern scientific
knowledge.
It is important to note recent research based on Schrödinger’s focusing on energy,
matter and thermodynamic imbalances provided by the environment,46 draws the attention to the fact that all organisms, including bacteria, are able to perform elementary cognitive functions because they “sense” the environment and process internal
information for “thriving on latent information embedded in the complexity of their
environment” (Ben Jacob, Shapira, and Tauber [2006, p. 496]). Indeed Schrödinger
maintained that life requires the consumption of negative entropy, i.e. the use of
thermodynamic imbalances in the environment. As a member of a complex superorganism – the colony, a multi-cellular community – each bacterium possesses the
ability to sense and communicate with the other units comprising the collective and
performs its work within a distribution task. Hence, bacterial communication entails
collective sensing and cooperativity through interpretation of chemical messages,
distinction between internal and external information, and a sort of self vs. non-self
distinction (peers and cheaters are both active).
In this perspective “biotic machines” are meaning-based forms of intelligence
to be contrasted with the information-based forms of artificial intelligence: biotic
machines generate new information, assigning contextual meaning to gathered information. Self-organizing organisms like bacte