Symbols, Computation & Intentionality – A Critique of the Computational Theory of Mind - Hardcover

Horst, Steven W

Hardcover

ISBN 10: 0520200527 ISBN 13: 9780520200524

Publisher: University of California Press, 1996

Synopsis

The computational theory of mind has been influential in philosophical studies of cognition. However, this book pronounces the theory deficient, refuting its claims and assumptions, particularly the assertion that symbolic representations need not have conventional meaning. The book goes on to sketch a new methodology for looking at the philosophy of psychology, one that provides a more fruitful way of comparing computational psychology with rival views emerging from connectionism and neuroscience.

About this title

About the Author

Steven W. Horst is Assistant Professor of Philosophy at Wesleyan University.

From the Back Cover

"A first-rate contribution to the literature on the foundations of cognitive science, philosophy of mind, and philosophy of psychology. It is clear, powerfully argued, highly original, and provides one of the best general critiques to date of the claims of the advocates of the computational theory of mind."—Jay L. Garfield, Hampshire College

From the Inside Flap

"A first-rate contribution to the literature on the foundations of cognitive science, philosophy of mind, and philosophy of psychology. It is clear, powerfully argued, highly original, and provides one of the best general critiques to date of the claims of the advocates of the computational theory of mind."Jay L. Garfield, Hampshire College

Excerpt. © Reprinted by permission. All rights reserved.

Symbols, Computation, and Intentionality: A Critique of the Computational Theory of Mind

By Steven Horst

University of California Press

Copyright 1996 Steven Horst
All right reserved.
ISBN: 0520200527
Chapter One
The Computational Theory of Mind

The past thirty years have witnessed the rapid emergence and swift ascendency of a truly novel paradigm for understanding the mind. The paradigm is that of machine computation, and its influence upon the study of mind has already been both deep and far-reaching. A significant number of philosophers, psychologists, linguists, neuroscientists, and other professionals engaged in the study of cognition now proceed upon the assumption that cognitive processes are in some sense computational processes; and those philosophers, psychologists, and other researchers who do not proceed upon this assumption nonetheless acknowledge that computational theories are now in the mainstream of their disciplines.

But if there is general agreement that the paradigm of machine computation may have significant implications for both the philosopher of mind and the empirical researcher interested in cognition, there is no such agreement about what these implications are. There is, perhaps, little doubt that computer modeling can be a powerful tool for the psychologist, much as it is for the physicist and the meteorologist. But not all researchers are agreed that the cognitive processes they may model on a computer are themselves computations, any more than the storms that the meteorologist models are computations.

Similarly, there is significant disagreement among philosophers about whether the paradigm of machine computation provides a literal characterization of the mind or merely an alluring metaphor. Three alternative ways of assessing the importance of the computer paradigm stand out. The most modest possibility is that the computer metaphor will

prove an able catalyst for generating theories in psychology, in much the sort of way that numerous other metaphors have so often played a role in the development of other sciences, yet in such a fashion that little or nothing about computation per se will be of direct relevance to the explanatory value of the resulting theories. A second and slightly stronger possibility is that the conceptual machinery employed in computer science will provide the right sorts of tools for allowing psychology (or at least parts of psychology) to become a rigorous science, in much the fashion that conceptual tools such as Cartesian geometry and the calculus provided a basis for the emergence of Newtonian mechanics, and differential geometry made possible the relativistic physics which supplanted it. On this view, which will be discussed in the final chapter of this book, what the computer paradigm might contribute is the basis for the maturation of psychology by way of the mathematization of its explanations and the connections between intentional explanation and explanation cast at the level of some lower-order (e.g., neurological) processes through which intentional states and processes are realized. This view is committed to the thesis that the mind is a computer only in the very weak sense that the interrelations between mental states have formal properties for which the vocabulary associated with computation provides an apt characterizationthat is, to the view that there is a description of the interrelations of mental states and processes that is isomorphic to a computer program. This thesis involves no commitment to the stronger view that terms like 'representation', 'symbol', and 'computation' play any stronger role in explaining why mental states and processes are mental states and processes, but only the weaker view that, given that we may posit such states and processes, their "form" may be described in computational terms. (You might say that, on this view, the mind is "computational" in the same sense that a relativistic universe is "differential.") The third and strongest view of the relevance of machine computation to psychologyone example of which will be the main focus of this bookis that notions such as "representation" and "computation" not only provide the psychologist with the formal tools she needs to do her science in a rigorous fashion, but also provide the philosopher with fundamental tools that allow for an analysis of the essential nature of cognition and for the solution of important and long-standing philosophical problems.

This book examines one particular application of the paradigm of machine computation to the study of mind: namely, the "Computational

Theory of Mind" (CTM) advocated in recent years by Jerry Fodor (1975, 1980a, 1981, 1987, 1990) and Zenon Pylyshyn (1980, 1984). Over the past two decades, CTM has emerged as the "mainstream" view of the significance of computation in philosophy. Its advocates have articulated a very strong position: namely, that cognition literally is computation and the mind literally is a digital computer. CTM is comprised of two theses. The first is a thesis about the nature of intentional states, such as individual beliefs and desires. According to CTM, intentional states are relational states involving an organism (or other cognizer) and mental representations. These mental representations, moreover, are to be understood on the model of representations in computer storage: in particular, they are symbol tokens that have both syntactic and semantic properties. These symbols include both semantic primitives and complex symbols whose semantic properties are a function of their syntactic structure and the semantic values of the primitives they contain. The second thesis comprising CTM is about the nature of cognitive processesprocesses such as reasoning to a conclusion, or forming and testing a hypothesis, which involve chains of beliefs, desires, and other intentional states. According to CTM, cognitive processes are computations over mental representations. That is, they are causal sequences of tokenings of mental representations in which the relevant causal regularities are determined by the syntactic properties of the symbols and are describable in terms of formal (i.e., syntactic) rules. The remainder of this chapter will be devoted to clarifying the nature and status of these two claims.

As we shall see in chapter 2, CTM's advocates have also made a very persuasive case that viewing the mind as a computer allows for the solution of significant philosophical problems: notably, they have argued (1) that it provides an account of the intentionality of mental states, and (2) that it shows that psychology can employ explanations in the intentional idiom without involving itself in methodological or ontological difficulties. The claims made on behalf of CTM thus fall into the third and strongest category of attitudes towards the promise of the computer paradigm. The task undertaken in the subsequent chapters of this book is to evaluate these claims that have been made on behalf of CTM and to provide the beginnings of an alternative understanding of the importance of the computer paradigm for the study of cognition. In particular, we shall examine (1) whether CTM succeeds in solving these philosophical problems, and (2) whether the weaker possibility of its providing the basis for a rigorous psychology in any way depends upon either the

understanding of cognition and computation endorsed by CTM or its ability to explain intentionality and vindicate intentional psychology.

1.1
Intentional States

CTM is a theory about the nature of intentional states and cognitive processes. To understand what this means, however, we must first become clear about the meanings of the expressions 'intentional state' and 'cognitive process'. The expression 'intentional state' is used as a generic term for mental states of a number of kinds recognized in ordinary language and commonsense psychology. Some paradigm examples of intentional states would be

believing (judging, doubting) that such-and-such is the case,

desiring that such-and-such should take place,

hoping that such-and-such will take place,

fearing that such-and-such will take place.

The characteristic feature of intentional states is that they are about something or directed towards something . This feature of directedness or intentionality distinguishes intentional states both from brute objects and from other mental phenomena such as qualia and feelings, none of which is about anything. The expressions 'intentional states' and 'cognitive states' denote the same class of mental states, but the two terms reflect different interests. The term 'intentionality' is employed primarily in philosophy, where it is used to denote specifically this directedness of certain mental states, a feature which is of importance in understanding several important philosophical problems, including opacity and transparency of reference and knowledge of extramental objects. The term 'cognition' is most commonly employed in psychology, where it is used to denote a domain for scientific investigation. As such, its scope and meaning are open to some degree of adjustment and change as the science of psychology progresses. A third term used to indicate this same domain is 'propositional attitude states'. This expression shows the influence of the widely accepted analysis of cognitive states as involving an attitude (such as believing or doubting) and a content that indicates the object or state of affairs to which the attitude is directed. Since the contents of mental states are often closely related to propositions, such attitudes are sometimes called propositional attitudes. These three ex-

pressions will be used interchangeably in the remainder of this book. In places where there is little danger of misunderstanding, the more general expression 'mental states' will also be used to refer specifically to intentional states.

1.2
Mental State Ascriptions in Intentional Psychology and Folk Psychology

Attributions of intentional states such as beliefs and desires play an important role in our ordinary understanding of ourselves and other human beings. We describe much of our linguistic behavior in terms of the expression of our beliefs, desires, and other intentional states. We explain our own actions on the basis of the beliefs and intentions that guided them. We explain the actions of others on the basis of what we take to be their intentional states. Such explanations reflect a general framework for psychological explanation which is implicit in our ordinary understanding of human thought and action. A cardinal principle of this framework is that people's actions can often be explained by their intentional states. I shall use the term 'intentional psychology' to refer to any psychology that (a ) makes use of explanations involving ascriptions of intentional states, and (b ) is committed to a realistic interpretation of at least some such ascriptions.

This usage of the expression 'intentional psychology' should be distinguished from the common usage of the currently popular expression 'folk psychology'. The expression 'folk psychology' is used by many contemporary writers in cognitive science to refer to a culture's loosely knit body of commonsense beliefs about how people are likely to think and act in various situations. It is called "psychology" because it involves an implicit ontology of mental states and processes and a set of (largely implicit) assumptions about regularities of human thought and action which can be used to explain behavior. It is called "folk" psychology because it is not the result of rigorous scientific inquiry and does not involve any rigorous scientific research methodology. Folk psychology, thus understood, is a proper subset of what I am calling intentional psychology. It is a subset of intentional psychology because it employs intentional state ascriptions in its explanations. It is only a proper subset because one could have psychological explanations cast in the intentional idiom that were the result of rigorous inquiry and were not committed to the specific set of assumptions characteristic of any given culture's commonsense views about the mind. Many of Freud's theories, for example,

fall within the bounds of intentional psychology, since they involve appeals to beliefs and desires; yet they fall outside the bounds of folk psychology because Freud's theories are at least attempts at rigorous scientific explanation and not mere distillations of commonsense wisdom. Similarly, many contemporary theories in cognitive psychology employ explanations in the intentional idiom that fall outside the bounds of folk psychology, in this case because the states picked out by their ascriptions occur at an infraconscious level where mental states are not attributed by commonsense understandings of the mind.

In understanding the importance of CTM in contemporary psychology and philosophy of mind, it would be hard to overemphasize this distinction between the more inclusive notion of intentional psychology, which embraces any psychology that is committed to a realistic construal of intentional state ascriptions, and the narrower notion of folk psychology, which is by definition confined to prescientific commonsense understandings of the mental. For CTM's advocates wish to defend the integrity of intentional psychology, while admitting that there may be significant problems with the specific set of precritical assumptions that comprise a culture's folk psychology. On the one hand, Fodor and Pylyshyn argue that the intentionally laden explanations present in folk psychology are quite successful,1 that folk psychology is easily "the most successful predictive scheme available for human behavior" (Pylyshyn 1984: 2), and even that intentional explanation is indispensable in psychology.2 On the other hand, advocates of CTM are often more critical of the specific generalizations implicit in commonsense understandings of mind. Folk psychology may provide a good starting point for doing psychology, much as animal terms in ordinary language may provide a starting point for zoological taxonomy or billiard ball analogies may provide a starting point for mechanics; but more rigorous research is likely to prove commonsensical assumptions wrong in psychology, much as it has in biology and physics.3 Folk psychology is thus viewed by these writers as a protoscience out of which a scientific intentional psychology might emerge. One thing that would be needed for this transition to a scientific intentional psychology to take place is rigorous empirical research of the sort undertaken in the relatively new area called cognitive psychology.4 Such empirical research would be responsible, among other things, for correcting such assumptions of common sense as may prove to be mistaken. What is viewed as the most significant shortcoming of commonsense psychology, however, is not that it contains erroneous generalizations, but that its generalizations are not united by a single theo-

retical framework.5 CTM is an attempt to provide such a framework by supplying (a ) an account of the nature of intentional states, and (b ) an account of the nature of cognitive processes.

1.3
CTM's Representational Account of Intentional States

The first thesis comprising CTM is a representational account of the nature of intentional states . Fodor provides a clear outline of the basic tenets of this account in the following five claims, offered in the introduction to RePresentations, published in 1981:

(a ) Propositional attitude states are relational.

(b ) Among the relata are mental representations (often called "Ideas" in the older literature).

(c ) Mental representation[s] are symbols: they have both formal and semantic properties.

(d ) Mental representations have their causal roles in virtue of their formal properties.

(e ) Propositional attitudes inherit their semantic properties from those of the mental representations that function as their objects. (Fodor 1981: 26)

Claims (a ) through (c ) provide Fodor's views upon the nature of intentional states, while claims (d ) and (e ) provide the means for connecting this representational account of intentional states with a computational account of cognitive processes and an account of the intentionality of the mental, respectively.

Fodor supplies a more formal account of the nature of intentional states in Psychosemantics, published in 1987. There he characterizes the nature of intentional states (propositional attitudes) as follows:

Claim 1 (the nature of propositional attitudes):

For any organism O , and any attitude A toward the proposition P , there is a ('computational'-'functional') relation R and a mental representation MP such that

MP means that P , and

O has A iff O bears R to MP . (Fodor 1987: 17)

On Fodor's account, Jones's believing that two is a prime number consists in Jones being in a particular kind of functional relationship R to a mental representation MP . This mental representation MP is a symbol token, presumably instantiated in some fashion in Jones's nervous system. MP has semantic properties: in particular, MP means that two is a

prime number. And Jones believes that two is a prime number when and only when he is relation R to MP .

There are some glaring unclarities about references to types and tokens of attitudes and representations in this formulation, but some of these are clarified when Fodor provides a "cruder but more intelligible" gloss upon his account of the nature of intentional states:

To believe that such and such is to have a mental symbol that means that such and such tokened in your head in a certain way; it's to have such a token 'in your belief box,' as I'll sometimes say. Correspondingly, to hope that such and such is to have a token of that same mental symbol tokened in your head, but in a rather different way; it's to have it tokened 'in your hope box.' . . . And so on for every attitude that you can bear toward a proposition; and so on for every proposition toward which you can bear an attitude. (Fodor 1987: 17)

On the basis of this gloss, it seems most reasonable to read Fodor's formulation as follows:

The Nature of Propositional Attitudes (Modified)

For any organism O , and any attitude-token a of type A toward the proposition P , there is a ('computational'-'functional') relation R and a mental representation token t of type MP such that

t means that P by virtue of being an MP -token, and

O has an attitude of type A iff O bears R to a token of type MP .6

While there are arguably some significant residual unclarities about Fodor's formulation in spite of these clarifications,7 Fodor does make the main point adequately clear: namely, that it is the relationship between the organism and its mental representations that is to account for the fact that intentional states have the semantic properties and intentionality that they have. In the passage already quoted from RePresentations, for example, he writes that intentional states "inherit their semantic properties from those of the mental representations that function as their objects" (Fodor 1981: 26). And in that essay he also writes that "the objects of propositional attitudes are symbols (specifically, mental representations)" and that "this fact accounts for their intensionality and semanticity" (ibid., 25, emphasis added).8

The first thesis comprising CTM is thus a representational account of the nature of intentional states . On this account, intentional states are relations to mental representations. These representations are symbol tokens having both syntactic and semantic properties, and intentional

Figure 1

states "inherit" their semantic properties and their intentionality from the representations they involve (see fig. 1).

1.4
Semantic Compositionality

An important feature of this account lies in the fact that the symbols involved in mental representation have both semantic and syntactic properties, and may be viewed as tokens in a "language of thought," sometimes called "mentalese." Viewing the system of mental representations as a language with both semantic and syntactic properties allows for the possibility of compositionality of meaning . That is, the symbols of mentalese are not all lexical primitives. Instead, there is a finite stock of lexical primitives which can be combined in various ways according to the syntactic rules of mentalese to form a potentially infinite variety of complex representations, just as in the case of natural languages it is possible to generate an infinite variety of meaningful utterances out of a finite stock of morphemes and compositional rules. Mentalese is thus viewed as having the same generative and creative aspects possessed by natural languages. So while the semantic properties of mental states are "inherited" from the representations they contain, those representations may themselves be either semantically primitive or composed out of semantic primitives by the application of syntactic rules.

1.5
Cognitive Processes

If a representational account of the mind provides a way of interpreting the nature of individual thoughts, it does not itself provide any comparable account of the nature of mental processes such as reasoning to a conclusion or forming and testing a hypothesis, and hence does not provide the grounds for a psychology of cognition. For a psychology of cognition, something more is needed: a theory of mental processes that uses

the properties of mental representations as the basis of a causal account of how one mental state follows another in a train of reasoning. Suppose, for example, that one wishes to explain why Jones has closed the window. An explanation might well be given along the following lines:

(1) Jones felt a chill.

(2) Jones noticed that the window was open.

(3) Jones hypothesized that there was a cold draft blowing in through the window.

(4) Jones hypothesized that this cold draft was the cause of his chill.

(5) Jones wanted to stop feeling chilled.

(6) Jones hypothesized that cutting off the draft would stop the chill.

so, (7) Jones formed a desire to cut off the draft.

(8) Jones hypothesized that closing the window would cut off the draft.

so, (9) Jones formed a desire to close the window.

so, (10) Jones closed the window.

Here we have not a random train of thought, but a sequence of thoughts in which the latter thoughts are plausibly viewed as both (a ) rational in light of those that have gone before them, and (b ) consequences of those previous statesJones formed a desire to close the window because he thought that doing so would cut off the draft. Moreover, a causal theory of inference would need to forge a close link between the semantic properties of individual states and their role in the production of subsequent states. It is changes in the content of Jones's beliefs and desires that we would expect to produce different trains of thought and different behaviors. If Jones had noticed the fan running instead of noticing an open window, we would expect him to entertain different hypotheses, form different desires, and act in a different way, all as a consequence of changing the content of his belief from "the window is open" to "the fan is running."

Now CTM's representational account of intentional states seems well suited to a discussion of the semantic relations between intentional states, since the semantic and intentional properties of intentional states are identified with those of the representations they involve. But when it

Figure 2

comes to the question of how intentional states can play a causal role in the etiology of a process that involves the generation of new intentional states, the notion of representation, in and of itself, has little to offer. Viewing intentional states as relations to representations allows us to locate the semantic relationships between intentional states in relationships between the representations they involve, but it does little to show how Jones's standing in relation R to a representation MP at time t can play a causal role in Jones coming to stand in relation Q to a representation MP * at t + .

This seems to present a problem. In order for a sequence of representations to make up a rational, cogent train of thought, the question of which representations should occur in the sequence should be determined by the meanings of the earlier representations. In order for the sequence of representations to make sense, the later representations need to stand in appropriate semantic relationships to the earlier ones. But in order for a sequence of representations to be a causal sequence, the question of what representations will occur later in the sequence must be determined by the causal powers of the earlier representations. Now intentional explanations pick out representations by their contentthat is, by their semantic properties. But if such explanations are to be causal explanations, they must pick out representations in a fashion that individuates them according to their causal powers. But this can be done only if the semantic values of representations can be linked to, or coordinated with, the causal roles they can play in the production of other representations and the etiology of behavior. This has been seen by some as a significant stumbling block to the possibility of a causal-nomological psychology, as it is notoriously problematic to view semantic relationships as causal relationships or to equate reasons with causes.9 The problem, then, for turning a representational theory of mental states into a psychological theory of mental processes is one of finding a way to link the semantic properties of mental representations to the causal powers of those representations (see fig. 2).

It is precisely at this point that the computer paradigm comes to be of interest. For computers are understood as devices that store and manipulate symbol tokens, and the manipulations that they perform are dependent upon what representations are already present, yet they are also completely mechanical and uncontroversially causal in nature. Machine computation provides a general paradigm for understanding symbol-manipulation processes in which the symbols already present play a causal role in determining what new symbols are to be generated. CTM seeks to provide an extension of this paradigm to mental representations, and thereby to supply an account of cognitive processes that can provide a way of discussing their etiology while also respecting the semantic relationships between the representations involved.

1.6
Formalization and Computation

CTM's advocates believe that machine computation provides a paradigm for understanding how one can have a symbol-manipulating system that can cause derivations of symbolic representations in a fashion that "respects" their semantic properties. More specifically, machine computation is believed to provide answers to two questions: (1) How can semantic properties of symbols be linked to causal powers that allow the presence of one symbol token s 1 at time t to be a partial cause of the tokening of a second symbol s 2 at time t + And (2) how can the laws governing the causal regularities also assure that the operations that generate new symbol tokens will "respect" the semantic relationships between the symbols, in the sense that the overall process will turn out to be, in a broad sense, rational?

The answers that CTM's advocates would like to provide for these questions can be developed in two stages. First, work in the formalization of symbol systems in nineteenth- and twentieth-century mathematics has shown that, for substantial (albeit limited) interpreted symbolic domains (such as geometry and algebra), one can find ways of carrying out valid derivations in a fashion that does not depend upon the mathematician's intuition of the meanings of the symbols, so long as (a ) the semantic distinctions between the symbols are reflected by syntactic distinctions, and (b ) one can develop a series of rules, dependent wholly upon the syntactic features of symbol structures, that will license those deductions and only those deductions that one would wish to have licensed on the basis of the meanings of the terms. Second, digital computers are devices that store and manipulate symbolic representations.

Their "manipulation" of symbolic representations, moreover, consists in creating new symbol tokens, and the regularities that govern what new tokens are to be generated may be cast in the form of derivation-licensing rules based upon the syntactic features of the symbols already tokened in computer storage. In a computer, symbols play causal roles in the generation of new symbols, and the causal role that a symbol can play is determined by its syntactic type. Formalization shows that (for limited domains) the semantic properties of a set of symbols can be "mirrored" by syntactic properties; digital computers offer proof that the syntactic properties of symbols can be causal determinants in the generation of new symbols. All in all, the computer paradigm shows that one can coordinate the semantic properties of representations with the causal roles they may play by encoding all semantic distinctions in syntax.

These crucial notions of formalization and computation will now be discussed in greater detail. These notions are, no doubt, already familiar to many readers. However, how one tells the story about these notions significantly influences the conclusions one is likely to draw about how they may be employed, and so it seems worthwhile to tell the story right from the start.

1.6.1
Formalization

In the second half of the nineteenth century, one of the most important issues in mathematics was the formalization of mathematical systems. The formalization of a mathematical system consists in the elimination from the system's deduction rules of anything dependent upon the meanings of the terms. Formalization became an important issue in mathematics after Gauss, Bolyai, Lobachevski, and Riemann independently found consistent geometries that denied Euclid's parallel postulate. This led to a desire to relieve the procedures employed in mathematical deductions of all dependence upon the semantic intuitions of the mathematician (for example, her Euclidean spatial intuitions). The process of formalization found a definitive spokesman in David Hilbert, whose book on the foundations of geometry, published in 1899, employed an approach to axiomatization that involved a complete abstraction from the meanings of the symbols. The formalization of logic, meanwhile, had been undertaken by Boole and later by Frege, Whitehead, and Russell, and the formalization of arithmetic by Peano.

While there were several different approaches to formalization in nineteenth-century mathematics, Hilbert's "symbol-game" approach is of

special interest for our purposes. In this approach, the symbols used in proofs are treated as tokens or pieces in a game, the "rules" of which govern the formation of expressions and the validity of deductions in that system. The rules employed in the symbol game, however, apply to formulae only insofar as the formulae fall under particular syntactic types. This ideal of formalization in a mathematical domain requires the ability to characterize, entirely in notational (symbolic and syntactic) terms, (a ) the rules for well-formedness of symbols, (b ) the rules for well-formedness of formulas, (c ) the axioms, and (d ) the rules that license derivations.

What is of interest about formalizability for our purposes is that, for limited domains, one can find methods for producing derivations that respect the meanings of the terms but do not rely upon the mathematician's knowledge of those meanings, because the method is based solely upon their syntactic features. Thus, for example, a logician might know a derivation-licensing rule to the effect that, whenever formulas of the form p and p q have been derived, he may validly derive a formula of the form q . To apply this rule, he need not know the interpretations of any of the substitution instances of p and q , or even know what relation is expressed by , but need only be able to recognize symbol structures as having the syntactic forms p and p q . As a consequence, one can carry out rational, sense- and truth-preserving inferences without attending toor even knowingthe meanings of the terms, so long as one can devise a set of syntactic types and a set of formal rules that capture all of the semantic distinctions necessary to license deductions in a given domain.

1.6.2
A Mathematical Notion of Computation

A second issue arising from turn-of-the-century mathematics was the question of what functions are "computable" in the sense of being subject to evaluation by the application of a rote procedure or algorithm. The procedures learned for evaluating integrals are good examples of computational algorithms. Learning integration is a matter of learning to identify expressions as members of particular syntactically characterized classes and learning how to produce the corresponding expressions that indicate the values of their integrals. One learns, for example, that integrals with the form have solutions of the form , and so on.

Such computational methods are formal, in the sense that a person's ability to apply the method does not require any understanding of the

meanings of the terms.10 To evaluate , for example, one need not know what the expression indicatesthe area under a curvebut only that it is of a particular syntactic type to which a particular rule for integration applies. Similarly, one might apply the techniques used in column addition (another algorithmic procedure) without knowing what numbers one was adding. For example, one might apply the method without looking to see what numbers were represented, or the numbers might be too long for anyone to recognize them. One might even learn the rules for manipulating digits without having been told that they are used in the representation of numbers. The method of column addition is so designed, in other words, that the results do not depend upon whether the person performing the computation knows the meanings of the terms. The procedure is so designed that applying it to representations of two numbers A and B will dependably result in the production of a representation of a number C such that A + B = C .

1.6.3
The Scope of Formal Symbol-Manipulation Techniques

It turns out that formal inference techniques have a surprisingly wide scope. In the nineteenth and early twentieth century it was shown that large portions of logic and mathematics are subject to formalization. And this is true not only in logic and number theory, which some theorists hold to be devoid of semantic content, but also in such domains as geometry, where the terms clearly have considerable semantic content. Hilbert (1899), for example, demonstrated that it is possible to formulate a collection of syntactic types, axioms, and derivation-licensing rules that is rich enough to license as valid all of the geometric derivations one would wish for on semantic grounds while excluding as invalid any derivations that would be excluded on semantic grounds.

Similarly, many problems lying outside of mathematics that involve highly context-specific semantic information can be given a formal characterization. A game such as chess, for example, may be represented by (1) a set of symbols representing the pieces, (2) expressions representing possible states of the board, (3) an expression picking out the initial state of the board, and (4) a set of rules governing the legality of moves by mapping expressions representing legal states of the board after a move m to the set of expressions representing legal successor states after move m + 1. Some games, such as tic-tac-toe, also admit of algorithmic strategies that assure a winning or nonlosing game. In addition to games, it is

also possible to represent the essential features of many real-world processes in formal models of the sorts employed by physicists, engineers, and economists. In general, a process can be modeled if one can find an adequate way of representing the objects, relationships, and events that make up the process, and of devising a set of derivation rules that map a representation R of a state S of the process onto a successor representation R * of a state S * just in case the process is such that S * would be the successor state to S . As a consequence, it is possible to devise representational systems in which large amounts of semantic information are encoded syntactically, with the effect that the application of purely syntactic derivation techniques can result in the production of sequences of representations that bear important semantic relationships: notably, sequences that could count as rational, cogent lines of reasoning.

1.6.4
Computing Machines

The formalizability of limited symbolic domains shows that semantic distinctions can be preserved syntactically and that the application of syntactic derivation rules can result in a semantically cogent sequence of representations. In crude terms, formalization shows us how to link semantics to syntax. What is required, however, is a way of linking the semantic properties of representations with their ability to play a causal role in the generation of new representations to which they bear interesting semantic relationships (see fig. 3). In and of themselves, formal proof methods and formal algorithms do not provide such a link, since they depend upon the actions of the human computer who applies them. It is the paradigm of machine computation that provides a way of connecting the causal roles played by representations with their syntactic properties, and thus indirectly linking semantics with causal role.

The crucial transition from formal techniques dependent upon a human mathematician to mechanical computation came in Alan Turing's "On Computable Numbers" (1936). This paper was framed as an answer to the mathematical problem of finding a general characterization of the class of functions that admit of computational (i.e., algorithmic) solutions. Turing's approach to this problem was to describe a machine that was capable of scanning and printing symbols printed on a tape and governed in part by internal mechanisms and in part by the specific symbols found on the tape. Some of the details of this machine are described in chapter 5, but for present purposes it suffices to say that Turing

Figure 3

showed that any computation that can be evaluated by application of a formal algorithm can be performed by a digital machine of the sort he specifies. The original intent of Turing's article was to provide a general description of all computable functions: a function is computable just in case it can be evaluated by a Turing machine. But in providing this answer to a problem in mathematics, Turing also showed something far more interesting for psychologists and philosophers: namely, that it is possible to design machines that not only passively store symbols for human use, but also actively distinguish symbols on the basis of their shape and their syntactic ordering, and indeed operate in a fashion that is partially determined by the syntactic properties of the symbols on which they operate. In short, Turing showed that it is possible to link syntax to causal powers in a computing machine.

A computing machine is a device that possesses several distinctive features. First, it contains media in which symbolic representations can be stored. These symbols, like written symbols, can be arranged into expressions having syntactic structures and may be assigned interpretations through an interpretation scheme. Second, a computer is capable of differentiating between representations in a fashion corresponding to distinctions in their syntactic "shape." Third, it can cause the tokening of new representations. Finally, the causal regularities that govern what new symbols the computer will cause to be tokened are dependent upon the syntactic form of the symbols already stored by the machine.

To take a simple example, suppose that a computer is programmed to sample two storage locations A and B where representations of integers are stored and to cause a tokening of a representation at a third

location C in such a fashion that the representation tokened at C will be a representation of the sum of the two numbers represented at A and B . The representations found at A , B , and C have syntactic structure: let us assume that each representation is a series of binary digits (1s and 0s). They also have semantic interpretations: namely, those assigned to them by the interpretation scheme employed by the designer of the program. Now when the computer executes the program, it will cause the tokening of a representation at C . Just what representation is tokened at C will depend upon what representations are found at A and B . More specifically, it will depend upon the syntactic type of the representations found at A and B namely, upon what sequences of binary digits are present at those locations. What the computer does in executing this program is thus analogous to the application of a formal algorithm (such as that employed in column addition), which is sensitive to the syntactic forms of the representations at A and B . If the program has been properly designed, the overall process will accurately mimic addition as well, in the sense that what is tokened at C will always be a representation of the sum of the two numbers represented at A and B . That is, if the program is properly designed, the syntactically dependent operations performed by the machine will ensure the production of a representation at C that bears the desired semantic relations to the representations at A and B as well.11 The semantic properties of the representations play no causal role in the processthey are etiologically inert. But since all semantic distinctions are preserved syntactically, and syntactic type determines what a representation can contribute causally, there is a correspondence between a representation's semantic properties and the causal role it can play.

This example illustrates three salient points. The first is the insight borrowed from formal logic and mathematics that at least some semantic relations can be reflected or "tracked" by syntactic relations. The second is the insight borrowed from computer science that machines can be made to operate upon symbols in such a way that the syntactic properties of the symbols can be reflected in their causal roles. Indeed, for any problem that can be solved by the application of a formal algorithm A , it is possible to design a machine M that will generate a series of representations corresponding to those that would be produced by the application of algorithm A . These two points jointly yield a third: namely, that it is possible for machines to operate upon symbols in a way that is, in Fodor's words, "sensitive solely to syntactic properties" of the symbols and "entirely confined to altering their shapes," while at the same time

Figure 4

the machine is so devised that it will transform one symbol into another if and only if the propositions
expressed by the symbols that are so transformed stand in certain semantic relationse.g.,
the relation that the premises bear to the conclusion of a valid argument. (Fodor 1987: 19)

In brief, "computers show us how to connect semantical with causal properties for symbols " (ibid.). And this completes the desired linkage between semantics and causality: for domains that can be formalized, semantic properties can be linked to causal properties by encoding semantic differences in syntax and designing a machine that is driven by the syntactic features of the symbols (see fig. 4).

1.7
The Computational Account of Cognitive Processes

We have seen that the first thesis comprising CTM was a representational account of the nature of intentional states: namely, that such states are relations to mental representations. The second thesis comprising CTM is a computational account of the nature of cognitive processes: namely, that cognitive processes are computations over mental representations, or "causal sequences of tokenings of mental representations" (Fodor 1987: 17). Fodor writes,

A train of thoughts, for example, is a causal sequence of tokenings of mental representations which express the propositions that are the objects of the thoughts. To a first approximation, to think 'It's going to rain; so I'll go indoors' is to have a tokening of a mental representation that means I'll go indoors caused, in a certain way, by a tokening of a mental representation that means It's going to rain . (ibid.)

This account may be broken down into several constituent claims. First, cognitive processes are sequences of intentional states. Now,

according to CTM, to be in a particular intentional state is just to be in a particular functional relation to a mental representation. So if an organism is undergoing a cognitive process, it is passing through a sequence of functional relations to mental representations. Second, there are causal relationships between the intentional states that make up a cognitive process. Being in relation R to a representation of type MP at time t (say, believing at 12:00 noon that it is going to rain) can be a partial cause of coming to be in relation R * to a representation of type MP * at time t + (e.g., coming to a decision at 12:01 to go indoors). Third, the causal connection between the states picked out is not merely incidental, but depends in a regular way upon the syntactic properties of the mental representations. It is because the organism stands in relation R to a token of (syntactic) type MP at t that it comes to stand in relation R * to a token of (syntactic) type MP * at t + , much as our adding program causes a particular representation to be tokened at C because representations with particular syntactic patterns are present at A and B . So just as the representations in computers can play a causal role in the generation of new representations, and do so by virtue of their syntactic form, so also "mental representations have their causal roles in virtue of their formal properties" (Fodor 1981: 26). Fourth, as in the case of a formal algorithm or a computer program, any semantic differences between mental representations are reflected by syntactic distinctions. So for any two mental representations MP and MP * to which a single organism O is related, if MP and MP * differ with respect to semantic properties, they must be of different syntactic types as well.

To view mental processes in this way is to treat the mind as being quite literally a digital computer. A computer is a device that performs symbol manipulations on the basis of the syntactic features of the symbols, and it can do so in a fashion that respects such semantic features as are encoded in the syntax. According to CTM, mental states involve symbolic representations from which they inherit their semantic properties. All semantic differences between representations are syntactically encoded, and the mind is a device whose causal regularities are determined by the syntactic properties of its representations.

This account of the nature of cognitive processes allows intentional state ascriptions to pick out intentional states by way of properties that are correlated with their causal powers. Intentional state ascriptions pick out intentional states by the semantic values of the representations they involve. These semantic values are not themselves causally efficient. But, according to CTM, the semantic properties of representations are cor-

related with their syntactic types. So when representations are picked out by their semantic value, their syntactic type is uniquely picked out as well. But the syntactic type of a representation is a determinant of the causal role it can play in causing tokenings of other representations and in the etiology of behavior. And so intentional state ascriptions can pick out causes, and indeed the semantic properties by which intentional states are picked out are correlated with the causal roles that they can play, because semantic properties are correlated with syntactic properties, and syntactic properties determine causal powers. This provides for the possibility of accounting for mental causation in a way that does not require semantic properties to be causally active, and yet correlates semantic value with causal role.

1.8
Summary: The Computational Theory of Mind

In summary, we have now seen that CTM consists in two main theses. The first thesis is a representational account of the nature of intentional states. On this view, intentional states are relations between an organism and mental representations. These representations are physically instantiated symbol tokens having both semantic and syntactic properties. The second thesis is a computational account of the nature of cognitive processes. Cognitive processes, according to CTM, are computations over mental representations. That is, they are sequences of tokenings of mental representations in which the presence of one representation can serve as a partial cause of the tokening of a second representation. Just what causal roles a representation may play in the generation of other representations and the etiology of behavior is determined by its syntactic properties, and not by its semantic value. But while a representation's semantic value does not influence what causal roles it can play, the semantic value is nonetheless coordinated with causal role, because all semantic differences between representations are preserved syntactically, and syntax determines causal role.

Continues...

Excerpted from Symbols, Computation, and Intentionality: A Critique of the Computational Theory of Mind by Steven Horst Copyright 1996 by Steven Horst. Excerpted by permission.
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Edition details

• Publisher: University of California Press
• Publication date: 1996
• Language: English
• ISBN 10: 0520200527
• ISBN 13: 9780520200524
• Binding: Hardcover
• Number of pages: 448