The Sourhern Journal of Phitosopby ( I 987) Supplement

TYE ON CONNECTIONISM Brian McLaughlin Rutgers University

that his primary concern is

to discuss whether there is really any incompatibiliry, at the representational level, between the hypothesis that there is an inner ‘language’ within which mental representation is confined (hereafter the language of cognition thesis) and either pictorialism or various connectionist theses.

He goes on to pursue two largely unrelated questions: (1) Are the language of cognition thesis and Kosslyn’s pictorialism compatible? (2) Are the language of cognition thesis and Smolensky’s tensor product connectionism compatible “at the representational level *’? He answers “yes”to ( I ) and “They may well be”to (2). I shall focus on his answer to (2) and also on the connectionism/language of thought controversy concerning the nature of mental representation. But first a few remarks about Tye’s answer to (1).

Pictorialism is, Tye says, “the thesis that mental images represent in the manner of pictures.” Kosslyn’s brand of pictorialism implies that a mental image is a quasi-picture (Kosslyn, 1980, 1983). Tye offers an explication of Kosslyn’s notion of a quasi-picture, the details of which need not concern us. The point to note is that quasi-pictures are nonlinguistic. Since mental images are mental representations, Kos- slyn’s brand of pictorialism is, claims Tye, incompatible with the language of cognition thesis, which Tye formulates as follows:

Language of Cognition Thesis. “there is an inner ‘language’within which mental representation is confined.”

Presumably, he intends this to imply that all mental representations are linguistic. If so, Kosslyn’s pictorialism thesis is indeed incompatible with it.

Any realist about mental images who maintains that all mental representations are linguistic should deny that mental images are quasi- pictures. The following question thus arises: Are mental images quasi- pictures? Tye’s explication of the notion of a quasi-picture is useful for anyone concerned to answer this question. While Tye sympathizes with the view that mental images are quasi-pictures, he does not attempt to defend an answer to the question. So I shall say no more about it.

It is worthwhile noting, however, that some language of thought enthusiasts, for example, Jerry Fodor, claim only that propositional

In “Representation in Pictorialism and Connectionism,”’ Tye says

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attitudes involve linguistic mental representations. According to him, a causally necessary and sufficient condition for one’s having a propo- sitional attitude (belief, desire, etc.) that p is one’s bearing a computational relation constitutive of the attitude in question to a sentence in one’s language of thought that means that p (Fodor, 1976). He allows, however, that mental images may be pictorial (Fodor, 1982). He does not accept Tye’s Language of Cognition Thesis since he does not hold that all mental representations are linguistic.

Tye sympathizes with the claim that propositional attitudes involve linguistic mental representations. He holds that a certain argument offered by Fodor and Pylyshyn* for this claim has “substantial force.” As we shall see, the argument bears on the connectionism/language of thought debate and on what Tye says about question ( 2 ) . In what follows, I shall first present the argument; then I shall say how Fodor and Pylyshyn invoke its conclusion in an argument against connec- tionist theories of mental representation; this will provide a context in which to consider finally Tye’s answer to ( 2 ) .

To begin, as Tye correctly points out, Fodor and Pylyshyn maintain that there is a broad range of “intrinsic connections” between abilities t o have certain propositional attitudes and abilities to have certain others. Here are some examples: if one can think the thought that Michael loves Mary, then one can think the thought that Mary loves Michael. If one can think that thought that Michael loves Mary and Mary loves him, then one can think the thought that Mary loves Michael. And if one can think the thought that Michael does not like McDonald hamburgers, then one can also think the thought that Michael does not like McDonald hamburgers. As Fodor and Pylyshyn put it: thought is, by causal necessity, systemalic.3 They maintain that the systematicity of thought is t o be explained by appeal to a system of mental repre- sentation that is systematic. The idea is that if, for example, the state of affairs consisting of Michael’s loving Mary can be represented in a system of mental representation M, then the state of affairs consisting of Mary’s loving Michael can be represented in M. While Tye does not mention this, Fodor and Pylyshyn also hold that a system of mental representation is, by causal necessity, productive: it can generate an infinite number of mental representations.

It is widely held that natural languages are both systematic and productive: there are widespread systematic relationships between sentences and natural languages contain infinitely many sentences. These properties of natural languages are standardly explained as follows: sentences are complex in that they have parts which have semantic values. Moreover, the semantically evaluable parts of sentences so constitute them that natural languages have a combina- torial syntax and semantics. The semantically evaluable parts of sentences are constituents of them. The systematicity of language is explained by appeal to shared constituents and the constituent

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structures of sentences. Productivity is explained by appeal t o recursive rules which generate infinitely many sentences from a finite base of basic constituents.

Fodor and Pylyshyn maintain that the systematicity and productivity of a system of mental representation are to be explained in the same way. There are mental representations which are complex in that they contain other mental representations as constituents. The constituent structure of complex mental representations is such that a system of mental representation will have a combinatorial syntax and semantics. Fodor and Pylyshyn maintain that a system of mental representation is a language, or, better, is language-like in that it will have a combinatorial syntax and semantics. And they hold that the constituent structure of a complex mental representation will determine its causal role cognitive processes.

According to Fodor and Pylyshyn, connectionist theories of mental representation d o not seem to have the explanatory resources to explain the systematicity and productivity of a system of mental representation. Some connectionists have denied that such systems are productive. But systematicity seems especially hard to deny. And Fodor and Pylyshyn hold that connectionist theories d o not hold promise of explaining systematicity. For this reason, among others, they deny that systems of mental representation are connectionist networks. ( I shall, hereafter, focus on systematicity.)

Let us consider a simple connectionist network and see why it lacks systematicity. On some connectionist theories, mental representations are individual units; such units are linked together in a largely parallel network; and units interact by exciting or inhibiting activity in one another. On such theories, all mental representations are atomic in that no mental representation contains another as a constitutent. The fact that such a network has a unit which represents Michael’s loving Mary, for example, is compatible with its failing to have one which represents Mary’s loving Michael. Thus such connectionists theories cannot appeal to constituent structure to explain systematicity.

Fodor and Pylyshyn do not purport to have shown a priori that the systematicity of mental representation can be explained only by appeal to a combinatorial syntax and semantics. They maintain rather that no one has a clue as to how else systematicity might be explained. So much, then, by way of presenting Fodor and Pylyshyn’s objections to connectionist theories of mental representation.

Tye seems to hold that (a) a system of mental representation is, by causal necessity, systematic, and that (b) Fodor and Pylyshyn’s argument for holding that systematicity is t o be explained by appeal t o constituent structure has “substantial force.” For this reason he holds that connectionists should “care whether their views on representation are compatible with those of advocates of the language of cognition hypothesis.”

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Turn, then, to question (2): Are the Language of Cognition Thesis and Smolensky’s tensor product connectionism compatible “at the repre- sentational level”? If 1 understand him, Tye intends to be asking whether the following two theses are compatible:

Tensor Product Connectionism Thesis. “A system of mental representation is a tensor product connectionist network.” The Language of Cognition Thesis. “There is a n inner ‘language’ within which mental representation is confined.”

Both theses are, I take, supposed to be causally necessary. Tye seems to maintain that these theses may well be compatible because mental representations in a tensor product connectionist network may well have linguistic structure.

I shall say what a tensor product connectionist network is ~ h o r t l y . ~ First, however, I want to note why I qualified my remarks about Tye in the preceding paragraph by saying ‘if 1 understand him.’ Tye does not himself formulate the Tensor Product Connectionism Thesis. And some of Tye’s remarks suggest that he may have a different proposition in mind. For example, he closes his paper by saying that:

the tensor product approach may be seen as providing a more basic ‘sub-symbolc’ model of representation out of which quasi-symbolic representation. . . emerge(s).

1 take it that the tensor product approach is supposed to be“more basic” than the language of thought approach to mental representation. O n the language of thought approach, of course, mental representations are symbols (or quasi-symbols). I a m uncertain, however, what is meant by a ‘sub-symbol.’ If a sub-symbol has a semantic value, what is the difference between a symbol and a sub-symbol? If sub-symbols d o not have semantic values, then mental representations are not sub-symbols. For mental representations have semantic values. If sub-symbols d o not have semantic values, what is meant by a sub-symbol model of representation? One thing that might be meant is a theory or model of how the operations of a system of mental representation carried out over symbols are implemented by processes involving sub-symbols; such a theory would explain how symbolic processes “emerge” from sub- symbolic ones. But such a sub-symbolic theory would not itself be a theory of mental representation. Rather, it would be a n implementation theory for a theory of mental representation.

If tensor product connectionism is proposed as a n implementation theory of this sort, then there is no incompatibility between the language of thought approach to mental representation and tensor product connectionism “at the representational level.” For, then, tensor product connectionism will not be a theory of processes a t the representational level, but rather a theory of processes at a more basic level. The thesis

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that the operations of a system of mental representation are imple- mented by the operations of a tensor product connectionist network is compatible with the Language of Cognition Thesis. Indeed, Fodor and Pylyshyn maintain that some connectionist theory may well provide an implementation theory for a theory of mental representation. (It should be noted that such an implementation theory would be a monumental conceptual achievement.)

But, again, if I understand Tye, he is claiming that a tensor product connectionist theory of mental representation is compatible with there being a language of thought. He is claiming that the Tensor Product Connectionism Thesis is compatible with the Language of Cognition Thesis. Given that both theses purport (1 take it) to express causally necessary truths, this consistency claim is striking and highly controversial.

If I understand him, Tye holds that a tensor product connectionism may well be able to explain systematicity by appeal to constituent structure. If he is right, this is a direct response to Fodor and Pylyshyn’s objection to connectionism. They maintain that connectionist theories of mental representation do not hold the promise of explaining systematicity. They hold this because they hold that (i) such theories lack the explanatory resource of a combinatorial syntax and semantics and that (ii) no one has the faintest idea how systematicity can be explained without such a resource. Tye seems to sympathize with (ii) but to think that (i) may well be false. He seems to hold that, contra Fodor and Pylyshyn, a connectionist theory of mental representation may well be able to avail itself of the explanatory resource of a combinatorial syntax and semantics and so explain systematicity in the familiar way.

A host of interesting questions arise which include these: (a) Can tensor product connectionism explain systematicity? (b) If so, can it explain systematicity by appeal to constituent structure? (c) If it can, can it do so without implying a standard language of thought theory of mental representation? One might well think that the answer to (c) is “no.”The central claims of a standard language of thought theory is that a system of mental representation has a combinatorial syntax and semantics and the causal role of complex mental representations in cognitive processes is determined by their constituent structure. (It is worth noting that the claim that the rules governing the operation of a system of mental representation must be represented in the system is not essential to the standard view. The standard view is compatible with the claim that all rules are, so to speak, implicit, “hard-wired in.”) Of course, a standard language of thought theory of mental representation combined with a tensor product connectionist implementation theory might be called a tensor product connectionist theory. But the theory of mental representation properly so-called would be the standard language of thought theory implied by the conjunctive theory in question.

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In any case, I confess that there is much that I a m uncertain about here, including what Tye would say in answer to (c). In what remains, 1 shall focus on (b). For Tye holds that the answer to (b) may well be “yes.”I will not try to settle whether his answer is correct; rather, I shall just try to highlight what is at issue.

The consituency relation is, of course, a part-whole relation. Part- whole relations are easy to come by within a connectionist framework. But it is far from clear how the relevant part-whole relation, the constituency relation, can be captured. It is instructive to consider two connectionist attempts to capture the constituency relation which fail. Suppose there is in a connectionist network a unit that represents the two-placed relation loving. One might take the representation of Michael’s loving Mary to be the set of these units. This is a notion of complexity, but not the right one. The subset relation does not suffice for the constituency relation. For, on this view, there is no distinguishing the representation of Michael’s loving Mary from the representation of Mary’s loving Michael. The same set of units corresponds to each. Suppose, then, that mental representations are sets of units and that a system contains a unit which represents Michael in the role of agent, another which represents him in the role of patient, one which represents Mary in the role of patient, another which represents her in the role of agent, and a unit which represents loving. Then, there will be distinct representations for Michael loves Mary and for Mary loves Michael. Such a connectionist model, however, still would not capture the notion of constituency. It could not, for example, distinguish a mental representatioin of Michael’s loving Mary and Bill’s hating Sam from a mental representation of Michael’s loving Sam and Bill’s hating Mary. For it provides no way to pair the right agents and patients. It thus does not capture constituent structure.

Turn, then, to Smolensky’s tensor product connectionism, which Tye claims can (or a t least may well be able to) capture constituent structure. Tye provides a detailed and lucid summary of tensor product connectionism, so I shall just briefly state its main features. O n this sort of connectionism, mental representations are vectors of units a t various levels of activity. These representations are “distributed,” since they are ordered sets of units. The units can have continuous levels of activation from 0 to 1. A pool or group of units can be filler units, or role units, or binding units. And activity vectors over binding units can be tensor products of activity vectors over filler and role units. To illustrate this model, consider a connectionist machine that can detect four letter words of English in its environment. The machine might be structured like this: it may have a group or pool of units some activity vectors of which represent the first letter position in a word, some activity vectors of which represent the second letter position in a word, some activity vectors which represent the third letter position in a word, and some activity vectors of which represent the fourth letter position in a word.

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This group of units is the group of role-units. The machine may also have a group of units activity vectors of which represent the various letters of the alphabet. This group is the group of filler-units. There may also be a third group of units whose activity vectors are tensor products of filler and role activity vectors. This group of units is the group of binding-units. Finally, there may be activity vectors over binding-units which are the superimposition vectors of tensor product vectors of filler and role units. Such activity vectors would represent four letter words. An important point should be noted: If certain conditions are satisfied, the filler and role activity vectors can be mathematically recovered from the tensor product activity vector.

Now, Tye maintains that if, for example, a system of mental representation is organized into filler, role, and binding units, then if it can represent the state of affairs of Michael’s loving Mary, it can represent the state of affairs of Mary’s loving Michael. More generally, he maintains that a tensor product connectionism may well be able to explain systematicity by appeal to constituent structure. But, of course, he has not shown that tensor product connectionism can explain the systematicity of mental representation by appeal to constituent structure.

As Smolensky explicitly notes, filler and role units can be “im- aginary.”That is to say, they need not actually be in the organism. It is clear why. The causal role of a tensor product activity vector over binding units in connectionist processes does not in any way depend on there actually being pools of role units and pools of filler units. Connectionist processes are exciting and inhibiting activities among units or pools of units. How a pool of binding units excites or inhibits other units or pools of units, will not depend on whether the role and filler activity vectors (of which activity vectors over binding units are tensor products) are themselves activity vectors over actual pools of units in the organism. On Smolensky’s view, then, a system of mental representation can contain a mental representation of Michael’s loving Mary without containing a representation of Michael, of loving, or of Mary. For mental representations are activity vectors over pools of units. And there may fail to be any pool of units whose activity vector is, for example, a representation of Michael.

Now one may, of course, require that there actually be pools of filler and role units in an organism. But, for one thing, I am uncertain what makes a pool of units a pool of filler units, a pool of role units, or a pool of binding units. If it is thecausal role of these units, one wold like to see the causal roles spelled out in detail. One wonders whether the causal roles will themselves constitute syntactic properties. But, in any case, as Smolensky notes, whether such pools of units are actually present or not will make no difference to the role of binding units in causal processes.

Constituency relations explain systematicity, in part, because the constituent structure of a complex mental representation determines its causal role in cognitive processes. On the standard language of thought

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view, a complex representation is a complex state that contains other mental representations as component states. And just as the syntactic properties of a complex representation are determined by its constituent structure, so the causal role of a complex representation is determined by the causal roles of its constituents. It is this correspondence between constituent syntactic structure and causal role that is invoked to explain systematicity. Smolensky’s tensor product connectionism, if I under- stand it, does not imply that the causal role of a complex mental representation is a function of the causal role of states which are mental representations and which are its components. Thus his tensor product connectionism does not have the explanatory resources of the standard language of thought view to appeal to in explaining systematicity. What is missing are appropriately constituent sensitive processes.5

NOTES

I This volume. 2 This argument and the views and arguments I attribute to Fodor and Pylyshyn below

can be found in Fodor and Pylyshyn, 1988. J Of course, a connectionist might grant that all minds happen to be systematic, but deny

that it is causally necessary that they are. 1 cannot pursue this here, however. 4 Smolensky presents his tensor product connectionism in Smolensky (a) and (b), both

forthcoming. I should note here that 1 shall be concerned exclusively with what Tye says about Smolensky’s theory and shall not be concerned with whether he has correctly interpreted Smolensky.

5 This paper has been improved as a result of discussions with Francis Egan, Jerry Fodor, Terence Horgan, Barry Loewer, Robert Mathews, and MichaelTye. 1 have drawn from lectures on connectionism given by Fodor at Rutgers University in the fall of 1987. He is, of course, in no way responsible for my interpretation of his views.

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BLOCK, Ned, 1982. Imagery. Cambridge, MIT Press

FODOR, Jerry, 1982. “Imagistic Representation,” in Block, 1982.

FODOR, Jerry, 1976. The Language of Thought, Cambridge, Harvard University Press.

FODOR, Jerryand Pylyshyn, Zenon, 1988. “Connectionism and Cognitive Architecture: A Critical Analysis,” Cognition 28, 3-71.

KOSSLYN, 1980. Image and Mind, Cambridge, Harvard.

KOSSLYN, 1983. Ghostsin the Mind’s Machine. New York, W. W. Norton.

McCLELLAND, J. L., Rumelhart, D. E., and Hinton, G. E. “The Appeal of Parallel Distributed Processing,” in Rumelhart and McClelland, Volume I .

RUMELHART and McClelland, and the P D P Research Group (eds.); 1986. Parallel Distributed Processing, Vol. I and Vol. 2 , Cambridge, MIT Press, Bradford Books.

SMOLENSKY, Paul. (a) Forthcoming, “A Method for Connectionist Variable Binding.”

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SMOLENSKY, Paul, (b) forthcoming. “On Variable Binding and the Representation of Symbolic Structures in Connectionist Systems.”

TY E, Michael. This volume, “Representation in Pictorialism and Connectionism.

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