The Systematicity Arguments is the only book-length treatment of the systematicity and productivity arguments.

Fodor and Pylyshyn (1988) have argued that the cognitive architecture is not Connectionist. Their argument takes the following form: (1) the cognitive architecture is Classical; (2) Classicalism and Connectionism are incompatible; (3) therefore the cognitive architecture is not Connectionist. In this essay I argue that Fodor and Pylyshyn's defenses of (1) and (2) are inadequate. Their argument for (1), based on their claim that Classicalism best explains the systematicity of cognitive capacities, is an invalid instance of inference to the best (...) explanation. And their argument for (2) turns out to be question-begging. The upshot is that, while Fodor and Pylyshyn have presented Connectionists with the important empirical challenge of explaining systematicity, they have failed to provide sufficient reason for inferring that the cognitive architecture is Classical and not Connectionist. (shrink)

Fodor and Pylyshyn's critique of connectionism has posed a challenge to connectionists: Adequately explain such nomological regularities as systematicity and productivity without postulating a "language of thought" (LOT). Some connectionists like Smolensky took the challenge very seriously, and attempted to meet it by developing models that were supposed to be non-classical. At the core of these attempts lies the claim that connectionist models can provide a representational system with a combinatorial syntax and processes sensitive to syntactic structure. They are not (...) implementation models because, it is claimed, the way they obtain syntax and structure sensitivity is not "concatenative," hence "radically different" from the way classicists handle them. In this paper, I offer an analysis of what it is to physically satisfy/realize a formal system. In this context, I examine the minimal truth-conditions of LOT Hypothesis. From my analysis it will follow that concatenative realization of formal systems is irrelevant to LOTH since the very notion of LOT is indifferent to such an implementation level issue as concatenation. I will conclude that to the extent to which they can explain the law-like cognitive regularities, a certain class of connectionist models proposed as radical alternatives to the classical LOT paradigm will in fact turn out to be LOT models, even though new and potentially very exciting ones. (shrink)

This paper offers both a theoretical and an experimental perspective on the relationship between connectionist and Classical (symbol-processing) models. Firstly, a serious flaw in Fodor and Pylyshyn’s argument against connectionism is pointed out: if, in fact, a part of their argument is valid, then it establishes a conclusion quite different from that which they intend, a conclusion which is demonstrably false. The source of this flaw is traced to an underestimation of the differences between localist and distributed representation. It has (...) been claimed that distributed representations cannot support systematic operations, or that if they can, then they will be mere implementations of traditional ideas. This paper presents experimental evidence against this conclusion: distributed representations can be used to support direct structure-sensitive operations, in a man- ner quite unlike the Classical approach. Finally, it is argued that even if Fodor and Pylyshyn’s argument that connectionist models of compositionality must be mere implementations were correct, then this would still not be a serious argument against connectionism as a theory of mind. (shrink)

1. I think that by emphasizing theoretical spaces of representations, Andy has put his finger on an issue that is key to connectionism's success, and whose investigation will be a key determinant of the field's further progress. I also think that if we look at representational spaces in the right way, we can see that they are deeply related to classical phenomenon of systematicity in representation. I want to argue that the key to understanding representational spaces, and in particular their (...) ability to capture the deep organization underlying various problems, lies in the idea of what I will call. (shrink)

There has been much interest in the possibility of connectionist models whose representations can be endowed with compositional structure, and a variety of such models have been proposed. These models typically use distributed representations that arise from the functional composition of constituent parts. Functional composition and decomposition alone, however, yield only an implementation of classical symbolic theories. This paper explores the possibility of moving beyond implementation by exploiting holistic structure-sensitive operations on distributed representations. An experiment is performed using Pollack’s Recursive (...) Auto-Associative Memory. RAAM is used to construct distributed representations of syntactically structured sentences. A feed-forward network is then trained to operate directly on these representations, modeling syn- tactic transformations of the represented sentences. Successful training and generalization is obtained, demonstrating that the implicit structure present in these representations can be used for a kind of structure-sensitive processing unique to the connectionist domain. (shrink)

This paper explores the difference between Connectionist proposals for cognitive a r c h i t e c t u r e a n d t h e s o r t s o f m o d e l s t hat have traditionally been assum e d i n c o g n i t i v e s c i e n c e . W e c l a i m t h a t t h (...) e m a j o r d i s t i n c t i o n i s t h a t , w h i l e b o t h Connectionist and Classical architectures postulate representational mental states, the latter but not the former are committed to a symbol-level of representation, or to a ‘language of thought’: i.e., to representational states that have combinatorial syntactic and semantic structure. Several arguments for combinatorial structure in mental representations are then reviewed. These include arguments based on the ‘systematicity’ of mental representation: i.e., on the fact that cognitive capacities always exhibit certain symmetries, so that the ability to entertain a given thought implies the ability to entertain thoughts with semantically related contents. We claim that such arguments make a powerful case that mind/brain architecture is not Connectionist at the cognitive level. We then consider the possibility that Connectionism may provide an account of the neural (or ‘abstract neurological’) structures in which Classical cognitive architecture is implemented. We survey a n u m b e r o f t h e s t a n d a r d a r g u m e n t s t h a t h a v e b e e n o f f e r e d i n f a v o r o f Connectionism, and conclude that they are coherent only on this interpretation. (shrink)

The paper examines an alleged distinction claimed to exist by Van Gelder between two different, but equally acceptable ways of accounting for the systematicity of cognitive output (two varieties of compositionality): concatenative compositionality vs. functional compositionality. The second is supposed to provide an explanation alternative to the Language of Thought Hypothesis. I contend that, if the definition of concatenative compositionality is taken in a different way from the official one given by Van Gelder (but one suggested by some of his (...) formulations) then there is indeed a different sort of compositionality; however, the second variety is not an alternative to the language of thought in that case. On the other hand, if the concept of concatenative compositionality is taken in a different way, along the lines of Van Gelder's explicit definition, then there is no reason to think that there is an alternative way of explaining systematicity. (shrink)

In his discussion of results which I (with Michael Hayward) recently reported in this journal, Kenneth Aizawa takes issue with two of our conclusions, which are: (a) that our connectionist model provides a basis for explaining systematicity within the realm of sentence comprehension, and subject to a limited range of syntax (b) that the model does not employ structure-sensitive processing, and that this is clearly true in the early stages of the network''s training. Ultimately, Aizawa rejects both (a) and (b) (...) for reasons which I think are ill-founded. In what follows, I offer a defense of our position. In particular, I argue (1) that Aizawa adopts a standard of explanation that many accepted scientific explanations could not meet, and (2) that Aizawa misconstrues the relevant meaning of structure-sensitive process. (shrink)

Fodor's and Pylyshyn's stand on systematicity in thought and language has been debated and criticized. Van Gelder and Niklasson, among others, have argued that Fodor and Pylyshyn offer no precise definition of systematicity. However, our concern here is with a learning based formulation of that concept. In particular, Hadley has proposed that a network exhibits strong semantic systematicity when, as a result of training, it can assign appropriate meaning representations to novel sentences (both simple and embedded) which contain words in (...) syntactic positions they did not occupy during training. The experience of researchers indicates that strong systematicity in any form is difficult to achieve in connectionist systems.Herein we describe a network which displays strong semantic systematicity in response to Hebbian, connectionist training. During training, two-thirds of all nouns are presented only in a single syntactic position (either as grammatical subject or object). Yet, during testing, the network correctly interprets thousands of sentences containing those nouns in novel positions. In addition, the network generalizes to novel levels of embedding. Successful training requires a, corpus of about 1000 sentences, and network training is quite rapid. The architecture and learning algorithms are purely connectionist, but classical insights are discernible in one respect, viz, that complex semantic representations spatially contain their semantic constituents. However, in other important respects, the architecture is distinctly non-classical. (shrink)

This paper investigates connectionism's potential to solve the frame problem. The frame problem arises in the context of modelling the human ability to see the relevant consequences of events in a situation. It has been claimed to be unsolvable for classical cognitive science, but easily manageable for connectionism. We will focus on a representational approach to the frame problem which advocates the use of intrinsic representations. We argue that although connectionism's distributed representations may look promising from this perspective, doubts can (...) be raised about the potential of distributed representations to allow large amounts of complexly structured information to be adequately encoded and processed. It is questionable whether connectionist models that are claimed to effectively represent structured information can be scaled up to a realistic extent. We conclude that the frame problem provides a difficulty to connectionism that is no less serious than the obstacle it constitutes for classical cognitive science. (shrink)

Fodor and Pylyshyn (1988), Fodor and McLaughlin (1990) and McLaughlin (1993) challenge connectionists to explain systematicity without simply implementing a classical architecture. In this paper I argue that what makes the challenge difficult for connectionists to meet has less to do with what is to be explained than with what is to count as an explanation. Fodor et al. are prepared to admit as explanatory, accounts of a sort that only classical models can provide. If connectionists are to meet the (...) challenge, they are going to have to insist on the propriety of changing what counts as an explanation of systematicity. Once that is done, there would seem to be as yet no reason to suppose that connectionists are unable to explain systematicity. (shrink)

In 1988 Fodor and Pylyshyn issued a challenge to the newly-popular connectionism: explain the systematicity of cognition without merely implementing a so-called classical architecture. Since that time quite a number of connectionist models have been put forward, either by their designers or by others, as in some measure demonstrating that the challenge can be met (e.g., Pollack, 1988, 1990; Smolensky, 1990; Chalmers, 1990; Niklasson and Sharkey, 1992; Brousse, 1993). Unfortu- nately, it has generally been unclear whether these models actually do (...) have this implication (see, for instance, the extensive philosophical debate in Smolensky, 1988; Fodor and McLaughlin, 1990; van Gelder, 1990, 1991; McLaughlin, 1993a, 1993b; Clark, 1993). Indeed, we know of no major supporter of classical orthodoxy who has felt compelled, by connectionist models and argu- ments, to concede in print that connectionists have in fact delivered a non-classical explanation of systematicity. (shrink)

One of the hallmarks of human cognition is the capacity to generalize over arbitrary constituents. Recently, Marcus (1998, 1998a, b; Cognition 66, p. 153; Cognitive Psychology 37, p. 243) argued that this capacity, called universal generalization (universality), is not supported by Connectionist models. Instead, universality is best explained by Classical symbol systems, with Connectionism as its implementation. Here it is argued that universality is also a problem for Classicism in that the syntax-sensitive rules that are supposed to provide causal explanations (...) of mental processes are either too strict, precluding possible generalizations; or too lax, providing no information as to the appropriate alternative. Consequently, universality is not explained by a Classical theory. (shrink)

In an influential critique, Jerry Fodor and Zenon Pylyshyn point to the existence of a potentially devastating dilemma for connectionism (Fodor and Pylyshyn [1988]). Either connectionist models consist in mere associations of unstructured representations, or they consist in processes involving complex representations. If the former, connectionism is mere associationism, and will not be capable of accounting for very much of cognition. If the latter, then connectionist models concern only the implementation of cognitive processes, and are, therefore, not informative at the (...) level of cognition. I shall argue that Fodor and Pylyshyn's argument is based on a crucial misunderstanding, the same misunderstanding which motivates the entire language of thought hypothesis. (shrink)

Martin Davies' criterion for the knowledge of implicit rules, viz. the causal systematicity of cognitive processes, is first exposed. Then the inference from causal systematicity of a process to syntactic properties of the input states is examined. It is argued that Davies' notion of a syntactic property is too weak to bear the conclusion that causal systematicity implies a language of thought as far as the input states are concerned. Next, it is shown that Davies' criterion leads to a counterintuitive (...) consequence: it groups together distributed connectionist systems with look-up tables. To avoid this consequence, a modified construal of causal systematicity is proposed and Davies' argument for the causal systematicity of thought is shown to be question-begging. It is briefly sketched how the modified construal links up with multiple dispositions of the same categorical base. Finally, the question of the causal efficacy of single rules is distinguished from the question of their psychological reality: implicit rules might be psychologically real without being causally efficacious. (shrink)

Department of Computer Science Philosophy Program, Research School of Social Sciences University of Skövde, S-54128, SWEDEN Australian National University, Canberra ACT 0200.

In 1988 Fodor and Pylyshyn issued a challenge to the newly-popular connectionism: explain the systematicity of cognition without merely implementing a so-called classical architecture. Since that time quite a number of connectionist models have been put forward, either by their designers or by others, as in some measure demonstrating that the challenge can be met (e.g., Pollack, 1988, 1990; Smolensky, 1990; Chalmers, 1990; Niklasson and Sharkey, 1992; Brousse, 1993). Unfortu- nately, it has generally been unclear whether these models actually do (...) have this implication (see, for instance, the extensive philosophical debate in Smolensky, 1988; Fodor and McLaughlin, 1990; van Gelder, 1990, 1991; McLaughlin, 1993a, 1993b; Clark, 1993). Indeed, we know of no major supporter of classical orthodoxy who has felt compelled, by connectionist models and argu- ments, to concede in print that connectionists have in fact delivered a non-classical explanation of systematicity. (shrink)

Figure 1: A pr ototyp ical exa mple of a three-layer feed forward network, used by Plunkett and M archm an (1 991 ) to simulate learning the past-tense of En glish verbs. The inpu t units encode representations of the three phonemes of the present tense of the artificial words used in this simulation. Th e netwo rk is trained to produce a representation of the phonemes employed in the past tense form and the suffix (/d/, /ed/, or /t/) (...) used on regular verbs. To run the network, each input unit is assigned an activation value o f 0 or 1 , dep ending on whethe r the featu re is present or not. Eac h input unit is conne cted to each of the 30 hidden units by a we ighted conn ection and p rovid es an inp ut to each hidden unit equal to the product of the input unit's activation and the weight. Each hidd en unit's activation is then determined by summing ov er the va lues co ming fro m each inp ut unit to deter mine a netinput, and then applying a non-linear function (e.g., the logistic function 1/(1+e^netinput). Th is whole proced ure is. (shrink)

The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the (...) fact that we have learned natural languages which are themselves syntactically structured. According to this view, symbols of natural language are external to the cognitive processing system and what the cognitive system must learn to do is produce and comprehend such symbols. In this paper I pursue that idea by arguing that ability in natural deduction itself may rely on pattern recognition abilities that enable us to operate on external symbols rather than encodings of rules that might be applied to internal representations. To support this suggestion, I present a series of experiments with connectionist networks that have been trained to construct simple natural deductions in sentential logic. These networks not only succeed in reconstructing the derivations on which they have been trained, but in constructing new derivations that are only similar to the ones on which they have been trained. (shrink)

Connectionism provides hope for unifying work in neuroscience, computer science, and cognitive psychology. This promise has met with some resistance from Classical Computionalists, which may have inspired Connectionists to retaliate with bold, inflationary claims on behalf of Connectionist models. This paper demonstrates, by examining three intimately connected issues, that these inflationary claims made on behalf of Connectionism are wrong. This should not be construed as an attack on Connectionism, however, since the inflated claims made on its behalf have the look (...) of cures for which there are no ailments. There is nothing wrong with Connectionism for its failure to solve illusory problems. (shrink)

Jerry Fodor and Ernest Lepore [(1992) Holism: a shopper's guide, Oxford: Blackwell; (1996) in R. McCauley (Ed.) The Churchlands and their critics , Cambridge: Blackwell] have launched a powerful attack against Paul Churchland's connectionist theory of semantics--also known as state space semantics. In one part of their attack, Fodor and Lepore argue that the architectural and functional idiosyncrasies of connectionist networks preclude us from articulating a notion of conceptual similarity applicable to state space semantics. Aarre Laakso and Gary Cottrell [(1998) (...) in M. A. Gernsbacher & S. Derry (Eds) Proceedings of the 20th Annual Conference of the Cognitive Science Society, Mahway, NJ: Erlbaum; Philosophical Psychology ] 13, 47-76 have recently run a number of simulations on simple feedforward networks and applied a mathematical technique for measuring conceptual similarity in the representational spaces of those networks. Laakso and Cottrell contend that their results decisively refute Fodor and Lepore's criticisms. Paul Churchland [(1998) Journal of Philosophy, 95, 5-32 ] goes further. He uses Laakso and Cottrell's neurosimulations to argue that connectionism does furnish us with all we need to construct a robust theory of semantics and a robust theory of translation. In this paper I shall argue that whereas Laakso and Cottrell's neurocomputational results may provide us with a rebuttal of Fodor and Lepore's argument, Churchland's conclusion is far too optimistic. In particular, I shall try to show that connectionist modelling does not provide any objective criterion for achieving a one-to-one accurate translational mapping across networks. (shrink)

As Ruben notes, the macrostrategy can allow that the distinction may also be drawn at some micro level, but it insists that descent to the micro level is ...

The character of computational modelling of cognition depends on an underlying theory of representation. Classical cognitive science has exploited the syntax/semantics theory of representation that derives from logic. But this has had the consequence that the kind of psychological explanation supported by classical cognitive science is

_conceptualist_:

psychological phenomena are modelled in terms of relations that hold between concepts, and between the sensors/effectors and concepts. This kind of explanation is inappropriate for the Proper Treatment of Connectionism (Smolensky 1988).

There has been a long-standing debate between symbolicists and connectionists concerning the nature of representation used by human cognizers. In general, symbolicist commitments have allowed them to provide superior models of high-level cognitive function. In contrast, connectionist distributed representations are preferred for providing a description of low-level cognition. The development of Holographic Reduced Representations (HRRs) has opened the possibility of one representational medium unifying both low-level and high-level descriptions of cognition. This paper describes the relative strengths and weaknesses of symbolic (...) and distributed representations. HRRs are shown to capture the important strengths of both types of representation. These properties of HRRs allow a rebuttal of Fodor and McLaughlin's (1990) criticism that distributed representations are not adequately structure sensitive to provide a full account of human cognition. (shrink)

Jerry Fodor and Ernest Lepore [(1992) Holism: a shopper's guide, Oxford: Blackwell; (1996) in R. McCauley (Ed.) The Churchlands and their critics , Cambridge: Blackwell] have launched a powerful attack against Paul Churchland's connectionist theory of semantics--also known as state space semantics. In one part of their attack, Fodor and Lepore argue that the architectural and functional idiosyncrasies of connectionist networks preclude us from articulating a notion of conceptual similarity applicable to state space semantics. Aarre Laakso and Gary Cottrell [(1998) (...) in M. A. Gernsbacher & S. Derry (Eds) Proceedings of the 20th Annual Conference of the Cognitive Science Society, Mahway, NJ: Erlbaum; Philosophical Psychology ] 13, 47-76 have recently run a number of simulations on simple feedforward networks and applied a mathematical technique for measuring conceptual similarity in the representational spaces of those networks. Laakso and Cottrell contend that their results decisively refute Fodor and Lepore's criticisms. Paul Churchland [(1998) Journal of Philosophy, 95, 5-32 ] goes further. He uses Laakso and Cottrell's neurosimulations to argue that connectionism does furnish us with all we need to construct a robust theory of semantics and a robust theory of translation. In this paper I shall argue that whereas Laakso and Cottrell's neurocomputational results may provide us with a rebuttal of Fodor and Lepore's argument, Churchland's conclusion is far too optimistic. In particular, I shall try to show that connectionist modelling does not provide any objective criterion for achieving a one-to-one accurate translational mapping across networks. (shrink)

A similarity space is a hyperspace in which the dimensions represent various dimensions on which objects may differ. The similarity space theory of concepts is the thesis that concepts are regions of similarity spaces that are somehow realized in the brain. Proponents of such a theory of concepts include Paul Churchland and Peter Gärdenfors. This paper argues that the similarity space theory of concepts is mistaken because regions of similarity spaces cannot serve as the components of judgments. It emerges that (...) although similarity spaces cannot model concepts, they may model a kind of nonconceptual representation. (shrink)