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 discusses the relation between cognitive and implementational levels of analysis. Chalmers (1990, 1993) argues that a connectionist implementation of a classical cognitive architecture possesses a compositional semantics, and therefore undercuts Fodor and Pylyshyn's (1988) argument that connectionist networks cannot possess a compositional semantics. I argue that Chalmers argument misconstrues the relation between cognitive and implementational levels of analysis. This paper clarifies the distinction, and shows that while Fodor and Pylyshyn's argument survives Chalmers' critique, it cannot be used to (...) establish the irrelevance of neurophysiological implementation to cognitive modeling; some aspects of Chater and Oaksford's (1990) response to Fodor and Pylyshyn, though not all, are therefore cogent. (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)

Robert Cummins has argued that Jerry Fodor’s well-known systematicity argument begs the question. I show that the systematicity argument for thought structure does not beg the question, nor run in either explanatory nor inferential circles, nor illegitimately project sentence structure onto thoughts. Because the evidence does not presuppose that thought has structure, connectionist explanations of the same interconnections between thoughts are at least possibilities. Butthey are likely to be ad hoc.

Instead of using low-level neurophysiology mimicking and exploratory programming methods commonly used in the machine consciousness field, the hierarchical Operational Architectonics (OA) framework of brain and mind functioning proposes an alternative conceptual-theoretical framework as a new direction in the area of model-driven machine (robot) consciousness engineering. The unified brain-mind theoretical OA model explicitly captures (though in an informal way) the basic essence of brain functional architecture, which indeed constitutes a theory of consciousness. The OA describes the neurophysiological basis of the (...) phenomenal level of brain organization. In this context the problem of producing man-made “machine” consciousness and “artificial” thought is a matter of duplicating all levels of the operational architectonics hierarchy (with its inherent rules and mechanisms) found in the brain electromagnetic field. We hope that the conceptual-theoretical framework described in this paper will stimulate the interest of mathematicians and/or computer scientists to abstract and formalize principles of hierarchy of brain operations which are the building blocks for phenomenal consciousness and thought. (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)

Classical computational modellers of mind urge that the mind is something like a von Neumann computer operating over a system of symbols constituting a language of thought. Such an architecture, they argue, presents us with the best explanation of the compositionality, systematicity and productivity of thought. The language of thought hypothesis is supported by additional independent arguments made popular by Jerry Fodor. Paul Smolensky has developed a connectionist architecture he claims adequately explains compositionality, systematicity and productivity without positing any language (...) of thought, and without positing any operations over a set of symbols. This architecture encodes the information represented in linguistic trees without explicitly representing those trees or their constituents, and indeed without employing any representational vehicles with constituent structure. In a recent article, Fodor (1997; Connectionism and systematicity, Cognition , 62, 109-119) argues that Smolensky's proposal does not work. I defend Smolensky against Fodor's attack, and use this interchange as a vehicle for exploring and criticising the “Language of Thought” hypothesis more generally and the arguments Fodor adduces on its behalf. (shrink)

This paper responds to criticisms levelled by Fodor, Pylyshyn, and McLaughlin against connectionism. Specifically, I will rebut the charge that connectionists cannot account for representational systematicity without implementing a classical architecture. This will be accomplished by drawing on Paul Smolensky's Tensor Product model of representation and on his insights about split-level architectures.

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)

This paper presents considerations in favour of the view that traditional (classical) architectures can be seen as emergent features of connectionist networks with distributed representation. A recent paper by William Bechtel (1988) which argues for a similar conclusion is unsatisfactory in that it fails to consider whether the compositional syntax and semantics attributed to mental representations by classical models can emerge within a connectionist network. The compatibility of the two paradigms hinges largely, I suggest, on how this question is answered. (...) Focusing on the issue of syntax, I argue that while such structure is lacking in connectionist models with local representation, it can be accommodated within networks where representation is distributed. I discuss an important paper by Smolenski (1988) which attempts to show how connectionists can incorporate the relevant syntactic structure, suggesting that some criticisms levelled against that paper by Fodor & Pylyshyn (1988) are wanting. I then go on to indicate a strategy by which a compositional syntax and semantics can be defined for the sort of network that Smolenski describes. I conclude that since the connectionist can respect the central tenets of classicism, the two approaches are compatible with one another. (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)

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)

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

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)