Christopher D. Green (1998) Statistical Analyses do not Solve Connectionism's Problem. Psycoloquy: 9(15) Connectionist Explanation (12)

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PSYCOLOQUY (ISSN 1055-0143) is sponsored by the American Psychological Association (APA).
Psycoloquy 9(15): Statistical Analyses do not Solve Connectionism's Problem

Reply to Medler & Dawson on Connectionist-Explanation

Christopher D. Green
Department of Psychology
York University
Toronto, Ontario M3J 1P3


Medler & Dawson (1998) claim (1) that I am just a closet implementationalist, (2) that I have ignored a range of statistical analyses that answer my challenge to connectionism, and (3) that only connectionist networks can produce explanatory models of cognition. I reply that I am not an implementationalist, that the statistical analyses to which they refer do not solve the problem I have posed, and that the question of whether a theory is explanatory is independent of the question of how it was generated.


artificial intelligence, cognition, computer modelling, connectionism, epistemology, explanation, methodology, neural nets, philosophy of science, theory.
1. Medler & Dawson (1998) argue that interpretations of the internal workings of connectionist networks other than neurological ones are possible and that my critique of connectionism (Green 1998a) accordingly fails. In particular, they promote "banding analysis" of hidden unit activities, developed by Berkeley, Dawson, Medler, Schopflocher, & Hornsby (1995). They go on to argue that this approach to theory development is actually preferable to the traditional approach to cognitive theorizing because it results in explanatory rather than merely descriptive theories. By contrast, I argue (1) that they have misunderstood a key portion of my argument; (2) that "banding analysis" and other statistical approaches to the interpretation of connectionist networks do not evade my critique; and (3) that it is neither true that traditional approaches to cognitive theorizing necessarily result in descriptive theories nor that the connectionist approach necessarily results in explanatory ones.

2. Medler & Dawson claim that I adopt the "mere-implementation argument of Fodor and Pylyshyn (1988)," and that I believe that connectionist networks "are a mere implementation of some cognitive theory" (para. 2). It is hard to know why they think this. I explicitly distance myself from the Fodor-Pylyshyn argument, and I never make any claims about implementation at all. Indeed, if I believed that connectionist networks must implement symbol systems, the answer to my question, "What theory, precisely, is embodied by the net?" would be entirely obvious: it would be the symbol system thus implemented, couched in the vocabulary of symbolic representations (beliefs, desires, etc.). In fact, this is precisely the claim of Fodor and Pylyshyn's "implementationalism" and, as far as I can tell, it evades my critique of connectionism entirely by offering a comprehensible interpretation of the activity of the network, one pitched more or less at the folk-psychological level. My critique only has force to the degree that connectionists reject Fodor and Pylyshyn's implementationalism (and they seem to, almost without exception). By contrast, my concern was with connectionists who, on the one hand, reject implementationalism and, on the other, are reluctant to argue that their models constitute serious attempts to model brain activity directly. These are the folks whose models would seem to have no domain, and I would venture to guess that they comprise the vast majority of connectionists.

3. Medler & Dawson go on to argue that there is a whole range of interpretational techniques with respect to connectionist networks that I have ignored and that, if acknowledged, would undercut my argument. These include cluster and factor analyses of network weights, as well as their own very intriguing "banding analysis." As far as I can tell, however, they have confused the techniques one uses to obtain a theory with the nature of the theory itself. To the degree that one takes the result of a multivariate statistical analysis seriously, one ends up with a fairly straightforward symbolic theory. Using NETtalk (Sejnowski & Rosenberg, 1987) as an example, what were found were statistical clusters corresponding more or less to the distinctions of traditional phonetics. The fact that the clusters did not correspond EXACTLY to traditional phonetics does not make the model any less symbolic; it is just a variant or "deviant" form of traditional phonetics. Note that I said this follows ONLY TO THE DEGREE THAT ONE TAKES THE RESULTS OF THE ANALYSIS SERIOUSLY. Most connectionists attempt to distance themselves from the results of such analyses in one way or another because to accept them at face value would be to accept nothing less than Fodor and Pylyshyn's implementationalism.

4. Clark's (1993) position on the NETtalk cluster analysis serves as a good example of this sort of ambivalence, and one I discussed in a reply to a previous psycoloquy commentator (Green, 1998b). On the one hand, Clark uses NETtalk as a prime instance of just how powerful connectionist networks can be, but then he warns his readers off, saying that such analyses "must be treated with caution" because they "typically transform dynamic processing characteristics of a network...into static structures" and "foster the illusion that the system has generated internal symbols" (p. 60). So what's it going to be? Either the analysis shows that the machine is, in effect, processing traditional phonetics, in which case one must swallow Fodor and Pylyshyn's implementationalism, or its advocates must find another domain for it to be modeling. If that "other" domain is not neural activity, then what is it? This is the challenge I posed to connectionists, and it remains, as far as I can see, unanswered by Medler & Dawson's commentary.

5. As for banding analysis, it is a truly fascinating innovation, but I do not think it shows what Medler & Dawson think it does. To review, Berkeley et al. (1995) showed that Bechtel and Abrahamsen's (1991) deductive reasoning network appears to use rules that are similar but not identical to those used in traditional propositional calculus (PC). Dawson, Medler, & Berkeley (1997) then urged that this outcome NOT be understood in implementationalist terms (i.e., that the network simply implements a symbolic quasi-logical system). That is, like many other connectionists, they tried to distance themselves from the apparently symbolic nature of their own results. Their argument, however, remains obscure to me. It seems as though Dawson et al. believe that simply because the rules the network appears to use differ somewhat from those of traditional PC it follows that the system is somehow not symbolic. I cannot see why this would be the case, however. The fact that the network implements a "deviant" logical system does not thereby make it non-symbolic. If the result is taken seriously, it is just as symbolic as, say, Wason and Johnson-Laird's (1972, pp. 90-92) "defective truth table" theory of reasoning. Its having been derived by a different method is neither here nor there with respect to the question of whether the theory is, in the end, symbolic.

6. There is of course a way out for Dawson et al. They can claim, as numerous connectionists have done in the past, that the symbolic bands they found only "approximate" the activity of the network; that they are not to be taken seriously as the theory of reasoning it embodies; that only the activity of the network itself, in all its variegated detail, is the real theory. But if they take this opening, then they are left facing the very challenge I posed in the target article: if it is not mentally represented quasi-logical rules that we are talking about then what exactly is the domain of your theory? Are the nodes and connections meant to map onto neurons? If the network maps neither onto beliefs about logic (in which case it would be symbolic), nor onto neurons or some similar elements of the brain (in which case it would essentially be eliminativist), then what exactly does it map onto with respect to cognition?

7. Last we come to the question of descriptive vs. explanatory theories. Medler & Dawson seem to claim that cognitive models as traditionally conceived must, for that very reason, be merely descriptive, whereas models conceived through a process of connectionist computation must, for that very reason, be explanatory. I can see no merit at all to this argument. Chomsky's theory of grammar is as traditional a symbolic theory as one is ever likely to see (no doubt in part because it virtually defines that tradition). Regardless of whether one adheres to it or not, it cannot be denied that its aim is to be explanatory. (Let us not confuse, here, the age-old issue of whether a theory is a legitimate CANDIDATE for being explanatory with the issue of whether it SUCCEEDS in doing so. Even among those theories that we believe to be false, we can distinguish those that WOULD HAVE BEEN explanatory if they had been true from those that would NOT have been explanatory, even if true. Chomsky's theory is surely to be placed among the former even by those would believe it to be false.)

8. Just to make the point a little sharper, Newton's laws of motion were derived in the traditional way, but few would deny that they are explanatory. Why should we treat cognitive science any differently? On the other side of the coin, there are all manner of connectionist networks whose outcomes are merely descriptive. Indeed, I would think that everyone who uses such nets as tools (e.g., as predictors of stock prices) would say that they merely "describe" stock fluctuations without explaining anything at all significant about the stock market. Indeed, in the absence of plausible, a priori, theoretical constraints, connectionist networks are little more than very powerful "curve-fitters" -- just about as Baconian as one can get. In fact, Medler & Dawson admit as much when, on the authority of Seidenberg (1993), they say that in order to be explanatory, connectionist models of cognition must be "neurobiologically relevant." But this is virtually the claim made in my original target article. So what exactly are we arguing about again?

9. To conclude, Medler & Dawson claimed that my argument amounts to little more than a repetition of Fodor and Pylyshyn's implementationalism. I disagreed, and argued, by contrast, that if I were an implementationalist, then the challenge I posed to connectionists would have no force. Second, they argued that I had ignored techniques for the interpretation of the activity of connectionist networks that undercut my challenge. I replied by showing that such techniques fail to respond adequately, and are sometimes used to obfuscate the real issue of just what domain is being modeled by connectionist networks. Third, they argued that traditional symbolic models result in merely descriptive theories, whereas connectionist models result in explanatory ones. I presented counterexamples refuting both sides of their claim.


Bechtel, W., & Abrahamsen, A. (1991). Connectionism and the MIND: an Introduction to Parallel Processing in Networks. Cambridge, MA: Blackwell.

Berkeley, I.S.N., Dawson, M.R.W., Medler, D.A., Schopflocher, D.P., & Hornsby, L. (1995) Density plots of hidden unit activations reveal interpretable bands. Connection Science, 7, 167-186.

Clark, A. (1993). Associative Engines: Connectionism, Concepts, and Representational Change. Cambridge, MA: MIT Press.

Dawson, M.R.W., Medler, D.A., & Berkeley, I.S.N. (1997). PDP networks can provide symbolic models that are nor mere implementations of classical theories. Philosophical Psychology, 10, 25-40.

Fodor, J. A. & Pylyshyn, Z. W. (1988) Connectionism and cognitive architecture: A critical analysis. Cognition, 28, 3-71.

Green, C. D. (1998a) Are connectionist models theories of cognition? PSYCOLOQUY 9(4)

Green, C. D. (1998b) Problems with the implementation argument. PSYCOLOQUY 9(8)

Medler, D. A. & Dawson, M. R. W. (1998) Connectionism and cognitive theories: Commentary on Green on connectionist- explanation. PSYCOLOQUY 9(11) psyc.98.9.11.connectionist-explanation.8.medler

Seidenberg, M. (1993). Connectionist models and cognitive science. Psychological Science, 4, 228-235.

Sejnowksi, T. & Rosenberg, C. (1987) Parallel networks that learn to pronounce English text. Complex Systems, 1, 145-168.

Wason, P. C. & Johnson-Laird, P. N. (1972). Psychology of Reasoning: Structure and Content. Cambridge, MA: Harvard University Press.

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