Systematicity and Cognitive Architecture

1. Systematicity and Cognitive Architecture • In “Connectionism and Cognitive Architecture: A Critical Analysis” (1988), Fodor and Pylyshyn pose several challenges for any connectionist theory of cognitive architecture.

2. The Systematicity Challenge • One is to explain the systematicity of thought without implementing a classical cognitive architecture.

3. The Language of Thought (LOT) • By `a classical cognitive architecture’ they mean a Language of Thought (LOT) architecture.

4. A LOT architecture includes a mental symbol system with a compositional semantics—so that the semantic value of a molecular mental symbol is a function of the semantic values of the atomic mental symbols that are its constituents together with the syntactic structure of the molecular symbol—, and includes computational operations that molecular symbols participate in in virtue of their syntactic and other formal properties.

5. By the LOT hypothesis, let’s mean the hypothesis that the cognitive architecture of beings with the ability to think includes a kind of LOT architecture.

6. A Dilemma • The systematicity challenge presents a dilemma. • If connectionism cannot explain the systematicity of thought, then it fails to offer an adequate theory of cognitive architecture; and • if it explains the systematicity of thought by implementing a LOT architecture, then it fails to offer an alternative to the LOT hypothesis.

7. Given that thought is systematic, connectionism can offer an adequate alternative to the LOT hypothesis only if it can meet this challenge.

8. Critical Reaction • Critical reaction to the challenge was divided. • Some critics tried to meet the challenge. • Some argued that it need not be met since thought is not in fact systematic. • And some claimed not to even understand the claim that thought is systematic.

9. What I’ll do today is defend the challenge by explicating the notion of systematicity in a way that I hope makes clear that thought is indeed systematic.

10. In their 1988 paper, Fodor and Pylyshyn claim both that thoughts and that linguist abilities are systematic, but they did not state non-circular necessary and sufficient conditions for the property of being systematic; nor has either of them offered such in any subsequent works.

11. A Complaint • Matthews (1994), Niklasson and van Gelder (1994), van Gelder and Niklason (1994), Hadley (1997), Johnson (2004) and others have complained about the lack of a definition of systematicity.

12. No Definition • I think that no definition is to be had.

13. However, that is no objection to the systematicity challenge. • How often can something a scientific theory is challenged to explain be characterized by non-circular necessary and sufficient conditions?

14. Still the locution `the systematicity of thought’ is a technical one, and the absence of a definition has led to much speculation about what the claim that thought is systematic means.

15. I’ll now begin to spell that out. • Then, I will discuss a misguided attempts to spell the thesis out by Kent Johnson (2004). • I’ll conclude with an explication of the systematicity challenge.

16. Issue Not Computational Power • It should be noted first of all that the systematicity challenge is not generated by skepticism about the computational powers of multi-layered connectionist networks.

17. Such networks are Turing-equivalent. • Computational power is thus not the issue. • The challenge is thus not, as some respondents have mistakenly thought (e.g., Chalmers 1990), to show that a connectionist network can compute certain functions, such as, for instance, linguistic functions.

18. Further, as is not doubt already obvious from how the systematicity challenge is stated, implementational connectionism is not at issue. • (It is worth noting that Turing machines and production systems have been implemented by connectionist architectures.)

19. Explaining Laws • The challenge is, rather, generated by skepticism about the prospects for explaining certain psychological laws by appeal to a connectionist architecture that does not implement a LOT architecture.

20. By `a psychological law’ I mean here simply a psychological generalization that is true (at least ceteris paribus) and counterfactual supporting. • Explaining the systematicity of thought is just matter of explaining the psychological laws in question.

21. Systematicity Laws • Let’s call the laws in question “systematicity laws.” • The thesis that thought is systematic amounts to the thesis that there is a family of systematicity laws. • The task of characterizing the systematicity of thought is thus that of saying what laws are systematicity laws.

22. Systematicity laws are correlation laws. • They assert the co-possession of the members of certain pairs of thought abilities. • They are all laws to the effect that ceteris paribus, a cognizer has a certain thought ability if and only if the cognizer has a certain other thought ability.

23. The thought abilities in question are abilities to think certain thoughts. • There are, however, no non-circular necessary and sufficient conditions for a pair of abilities to think certain thoughts being one of the pairs in question; as least none that would not be regarded by some as question-begging in the present dialectical context; and so there are no non-circular necessary and sufficient conditions for being a systematicity law.

24. But I think that enough can be said by way of indicating the sorts of laws in question for the purpose of posing the systematicity challenge. • Of that, more later.

25. Productivity of Thought • Fodor and Pylyshyn (1988) pose the systematicity challenge after posing the productivity challenge: the challenge to explain the productivity of thought by appeal to a connectionist architecture that does not implement a LOT architecture. • The claim that thought is productive is the claim that a thinker is, in principle, able to think an unbounded number of thoughts.

26. Constituent Structures • Fodor and Pylyshyn press the productivity challenge to make apparent the need to postulate mental representations with constituent structures.

27. Idealization • But the claim that thought is productive involves idealization. • A human, being a finite creature, can’t actually think an unbounded number of thoughts.

28. Acknowledging that some connectionists (e.g., Rumelhart and McClelland (1986, p. 191)) reject idealizations to unbounded cognitive abilities, Fodor and Pylyshyn claim that appeal to the systematicity of thought, which involves no such idealization, suffices to make the case that mental representations have constituent structures.

29. The idea of thought-productivity is that any being able to have a thought would in principle be able to have an unbounded number of thoughts. • The kernal of the idea that thought is systematic is that any being able to have a thought would be able to have a family of other thoughts, whose members have related (though non-equivalent) contents.

30. Abilities to have thoughts come in clusters, so that there are no cognizers with punctuate thought abilities or the ability to think, say, 27 semantically unrelated thoughts.

31. The idea that thought abilities come in clusters can be captured by saying that they come in pairs, where it is understood that a given thought ability can be a member of more than one pair. • The pairs are such that ceteris paribus, a cognizer has one member if and only if the cognizer has the other.

32. A Paradigm • A paradigm example from the literature of a pair of systematically related thought abilities is the ability to think the thought that John loves Mary and the ability to think the thought that Mary loves John. • One can of course think that John loves Mary without thinking that Mary loves John. • But the idea is that ceteris paribus, anyone able to think the one thought would be able to think the other.

33. A Schema • This idea can be generalized by appeal to a predicate logic sentence schema: `Ceteris paribus, a cognizer is able to think the thought that aRb if and only if the cognizer is able to think the thought that bRa’. • The claim is that generalizations that are instances of this schema are true and counterfactual supporting, and so are in that sense psychological laws. • Instances of this schema are members the family of systemacity laws, and so are among the psychological laws that connectionism is being challenged to explain.

34. Other laws of systematicity are, like the instances of this of schema, quite low-level laws. • They all specify what it is the thought abilities they cite are abilities to think, rather than quantifying over what the thought abilities are abilities to think. • They are laws, to repeat, in the sense that they are true, counterfactual supporting generalizations.

35. Strategy • I have here employed a strategy common in the literature for identifying systematicity laws. • The strategy is to identify them by appeal to sentence schemata the instances of which are systematicity laws.

36. In their 1988 paper, Fodor and Pylyshyn appealed to a schema only once in their discussion of the systematicity of thought (p.30).

37. But schemata are widely used elsewhere in the literature on systematicity; see, for example, McLaughlin (1987), Fodor and McLaughlin (1990), Fodor and Lepore (1992), McLaughlin (1993a), (1993b), (1997), and Aizawa (2003). • I will state further such schemata later.

38. I have here also followed Fodor and Pylyshyn’s practice of characterizing the thought abilities in question as abilities to think certain thoughts.

39. Use of the locution `think the thought that’ has, however, led to misunderstandings in some quarters. • This expression suggests the ability to occurently think something or to believe something. • But in fact that is not what is intended.

40. Representational Theory of Mind • Fodor and Pylyshyn embrace a representational theory of mind. • According that theory, believing that p, occurrently thinking that p, desiring that p, intending that p, imagining, hoping, wishing, fearing, considering whether p, as well as simply entertaining the thought that p, all involve mentally representing that p.

41. By `think the thought that p’ Fodor and Pylyshyn mean mentally represent that p. • And they take mentally representing that p to involve having a mental representation that means that p. • What makes the type of representation in question a mental representation is that it can function in the cognizer’s cognitive economy in such a way that its content is the content of a propositional attitude of the cognizer.

42. The relevant thought abilities—the ones that are systematically related, related by systematicity laws—are thus abilities to have mental representations with propositional contents (contents expressible by that-clauses) that are the contents of propositional attitudes the cognizer is able to have.

43. Failure to appreciate that `thinks the thought that’ is to be understood as `mentally represent that’ has led to some misguided objections to the schema stated earlier, namely • `Ceteris paribus, a cognizer is able to think the thought that aRb if and only if the cognizer is able to think the thought that bRa’.

44. Matthews (1994) claims that someone can think that x is the sole member of {x} yet be unable to think that {x} is the sole member of x. • Here `think that’ is used to mean believe that (or occurrently think that), rather than to mean mentally represent that.

45. But given how `thinks the thought that’ is to be understood, the relevant schema is actually this: `Ceteris paribus, anyone able to mentally represent that aRb is able to mentally represent that bRa’.

46. Even where `Tom’ is, say, the name of a person, the sentence `Ceteris paribus, a cognizer is able to mentally represent that Tom is the sole member of {Tom} if and only if the cognizer is able to mentally represent that {Tom} is the sole member of Tom’ is an instance of this schema. • And that generalization is true and counterfactual supporting.

47. One mentally represents that {Tom} is the sole member of Tom when one disbelieves that {Tom} is the sole member of Tom (perhaps taking it to be necessarily false that Tom even has members in the sense in question). • Disbelief differs of course from non-belief. • One disbelieves that p if and only if one believes that not-p.

48. Given the reading that `thinks the thought that’ naturally invites, the misunderstanding in question is perhaps understandable (though I believe that typically surrounding texts in the relevant literature should have made the intended interpretation clear). • As we’ll see later, however, some other misunderstandings of such schemata in the literature are harder to understand, and seem to be the result of misunderstandings of how schemata are used.

49. Connectionists that deny that there are mental representations will of course reject the systematicity challenge on the grounds that there are no mental representations to be systematically related.

50. But the systematicity challenge is aimed at connectionists that posit mental representations, whether they take a mental representation to be an activated unit in a connectionist network (and so “local”) or instead to be a pattern of activation over a groups of units in a network (and so “distributed”).