Functional Combinatorialism

Abstract

One of the leading Connectionist responses to the systematicity arguments is to postulate that cognition involves functionally combinatorial representations rather than Classical concatenative representations. In a functionally combinatorial representation, no token of a syntactic and semantic atom need be a literal part of a token of a syntactic and semantic molecule to which it gives rise. Rather, a syntactic and semnatic atom is merely an argument to a function whose value is a syntactic and semantic molecule.1 Gödel numberings and Smolensky’s Tensor Product Theory are often offered as examples illustrating this idea.2 In this chapter, we shall consider what potential Gödel numberings and Tensor Product Theory have for explaining the numerous productive and systematic characteristics of thought. What we shall find is that, where Gödel numbers can explain the productivity of thought to the standard implicit there, neither theory of cognitive representation can explain the familiar systematic relations in thought. Further, neither of these forms of functionally combinatorial representations can explain the co-occurrence of the counterfactual dependence and content relatedness of possible occurrent thoughts. There is, therefore, some defeasible reason to prefer a Classical theory of cognition over a Functionally Combinatorial theory.