Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of (...) composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complex has a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called 'strong compositionality'. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl. (shrink)

In "Representations without Rules, Connectionism and the Syntactic Argument'', Kenneth Aizawa argues against the view that connectionist nets can be understood as processing representations without the use of representation-level rules, and he provides a positive characterization of how to interpret connectionist nets as following representation-level rules. He takes Terry Horgan and John Tienson to be the targets of his critique. The present paper marshals functional and methodological considerations, gleaned from the practice of cognitive modelling, to argue against Aizawa's characterization of (...) how connectionist nets may be understood as making use of representation-level rules. (shrink)