So, if we have a semantic interpretation of atomic symbols (if we have symbols whose reference and extension are fixed at the first stage by whatever naturalistic mechanism turns out to govern it), then the combinatorial syntax will take over and effectively determine the semantic interpretation (truth-conditions) of the complex sentences they are constituents of.
The combinatorial syntax not only gives us a criterion of well-formedness for mental expressions, but it also defines the logical form or syntactic structure for each well-formed expression.
Third, the combinatorial, syntax-like, proof-theoretical aspects of information can be brought to this setting in various ways.
The rules of combinatorial syntax determine the syntactic or formal structure of complex mental representations.
Whereas the former involves discrete symbols and a combinatorial syntax, the latter involves action potentials, spiking frequencies and spreading activation.
The classical explanation LOTH offers is to postulate a system of representations with combinatorial syntax exactly as in the case of the explanation of the linguistic systematicity.
This is what the postulation of a combinatorial semantics in conjunction with a combinatorial syntax buys for LOT-theorists in adequately explaining the empirical regularity in question.
This language consists of a system of representations that is physically realized in the brain of thinkers and has a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations.
This is what Fodor and Pylyshyn call 'the principle of compositionality'.[22] In brief, it is an argument for LOTH that it offers a cogent and principled solution to the systematicity and compositionality of cognitive capacities by postulating a system of representations that has a combinatorial syntax and semantics, i.e., a system of representations that satisfies at least (B1).
If the system of mental representations does have a combinatorial syntax, then there is a set of rules, psychosyntactic formation rules, so to speak, that govern the construction of well-formed expressions in the system.
