The creative aspect of language use provides a set of phenomena that a science of language must explain. It is the “central fact to which any signi- ficant linguistic theory must address itself” and thus “a theory of language that neglects this ‘creative’ aspect is of only marginal interest” (Chomsky 1964: 7–8). Therefore, the form and explanatory depth of linguistic science is restricted in accordance with this aspect of language. In this paper, the implications of the creative aspect of language (...) use for a scientific theory of language will be discussed, noting the possible further implications for a science of the mind. It will be argued that a corollary of the creative aspect of language use is that a science of language can study the mechanisms that make language use possible, but that such a science cannot explain how these mechanisms enter into human action in the form of language use. (shrink)

One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)