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A Cognitive Approach To Benacerraf’S Dilemma, Luke V. Jerzykiewicz

Digitized Theses

One of the important challenges in the philosophy of mathematics is to account for the se­ mantics 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 …