Date of Award


Degree Type


Degree Name

Doctor of Philosophy




Robert Stainton


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 of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt Godel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms



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