The dominant approach to analyzing the meaning of natural language sentences that express mathematical knowledge relies on a referential, formal semantics Below, I discuss an argument against this approach and in favour of an internalist, conceptual, intensional alternative The proposed shift in analytic method offers several benefits, including a novel perspective on what is required to track mathematical content, and hence on the Benacerraf dilemma The new perspective also promises to facilitate discussion between philosophers of mathematics and cognitive scientists working on topics of common interest

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Mathematical realism and conceptual semantics

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Mathematical realism and conceptual semantics