The Philosophinity Guide to: Philosophy of Mathematics

Epistemic Access. What is the difference between Hartry Field’s version of the epistemic access problem for platonism and the original Paul Benacerraf version? Why was this change seen to be necessary?

In ‘Mathematical Truth’, Benacerraf (1973) presents two challenges that any credible philosophy of mathematics must meet: firstly, it must enable a coherent semantics, one that describes mathematics in a way that is uniform (or continuous with) non-mathematics; secondly, it must explain how it is the case that under the spectre of the causal theory of knowledge we come by mathematical entities in the first instance. This second challenge, however, or at least Benacerraf’s exposition of it, came to exclude important issues, and so had to be recast, a task eventually taken up by Hartry Field.

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