Abstract
Part II (chapters 3-7) of the book developed and defended an inferentialist/conventionalist theory of logic. In this, the opening chapter of part III, it is explained why the extension of part II’s approach from logic to mathematics faces significant philosophical challenges. The first major challenge concerns the ontological commitments of mathematics. It is received wisdom in philosophy that existence claims cannot be analytic or trivially true, making it difficult to see how a conventionalist account of mathematics could possibly be viable. The second major challenge concerns mathematical truth. Unlike (first-order) logical truth, mathematical truth, even in basic arithmetic, is computationally rich. There are serious challenges for conventionalists in trying to capture our intuition that mathematical truth is fully determinate, in light of this feature.
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