Epistemic mathematical realism: a minimalist reading of indispensability arguments

Mr Cristian Soto (University of Melbourne)

In this paper, I put forward a form of epistemic mathematical realism, which attempts to reconcile realism about science with a minimalist form of realism about the contributions mathematics makes to the epistemic success of science. I examine several forms of indispensability arguments (IA), viz., the Quine-Putnam IA, the pragmatic IA, and the explanationist IA. I claim these arguments fail to make a compelling case for both the reality of mathematical entities and the truth of mathematical statements. Along this paper, I focus my argument in the elaboration and defence of what I call epistemic IA. A robust realism about the epistemic contribution of mathematics to the success of science, so I argue, should satisfy the realist inclinations of those who endorse realism about science overall.