Title

Mathematical Skepticism

Document Type

Article

Publication Date

2008

Published In

Acta Universitatis Latviensis

Abstract

Platonism in the philosophy of mathematics is the view that mathematical statements aim to give a literally true description of a realm of abstract mathematical objects. In this paper I compare a recent epistemological challenge to mathematical platonism with traditional skeptical arguments about the existence of the external world. The epistemological challenge is based on the claim that whether mathematical objects exist or not makes no difference to the concrete, physical world. The way was opened for this style of argument by the rise of indispensabilist platonism, which abandons the presupposition that mathematical objects exist necessarily. I conclude that the ‘Makes No Difference’ argument against platonism faces its own distinct hurdles if it is to successfully gain epistemological traction against the core metaphysical issues in the philosophy of mathematics.

Keywords

philosophy of mathematics, platonism, scepticism