On Reality of Numbers

Abstract

There are at least two recent distinct physicalist approaches to mathematics. First, there is Maddy’s set theoretic realism. This does not concern us here. Second, there is Bigelow’s approach as it was put forward in his book “The Reality of Numbers”. In my paper, I discuss some major difficulties concerning Bigelow’s physicalism in general, and argue that it is problematic to construe all numbers on his methodology. In particular, there are some difficulties concerning infinite numbers. Besides, some transcendental reals like e and many logarithms may not exist in physical space-time as lengths in Bigelow’s sense.