Can mathematical objects be causally efficacious?

Abstract

Callard argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: Why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object and how we can have knowledge about an unchanging object.