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.

Keywords:

• Mathematical causalism
• mathematical object
• mathematical realism

Acknowledgements

This paper improved a lot thanks to anonymous referees’ useful comments.

Additional information

Funding

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea [grant number NRF-2016S1A5A2A01022592].