Michelangelo's Stone: an Argument against Platonism in Mathematics

TL;DR

This paper challenges mathematical Platonism by arguing that the universe of mathematical facts is either too large and uninteresting or too small and dependent on us, highlighting the contingency of mathematical truths.

Contribution

It offers a philosophical critique of Platonism by examining the implications of the size and independence of the mathematical universe.

Findings

Contingent aspects of classical geometry, arithmetic, and linear algebra.

Mathematical universality may be a prejudice.

Size of the mathematical universe affects its philosophical interpretation.

Abstract

If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent from us. Both alternatives challenge mathematical platonism. I suggest that the universality of our mathematics may be a prejudice hiding its contingency, and illustrate contingent aspects of classical geometry, arithmetic and linear algebra.