Michelangelo’s Stone: an Argument against Platonism in Mathematics

Publication Year:
Usage 594
Downloads 594
Repository URL:
preprint description
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 of 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.