Michelangelo's Stone: an Argument against Platonism in Mathematics
History and Overview
2018-04-23 v2
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.
Keywords
Cite
@article{arxiv.1508.00001,
title = {Michelangelo's Stone: an Argument against Platonism in Mathematics},
author = {Carlo Rovelli},
journal= {arXiv preprint arXiv:1508.00001},
year = {2018}
}
Comments
7 pages, 3 figures