Abstract

If there is a ‘platonic world’ \ of mathematical facts, what does \ contain precisely? I observe that if \ 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 and illustrate contingent aspects of classical geometry, arithmetic and linear algebra, making the case that what we call “mathematics” is always contingent.