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Michelangelo's Stone: an Argument against Platonism in Mathematics (1508.00001v2)
Published 2 Aug 2015 in math.HO
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.