Why Can’t There Be Numbers?

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Abstract
Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to precisify the widespread intuition that mathematical objects are somehow ‘spooky’ or ‘mysterious’.
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Archival date: 2021-03-03
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