Frontiers of Philosophy in China 2 (4):614-628 (2007)
|Abstract||The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions.|
|Keywords||philosophy of mathematics indispensability argument anti-realism nominalism realism Quine 数学哲学 不可或缺性论证 反实在论 唯名论 实在论 奎因|
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