"不可或缺性论证"与反实在论数学哲学 |
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收稿时间: | 24 October 2006 |
Indispensability argument and anti-realism in philosophy of mathematics |
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Authors: | Feng Ye |
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Institution: | (1) Department of Philosophy, Peking University, Beijing, 100871, China |
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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.
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Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2006, (8): 74–83 |
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Keywords: | philosophy of mathematics indispensability argument anti-realism nominalism realism Quine |
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