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Frontiers of Philosophy in China

Front. Philos. China    2007, Vol. 2 Issue (4) : 614-628     https://doi.org/10.1007/s11466-007-0040-0
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Indispensability argument and anti-realism in philosophy of mathematics
YE Feng
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.
Issue Date: 05 December 2007
 Cite this article:   
YE Feng. Indispensability argument and anti-realism in philosophy of mathematics[J]. Front. Philos. China, 2007, 2(4): 614-628.
 URL:  
http://journal.hep.com.cn/fpc/EN/10.1007/s11466-007-0040-0
http://journal.hep.com.cn/fpc/EN/Y2007/V2/I4/614
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