Frontiers of Philosophy in China 2 (4):614-628 (2007)

Authors
Feng Ye
Capital Normal University, Beijing, China
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
Categories (categorize this paper)
DOI 10.1007/s11466-007-0040-0
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,959
Through your library

References found in this work BETA

From a Logical Point of View.W. V. O. Quine - 1953 - Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.

View all 24 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
98 ( #119,122 of 2,504,815 )

Recent downloads (6 months)
3 ( #209,949 of 2,504,815 )

How can I increase my downloads?

Downloads

My notes