David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Frontiers of Philosophy in China 2 (4):614-628 (2007)
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Otávio Bueno (2003). Quine's Double Standard: Undermining the Indispensability Argument Via the Indeterminacy of Reference. Principia 7 (1-2):17-39.
Mark Colyvan (1998). In Defence of Indispensability. Philosophia Mathematica 6 (1):39-62.
Feng Ye (2011). Naturalism and Abstract Entities. International Studies in the Philosophy of Science 24 (2):129-146.
Christopher Pincock (2004). A Revealing Flaw in Colyvan's Indispensability Argument. Philosophy of Science 71 (1):61-79.
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
Michael Resnik (1995). Scientific Vs. Mathematical Realism: The Indispensability Argument. Philosophia Mathematica 3 (2):166-174.
Added to index2009-01-28
Total downloads18 ( #94,242 of 1,102,698 )
Recent downloads (6 months)4 ( #84,424 of 1,102,698 )
How can I increase my downloads?