What anti-realism in philosophy of mathematics must offer

Synthese 175 (1):13 - 31 (2010)
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Abstract

This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs to anti-realism, but can meet those challenges and can perhaps convince some realists, at least those who are also naturalists.

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Feng Ye
Capital Normal University, Beijing, China

Citations of this work

Fictionalism.E. C. Bourne - 2013 - Analysis 73 (1):147-162.
Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.

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References found in this work

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 - New York: Oxford University Press.
A subject with no object: strategies for nominalistic interpretation of mathematics.John P. Burgess & Gideon Rosen - 1997 - New York: Oxford University Press. Edited by Gideon A. Rosen.

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