What anti-realism in philosophy of mathematics must offer

Synthese 175 (1):13 - 31 (2010)
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.
Keywords Philosophy of mathematics  Anti-realism  Realism  Naturalism
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DOI 10.1007/s11229-009-9535-7
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References found in this work BETA
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
Science Without Numbers.Hartry Field - 1980 - Princeton University Press.

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Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.

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