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What anti-realism in philosophy of mathematics must offer

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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Correspondence to Feng Ye.

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Ye, F. What anti-realism in philosophy of mathematics must offer. Synthese 175, 13–31 (2010). https://doi.org/10.1007/s11229-009-9535-7

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Keywords

  • Philosophy of mathematics
  • Anti-realism
  • Realism
  • Naturalism