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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    References found in this work BETA
    Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
    John P. Burgess (2004). Mathematics and Bleak House. Philosophia Mathematica 12 (1):18-36.
    Charles Chihara (2005). Nominalism. In Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. 483--514.

    View all 23 references

    Citations of this work BETA
    Feng Ye (2011). Naturalism and Abstract Entities. International Studies in the Philosophy of Science 24 (2):129-146.
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