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. © Springer Science+Business Media B.V. 2009.
Ye, F. (2010). What anti-realism in philosophy of mathematics must offer. Synthese, 175(1), 13–31. https://doi.org/10.1007/s11229-009-9535-7