David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 175 (1):13 - 31 (2010)
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
Alan Baker (2005). Are There Genuine Mathematical Explanations of Physical Phenomena? Mind 114 (454):223-238.
Alan Baker (2001). Mathematics, Indispensability and Scientific Progress. Erkenntnis 55 (1):85-116.
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.
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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