David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
Penelope Maddy (1997). Naturalism in Mathematics. Oxford University Press.
Alan Baker (2005). Are There Genuine Mathematical Explanations of Physical Phenomena? Mind 114 (454):223-238.
Hartry Field (1980). Science Without Numbers. Princeton University Press.
John P. Burgess & Gideon A. Rosen (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford University Press.
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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