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
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.
George Lakoff & Rafael E. Núñez (2000). Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.
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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