Synthese 175 (1):13 - 31 (2010)
AbstractThis 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.
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References found in this work
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Philosophical Naturalism. Philosophical Naturalism.David Papineau - 1993 - Blackwell.
A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon Rosen - 1997 - Oxford, England: Oxford University Press.
Citations of this work
Strict Finitism and the Logic of Mathematical Applications.Feng Ye - 2011 - Dordrecht, Netherland: Springer.
Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
Feng Ye. Strict Finitism and the Logic of Mathematical Applications.Nigel Vinckier & Jean Paul Van Bendegem - 2016 - Philosophia Mathematica 24 (2):247-256.
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