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Philosophia Mathematica Advance Access originally published online on March 5, 2008
Philosophia Mathematica 2008 16(2):209-226; doi:10.1093/philmat/nkm050
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Copyright © The Author 2008. Published by Oxford University Press.

A Puzzle About Ontological Commitments{dagger}

Philip A. Ebert*

* Department of Philosophy, University of Stirling, Stirling FK9 4LA, U.K.

Correspondence: p.a.ebert{at}stir.ac.uk

This paper raises and then discusses a puzzle concerning the ontological commitments of mathematical principles. The main focus here is Hume's Principle—a statement that, embedded in second-order logic, allows for a deduction of the second-order Peano axioms. The puzzle aims to put pressure on so-called epistemic rejectionism, a position that rejects the analytic status of Hume's Principle. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the neo-Fregeans, defenders of the analytic status of Hume's Principle, which will provide a new angle from which properly to assess and re-evaluate the current debate.

{dagger} I wish to thank the audience of various Arché Seminars in St Andrews for their comments and discussion. Special thanks to Roy T. Cook, Marcus Rossberg, and Crispin Wright for commenting and discussing earlier drafts of this paper. Also, I wish to thank two anonymous referees for their very helpful comments.


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