A puzzle about ontological commitments

Philip Alexander Ebert

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)209-226
JournalPhilosophia Mathematica
Volume16
Issue number2
DOIs
Publication statusPublished - Jun 2006

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