A Puzzle About Ontological Commitments

Philosophia Mathematica 16 (2):209-226 (2008)

Authors
Philip A. Ebert
University of Stirling
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
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DOI 10.1093/philmat/nkm050
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References found in this work BETA

Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Fixing Frege.John P. Burgess - 2006 - Tijdschrift Voor Filosofie 68 (3):665-665.
Logic, Logic and Logic.George Boolos & Richard C. Jeffrey - 1998 - Studia Logica 66 (3):428-432.

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Citations of this work BETA

A Puzzle About Ontological Commitments: Reply to Ebert.Ivan Kasa - 2010 - Philosophia Mathematica 18 (1):102-105.

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