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2010 Numerical Abstraction via the Frege Quantifier
G. Aldo Antonelli
Notre Dame J. Formal Logic 51(2): 161-179 (2010). DOI: 10.1215/00294527-2010-010

Abstract

This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard (but still first-order) cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.

Citation

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G. Aldo Antonelli. "Numerical Abstraction via the Frege Quantifier." Notre Dame J. Formal Logic 51 (2) 161 - 179, 2010. https://doi.org/10.1215/00294527-2010-010

Information

Published: 2010
First available in Project Euclid: 11 June 2010

zbMATH: 1205.03055
MathSciNet: MR2667904
Digital Object Identifier: 10.1215/00294527-2010-010

Subjects:
Primary: 03C80, 03C99

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 2 • 2010
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