A Note on Induction, Abstraction, and Dedekind-Finiteness

Notre Dame Journal of Formal Logic 53 (2):187-192 (2012)
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Abstract

The purpose of this note is to present a simplification of the system of arithmetical axioms given in previous work; specifically, it is shown how the induction principle can in fact be obtained from the remaining axioms, without the need of explicit postulation. The argument might be of more general interest, beyond the specifics of the proposed axiomatization, as it highlights the interaction of the notion of Dedekind-finiteness and the induction principle

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G. Aldo Antonelli
University of California, Davis

Citations of this work

Is Frege's Definition of the Ancestral Adequate?Richard G. Heck - 2016 - Philosophia Mathematica 24 (1):91-116.

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References found in this work

Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Notions of Invariance for Abstraction Principles.G. A. Antonelli - 2010 - Philosophia Mathematica 18 (3):276-292.
Numerical Abstraction via the Frege Quantifier.G. Aldo Antonelli - 2010 - Notre Dame Journal of Formal Logic 51 (2):161-179.
The Nature and Purpose of Numbers.G. Aldo Antonelli - 2010 - Journal of Philosophy 107 (4):191-212.

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