Notions of Invariance for Abstraction Principles

Philosophia Mathematica 18 (3):276-292 (2010)
Abstract
The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each
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References found in this work BETA
G. Aldo Antonelli (2010). Numerical Abstraction Via the Frege Quantifier. Notre Dame Journal of Formal Logic 51 (2):161-179.
G. Aldo Antonelli & Robert C. May (2005). Frege's Other Program. Notre Dame Journal of Formal Logic 46 (1):1-17.
Denis Bonnay (2006). Logicality and Invariance. Bulletin of Symbolic Logic 14 (1):29-68.
Richard Heck (2000). Syntactic Reductionism. Philosophia Mathematica 8 (2):124-149.

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Citations of this work BETA
Eric Thomas Updike (2012). Abstraction in Fitch's Basic Logic. History and Philosophy of Logic 33 (3):215-243.
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