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2015 Extensionalizing Intensional Second-Order Logic
Jonathan Payne
Notre Dame J. Formal Logic 56(1): 243-261 (2015). DOI: 10.1215/00294527-2835092

Abstract

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity X, there may be an object εX, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities.

This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either is more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the ε operator can have the effect of “extensionalizing” intensional second-order entities.

Citation

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Jonathan Payne. "Extensionalizing Intensional Second-Order Logic." Notre Dame J. Formal Logic 56 (1) 243 - 261, 2015. https://doi.org/10.1215/00294527-2835092

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1371.03015
MathSciNet: MR3326597
Digital Object Identifier: 10.1215/00294527-2835092

Subjects:
Primary: 03A05
Secondary: 00A30

Keywords: abstraction , modal set theory , plural logic , second-order logic

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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