Notre Dame Journal of Formal Logic 56 (1):243-261 (2015)

Authors
Jonathan Payne
University of Sheffield (PhD)
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 $\varepsilon X$, 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 $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities.
Keywords modal set theory   abstraction   second-order logic   plural logic
Categories (categorize this paper)
DOI 10.1215/00294527-2835092
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Basic Laws of Arithmetic.Gottlob Frege - 1893 - Berkeley: University of California Press.
Philosophy of Logic.W. V. Quine - 1999 - In Simon Blackburn & Keith Simmons (eds.), Truth. Oxford University Press.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.

View all 17 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Modal Object Calculus and its Interpretation.Edward N. Zalta - 1997 - In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer Academic Publishers. pp. 249--279.
Toward Model-Theoretic Modal Logics.Minghui Ma - 2010 - Frontiers of Philosophy in China 5 (2):294-311.
Modal Logic and Model Theory.Giangiacomo Gerla & Virginia Vaccaro - 1984 - Studia Logica 43 (3):203 - 216.
First-Order Intensional Logic.Melvin Fitting - 2004 - Annals of Pure and Applied Logic 127 (1-3):171-193.

Analytics

Added to PP index
2015-03-25

Total views
211 ( #47,641 of 2,445,402 )

Recent downloads (6 months)
9 ( #76,488 of 2,445,402 )

How can I increase my downloads?

Downloads

My notes