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2018 A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”
Simon Hewitt
Notre Dame J. Formal Logic 59(3): 455-459 (2018). DOI: 10.1215/00294527-2018-0005


Gabriel Uzquiano has offered an account of indefinite extensibility for sets in the context of a modal logic. The modal operators are interpreted in terms of linguistic extensibility. After reviewing the proposal, I argue that the view should be understood as a version of in rebus structuralism about set theory. As such it is subject to the usual problems for in rebus structuralism. In particular, there is no good extra set-theoretic reason to assent to an ontology of sufficient cardinality to make true the theorems of ZFC.


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Simon Hewitt. "A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”." Notre Dame J. Formal Logic 59 (3) 455 - 459, 2018.


Received: 4 August 2015; Accepted: 17 April 2016; Published: 2018
First available in Project Euclid: 20 June 2018

zbMATH: 06939331
MathSciNet: MR3832092
Digital Object Identifier: 10.1215/00294527-2018-0005

Primary: 03A05
Secondary: 00A30

Keywords: indefinite extensibility , philosophy of mathematics , philosophy of set theory , plural logic , structuralism , Uzquiano

Rights: Copyright © 2018 University of Notre Dame


Vol.59 • No. 3 • 2018
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