Notre Dame Journal of Formal Logic

A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”

Simon Hewitt

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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.

Article information

Notre Dame J. Formal Logic, Volume 59, Number 3 (2018), 455-459.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 00A30: Philosophy of mathematics [See also 03A05]

philosophy of mathematics philosophy of set theory structuralism plural logic indefinite extensibility Uzquiano


Hewitt, Simon. A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”. Notre Dame J. Formal Logic 59 (2018), no. 3, 455--459. doi:10.1215/00294527-2018-0005.

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