Quantifier Variance and Indefinite Extensibility

Philosophical Review 126 (1):81-122 (2017)
  Copy   BIBTEX

Abstract

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 98,219

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”.Simon Hewitt - unknown - Notre Dame Journal of Formal Logic 59 (3):455-459.
Dummett on Indefinite Extensibility.Øystein Linnebo - 2018 - Philosophical Issues 28 (1):196-220.
Indefinite Extensibility.Royt Cook - 2013 - In Christy Mag Uidhir (ed.), Art & Abstract Objects. Oxford University Press. pp. 87.

Analytics

Added to PP
2016-12-23

Downloads
563 (#41,074)

6 months
47 (#100,060)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Jared Warren
Stanford University

Citations of this work

Everything, More or Less: A Defence of Generality Relativism.James Studd - 2019 - Oxford, England: Oxford University Press.
Ontology and Arbitrariness.David Builes - 2022 - Australasian Journal of Philosophy 100 (3):485-495.
Quantifier Variance and the Demand for a Semantics.Eli Hirsch & Jared Warren - 2017 - Philosophy and Phenomenological Research 98 (3):592-605.

View all 14 citations / Add more citations

References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
Philosophical Investigations.Ludwig Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell. Edited by G. E. M. Anscombe.
Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. New York: Oxford University Press. pp. 481-563.
Inquiries Into Truth And Interpretation.Donald Davidson - 1984 - Oxford, GB: Oxford University Press.

View all 126 references / Add more references