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2015 Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections
Toby Meadows
Notre Dame J. Formal Logic 56(1): 191-212 (2015). DOI: 10.1215/00294527-2835074

Abstract

This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday mathematical practice.

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Toby Meadows. "Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections." Notre Dame J. Formal Logic 56 (1) 191 - 212, 2015. https://doi.org/10.1215/00294527-2835074

Information

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

zbMATH: 1371.03011
MathSciNet: MR3326595
Digital Object Identifier: 10.1215/00294527-2835074

Subjects:
Primary: 03A05 , Y002
Secondary: 03E99

Keywords: Cantor’s theorem , Forcing , generic elements , Kripkean truth , Set theory , Tarski , the liar paradox , Truth

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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