Notre Dame Journal of Formal Logic 56 (1):191-212 (2015)

Toby Meadows
University of California, Irvine
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.
Keywords Cantor’s theorem   set theory   the liar paradox   truth   Tarski   Kripkean truth   forcing   generic elements
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DOI 10.1215/00294527-2835074
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Semantic Conception of Truth and the Foundations of Semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
The Set-Theoretic Multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.
Inconsistent Languages.Matti Eklund - 2002 - Philosophy and Phenomenological Research 64 (2):251-275.

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Citations of this work BETA

Can All Things Be Counted?Chris J. Scambler - 2021 - Journal of Philosophical Logic 50 (5):1079-1106.
Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.
Might All Infinities Be the Same Size?Alexander R. Pruss - 2020 - Australasian Journal of Philosophy 98 (3):604-617.
In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.

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