Naive infinitism: the case for an inconsistency approach to infinite collections

Meadows, Toby (2015) Naive infinitism: the case for an inconsistency approach to infinite collections. Notre Dame Journal of Formal Logic, 56 1: 191-212. doi:10.1215/00294527-2835074


Author Meadows, Toby
Title Naive infinitism: the case for an inconsistency approach to infinite collections
Journal name Notre Dame Journal of Formal Logic   Check publisher's open access policy
ISSN 1939-0726
0029-4527
Publication date 2015
Year available 2015
Sub-type Article (original research)
DOI 10.1215/00294527-2835074
Open Access Status Not Open Access
Volume 56
Issue 1
Start page 191
End page 212
Total pages 22
Place of publication Durham, NC, United States
Publisher Duke University Press
Language eng
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.
Keyword Cantor's theorem
Forcing
Generic elements
Kripkean truth
Set theory
Tarski
The liar paradox
Truth
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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