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Paradoxical Partners: Semantical Brides and Set-theoretical Grooms

Goldstein, Laurence (2013) Paradoxical Partners: Semantical Brides and Set-theoretical Grooms. Analysis, 73 (1). pp. 33-37. ISSN 0003-2638. (doi:10.1093/analys/ans130)

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Abstract

I supply a simple key for ‘translating’ some semantical paradoxes into set-theoretical counterparts and vice-versa. This suggests a unified solution of these paradoxes, one which becomes particularly easy to see, because the ‘partners’ of some deep paradoxes are fairly trivial. One upshot of the investigation is that it is illicit, because circular, stipulation that gives rise to standard and ‘truth-teller’ paradoxes, and that there is a clear and natural restriction that prevents such circularity. In set theory, what we require are not new foundations for a consistent axiomatic system but only a minor restriction on the comprehension principle of naïve set theory that preserves our naïve intuitions.

Item Type: Article
DOI/Identification number: 10.1093/analys/ans130
Uncontrolled keywords: paradox semantics naive set theory unified
Subjects: B Philosophy. Psychology. Religion > BC Logic
Divisions: Faculties > Humanities > School of European Culture and Languages > Philosophy
Depositing User: Laurence Goldstein
Date Deposited: 19 Apr 2013 08:34 UTC
Last Modified: 29 May 2019 10:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/33642 (The current URI for this page, for reference purposes)
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