'Sometime a paradox', now proof: Yablo is not first order. (28th October 2020)
- Record Type:
- Journal Article
- Title:
- 'Sometime a paradox', now proof: Yablo is not first order. (28th October 2020)
- Main Title:
- 'Sometime a paradox', now proof: Yablo is not first order
- Authors:
- Salehi, Saeed
- Abstract:
- Abstract: Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell's paradox, which overthrew Frege's logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar's paradox has been used in the classical proof of Tarski's theorem on the undefinability of truth in sufficiently rich languages. This paradox (as well as Richard's paradox) appears implicitly in Gödel's proof of his celebrated first incompleteness theorem. In this paper, we study Yablo's paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo's paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984).
- Is Part Of:
- Logic journal of the IGPL. Volume 30:Number 1(2022)
- Journal:
- Logic journal of the IGPL
- Issue:
- Volume 30:Number 1(2022)
- Issue Display:
- Volume 30, Issue 1 (2022)
- Year:
- 2022
- Volume:
- 30
- Issue:
- 1
- Issue Sort Value:
- 2022-0030-0001-0000
- Page Start:
- 71
- Page End:
- 77
- Publication Date:
- 2020-10-28
- Subjects:
- Yablo's paradox -- non-first-orderizability
Logic, Symbolic and mathematical -- Periodicals
511.3 - Journal URLs:
- http://jigpal.oxfordjournals.org/ ↗
http://www3.oup.co.uk/igpl/contents ↗
http://ukcatalogue.oup.com/ ↗ - DOI:
- 10.1093/jigpal/jzaa051 ↗
- Languages:
- English
- ISSNs:
- 1367-0751
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5292.308290
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 20373.xml