Jump Liars and Jourdain’s Card via the Relativized T-scheme

Studia Logica 91 (2):239-271 (2009)
Authors
Ming Hsiung
Zhongshan University
Abstract
A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain's card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic  Liar Paradox  Tarski's T-scheme  Possible World
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DOI 10.1007/s11225-009-9174-5
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References found in this work BETA

Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
Recent Essays on Truth and the Liar Paradox.Robert L. Martin (ed.) - 1984 - Oxford University Press.

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Citations of this work BETA

Equiparadoxicality of Yablo's Paradox and the Liar.Ming Hsiung - 2013 - Journal of Logic, Language and Information 22 (1):23-31.
Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - forthcoming - Journal of Philosophical Logic:1-9.
Tarski's Theorem and Liar-Like Paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.

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