Infinitary Tableau for Semantic Truth

Toby Meadows

doi:10.1017/S175502031500012X

Infinitary Tableau for Semantic Truth

Toby Meadows

Philosophy

Research output: Contribution to journal › Article

3 Citations (Scopus)

5 Downloads (Pure)

Abstract

We provide infinitary proof theories for three common semantic theories of truth: strong Kleene, van Fraassen supervaluation and Cantinisupervaluation. The value of these systems is that they provide an easy method of proving simple facts about semantic theories. Moreover we shall show that they also give us a simpler understanding of the computational complexity of these definitions and provide a direct proof that the closure ordinal for Kripke’s definition is ωCK1. This work can be understood as an effort to provide a proof-theoretic counterpart to Welch’s game theoretic (Welch, 2009).

Original language	English
Pages (from-to)	207-235
Number of pages	29
Journal	Review of Symbolic Logic
Volume	8
Issue number	2
Early online date	8 Apr 2015
DOIs	https://doi.org/10.1017/S175502031500012X
Publication status	Published - Jun 2015

Keywords

Semantic Theories of Truth

Access to Document

10.1017/S175502031500012XLicence: Unspecified

Infinitary Tableau for Semantic Truth
This is the author's accepted manuscript of an article accepted for publication in The Review of Symbolic Logic. © Cambridge University Press 2015 The Review of Symbolic Logic can be viewed here: http://journals.cambridge.org/action/displayJournal?jid=RSL
Accepted author manuscript, 459 KB

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Meadows, T. (2015). Infinitary Tableau for Semantic Truth. Review of Symbolic Logic, 8(2), 207-235. https://doi.org/10.1017/S175502031500012X

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abstract = "We provide infinitary proof theories for three common semantic theories of truth: strong Kleene, van Fraassen supervaluation and Cantinisupervaluation. The value of these systems is that they provide an easy method of proving simple facts about semantic theories. Moreover we shall show that they also give us a simpler understanding of the computational complexity of these definitions and provide a direct proof that the closure ordinal for Kripke{\textquoteright}s definition is ωCK1. This work can be understood as an effort to provide a proof-theoretic counterpart to Welch{\textquoteright}s game theoretic (Welch, 2009).",

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note = " Acknowledgements I would like to thank Philip Welch for his assistance and acknowledge the late Greg Hjorth for the time he spent in helping me learn how to use the tools used in the paper. I would also like to thank Hannes Leitgeb for giving me the opportunity to present this material and for providing me with valuable feedback. And I would like to thank Benedict Eastaugh and Marcus Holland for helping make the final sections of this paper more accessible in the way it was intended.",

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