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Saving Truth From Paradox$
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Hartry Field

Print publication date: 2008

Print ISBN-13: 9780199230747

Published to Oxford Scholarship Online: May 2008

DOI: 10.1093/acprof:oso/9780199230747.001.0001

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Fixed Points and Revision Rules for Conditionals

Fixed Points and Revision Rules for Conditionals

(p.242) 16 Fixed Points and Revision Rules for Conditionals
Saving Truth From Paradox

Hartry Field (Contributor Webpage)

Oxford University Press

This chapter looks at two ways of meeting the goal of naïvety. Yablo's is technically simpler, but involves extreme failures of intersubstitutivity of logical truths within conditionals. The alternative involves a revision-theoretic ideas, but applied to the conditional instead of the truth predicate, in combination with an iterated Kripke fixed point construction. A general non-triviality theorem is proved, and examples are given, especially to a ‘transfinite Liar hierarchy’.

Keywords:   Yablo, Kripke, fixed points, revision rules, conditionals, acceptable ordinal, transfinite Liar hierarchy

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