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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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Truth‐Value Gaps in Classical Theories

Truth‐Value Gaps in Classical Theories

(p.121) 7 Truth‐Value Gaps in Classical Theories
Saving Truth From Paradox

Hartry Field (Contributor Webpage)

Oxford University Press

This chapter deals with classical theories that postulate truth value gaps, especially theories that accept the left-to-right half of the Tarski biconditionals. The theories divide into two types: Kleene-style gap theories and supervaluation-style gap theories (though the latter includes revision-theoretic gap theories as well); these are all ‘external theories’ of the corresponding model-theoretic constructions. Focus is put on the fact that all such theories declare themselves untrue. It is argued that saying that the problematic sentences ‘don't express propositions’ is unhelpful.

Keywords:   Kleene-style gap theories, supervaluation-style gap theories, propositions, Kripke-Feferman theory

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