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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

Chapter:
(p.121) 7 Truth‐Value Gaps in Classical Theories
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0008

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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