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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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Kripke's Theory of Truth (Strong Kleene Version)

Kripke's Theory of Truth (Strong Kleene Version)

(p.56) 3 Kripke's Theory of Truth (Strong Kleene Version)
Saving Truth From Paradox

Hartry Field (Contributor Webpage)

Oxford University Press

This chapter is an exposition of the strong Kleene version of Kripke's fixed point semantics, and the theories of truth that can be obtained from it. Emphasis is put on the distinction between ‘external’ and ‘internal’ theories of the fixed points: the external theories keep classical logic, posit truth value gaps, and deny the existence of truth value gluts; whereas the internal theories are non-classical and neither assert nor deny the existence of gaps or of gluts. In fact, ‘gap’ and ‘glut’ are equivalent within these theories. The advantages of the internal theories over the external are stressed: primarily, internal theories make True(p) intersubstitutable with p, whereas external theories don't. At the same time, the internal Kripke theories are seriously lacking in expressive power.

Keywords:   Kripke, Kleene, fixed point, truth value gap, truth value glut, internal fixed point theory, external fixed point theory, conservativeness, Intersubstitutivity Principle, degree of belief

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