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Understanding Truth$
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Scott Soames

Print publication date: 1999

Print ISBN-13: 9780195123357

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0195123352.001.0001

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Truth, Paradox, and Partially Defined Predicates

Truth, Paradox, and Partially Defined Predicates

Chapter:
(p.163) Six Truth, Paradox, and Partially Defined Predicates
Source:
Understanding Truth
Author(s):

Scott Soames (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195123352.003.0007

Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it conforms to this model. On this view, there are sentences, including Liar sentences like this sentence is not true and “Truth Tellers” like This sentence is true, about which the rules determining whether or not a sentence is true provide no result (either to the effect that it is true, or to the effect that it is not true) – thereby blocking the usual derivation of the paradox. However, despite these promising results, it is shown that a general solution to the Liar paradox is not forthcoming, since the very activity of solving the paradox in a particular limited case provides material for recreating it in a new and strengthened form. In the second half of the chapter, it is argued that this philosophical model provides the best way of understanding Saul Kripke's formal theory of truth (despite certain uncharacteristically misleading remarks of his to the contrary). In addition to laying out the philosophical basis for Kripke's theory of truth, explanations are given of his basic technical apparatus and formal results – including fixed points, minimal fixed points, monotonicity, intrinsic fixed points, ungrounded sentences, and paradoxical sentences.

Keywords:   fixed points, Kripke, Liar's paradox, monotonicity, paradoxical sentences, partially defined predicates, truth, ungrounded sentences

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