Chapter

Truth, Paradox, and Partially Defined Predicates

Scott Soames

in Understanding Truth

Published in print January 1999 | ISBN: 9780195123357
Published online November 2003 | e-ISBN: 9780199872114 | DOI: http://dx.doi.org/10.1093/0195123352.003.0007
 Truth, Paradox, and Partially Defined Predicates

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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

Chapter.  21049 words.  Illustrated.

Subjects: Philosophy of Language

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