How truthlike can a predicate be? A negative result
type: Item
instance of: scholarly article
title: How truthlike can a predicate be? A negative result
zbMATH Open document ID: 0583.03002
DOI: 10.1007/BF00649483
author: Vann McGee
published in: Journal of Philosophical Logic
publication date: 1985-01-01T00:00:00Z
review text: Tarski showed that a theory of truth for a language, formulated within that very language, that entails all instances of the schema \(^{\ulcorner \ulcorner}\phi^{\urcorner}\) is true iff \(\phi^{\urcorner}\) will be inconsistent with Peano arithmetic. This paper presents a further result along the same lines, showing that, if \(\Gamma\) is a theory of truth that contains Robinson's Q, is closed under first-order consequence and under the rule that from \(^{\ulcorner}\phi^{\urcorner}\) one may infer \(^{\ulcorner \ulcorner}\phi^{\urcorner}\) is \(true^{\urcorner}\), and contains all instances of the schemata asserting that a true conditional with a true antecedent has a true consequent, that a sentence and its negation are not both true, and that a generalization beginning ''for each natural number x'' is true if all of its numerical instances are, then \(\Gamma\) is \(\omega\)-inconsistent. Implications for recent theories of truth, such as those of Kripke, Gupta, and Herzberger, are discussed.
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 3933025
zbMATH Keywords: antinomy
zbMATH Keywords: paradox
zbMATH Keywords: omega consistency
zbMATH Keywords: truth
zbMATH Keywords: Robinson's Q
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3933025