Maximal consistent sets of instances of Tarski's schema (T)
type: Item
instance of: scholarly article
title: Maximal consistent sets of instances of Tarski's schema (T)
zbMATH Open document ID: 0773.03003
DOI: 10.1007/BF00260929
author: Vann McGee
published in: Journal of Philosophical Logic
publication date: 1993-01-16T00:00:00Z
review text: As is well known, Tarski's schema \[ \text{Tr }\ulcorner s\urcorner \text{ if and only if } s \tag{T} \] for the truth predicate Tr of sentences \(s\), implies that there can be no theory which contains its own truth predicate satisfying (T). A meta-theory is required. Under circumstances where one wants to develop a semantic theory of a language within that very language, one may deal with Tr as a partial predicate, thereby cutting down on (T). The strategy which the author studies, is to look for maximal sets of sentences which do satisfy (T) and are consistent with the basic laws of arithmetic. He shows that such maximal sets of instances of (T) do exist, although beyond axiomatization. The author concludes: ``Thus the requirement that our theory of truth should entail a maximal consistent set of instances of (T) is both too weak and too strong. It is too strong because we cannot hope actually to construct a theory that meets the requirement. It is too weak because \dots even if, by some superhuman agency, we got hold of a theory that meet the requirement, we would have no reason to suppose that the theory captured any of the useful features of our ordinary notion of truth''.
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 92833
zbMATH Keywords: truth predicate
zbMATH Keywords: theory of truth
zbMATH Keywords: maximal consistent set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 92833