Truth without satisfaction
type: Item
instance of: scholarly article
title: Truth without satisfaction
zbMATH Open document ID: 0556.03010
DOI: 10.1007/BF00247713
author: Kit Fine
author: Timothy McCarthy
published in: Journal of Philosophical Logic
publication date: 1984-01-01T00:00:00Z
review text: Tarski's definition of truth is given by using the concept of satisfaction. This paper studies systematically the conditions for the possibility of defining truth without satisfaction. The authors state results for the case, where the object language is a classical first- order language L and the meta-language is a many-sorted first-order language \(L_ M\). A meta-theory M in \(L_ M\) is said to be over a theory T in L if every theorem of T is a theorem of M. Theorem 8 says that there exists a metatheory M over T such that M defines truth but not satisfaction (for formulas with n free variables) if and only if T does not admit only finitely many n-types. Such a ''non-Tarskian\(_ n\)'' metatheory which is also finitely axiomatizable exists if T has a complete and axiomatizable extension that does not admit only finitely many n-types (Theorem 20). These results imply that there is a non- Tarskian\(_ n\) metatheory (finitely axiomatizable or not) for the language L if and only if L is not purely monadic, i.e., L contains other non-logical constants then one-place predicates and individual constants (Theorems 12 and 22).
Mathematics Subject Classification ID: 03B10
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03C99
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 3885862
zbMATH Keywords: semantics
zbMATH Keywords: truth
zbMATH Keywords: satisfaction
zbMATH Keywords: types
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3885862