Modality, invariance, and logical truth
type: Item
instance of: scholarly article
title: Modality, invariance, and logical truth
zbMATH Open document ID: 0635.03010
DOI: 10.1007/BF00431187
published in: Journal of Philosophical Logic
publication date: 1987-01-01T00:00:00Z
review text: I shall discuss the conditions under which a model-theoretic characterization of validity for a language leads to a class of logical truths which exemplify certain necessity properties. Our question is this. Let us think of a notion of possibility for a language L as being characterized by a class \({\mathbb{M}}\) of theories in L; a statement of L is possible (in the sense of \({\mathbb{M}})\) if it occurs in some theory in \({\mathbb{M}}\) and is necessary if its negation is not possible. Under what conditions will the model-theoretically valid statements of L be necessary? This question will receive a general answer in terms of certain properties of the expressions of L which are treated as constants in the characterization of validity. Each notion of possibility \({\mathbb{M}}\) for L will be associated with a property, to be termed invariance over \({\mathbb{M}}\), defined for expressions in L. In Section 4 it is shown that if the logical expressions of L are invariant over \({\mathbb{M}}\), then a sentence is valid in L only if it is necessary in the sense of \({\mathbb{M}}\). The languages which I consider arise by supplementing first-order logic with generalized quantifiers. The results can, however, be extended to other languages.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03C80
zbMATH DE Number: 4033696
zbMATH Keywords: model-theoretic characterization of validity for a language
zbMATH Keywords: necessity
zbMATH Keywords: possibility
zbMATH Keywords: invariance
zbMATH Keywords: first-order logic with generalized quantifiers
author: Timothy McCarthy
MaRDI profile type: Publication
cites work: Pragmatics and intensional logic
cites work: On a generalization of quantifiers
description: scientific article; zbMATH DE number 4033696