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Series:   Elements in Philosophy and Logic

Logical Consequence

Published online by Cambridge University Press:  20 August 2022

Gila Sher
Gila Sher
Affiliation:
University of California, San Diego

Summary

To understand logic is, first and foremost, to understand logical consequence. This Element provides an in-depth, accessible, up-to-date account of and philosophical insight into the semantic, model-theoretic conception of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. The topics discussed include: (i) the passage from Tarski's definition of truth (simpliciter) to his definition of logical consequence, (ii) the need for a non-proof-theoretic definition, (iii) the idea of a semantic definition, (iv) the adequacy conditions of preservation of truth, formality, and necessity, (v) the nature, structure, and totality of models, (vi) the logicality problem that threatens the definition of logical consequence (the problem of logical constants), (vii) a general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality, (viii) philosophical background and justification of the isomorphism-invariance criterion, and (ix) major criticisms of the semantic definition and the isomorphism-invariance criterion.
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Keywords

logical consequencelogical semanticsmodel theorycriterion of logicalityinvariance under
Type
Element
Information
Series: Elements in Philosophy and Logic
Online ISBN: 9781108981668
Publisher: Cambridge University Press
Print publication: 08 September 2022

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Logical Consequence
  • Gila Sher, University of California, San Diego
  • Online ISBN: 9781108981668
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Logical Consequence
  • Gila Sher, University of California, San Diego
  • Online ISBN: 9781108981668
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Logical Consequence
  • Gila Sher, University of California, San Diego
  • Online ISBN: 9781108981668
Available formats
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