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  3. Logical Consequence
  • Cited by 12
  • Gila Sher, University of California, San Diego
Publisher:
Cambridge University Press
Online publication date:
August 2022
Print publication year:
2022
Online ISBN:
9781108981668
DOI:
https://doi.org/10.1017/9781108981668
Series:
Elements in Philosophy and Logic
Subjects:
Logic, Philosophy
Information

Book description

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.

References

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