Logical Consequence

The Element provides an in-depth account of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. It discusses the passage from Tarski's definition of truth to his definition of logical consequence, the need for a non-proof-theoretic definition, the idea of a semantic definition, the adequacy conditions of preservation of truth, formality, and necessity, the nature, structure, and totality of models, the logicality problem, a general solution to the logicality, formality, and necessity problems, and the philosophical background and justification of the isomorphism-invariance criterion.

Format: Paperback / softback
Length: 75 pages
Publication date: 08 September 2022
Publisher: Cambridge University Press

Understanding 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:

The passage from Tarski's definition of truth (simpliciter) to his definition of logical consequence.

The need for a non-proof-theoretic definition.

The idea of a semantic definition.

The adequacy conditions of preservation of truth, formality, and necessity.

The nature, structure, and totality of models.

The logicality problem that threatens the definition of logical consequence (the problem of logical constants).

A general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality.

Philosophical background and justification of the isomorphism-invariance criterion.

Major criticisms of the semantic definition and the isomorphism-invariance criterion.

Weight: 147g
ISBN-13: 9781108986847