Logical Consequence

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.