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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