On the concept of logical consequence

Tarski, A. (1936). On the concept of logical consequence. Logic, Semantics, Metamathematics.

Type

Book chapter

Intellectual base

Review or monograph

Year

1936

Link

https://plato.stanford.edu/entries/logical-consequence/

Cited from

linguistics_semiotics, philosophy, systems_cybernetics

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Deductive Reasoning
  • ) or model-theoretically (as semantic entailment, where a conclusion holds in all models satisfying the premises — Tarskian semantics

    This sourceGives the model-theoretic (Tarskian) account: X is a logical consequence of Γ iff every model of Γ is a model of X. WebSearch confirmed Tarski's 1936 definition of logical consequence as truth-in-every-model.

• Meta-Symbolic Reflection
  • The meta-level may be formally distinct (Tarski's metalanguage hierarchy, 1936

    This sourceFoundational model-theoretic account of logical consequence (entailment); makes the dependency of a conclusion on its premises precise in terms of truth-preservation across all models.

• Reflexivity (Self-Reference)
  • Logic and mathematics: Russell's paradox (a set of all sets not containing themselves—contradictory under unrestricted comprehension); Gödel's incompleteness theorems (mathematical theories sufficient to express self-reference cannot prove their own consistency); Tarski's undefinability theorem (truth cannot be defined within the language it applies to)

    This sourceFoundational model-theoretic account of logical consequence (entailment); makes the dependency of a conclusion on its premises precise in terms of truth-preservation across all models.

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