On the concept of logical consequence

Tarski, A. (1956). On the concept of logical consequence. Logic, Semantics, Metamathematics.

Type

Book chapter

Intellectual base

Review or monograph

Year

1956

Pages cited

409-420

Link

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

Cited from

computer_science, linguistics_semiotics, philosophy, systems_cybernetics

Cited by

4 citations across 4 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.

• Dependency
  • The relation has been formalized independently in five distinct intellectual traditions: graph-theoretic dependency analysis in compiler design (Aho, Lam, Sethi, and Ullman 2006), task-precedence modeling in operations research (Kelley and Walker 1959, who introduced the Critical Path Method), logical entailment in formal logic (Tarski 1936), semantic presupposition in philosophy of language (Strawson 1950), and obligate dependency in ecology (Janzen 1980).
• 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.

Verification

Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.

Does it back the claim? Not recorded. Neither this nor any other of the 4 citations of this work carries a recorded support check.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://philpapers.org/rec/TARLSM ×1

Registry ID ref:2827a81f1120 · see in the full table