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The text I'm reading distinguishes logical necessity, logical consequence, logical truth, and tautology from one another; however it doesn't make their distinctions especially perspicuous.

As far as I interpreted it,

  • Logical consequence: truth of the antecedent or premises guarantees the truth of the consequent or conclusions.
  • Logical truth: Any statement that must be valuated true, even if the set of premises is the empty set. (3=3, p v ~p, etc)
  • Tautology: Any statement that must be valuated true, but only when the statement is stated. (as opposed to logical truths)
  • Logical necessity: for any set of statements containing the logically necessary statement in question, the logically necessary statement can be evaluated as true under at least one valuation.
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    You can see in SEP the following entries : Logical Truth and Logical Consequence. Tautology is a technical term (in propositional logic) without "philosophical" connotations. Logical consequence is a technical term with "philosophical" connotations. Logical truth may be equated with validity, and so is a technical term, but has some deep aspects and implications. Logical necessity involves modal logic. – Mauro ALLEGRANZA Mar 21 '14 at 9:38
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Tautologies are logical truths in the context of propositional logic:

φ is a tautology       =def   φ is assigned ⊤ by all rows of the truth-table for φ.

Logical truths are something more general, and can be defined as follows:

φ is a logical truth   =def   a true interpretation of the logical constants occurring in φ makes φ true.

Logical consequence is similar to that:

φ is a logical consequence of ψ   =def   every true interpretation of ψ makes φ true.

Logical necessity is a modal notion, and can be defined using state-descriptions:

φ is logically necessary   =def   φ is true in all state-descriptions.

All of these definitions are inspired by Carnap, but may differ from his actual definitions.

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