more from John P. Burgess

Single Idea 15417

[catalogued under 10. Modality / A. Necessity / 6. Logical Necessity]

Full Idea

Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension.

Gist of Idea

Logical necessity has two sides - validity and demonstrability - which coincide in classical logic


John P. Burgess (Philosophical Logic [2009], 3.3)

Book Reference

Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.46

A Reaction

They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'.

Related Idea

Idea 15418 Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]