Single Idea 8375

[catalogued under 10. Modality / A. Necessity / 2. Nature of Necessity]

Full Idea

'Necessary' is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments. Thus 'If x is a man, x is mortal' is necessary, because it is true for any possible value of x.

Gist of Idea

'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument

Source

Bertrand Russell (On the Notion of Cause [1912], p.175)

Book Reference

Russell,Bertrand: 'Mysticism and Logic' [Unwin 1989], p.175


A Reaction

This is presumably the intermediate definition of necessity, prior to modern talk of possible worlds. Since it is a predicate about functions, it is presumably a metalinguistic concept, like the semantic concept of truth.