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.