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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 Ref
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.
| 4396 | The law of causality is a source of confusion, and should be dropped from philosophy [Russell] |
| 8375 | 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell] |
| 8376 | If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell] |
| 8378 | Philosophers usually learn science from each other, not from science [Russell] |
| 8379 | In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell] |
| 8380 | Striking a match causes its igniting, even if it sometimes doesn't work [Russell] |
| 8381 | The constancy of scientific laws rests on differential equations, not on cause and effect [Russell] |