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Single Idea 8375

[filed under theme 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 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.

The 24 ideas with the same theme [understanding the concept of necessity]:

12611 Necessity makes alternatives impossible [Aristotle]
12381 What is necessary cannot be otherwise [Aristotle]
12734 Every necessary proposition is demonstrable to someone who understands [Leibniz]
13828 Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking]
12190 Necessity is what will be, despite any alternative suppositions whatever [Mill]
22623 Necessity can only mean what must be, without conditions of any kind [Mill]
16013 Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
24077 Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche]
7134 Something can be irrefutable; that doesn't make it true [Nietzsche]
8375 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
6099 Modal terms are properties of propositional functions, not of propositions [Russell]
11002 Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]
10921 Necessity can attach to statement-names, to statements, and to open sentences [Quine]
11880 Kripke says his necessary a posteriori examples are known a priori to be necessary [Kripke, by Mackie,P]
15290 What reduces the field of the possible is a step towards necessity [Harré/Madden]
8822 Statements about necessities need not be necessarily true [Pollock]
15086 Absolute necessity might be achievable either logically or metaphysically [Hale]
11001 Equating necessity with truth in every possible world is the S5 conception of necessity [Read]
5738 We may be sure that P is necessary, but is it necessarily necessary? [Melia]
11083 A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna]
16346 Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach]
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
19008 The modern revival of necessity and possibility treated them as special cases of quantification [Vetter]
19029 It is necessary that p means that nothing has the potentiality for not-p [Vetter]