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10. Modality / A. Necessity / 2. Nature of Necessity

[understanding the concept of necessity]

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