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Single Idea 12734

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

Full Idea

Every necessary proposition is demonstrable, at least by someone who understands it.

Gist of Idea

Every necessary proposition is demonstrable to someone who understands

Source

Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6

Book Ref

Garber,Daniel: 'Leibniz: Body, Substance, Monad' [OUP 2009], p.238

A Reaction

This kind of optimism leads to the crisis of the Hilbert Programme in the 1930s. Gödel seems to have conclusively proved that Leibniz was wrong. What would Leibniz have made of Gödel?

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]