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Single Idea 13828
[filed under theme 10. Modality / A. Necessity / 2. Nature of Necessity
]
Full Idea
Leibniz argued that the necessary truths are just those which can be proved from identities by pure logic in a finite number of steps. ...[232] this claim is vindicated by Gentzen's sequent calculus.
Gist of Idea
Necessary truths are those provable from identities by pure logic in finite steps
Source
report of Gottfried Leibniz (works [1690]) by Ian Hacking - What is Logic? §01
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.226
A Reaction
This seems an odd idea, as if there were no necessary truths other than those for which a proof could be constructed. Sounds like intuitionism.
The
25 ideas
with the same theme
[understanding the concept of necessity]:
24236
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Some statements about what is obvious and stable are as irrefutable as possible
[Plato]
|
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]
|