display all the ideas for this combination of philosophers
3 ideas
| 12734 | Every necessary proposition is demonstrable to someone who understands [Leibniz] |
| Full Idea: Every necessary proposition is demonstrable, at least by someone who understands it. | |
| From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6 | |
| 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? |
| 13828 | Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking] |
| 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. | |
| From: report of Gottfried Leibniz (works [1690]) by Ian Hacking - What is Logic? §01 | |
| 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. |
| 5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
| Full Idea: Although the world is not metaphysically necessary, such that its contrary would imply a contradiction or logical absurdity, it is necessary physically, that is, determined in such a way that its contrary would imply imperfection or moral absurdity. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.139) | |
| A reaction: How does Leibniz know things like this? The distinction between 'metaphysical' necessity and 'natural' (what he calls 'physical') necessity is a key idea. But natural necessity is controversial. See 'Essentialism'. |