display all the ideas for this combination of texts
9 ideas
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. |
13084 | How can things be incompatible, if all positive terms seem to be compatible? [Leibniz] |
Full Idea: It is yet unknown to me what is the reason of the incompossibility of things, or how it is that different essences can be opposed to each other, seeing that all purely positive terms seem to be compatible. | |
From: Gottfried Leibniz (works [1690], G VII:194), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.4.4 | |
A reaction: Since 'heavy' seems straightforwardly opposed to 'light', we would have to ask what he means by 'positive'. The suspicion is that all things are compossible by definition, so it is not surprising that impossibilities are a bit puzzling. |
4307 | A reason must be given why contingent beings should exist rather than not exist [Leibniz] |
Full Idea: A reason must be given why contingent beings should exist rather than not exist. | |
From: Gottfried Leibniz (works [1690]) | |
A reaction: Spinoza rejects all contingency, but this seems an interesting support for it, even though we may need a reason for something where God does not because it is self-evident. |
6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
Full Idea: Modality has a special ontological category: it consists neither in objects (possible worlds theory) nor in properties (predicate modifier view), but items I have called 'modes', ..which can be hard/soft/rigid/pliable binding of objects to properties. | |
From: Colin McGinn (Logical Properties [2000], Ch.4) | |
A reaction: As so often, McGinn is very persuasive. Essentially he is proposing that modality is adverbial. He associates the middle view with David Wiggins. |
15883 | Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility [Leibniz, by Harré] |
Full Idea: Leibniz sets up increasingly stringent conditions possible worlds must meet. The weakest is non-contradiction, for truths of reason; then sufficient reason, for rational worlds; then identity of indiscernibles, for duplicates; then compossibility. | |
From: report of Gottfried Leibniz (works [1690]) by Rom Harré - Laws of Nature 4 | |
A reaction: [my summary of a very nice two pages by Harré] God is the source of the principles which do the narrowing down. |
18822 | Each monad expresses all its compatible monads; a possible world is the resulting equivalence class [Leibniz, by Rumfitt] |
Full Idea: Leibniz argued that each monad mirrors or expresses every monad with which it is compossible. Hence compossibility is an equivalence relation among monads; possible worlds may then be identified as the corresponding equivalence classes. | |
From: report of Gottfried Leibniz (works [1690]) by Ian Rumfitt - The Boundary Stones of Thought 6.1 | |
A reaction: [Rumfitt cites Benson Mates 1986:IV.1 for this claim] There is an analogous world of all the human minds that are in communication with one another - something like a 'culture'. |
7837 | Leibniz proposed possible worlds, because they might be evil, where God would not create evil things [Leibniz, by Stewart,M] |
Full Idea: In his early writings the principle of sufficient reason made it difficult for Leibniz to conceive of possible things;...raising this to possible worlds means God does not choose things that are evil, but chooses a world which must have evil in it. | |
From: report of Gottfried Leibniz (works [1690]) by Matthew Stewart - The Courtier and the Heretic Ch.14 | |
A reaction: Where we think of possible worlds as explanations for conditional and counterfactual truths (I take it), Leibniz developed the original idea as part of his huge effort to achieve a consistent theodicy. |
6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
Full Idea: If we replace modal words like 'possible' with quantification across worlds, clearly the notion of 'world' must exclude impossible worlds, otherwise 'possibly p' will be true if 'p' holds in an impossible world. | |
From: Colin McGinn (Logical Properties [2000], Ch.4) | |
A reaction: The point here, of course, is that the question is being begged of what 'possible' and 'impossible' actually mean. |
13080 | Leibniz has a counterpart view of de re counterfactuals [Leibniz, by Cover/O'Leary-Hawthorne] |
Full Idea: When Leibniz has the grounds of de re counterfactuals in mind, a counterpart picture, we have argued, is at work. | |
From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.2.2 | |
A reaction: If Leibniz were a 'superessentialist', then individuals would be totally worldbound (because their relations would be essential). Cover/Hawthorne argue that he is just a 'strong' essentialist, allowing possible counterparts. Quite persuasive. |