8 ideas
| 10163 | Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman] |
| Full Idea: At the age of 19 Saul Kripke published a completeness proof of propositional modal logic. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V |
| 10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
| Full Idea: Kripke gave a possible worlds semantics to a whole range of modal logics, and S4 and S5 turned out to be both sound and complete with this semantics. Hence more systems could be designed. S1-S3 failed in soundness, leading to 'impossible worlds'. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Marcus Rossberg - First-order Logic, 2nd-order, Completeness §4 |
| 16189 | The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen] |
| Full Idea: Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3 | |
| A reaction: [p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects. |
| 15132 | The Barcan formulas fail in models with varying domains [Kripke, by Williamson] |
| Full Idea: Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1 | |
| A reaction: I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm… |
| 22485 | Non-cognitivists give the conditions of use of moral sentences as facts about the speaker [Foot] |
| Full Idea: What all these [non-cognitivist] theories try to do is to give the conditions of use of sentences such as 'It is morally objectionable to break promises', in terms of something which must be true about the speaker. | |
| From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.192) | |
| A reaction: A wonderfully simple and accurate analysis of this view. Compare analysing 'there is a bus coming towards you' in the same way. Sounds silly, but lots of modern philosophers see things that way. |
| 22486 | The mistake is to think good grounds aren't enough for moral judgement, which also needs feelings [Foot] |
| Full Idea: The mistake is to think that whatever 'grounds' for a moral judgement may have been given, someone may be unready, indeed unable, to make the moral judgement, because he has not got the attitude or feeling. | |
| From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.192) | |
| A reaction: This is roughly the Frege-Geach problem for expressivism, of how we still make moral judgements about situations where we ourselves are entirely disinterested (such as ancient historical events). |
| 22487 | Moral arguments are grounded in human facts [Foot] |
| Full Idea: The grounding of a moral argument is ultimately in facts about human life. | |
| From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.207) | |
| A reaction: The best slogan I can find for summarising Foot's metaethics. The facts she refers to the basic human needs. She is right, and this almost bridges the fact-value divide (as long as you give a damn about human needs). |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |