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… |
| 21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
| Full Idea: Some philosophers maintain that we literally perceive proportions and other internal relations. These relations must exist, otherwise we couldn't perceive them. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: [He cites Mulligan 1991, and Hochberg 2013:232] This seems a rather good point. You can't perceive the differing heights of two people, yet fail to perceive that one is taller. You also perceive 'below', which is external. |
| 21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
| Full Idea: Internal relations are determined either by the mere existence of the things they relate, or by their intrinsic characters, or they supervene on the intrinsic characters of the things they relate. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: Suggesting that they 'supervene' doesn't explain anything (and supervenience never explains anything). I vote for the middle one - the intrinsic character. It has to be something about the existence, and not the mere fact of existence. |
| 21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
| Full Idea: A 'unigrade' relation R has a definite degree or adicity: R is binary, or ternary....or n-ary (for some unique n). By contrast a relation is 'multigrade' if it fails to be unigrade. Causation appears to be multigrade. | |
| From: Fraser MacBride (Relations [2016], 1) | |
| A reaction: He also cites entailment, which may have any number of premises. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |