10 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… |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| Full Idea: Ramsey's Test for conditionals is that a conditional should be believed if a belief in its antecedent would commit one to believing its consequent. | |
| From: report of Frank P. Ramsey (Law and Causality [1928]) by Stephen Read - Thinking About Logic Ch.3 | |
| A reaction: A rather pragmatic approach to conditionals |
| 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
| Full Idea: If two people are arguing 'If p, will q?' and are both in doubt as to p, they are adding p hypothetically to their stock of knowledge, and arguing on that basis about q; ...they are fixing their degrees of belief in q given p. | |
| From: Frank P. Ramsey (Law and Causality [1928], B 155 n) | |
| A reaction: This has become famous as the 'Ramsey Test'. Bennett emphasises that he is not saying that you should actually believe p - you are just trying it for size. The presupposition approach to conditionals seems attractive. Edgington likes 'degrees'. |
| 6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
| Full Idea: Ramsey Sentences are his technique for eliminating theoretical terms in science (and can be applied to mental terms, or to social rights); a term in a sentence is replaced by a variable and an existential quantifier. | |
| From: Frank P. Ramsey (Law and Causality [1928]), quoted by Thomas Mautner - Penguin Dictionary of Philosophy p.469 | |
| A reaction: The technique is used by functionalists and results in a sort of eliminativism. The intrinsic nature of mental states is eliminated, because everything worth saying can be expressed in terms of functional/causal role. Sounds wrong to me. |
| 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'). |
| 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
| Full Idea: Even if we knew everything, we should still want to systematize our knowledge as a deductive system, and the general axioms in that system would be the fundamental laws of nature. | |
| From: Frank P. Ramsey (Law and Causality [1928], §A) | |
| A reaction: This is the Mill-Ramsey-Lewis view. Cf. Idea 9420. |
| 9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |
| Full Idea: Causal laws are consequences of those propositions which we should take as axioms if we knew everything and organized it as simply as possible in a deductive system. | |
| From: Frank P. Ramsey (Law and Causality [1928], §B) | |
| A reaction: Cf. Idea 9418. |