15 ideas
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 16616 | Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius] |
| Full Idea: It is proper to substance both to stretch out or exist beneath accidents, which is to substand, and to exist per se and not in another, which is to subsist. | |
| From: Eustachius a Sancto Paulo (Summa [1609], I.1.3b.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 06.2 | |
| A reaction: This reflects Aristotle wavering between 'ousia' being the whole of a thing, or the substrate of a thing. In current discussion, 'substance' still wavers between a thing which 'is' a substance, and substance being the essence. |
| 16585 | Prime matter is free of all forms, but has the potential for all forms [Eustachius] |
| Full Idea: Everyone says that prime matter, considered in itself, is free of all forms and at the same time is open to all forms - or, that matter is in potentiality to all forms. | |
| From: Eustachius a Sancto Paulo (Summa [1609], III.1.1.2.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
| A reaction: This is the notorious doctrine developed to support the hylomorphic picture derived from Aristotle. No one could quite figure out what prime matter was, so it faded away. |
| 8430 | Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim] |
| Full Idea: The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.207) | |
| A reaction: He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little. |
| 8396 | Many counterfactuals have nothing to do with causation [Kim, by Tooley] |
| Full Idea: Kim has pointed out that there are a number of counterfactuals that have nothing to do with causation. If John marries Mary, then if John had not existed he would not have married Mary, but that is not the cause of their union. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973], 5.2) by Michael Tooley - Causation and Supervenience | |
| A reaction: One might not think that this mattered, but it leaves the problem of distinguishing between the causal counterfactuals and the rest (and you mustn't mention causation when you are doing it!). |
| 8429 | Counterfactuals can express four other relations between events, apart from causation [Kim] |
| Full Idea: Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: [Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'. |
| 8428 | Causation is not the only dependency relation expressed by counterfactuals [Kim] |
| Full Idea: The sort of dependency expressed by counterfactual relations is considerably broader than strictly causal dependency, and causal dependency is only one among the heterogeneous group of dependency relationships counterfactuals can express. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: In 'If pigs could fly, one and one still wouldn't make three' there isn't even a dependency. Kim has opened up lines of criticism which make the counterfactual analysis of causation look very implausible to me. |
| 4781 | Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos] |
| Full Idea: Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3 | |
| A reaction: This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is. |