9 ideas
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion. | |
| From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'. |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'. |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
| 15464 | The distinction between dispositional and 'categorical' properties leads to confusion [Lewis] |
| Full Idea: To avoid the danger of claiming that dispositions are their own categorical bases, we do better to eschew the alleged distinction between dispositional and 'categorical' properties altogether. | |
| From: David Lewis (Finkish dispositions [1997], II) | |
| A reaction: Since I have been unable to form any intuitive notion of what a 'categorical' property is, I like this, though not necessarily for his reason. |
| 15463 | All dispositions must have causal bases [Lewis] |
| Full Idea: Prior, Pargetter and Jackson have argued convincingly for the thesis that all dispositions must have causal bases. | |
| From: David Lewis (Finkish dispositions [1997], II) | |
| A reaction: [Their paper is 1982] This key thesis is tackled by modern defenders of powers. The question is not who has the best arguments, but who offers the most coherent picture. What is a 'causal basis'? What sort of thing could be primitive or fundamental? |
| 15461 | A 'finkish' disposition is real, but disappears when the stimulus occurs [Lewis] |
| Full Idea: A disposition which would straight away vanish if put to the test is called 'finkish'. A finkishly fragile thing is fragile so long as it is not struck. But if it were struck, it would straight away cease to be fragile, and it would not break. | |
| From: David Lewis (Finkish dispositions [1997], I) | |
| A reaction: There are also 'antidotes'. Finks kill the disposition, antidotes kill the effect. These cases are problems for the simple conditional analysis of a disposition - because we never achieved the consequent. |
| 15462 | Backtracking counterfactuals go from supposed events to their required causal antecedents [Lewis] |
| Full Idea: 'Backtracking' counterfactual reasoning runs from a counterfactually supposed event to the causal antecedents it would have to have had. | |
| From: David Lewis (Finkish dispositions [1997], I) | |
| A reaction: Why not call it a 'transcendental' counterfactual? Presumably you go thisworld>> counterfactualevent>> worldneededtocauseit. It conjures up two possible worlds instead of one. |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| Full Idea: A class of sentences can be called 'analytical' if every sequence of objects is a model of it. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.418) | |
| A reaction: See Idea 13344 and Idea 13343 for the context of this assertion. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |