6 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. |
| 16705 | Whiteness isn't created in an alteration, because it is just this-being-white [Oresme] |
| Full Idea: If it is said that whiteness begins to be through alteration, this does not hold, because whiteness is nothing other than this-being-white. | |
| From: Nicole Oresme (On 'Generation and Corruption' [1349], I.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.3 | |
| A reaction: This innocent-looking remark is dynamite, because it rejects the separability of qualities, which threatens the doctrine of Transubstantiation. |
| 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. |
| 20544 | Berlin distinguishes 'negative' and 'positive' liberty, and rejects the latter [Berlin, by Swift] |
| Full Idea: Isaiah Berlin draws a famous distinction between 'negative' and 'positive' concepts of liberty, and argues that the latter should be seen as a wrong turning (because totalitarian regimes have invoked it). | |
| From: report of Isaiah Berlin (Two Concepts of Liberty [1958]) by Adam Swift - Political Philosophy (3rd ed) 2 'Intro' | |
| A reaction: Swift argues against him, saying that positive liberty is not a single concept (it's three), and has aspects that should be defended. I think I'm with Swift on that. Is religious freedom a freedom 'from' something, or a freedom 'to do' something? |