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. |
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. |
7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
Full Idea: Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius. | |
From: report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
A reaction: This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny. |
9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection). | |
From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature |