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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.
Gist of Idea
X follows from sentences K iff every model of K also models X
Source
Alfred Tarski (The Concept of Logical Consequence [1936], p.417)
Book Ref
Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], 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'.
Related Idea
Idea 13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |