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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.
Gist of Idea
Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match
Source
report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.73
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'.
Related Idea
Idea 18811 Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
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] |