### Ideas from 'The Concept of Logical Consequence' by Alfred Tarski [1936], by Theme Structure

#### [found in 'Logic, Semantics, Meta-mathematics' by Tarski,Alfred [Hackett 1956,0-915144-76-x]].

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###### 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
 18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match
 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'.
###### 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
 13344 X follows from sentences K iff every model of K also models X
 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'.
###### 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
 13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions
 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.
###### 19. Language / E. Analyticity / 1. Analytic Propositions
 13345 Sentences are 'analytical' if every sequence of objects models them
 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.