more from Alfred Tarski

Single Idea 13344

[catalogued under 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=]

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


Alfred Tarski (The Concept of Logical Consequence [1936], p.417)

Book Reference

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]