more from Alfred Tarski

Single Idea 19191

[catalogued under 3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth]

Full Idea

To define satisfaction we indicate which objects satisfy the simplest sentential functions, then state the conditions for compound functions. This applies automatically to sentences (with no free variables) so a true sentence is satisfied by all objects.

Gist of Idea

Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects


Alfred Tarski (The Semantic Conception of Truth [1944], 11)

Book Reference

'Semantics and the Philosophy of Language', ed/tr. Linsky,Leonard [University of Illinois 1972], p.25

A Reaction

I presume nothing in the domain of objects can conflict with a sentence that has been satisfied by some of them, so 'all' the objects satisfy the sentence. Tarski doesn't use the word 'domain'. Basic satisfaction seems to be stipulated.

Related Idea

Idea 19174 Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson]