more from Donald Davidson

Single Idea 19174

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

Full Idea

Axioms specify how each unstructured predicate is satisfied by a particular sequence. Then recursive axioms characterise complex sentences built from simpler ones. Closed sentences have no free variables, so true sentences are satisfied by all sequences.

Gist of Idea

Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths


Donald Davidson (Truth and Predication [2005], 7)

Book Reference

Davidson,Donald: 'Truth and Predication' [Belknap Harvard 2005], p.160

A Reaction

I take 'all sequences' to mean all combinations of objects in the domain. Thus nothing in domain contradicts the satisfied sentences. Hence Tarski's truth is said to be 'true in a model', where the whole system vouches for the sentence.

Related Ideas

Idea 19175 Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]

Idea 19191 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]