more from Peter Smith

### Single Idea 10087

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 7. Decidability]

Full Idea

A theory is 'decidable' iff there is a mechanical procedure for determining whether any sentence of its language can be proved.

Gist of Idea

A theory is 'decidable' if all of its sentences could be mechanically proved

Source

Peter Smith (Intro to Gödel's Theorems [2007], 03.4)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.24

A Reaction

Note that it doesn't actually have to be proved. The theorems of the theory are all effectively decidable.