more from A.George / D.J.Velleman

Single Idea 10127

[catalogued under 5. Theory of Logic / K. Features of Logics / 4. Completeness]

Full Idea

If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'.

Gist of Idea

A 'complete' theory contains either any sentence or its negation


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.177

A Reaction

Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences....