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
Source
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....