Full Idea
If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'.
Gist of Idea
A 'consistent' theory cannot contain both a sentence and 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