NOUN (2)

1. the state of being complete and entire; having everything that is needed;

2. (logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system;

The Collaborative International Dictionary of English v.0.48:

Completeness \Com*plete"ness\, n.
   The state of being complete.
   [1913 Webster]