Etymology
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completeness (n.)

"state or quality of being complete," 1620s, from complete (adj.) + -ness.

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Definitions of completeness

completeness (n.)
the state of being complete and entire; having everything that is needed;
completeness (n.)
(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;
From wordnet.princeton.edu