1. 
[syn: awareness, consciousness, cognizance, cognisance, knowingness]
2.  shrewdness demonstrated by knowledge; 
The Collaborative International Dictionary of English v.0.48:
Knowingness \Know"ing*ness\, n.
   The state or quality of being knowing or intelligent;
   shrewdness; skillfulness.
   [1913 Webster]
WordNet (r) 3.0 (2006):
knowingness
    n 1: having knowledge of; "he had no awareness of his mistakes";
         "his sudden consciousness of the problem he faced"; "their
         intelligence and general knowingness was impressive" [syn:
         awareness, consciousness, cognizance, cognisance,
         knowingness] [ant: incognizance]
    2: shrewdness demonstrated by knowledge