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keenness (n.)

"state or quality of being keen," 1520s, from keen (adj.) + -ness.

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Definitions of keenness from WordNet

keenness (n.)
a quick and penetrating intelligence;
I admired the keenness of his mind
Synonyms: acuteness / acuity / sharpness
keenness (n.)
a positive feeling of wanting to push ahead with something;
Synonyms: eagerness / avidity / avidness
keenness (n.)
thinness of edge or fineness of point;
Synonyms: sharpness
From wordnet.princeton.edu