keenness

noun

1. A cutting quality: bite, edge, incisiveness, sharpness, sting. See sharp/dull.
2. Skill in perceiving, discriminating, or judging: acumen, astuteness, clear-sightedness, discernment, discrimination, eye, nose, penetration, perceptiveness, percipience, percipiency, perspicacity, sagacity, sageness, shrewdness, wit. See ability/inability, careful/careless.

The noun has 3 meanings:

Meaning #1: a quick and penetrating intelligence
  Synonyms: acuteness, acuity, sharpness

Meaning #2: a positive feeling of wanting to push ahead with something
  Synonyms: eagerness, avidity, avidness

Meaning #3: thinness of edge or fineness of point
  Synonym: sharpness