perceptiveness

noun

Skill in perceiving, discriminating, or judging: acumen, astuteness, clear-sightedness, discernment, discrimination, eye, keenness, nose, penetration, percipience, percipiency, perspicacity, sagacity, sageness, shrewdness, wit. See ability/inability, careful/careless.

The noun has 4 meanings:

Meaning #1: a feeling of understanding
  Synonyms: insight, perceptivity

Meaning #2: delicate discrimination (especially of aesthetic values)
  Synonyms: taste, appreciation, discernment

Meaning #3: perception of that which is obscure
  Synonym: discernment

Meaning #4: the quality of insight and sympathetic understanding
  Antonym: unperceptiveness (meaning #1)