The Collaborative International Dictionary of English v.0.48:

Acuteness \A*cute"ness\, n.
   1. The quality of being acute or pointed; sharpness; as, the
      acuteness of an angle. AS
      [1913 Webster]

   2. The faculty of nice discernment or perception; acumen;
      keenness; sharpness; sensitiveness; -- applied to the
      senses, or the understanding. By acuteness of feeling, we
      perceive small objects or slight impressions: by acuteness
      of intellect, we discern fine distinctions.
      [1913 Webster]

            Perhaps, also, he felt his professional acuteness
            interested in bringing it to a successful close.
                                                  --Sir W.
                                                  Scott.
      [1913 Webster]

   3. Shrillness; high pitch; -- said of sounds.
      [1913 Webster]

   4. (Med.) Violence of a disease, which brings it speedily to
      a crisis. AS
      [1913 Webster]

   Syn: Penetration; sagacity; keenness; ingenuity; shrewdness;
        subtlety; sharp-wittedness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

acuteness
    n 1: a sensitivity that is keen and highly developed; "dogs have
         a remarkable acuteness of smell"
    2: a quick and penetrating intelligence; "he argued with great
       acuteness"; "I admired the keenness of his mind" [syn:
       acuteness, acuity, sharpness, keenness]
    3: the quality of having a sharp edge or point [ant:
       obtuseness]