Source : Webster's Revised Unabridged Dictionary (1913)

Inquisitiveness \In*quis"i*tive*ness\, n.
   The quality or state of being inquisitive; the disposition to
   seek explanation and information; curiosity to learn what is
   unknown; esp., uncontrolled and impertinent curiosity.

         Mr. Boswell, whose inquisitiveness is seconded by great
         activity, scrambled in at a high window. --Johnson.

         Curiosity in children nature has provided, to remove
         that ignorance they were born with; which, without this
         busy inquisitiveness, will make them dull. --Locke.

Source : WordNet®

inquisitiveness
     n : a state of active curiosity [syn: {curiousness}]