Source : Webster's Revised Unabridged Dictionary (1913)

Destructiveness \De*struc"tive*ness\, n.
   1. The quality of destroying or ruining. --Prynne.

   2. (Phren.) The faculty supposed to impel to the commission
      of acts of destruction; propensity to destroy.

Source : WordNet®

destructiveness
     n : the quality of causing destruction [ant: {constructiveness}]