The Collaborative International Dictionary of English v.0.48:

Inanimateness \In*an"i*mate*ness\, n.
   The quality or state of being inanimate.
   [1913 Webster]

         The deadness and inanimateness of the subject. --W.
                                                  Montagu.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inanimateness
    n 1: not having life [syn: inanimateness, lifelessness]
         [ant: aliveness, animateness, liveness]