Source : Webster's Revised Unabridged Dictionary (1913)

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

         The deadness and inanimateness of the subject. --W.
                                                  Montagu.

Source : WordNet®

inanimateness
     n : not having life [syn: {lifelessness}] [ant: {animateness}]