The Collaborative International Dictionary of English v.0.48:

Insignificance \In`sig*nif"i*cance\, n.
   1. The condition or quality of being insignificant; lack of
      significance, sense, or meaning; as, the insignificance of
      words or phrases.
      [1913 Webster]

   2. Lack of force or effect; unimportance; pettiness;
      inefficacy; as, the insignificance of human art.
      [1913 Webster]

   3. Lack of claim to consideration or notice; lack of
      influence or standing; meanness.
      [1913 Webster]

            Reduce him, from being the first person in the
            nation, to a state of insignificance. --Beattie.
      [1913 Webster]

WordNet (r) 3.0 (2006):

insignificance
    n 1: the quality of having little or no significance [ant:
         significance]