Source : Webster's Revised Unabridged Dictionary (1913)

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

   2. Want of force or effect; unimportance; pettiness;
      inefficacy; as, the insignificance of human art.

   3. Want of claim to consideration or notice; want of
      influence or standing; meanness.

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

Source : WordNet®

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