Source : Webster's Revised Unabridged Dictionary (1913)

Incomprehensibility \In*com`pre*hen`si*bil"i*ty\, n. [Cf. F.
   incompr['e]hensibilit['e].]
   The quality of being incomprehensible, or beyond the reach of
   human intellect; incomprehensibleness; inconceivability;
   inexplicability.

         The constant, universal sense of all antiquity
         unanimously confessing an incomprehensibility in many
         of the articles of the Christian faith.  --South.

Source : WordNet®

incomprehensibility
     n : the quality of being incomprehensible [ant: {comprehensibility}]