The Collaborative International Dictionary of English v.0.48:

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.
   [1913 Webster]

         The constant, universal sense of all antiquity
         unanimously confessing an incomprehensibility in many
         of the articles of the Christian faith.  --South.
   [1913 Webster]

WordNet (r) 3.0 (2006):

incomprehensibility
    n 1: the quality of being incomprehensible [ant:
         comprehensibility, understandability]