Source : Webster's Revised Unabridged Dictionary (1913)

Incompatibility \In`com*pat`i*bil"i*ty\, n.; pl. {-ties}. [Cf.
   F. incompatibilit['e].]
   The quality or state of being incompatible; inconsistency;
   irreconcilableness.

Source : WordNet®

incompatibility
     n 1: the relation between propositions that cannot both be true
          at the same time [syn: {mutual exclusiveness}, {inconsistency},
           {repugnance}]
     2: (immunology) the degree to which the body's immune system
        will try to reject foreign material (as transfused blood
        or transplanted tissue)
     3: the quality of being unable to exist or work in congenial
        combination [ant: {compatibility}]