Source : Webster's Revised Unabridged Dictionary (1913)

Irrationality \Ir*ra`tion*al"i*ty\, n.
   The quality or state of being irrational. ``Brutish
   irrationaliity.'' --South.

Source : WordNet®

irrationality
     n : the state of being irrational; lacking powers of
         understanding [syn: {unreason}]