The Collaborative International Dictionary of English v.0.48:
irrationality \ir*ra`tion*al"i*ty\, n. The quality or state of being irrational; absence of rationality. "Brutish irrationaliity." --South. [1913 Webster]WordNet (r) 3.0 (2006):
irrationality n 1: the state of being irrational; lacking powers of understanding [syn: irrationality, unreason]