irrationality

Short definition from Wiktionary

Noun

1. 1
   The quality or state of being irrational: The state of being illogical or absurd.
2. 2
   The quality or state of being irrational: The property of being an irrational number.
3. 3
   The quality or state of being irrational: The state of being incapable of reason or abstract thought.
4. 4
   Something that is irrational; the result of an illogical or absurd thought or action.