Irrationality

noun

1. The state or quality of being irrational.
2. An irrational idea, expression, or act.
3. In mathematics, incommensurability.
4. The condition of being irrational; want of the faculty or the quality of reason; fatuity: as, the irrationality of brutes; the irrationality of a scheme.
5. That which is irrational; an irrational thought, action, or thing.