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What does irrationality mean?

Looking for the meaning or definition of the word irrationality? Here's what it means.

Noun
  1. The quality or state of being irrational; want of the faculty or the quality of reason; fatuity.
  2. Something which is irrational or brought forth by irrational action, judgement, idea or thought.
  3. (mathematics) The property of being irrational.
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Examples
Like most approaches grounded in irrationality, this one hasn't worked either.
What interests us here is not so much the completely irrationality of Carr's ravings, but the underlying reason for it.
I stand four-square for reason, and object to what seems to me to be irrationality, whatever the source.
The author shows how gaslight gave the night walker the experience of poetry and irrationality.
It is tempting to criticize the trial by ordeal, wager of law and judicial combat for their apparent irrationality and cruelty.
He railed against the creation of artificial dichotomies, such as head versus heart, reason versus irrationality.

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