noun
the quality or state of being irrational; lack of rationality or reason
adjective
irrational
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The decision was based on pure irrationality and lacked any logical reasoning.
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Her fear of spiders was just pure irrationality, she knows they can't hurt her.
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Stop being so irrational, there's no need to overreact like that.
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The irrationality of his actions left everyone puzzled and confused.