Irrationality is the noun: the state or quality of not being based on clear thought. You use it when you want to name the thing itself — the irrationality of a panic, of a rumour, of a rule that nobody can explain. It is more formal than “being unreasonable,” and you meet it in essays, news, and talk about the mind more than in kitchen chat. It can point to one wild act, or to a whole way of thinking. It does not, by itself, mean “madness.” It means the thinking is not sitting on reason. You can speak of someone recognising their own irrationality later, when the heat has gone.

不理性、非理性（名詞；偏書面）