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Longman Dictionary of Contemporary English
irrational
adjective
COLLOCATIONS FROM OTHER ENTRIES
an irrational fear (=one that is not reasonable)
▪ He grew up with an irrational fear of insects.
COLLOCATIONS FROM CORPUS
■ ADVERB
as
▪ First, deficit cultures are portrayed as irrational, as based on ignorance.
▪ I become now as irrational as I was then.
▪ He argued that it is too simplistic, and indeed ethnocentric, to dismiss such peoples as irrational and unscientific.
▪ Blaming parents can be as irrational as suggesting that more family time can prevent asthma or diabetes.
▪ Instead of rejecting religion out of hand as irrational, he enquired about it.
▪ But, importantly, they can not be ignored nor can they be dismissed easily as irrational fabrications.
▪ One can argue with Czerny's and Hummel's metronome markings, but on no grounds can they be dismissed as irrational.
■ NOUN
behaviour
▪ Cognition is to do with the rational domain: logic, reasoning and problem solving uncomplicated by irrational behaviour.
▪ By implication, other approaches were based on irrational behaviour.
▪ But Bruce's irrational behaviour spoiled it all.
▪ In the Cold War irrational behaviour like this acquired a sort of sacred aura.
fear
▪ She kept repeating to herself that it was an irrational fear, but logic did nothing to quell the lurking terror.
▪ Even among those not so badly affected, ignorance about radiation produces powerful if sometimes irrational fear.
▪ If your subject to these irrational fears, then use that fear as a trigger to change your attitude.
▪ I have an irrational fear that Lucker will blank me.
▪ It seems that anxious people condition most easily and it is thought that irrational fears are established in this way.
▪ Again, careful teaching is important as well as loving discussion of these often irrational fears.
EXAMPLES FROM OTHER ENTRIES
▪ His behaviour can be somewhat irrational at times.
▪ If Dane drinks even a couple of beers, he becomes irrational and even violent.
▪ Jane's irrational hopes began to rise as she listened to him.
▪ She struggled to overcome her irrational fear of the dark.
▪ Vance is becoming increasingly irrational.
EXAMPLES FROM CORPUS
▪ A man once famed for his intolerance, xenophobia and irrational rages has become a husk of his former self.
▪ Fighting hard to prevent such losses is not irrational.
▪ I knew I was being irrational but I began to fear the worst.
▪ In retrospect their structure seems irrational with no clear division between territorial and functional responsibilities.
▪ It was a pathetic gesture on my part, an irrational breach of the wall.
▪ This never worked, but I did it every time: tried to talk her out of her irrational ways.
▪ This, you understand, is purely sentimental and wholly irrational.
▪ Yet although these medical theories were wrong, they weren't altogether irrational.
The Collaborative International Dictionary
irrational

irrational \ir*ra"tion*al\ ([i^]r*r[a^]sh"[u^]n*al), a. [L. irrationalis: cf. F. irrationnel. See In- not, and Rational.]

  1. Not rational; void of reason or understanding; as, brutes are irrational animals.

  2. Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs. Hence, of actions: foolish; unreasonable.

    It seemed utterly irrational any longer to maintain it.
    --I. Taylor.

  3. (Math.) Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; -- said especially of roots. See Surd.

    Syn: Absurd; foolish; preposterous; unreasonable; senseless. See Absurd.

Douglas Harper's Etymology Dictionary
irrational

late 15c., "not endowed with reason" (of beats, etc.); earlier (of quantities) "inexpressible in ordinary numbers" (late 14c.); from Latin irrationalis "without reason," from assimilated form of in- "not, opposite of" (see in- (1)) + rationalis "reason" (see rational). Meaning "illogical, absurd" is attested from 1640s. Related: Irrationally.\n

Wiktionary
irrational

a. 1 Not rational; unfounded or nonsensical. 2 (context mathematics arithmetic number theory not comparable English) Of a real number, that cannot be written as the ratio of two integers. n. A real number that can not be expressed as the quotient of two integers, an irrational number.

WordNet
irrational
  1. adj. not consistent with or using reason; "irrational fears"; "irrational animals" [ant: rational]

  2. real but not expressible as the quotient of two integers; "irrational numbers" [ant: rational]

Wikipedia

Usage examples of "irrational".

He also related almost all the adventures that Sancho had recounted, which both astonished them and made them laugh, for they thought what everyone thought: it was the strangest kind of madness that had ever afflicted an irrational mind.

It seems, therefore, that just as irrational animals are not baptized, so neither should madmen and imbeciles in those cases be baptized.

The essential thing is that every obstacle should be denied and that the irrational should be triumphant.

It was probably sheer irrational instinct which made us dim our single torch--tempted no longer by the decadent and sinister sculptures that leered menacingly from the oppressive walls--and which softened our progress to a cautious tiptoeing and crawling over the increasingly littered floor and heaps of debris.

He felt some irrational hope that Daneel had come to take him away, to tell him the Plan was fulfilled and he did not have to stand trial, did not have to live in the shadow of the displeasure of Linge Chen.

Sasquatch on the grounds that the film would be difficult to fake, to one of irrational rejection based on an emotional response to the possibility that the Sasquatch actually exists.

Was he ashamed of grassing, even on so unattractive a character as Neville Skeate, or did he feel, as even proven liars sometimes do in the witness box, a sudden, irrational urge to tell the truth?

As the second version of his tendentious anecdote shows, he goes on to proclaim that Islam is an irrational herd or mass phenomenon, ruling Muslims by passions, instincts, and unreflecting hatreds.

Granting that there was a womanly intelligence there, as yet unquickened, he was not so irrational as to imagine he could jostle it into illumining activity in one short hour, or day, or week.

It has deep significance for those who have lived through social chaos, uprootedness, irrational torture, and this accounts for the pessimism and nightmarish imagery that pervade much Existentialist writing.

Carcassone, named Loba, or the Wolfess, the excess of his passion drove him over the country, howling like a wolf, and demeaning himself more like an irrational beast than a rational man.

An irrational instinct had rendered the painter and his paintings antipathetic to him at their first meeting.

The Yahoos, regarded as a distinct species, humanoid rather than equine, represent the irrational bestiality that the Houyhnhnms reject.

He worried for fear he would do something irrational while the attack was upon him, and ostracize himself in the village.

She did not demand that they be important to anyone else, yet it galled her that the world had passed through those years of ordeal without significant scars, and it also imbued her with the irrational fear that if she were to enter the village, she might suffer some magical slippage back through time and reinhabit her old life.