Adjective : an illogical reply.    From Dictionary.com. 

I don't want to fail at everything worth anything. (illogicalness).    From Wordnik.com.  [hemopoetic Diary Entry] Reference

Morettina, and by a very strange illogicalness never was the name of the brother of La Morettina mentioned without a formula of friendship.    From Wordnik.com.  [The French Immortals Series — Complete] Reference

She lied with the absurd and barefaced illogicalness of one finding herself in danger of death.    From Wordnik.com.  [Mare Nostrum (Our Sea) A Novel] Reference

The parallel between the the ambitions and the futility of the goat, and the present speaker's late advice is so obvious that only the illogicalness of woman can account for my cherishing a hope that I may be spared the fate of the indiscreet Billy.    From Wordnik.com.  [Library Work with Children] Reference

Regret as we sometimes must the illogicalness of the human mind, yet it is a providential characteristic of our as yet defective nature; for thanks to it few men or nations carry out to their complete logical results erroneous opinions and metaphysical speculations.    From Wordnik.com.  [Evolution Of The Japanese, Social And Psychic] Reference

But apart from the vagueness and illogicalness of several of the statements, the foregoing effusion is curious as a whole: the thoughts turn up one does not know where, how, or why ” their course is quite unaccountable; and if they passed through his mind in an unbroken connection, he fails to give the slightest indication of it.    From Wordnik.com.  [Frederic Chopin as a Man and Musician]

Human illogicalness providential -- Some devices for avoiding the evils of logical conclusions -- Buddhistic actual appeal to personal self-activity -- Practical Confucianism an antidote to Buddhist poison -- Confucian ethics produced strong persons -- The personal conception of deity is widespread -- Shinto gods all persons -- Popular.    From Wordnik.com.  [Evolution Of The Japanese, Social And Psychic] Reference