Douglas Harper's Etymology Dictionary
Wiktionary
arational
a. (context chiefly philosophy English) Not within the domain of what can be understood or analyzed by reason; not rational, outside the competence of the rules of reason. (from 20th c.)
Usage examples of "arational".
Regarded with the objectivity of hindsight, the illusion appears arational, almost literally fantastic: it would be like being able both to lie and to trust other people at the same time.
South, plus Penn's arational lobbing at an Israel that at the summit was explicitly placed under AMNAT's mutual-defense umbrella, has used these as golden tactical geese, racking up serious INDDIR-points against a SOUTHAF and INDPAK whose hasty defensive alliance and shaky aim produce nothing more than a lot of irradiated cod off Gloucester.