Non-rational

Indeed, the tirade against information in effect serves to justify the constriction of the area of rationality and scientific approach, in order to find room for all kinds of non-rational sources of "knowledge."

Source: wiktionary

But what of non-rational beings—the animal or infant-man of attuition?

Source: wiktionary

In the total artistic process the two phases—rational and non-rational, planful and inspirational—may be successive or simultaneous.

Source: wiktionary

Holton, a Harvard physicist and science historian, introduces us to the two extremist factions he sees attacking science from both sides: the "new Dionysians" who would widen the spectrum of scientific knowledge to include nonrational experience and the "new Apollonians" who would restrict scientific investigation to dealing only with those questions that seem to guarantee rational solution from the outset.

Source: wiktionary