noun
Refers to something that goes against reason or logic; often used in formal or written contexts.
彼の要求は非理だと思う。
I think his demand is unreasonable.
その議論には非理な点が多い。
There are many illogical points in that argument.
Compound of 非 (hi, 'non-', 'un-') and 理 (ri, 'reason', 'logic'). The exact historical derivation is uncertain, but the word follows a common Sino-Japanese pattern for negation.