'anti-rational' originates from Modern English, combining the prefix 'anti-' (from Greek 'anti-' meaning 'against') and 'rational' (from Latin 'rationalis' meaning 'pertaining to reason').

'rational' derives from Latin 'ratio/ rationalis' and passed into Old French and Middle English as 'rational', and the combining prefix 'anti-' (Greek) was later attached in Modern English to form 'anti-rational'; adding '-ly' creates the adverb 'anti-rationally'.

Initially components meant 'against' and 'pertaining to reason'; the combined modern usage came to mean 'opposed to rationalism or rational methods' and the adverb now means 'in a way that rejects or opposes reason'.