'antilogistic' originates from Greek elements: 'anti-' meaning 'against' and 'logistikos' (through Latin/Medieval usage) related to 'logos' meaning 'reason' or 'word'.

'antilogistic' is a modern formation from the prefix 'anti-' + 'logistic'/'logisticus' (from Greek 'logistikos' via Latin), combining to mean 'against reason'; it entered English as a coined adjective rather than through an older single-source inherited form.

Initially formed to convey 'against calculation/reason' in a literal compositional sense; over time it has been used to mean more generally 'contrary to logic' or 'illogical'.