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Absurd, illogical. Compare paradoxal , "paradoxical".
Mid 17th century; earliest use found in John Gaule (1603/4–1687), Church of England clergyman and author. Originally either from adox + -al or from classical Latin adoxus or its etymon ancient Greek ἄδοξος (both adjectives) + -al, after orthodoxal, paradoxal, etc.