Early 17th century; earliest use found in Richard Bernard (bap. 1568, d. 1641), Church of England clergyman and religious writer. From unlogical + -ly.
Definition of unlogically in US English:
unlogically
adverb(ˌ)ʌnˈlɒdʒɪkli
Not logically, illogically; without logic.
Origin
Early 17th century; earliest use found in Richard Bernard (bap. 1568, d. 1641), Church of England clergyman and religious writer. From unlogical + -ly.