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Webster 1828 Edition

adv.

In a manner contrary to the rules of correct reasoning.

illogically ‎(comparative more illogically, superlative most illogically)

In an illogical manner, without following methods of sane and correct reasoning, in a manner lacking thought or logic.
You are behaving illogically. Your plan is emotionally sound, but not well thought out.

in an illogical manner