illogically

from WordNet (r) 3.0 (2006)

illogically
    adv 1: in an illogical manner; "she acted illogically under the
           pressure" [ant: {logically}]

from The Collaborative International Dictionary of English v.0.48

Illogical \Il*log"ic*al\, a.
   Ignorant or negligent of the rules of logic or correct
   reasoning; as, an illogical disputant; contrary of the rules
   of logic or sound reasoning; as, an illogical inference. --
   {Il*log"ic*al*ly}, adv. -- {Il*log"ic*al*ness}, n.
   [1913 Webster]