Source : Webster's Revised Unabridged Dictionary (1913)

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.

Source : WordNet®

illogical
     adj 1: lacking in correct logical relation [syn: {unlogical}] [ant:
             {logical}]
     2: lacking orderly continuity; "a confused set of
        instructions"; "a confused dream about the end of the
        world"; "disconnected fragments of a story"; "scattered
        thoughts" [syn: {confused}, {disconnected}, {disjointed},
        {disordered}, {garbled}, {scattered}, {unconnected}]