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.
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  illogicalness
       n : invalid or incorrect reasoning [syn: illogicality, illogic]
           [ant: logicality, logicality]