Webster's English Dictionary

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illogical

il.log.i.cal \-i-k*l\ \(.)il-.a:j-i-'kal-*t-e-\ \(')il-'(l)a:j-i-k(*-)le-\ 
   \-k*l-n*s\ aj 1: not observing the principles of logic  2: devoid of logic 
   : SENSELESS  - il.log.i.cal.i.ty n