illogical

[ih-loj-i-kuhl]
adjective
not logical; contrary to or disregardful of the rules of logic; unreasoning: an illogical reply.

Origin:
1580–90; il-2 + logical

illogically, adverb
illogicalness, noun


unsound, absurd, preposterous.
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World English Dictionary
illogical (ɪˈlɒdʒɪkəl)
 
adj
1.  characterized by lack of logic; senseless or unreasonable
2.  disregarding logical principles
 
illogicality
 
n
 
il'logicalness
 
n
 
il'logically
 
adv

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
Some of their proposed usages are internally illogical.
Even arguments for academic freedom, he said, risk straying into illogical
  territory.
Your illogical misadventures should highlight it for her nicely.
What some have pointed out is that his argument is illogical.
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