illogic

[ih-loj-ik]
noun
the state or quality of being illogical; illogicality: His speech was full of illogic.

Origin:
1855–60; il-2 + logic

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World English Dictionary
illogic (ɪˈlɒdʒɪk)
 
n
reasoning characterized by lack of logic; illogicality

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Example sentences
Each step seems logical, while the illogic of it all evades them.
The problem with your illogic is that it will be too late to do anything then.
Logic performs well but fails poorly, illogic performs poorly but fails well.
If one thing is certain birds demonstrate the nonsense illogic behind the
  research.
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