illogicality

[ih-loj-i-kal-i-tee]
noun, plural illogicalities.
2.
an example of illogic: an argument notable for its illogicalities.

Origin:
1820–30; illogical + -ity

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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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
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Example sentences
The illogicality of punishing those who are here in an effort to deter those who might come should always have been obvious.
The book is sprinkled with enough pretentious jargon, factual error and illogicality to infuriate and baffle the unwary.
But let us focus on the illogicality of your arguments.
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