illogic
Definitions
The state or quality of being illogical; lack of sound reasoning.
An instance or example of faulty or irrational thinking.
Examples
The sheer illogic of his argument made it impossible for the committee to take his proposal seriously.
She pointed out the illogic in the company's new policy, noting that it would actually decrease productivity rather than improve it.
Synonyms
irrationality incoherence absurdity fallacy unreasonableness inconsistency senselessness