In an illogical manner, without following methods of sane and correct reasoning, in a manner lacking thought or logic.(adverb)
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Use "illogically" in a sentence
"He illogically compared the criticsms of the entire DoJ in having their own lawyers defend the accused to the criticisms leveled at Yoo and Addington."
"And she was also illogically infuriated by the fact that the company demanding so much of her hard-earned money was French."
"I am sprawled on the floor, illogically looking for cool air from the wooden planks."