Contradicting or disregarding the principles of logic.(adjective)
Without logic; senseless.(adjective)
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Use "illogical" in a sentence
"The report also cited what it described as illogical actions by the crew."
"The president's mentor, Ayatollah Mohammad Taqi Mesbah Yazdi, said Ahmadinejad is increasingly turning friends into enemies and demonstrating what he called "illogical and cheap" behavior."
"Dear St. Thomas, how sad that someone so illogical is masquerading as you."