Illogical means something doesn't make sense or follow the rules of reason. When an argument is illogical, its conclusions don't follow from its premises, like saying “All cats have tails, my dog has a tail, therefore my dog is a cat.” The pieces don't fit together properly.

Logic is the science of correct reasoning, so something illogical violates those principles. If your friend insists they can't be hungry because they ate breakfast three days ago, that's illogical reasoning. If a character in a story is terrified of harmless butterflies but fearlessly wrestles alligators, their behavior seems illogical.

Sometimes people confuse illogical with unlikely or surprising, but they're different. It might be unlikely that you'll find a twenty-dollar bill on the sidewalk, but there's nothing illogical about it. However, if someone claimed they found the same twenty-dollar bill in five different cities on the same day, that would be illogical.

The opposite is logical, meaning something follows clear reasoning and makes sense. When you solve a math problem step by step, you're using logical thinking. When scientists form hypotheses based on evidence, they're being logical. Spotting illogical arguments helps you think more clearly and avoid being fooled by reasoning that sounds good but actually falls apart when you examine it carefully.