Illogic

Overview
Illogic is the use of illogical statements to come to a logical conclusion. It can be used to confuse or distort, but usually is unintentionally created by a brain short-circuit or used for fun. A good example of illogic is this conversation:

"Slow down so I can talk to you!"

"No! I'm too lazy!  You speed up!"

Aliens
Spock is in this article for good reason. Vulcans' minds are physically damaged when exposed to illogic. The famed hand sign was actally a ward against illogic in ancient times.