Originally Posted by WillCAD

Tisk, tisk - you're mixing up two episodes.

Nomad destroyed anything that it believed to be "less than perfect", so Kirk tricked it into destroying itself when he revealed to it that it had made a major error, in mistaking Kirk for its original creator. It then intentionally activated a self-destruct, committing suicide because it thought itself to be unforgivably flawed.

However, in "I, Mudd", Kirk and company used logic to confound the thinking of a group of androids who wanted to take over the galaxy. They were unfailingly logical and couldn't comprehend the illogic of a group of emotional humans, so Kirk and his crew simply acted like raving lunatics, which confused most of the androids so badly that they had to shut down. The coup de grace, of course, was then they told the head android, Norman, "Everything that Harry Mudd says is a lie." Then Harry said, "Listen very carefully, Norman: I am LYING."

"You say you are lying, but if everything you say is a lie, then you are telling the truth, but you cannot tell the truth because you always lie... illogical! Illogical! Please explain! You are human; only humans can explain! Illogical!"