This episode also involves an amusingly naive version of the old SF motif "why an AI can never love / think / laugh / understand people." Eventually, both Mudd and the Enterprise crew find themselves wanting to leave the planet, but the androids prevent them. The crew determines that the androids have highly rigid expectations for how those around them should act, and will overheat (losing their magic blue smoke in the process) if they are sufficiently confused. They take down a few of the androids by asserting that humans shun pleasure and desire pain, but Norman, the head android, is too resistant. Finally, they get him by telling him that Mudd is a notorious liar, who never says anything true. When Norman has accepted this, Mudd steps forward and says "I am lying." Norman fries.
(unlike TNG, this episode showed little concern about the morality of killing an intelligent artificial life form).

This is naive, of course, because humans have known about Gödel's incompleteness theorem since 1931, and would surely have programmed its AIs to recognize self-falisfying statements and cease evaluating them before doing themselves harm.

See also: Epimenides paradox, Liar paradox, the smallest unnoded natural number.