Writers on ancient laughter often speak in the singular of the “ancient theory of laughter.” What they usually mean is Aristotle’s theory of laughter.
Mary Beard (Laughter in Ancient Rome) doesn’t think either of these things exists – there was no single ancient theory, and what Aristotle said about laughter (in the extant sources, excluding the legendary lost book on comedy) doesn’t amount to a theory.
Aristotle’s most extensive discussion of the topic appears in the Nicomachean Ethics, where he predictably enough suggests that wit is the mean between buffoonery and boorishness (Beard, 32).
His famous claim that humans are the only animals that laugh is part of a discussion of the diaphragm: “In a perilously circular explanation, he asserts that the fact that ‘humans alone are susceptible to tickling is due (a) to the fineness of their skin and (b) to their being the only living things that laugh.’ There is in this no suggestion that laughter is a distinguishing property of the human being. Despite the popular assumption about this aspect of his ‘theory,’ he is certainly not defining man as ‘the animal that laughs’” (32).
The other thing that everyone knows about Aristotle’s theory of laughter is that he saw it as an act of superiority and derision. Two passages form the basis of this notion. In the Poetics, he speaks of comedy in this fashion: “a representation of people worse than us, not in the full sense of bad, but what we laugh at, is a subdivision of the ugly/shameful. The laughable is some kind of fault and ugliness/shame that involves no pain or harm – such as, obviously, a comic mask, which is ugly and distorted but free of pain.” In the Rhetoric, he suggests (in Beard’s translation” that the young “are fond of laughter, and therefore witty. For wit is educated insolence” (quoted 32-3).
In all this, Beard argues, “there is rather less about derision than is usually supposed.” The laughter described in Poetics is explicitly a laughter that doesn’t cause pain. More importantly, there is nothing in either passage to indicate that Aristotle believes that ridicule is “laughter’s only cause, function, or stylistic register.” Like other Greeks, he was aware of “good-natured laughter,” and in Rhetoric he categorizes “laughter and the laughable into the class of ‘pleasant things’” (33).
So, no ancient theory of laughter, only theories.