What is humor? Henri Bergson's Laughter: An Essay on the Meaning of the Comic (1900) states that humor is a social tool by which we mildly scold each other for being insufficiently adaptive and flexible. On this account, the paradigm of humor is the absent-minded person, but any form of idiocy or freakishness or social ineptness also works: what's funny is the disconnect between the logic of the clown's behavior and what's actually called for socially in the situation.
One key way such a disconnect can be brought about is through the divergence of body and spirit, or more generally between one's intent and an opposing material reality. So a minister farting while giving a sermon would be especially funny.
Much of the book is taken up with stretching this theory to show how different types of humor relate to it. While he sees character humor as I've described above as central, there are derivative types: a funny coincidence mirrors the disconnect we see in character humor. Dramatic irony likewise involves the characters' intent clashing with circumstances of which they are unaware.
Bergson compares a pun or double entendre to the "absent-mindedness of language," where the two disconnected meanings converge interestingly. Sarcasm or verbal irony would involve a comparable kind of clash between meanings. However, Bergson wants to make sure we understand that such a clash itself is not sufficient for humor: an expression's having two meanings is not in itself funny, but only becomes funny because of the relation of those meanings to our interests, e.g. what we say is in direct contrast to what we mean to say and defeats our purposes.
Stretching the theory to fit physical humor, you can see how clumsiness/pratfalls would fall into the same category as absentmindedness and the inappropriate insertion of the body into a situation. Bergson characterizes this as the mechanical in contrast to the organic. A funny face, on this theory, is one that looks stuck in some way, like someone is perpetually surprised, or wincing, or falling asleep. He even says that clothes are inherently funny, given how their texture contrasts with our natural body, but that we get used to it and don't notice unless someone is wearing an unusual fashion (think bell bottoms or a top hat), in which case the strangeness reveals the humor, though again, the strangeness is not itself sufficient for the humor; merely looking strange is not the same as looking funny. He thinks the funny "deformities" are the ones that we could adopt by imitation, so someone missing his legs isn't funny, but hunchbacks, whoa those are hilarious (yes, this is one of his actual examples).
The regular four were joined for this discussion by comedienne Jennifer Dziura, and used Bergson's theory as a launching point to spout off about what is funny, why people's senses of humor differ, and why a theory of humor might not be possible. We didn't get to the bottom of the issue, and I anticipate that there will be at least one more episode on this topic (reading Freud).