I learn from Hugh’s comment to my post here that it is possible – and not only in German – “to play with words that [sound] alike, but [are] spelled differently.”

I have never seen this done, or knowingly done it myself. I know that there are some words that sound alike and are spelt differently, but this is rather a nuisance to be overcome than material for “play”, still less amusement. I hope that puns remain deservedly rare, a hope that I think is shared by Thomas C Veatch:

The pun is a form of humor involving linguistic ambiguity. Ambiguity is of course a major means of constructing humorous speech acts, since a violation in one interpretation may be disguised by the "straight" N interpretation in the other. Punning is done differently in different cultures, where the hilariously ambiguous turn of phrase or innuendo can be a widely acknowledged and highly respected form of verbal art. In this section, however, I will only discuss the punning practices I am familiar with in my culture. These involve speech events of a certain type, similar to the set joke or riddle. They are of interest because they have often been proposed as counterexamples to the present theory, because people often find it difficult to see any moral violation in them. Consider first an example of this genre, chosen for its apparent lack of affective implications.

Q: ``When is a door not a door?'
A: ``When it's ajar.'

[…]

Consider how these observations (one at a time) can be derived from a moral theory of humor by examining the above example. A related proof will clarify the logic used. Note the ambiguity in step 2 (observation 4):

1. X is a door (Given by Q)
2. a) X is ajar, AND b) X is a jar (the ambiguity given in A)
3. If X is a jar, X is not a door. (By definition of ``door' and ``jar')
4. Therefore, X is not a door. (by 3 and 2b)
1 and 4 are logically inconsistent.

Logical inconsistency by itself, or at least the blatant expression of faulty reasoning, is indeed a moral violation to most people, though usually only a mild violation having to do with the proper conduct of discourse. This satisfies the requirement in this example for a V interpretation in humor perception. At the same time, the ambiguity of the spoken form between ``a jar' and ``ajar', where both statements in step 2 are claimed at once, provides a path of apparently legitimate reasoning (through step 4) to the conclusion, which through this path seems perfectly normal and correct. Thus a (mild) moral violation and an (only apparently) normal interpretation coincide in this text. So much for its humor.

This possibly humorous interpretation notwithstanding, the listener may rapidly recognize the two meanings of the ambiguous form and thereby recognize the mistake in the reasoning (specifically, both meanings of an ambiguous statement are not necessarily asserted when the statement is made; instead, the second part of step 2 is false, since ``It is ajar' where ``it' refers to a door, can hardly mean ``It is a jar'), so that the legitimacy of the N interpretation is lost, and the text is seen as simply wrong. Once this is recognized, actual humor perception cannot remain, leaving only the possible recognition that an attempt at humor had been made.

This pattern, which applies to innumerable similar examples, lets us see why puns like this are only partly funny and why they generate a sense of failed humor, two of the main properties observeable in set-joke-style puns in my culture. Under one (clearly stupid) interpretation it is mildly funny, while under another (more clearheaded) view, it is simply wrong.

Next, when the speaker performs a pun, s/he makes an implicit claim on listeners to be cooperative, that is, to see it as funny. But to do that one must pretend not to see the obvious. So in effect the subtext of a pun is, "Go along me; act stupid." The offensiveness of this implicit request explains another of the observations, that listeners may express apparent unhappiness with groans and disparaging comments.

In creating a pun, the speaker discovers a linguistic ambiguity and a way of exploiting it in constructing a described situation that contains a moral violation of some kind but that appears normal because of the ambiguity. This intellectual feat, like that of creating any joke, is grounds for a creative glow of accomplishment.

These remarks provide plausible explanations for all of the general observations made above about this kind of pun: they are partly funny, partly failed, self-consciously humorous performances based on linguistic ambiguity, which result in a mixed unhappy response in listeners due to the implicit request to go along with stupid and faulty reasoning, as well as a glow of accomplishment in the creater/speaker. As shown here, these properties are all explained within the present moral theory of humor.