Words on a wall

The latest xkcd (#1860):


That’s Lewis Carroll’s Humpty Dumpty on that wall, discoursing on semantics as in Through the Looking-Glass. The stand-in for the baffled Alice in the book is the aggressively disputatious Science Girl of xkcd.

Background from Wikipedia:

Humpty Dumpty is a character in an English nursery rhyme, probably originally a riddle and one of the best known in the English-speaking world. He is typically portrayed as a personified egg, though he is not explicitly described so. The first recorded versions of the rhyme date from late eighteenth-century England and the tune from 1870 in James William Elliott’s National Nursery Rhymes and Nursery Songs. Its origins are obscure and several theories have been advanced to suggest original meanings.

Humpty Dumpty sat on a wall,
Humpty Dumpty had a great fall.
All the king’s horses and all the king’s men
Couldn’t put Humpty together again.

Humpty appears in Lewis Carroll’s Through the Looking-Glass (1872), where he discusses semantics and pragmatics with Alice.

(#2) Illustration by John Tenniel

“I don’t know what you mean by ‘glory,’ ” Alice said.
Humpty Dumpty smiled contemptuously. “Of course you don’t — till I tell you. I meant ‘there’s a nice knock-down argument for you!’ ”
“But ‘glory’ doesn’t mean ‘a nice knock-down argument’,” Alice objected.
“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean — neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be master — that’s all.”

Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. “They’ve a temper, some of them — particularly verbs, they’re the proudest—adjectives you can do anything with, but not verbs — however, I can manage the whole lot! Impenetrability! That’s what I say!”

This passage was used in Britain by Lord Atkin in his dissenting judgement in the seminal case Liversidge v. Anderson (1942), where he protested about the distortion of a statute by the majority of the House of Lords. It also became a popular citation in United States legal opinions, appearing in 250 judicial decisions in the Westlaw database as of 19 April 2008, including two Supreme Court cases (TVA v. Hill and Zschernig v. Miller).

Here’s some discussion from the explain xkcd wiki, with a crucial sentence boldfaced:

Humpty declares to Alice “There’s glory for you”. Alice doesn’t understand what Humpty means by “glory”. Humpty explains that he can make words mean whatever he chooses to mean. By “glory” he meant “a nice knock-down argument”. And he adds: “When I use a word, it means just what I choose it to mean. Neither more nor less.”

In the comic Humpty is explaining to “Alice” (portrayed by Science Girl) that he can choose meanings for his words. “Alice” wonders what meaning should be given to that utterance, and decides it means “Please take all my belongings”. [If Humpty can stipulate meanings, so can she. Take that, Egg Man!]  Humpty realizes he has been caught in a trap, but now Alice is choosing meanings, and even his protests are taken to mean “take my car too”.

While it seems that Alice chooses these specific meanings of words to educate Humpty Dumpty about the mistake in his way of thinking, she could as well inform him about planned theft with random, meaningless words or not at all. After all, she got “permission”. Also, even though Humpty Dumpty decides about the meanings of words by himself, he “accidentally” chooses the normal meanings of all of Alice’s words, because otherwise he wouldn’t be informed about the planned theft and wouldn’t be able to react to this with “What!? No!”.

Carroll’s Humpty Dumpty is a parody of people who use technical language without defining their terms, and expect others to understand. The title text continues this. By Humpty insisting that he is not responsible for others understanding him he is unable to get help getting down from the wall, which will lead to his inevitable demise.

The explain xkcd site emphasizes the two-sided nature of communication, but of course that’s inadequate: both Humpty and Alice/”Alice” are calling upon an elaborate sytem of words and their meanings that is shared knowledge between them (them and a much larger speech community), or that each has knowledge of by virtue of their experience with variation within the speech community (even if you don’t use W to mean M, you’re aware that other people in the community do.)

Humpty’s error here could then be seen, not as a failure to define technical terms, but as inappropriately behaving, in an everyday conversational context, like a mathematician (which Lewis Carroll was) in technical discourse, where a speaker or writer is free to stipulate words and their meanings.

Mathematicians are given to wrenching words from ordinary language and just assigning them special technical senses. Which words get this treatment and why is sometimes a mystery, but it results in things like the French noun groupe getting taken over as a technical term in abstract algebra (and then taken over as English group and German Gruppe). From Wikipedia:

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

Closure: For all ab in G, the result of the operation, a • b, is also in G.

Associativity: For all ab and c in G, (a • b) • c = a • (b • c).

Identity element: There exists an element e in G such that, for every element a in G, the equation e • a = a • e = a holds. Such an element is unique, and thus one speaks of the identity element.

Inverse element: For each a in G, there exists an element b in G, commonly denoted a−1 (or −a, if the operation is denoted “+”), such that a • b = b • a = e, where e is the identity element.

(I go into such detail in part because group is a central concept in algebra, in part because I think (algebraic) groups are really cool.)

In this case, in this context, when I use the word group, it means just what I choose it to mean — neither more nor less.

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