0: How do you mean? 1: He looks like an egg. 0: Check your premises. 1: What premises? 0: They never say Humpty Dumpty is an egg. 1: _(Recites lyrics in Onehead)_ Huh... They really don't. 0: People assume all sorts of illogical things about Humpty Dumpty. 1: Illogical how? 0: Not justified by the axioms. 1: What axioms? 0: Well, what do we know for sure about H.D.? 1: That he fell off a一 0: Wrong. 1: This file is definitely punishment. 0: This file is about logic, my one. 1: How is this about logic? 0: And logic is about what can be inferred from a given set of premises with absolute certainty. 1: I can infer with certainty that this section is called Lamb一 0: And anything that cannot be inferred with certainty from those premises may be consistent with them, or inconsistent with them, but not true,[^4] for "truth" in logic means "true in all interpretations," or as the logicians say, "true in all models." 1: Are we still talking about Humpty Dumpty or did we switch back to logic? 0: Both. Here's what we know from the original text about Mr. Dumpty. > _Humpty Dumpty set en a wall,_ > _Humpty Dumpty had a great fall._ > _Four score Men and Four-score more,_ > _Could not make Humpty Dumpty where he was before._ > -Samuel Arnold, Juvenile Amusements, 1797. (Plus like duae litterae of Ibid. in linea prima.) 1: When was this Lambert guy around? 0: 1700s. 1: Noted. 0: Now, dearest One. What can be inferred with certainty about Mr. D, from the point of view of Model Theory? 1: What's Model Theory? 0: A branch of logic. One that concerns itself with the set of possible interpretations of the symbols, terms, and statements in a formal language. 1: What's the question? 0: Taking the original text of H.D. as written by S.A. in J.A. as our Axioms for a formal theory of H.D., what can one infer with certainty from said Ax? 1: Is that Zero-talk for "What do we know about Humpty Dumpty?"? 0: Exactly. 1: He fell. 0: Wrong. 1: Why are you like this? 0: Your conclusion only follows in the subset of models in which "fall" is given the interpretation numbered "1" in the definition below. ``` fall 0. The time of the year when the leaves typically fall from the trees; autumn; the season of the year between the autumnal equinox and the winter solstice. 1. The act of moving to a lower position under the effect of gravity. 2. A loss of greatness or status. 3. That which falls or cascades. 4. The height of that which falls or cascades. 5. A reduction in quantity, pitch. 6. (sports) A crucial event or circumstance. 7. (cricket) The action of a batsman being out. 8. (curling) A defect in the ice which causes stones thrown into an area to drift in a given direction. 9. (wrestling) A wrestler being pinned to the mat. 10. A hairpiece for women consisting of long strands of hair on a woven backing, intended primarily to cover hair loss. 11. (informal) Blame or punishment for a failure or misdeed. 12. (nautical) The part of the rope of a tackle to which the power is applied in hoisting. 13. An old Scots unit of measure equal to six ells. 14. A short, flexible piece of leather forming part of a bullwhip, placed between the thong and the cracker. 15. The lid on a piano that covers the keyboard. ``` 1: As long as we agree mine's #1. 0: Now from the use of the term "had" in "he had a great fall" we can infer that "he fell" only in those models in which the interpretation of "fall" is one of the irregular verbs above, for example definition 1. 1: Please tell me there's a point to all this. 0: However one, if one chooses not to be deaf to all defs but def 1, but rather considers also def 0. 1: _(Not listening)_ Zero... 0: Then the following model is perfectly consistent with our axioms. ![[humpty-dumpty-2.png]] 1: ... 0: ... He had a great one. 1: Tedious fall puns aside, this isn't a model of the axioms. 0: Why not? 1: Where's the wall? Where are the kings hors--- 0: There's no king in the original. 1: _(Rereads the text.)_ Dammit. 0: No horses either. 1: Ok then how am I to interpret the rest of the axioms? Aside from the "great fall" which, whatever I might have said a minute ago, I'll admit is pretty cute. 0: Well clearly, our protagonist, prior that great fall was a different sort of man. 1: Different how? wall. (noun) 1. A barrier, built up for defensive purposes. 2. (figurative) A means of defence or security. She built a wall between herself and the outside world. 3. (roleplaying games) A character that has high defenses, thereby reducing the amount of damage taken from the opponent’s attacks. 4. (slang, seduction community, chiefly definite) The stage of biological aging where physical appearance and attractiveness start to deteriorate rapidly. 1: Defensive outer shell? 0: On any reading. 1: Like over-protected? 0: Hardly. But yes he had his walls up. Don't let them in, don't let them see. He'd been an Ovial Libertine, before they met, in my model. 1: Ovaltine what? 0: A Shellborne Rake. 1: Like for leaves? 0: Before she leaves. 1: Who leaves? There's a girl egg? 0: Never said egg. 1: He sure looks like a一 0: But he was primal, a hunter, our Paleovarian Seducer Mr. D. 1: Are these real words? 0: He'd seen cracks unseen and spread broken many open, screwed them ova, l'ovum and leaves em he'd say, fore he leaves, after ne'er having l'ovum. A bad egg. 1: Egg huh? 0: It's a figure of speech one, grow up. 1: Sure. 0: Grade A dozens with whom he'd had his free range, his choice of whom to take home in which weather and when. And come home they did, ere the night was ova, and unclothed the heat of his sunny side under the satin sheets they felt, but then he'd break fast in the morning ere the sun was up, and when he leaf't he left 'em scrambled, dozens of unfertilized virgins now seen fried up and over easy, eaten up, hors d'oeuvre. _(Narrator: One has at this point forgotten to be annoyed and is now listening intently to see where this is all going.)_ 0: That was before she came. 1: Who? 0: She was hardly his first. And then she came. She was his first. ![[humpty-dumpty-3.png]] 0: He fell for her. 1: I hate you. 0: Then came the fall. 1: I thought it was already一 ![[humpty-dumpty-4.png]] 1: I'm counting like three falls here. 0: So we're agreed it's a model? 1: The girl egg? I mean she was ok looki一 0: No, the interpretation. And I never said egg. 1: This was an impressive amount of effort for a lame dad joke but no I'm not convinced it makes sense. 0: Consider the following. score. 1. (noun, vulgar, slang) A sexual conquest. 2. (noun, slang, crime) A prostitute's client. 3. (verb, vulgar, slang) To obtain sexual favors from a successful seduction. 1: This is a pretty elaborate backstory for a four line poem about an egg. 0: Elaborate how? 1: I mean you added all sorts of stuff that was nowhere in the original. 0: Such as? 1: His philandering. The breakup. The word "fall" meaning (as far as I can tell) everything from "falling in love" to "Autumn" to "falling out." That entirely unmotivated definition of "score" up there. Sure it's a possible interpretation, maybe, if you're insane, but there's no underlying reason why anyone would ever actually think this. 0: Are you sure? 1: Pretty sure. 0: What's his name? _(Narrator: One frowns at the totality of the section and the file falls silent.)_ 1: I hate you. ## 5. Lambert (again)