704: Principle of Explosion

Explain xkcd: It's 'cause you're dumb.
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Principle of Explosion
You want me to pick up waffle cones? Oh, right, for the wine. One sec, let me just derive your son's credit card number and I'll be on my way.


Cueball explains the principle of explosion, a classical law of logic, that says that if you start out with premises (axioms) that are contradictory, it is possible to derive (prove) any statement in the language you are working in, true or false. (In math for example, if you assume that √2 is a rational number, you can prove things that are obviously false. Consequently you draw the conclusion that √2 is an irrational number. This is how proof by contradiction works.)

His friend misinterprets this to mean that you can derive any fact about the physical world. He starts with a formula of propositional logic that says "P and not-P", where P is a proposition. To say that P is both true and false is a contradiction, it's false regardless of whether P is true or false. To Cueball's bewilderment he then successfully derives his mom's phone number. His mom turns out to be Miss Lenhart (now a Mrs?), and to his vexation she asks his friend out.


Cueball: If you assume contradictory axioms, you can derive anything. It's called the principle of explosion.
Friend: Anything? Lemme try.
Friend: Hey, you're right! I started with P∧¬P and derived your mom's phone number!
Cueball: That's not how it works.
Cueball: Wait, this is her number! How–
Friend: Hi, I'm a friend of– Why, yes, I am free tonight!
Cueball: Mom!
Friend: No, box wine sounds lovely!



Could Mrs Lenhart be Miss Lenhart's mother, perhaps? This makes Cueball-1 Miss Lenhart's brother (and thus possibly "Cueball Lenhart", unless he's a half-brother or step-brother or the like). Of course with provably two Cueballs in this situation (and assuming they aren't twins, unless #2... no, we won't go there) we can't therefore assume that any particular lone Cueball is related. However, if "Cueball is a Lenhart AND Cueball is not a Lenhart" then.... well, lock up your mothers... <smirk> 22:01, 7 May 2013 (UTC)

^ genealogy makes my head durt. 20:22, 19 October 2013 (UTC)

Hey, what do waffle cones and box wine have to do with each other? Wouldn't the cones just get soggy? Just wondering. Anonymous 18:30, 9 December 2014 (UTC)

This is what I came here to figure out. "Oh, right, for the wine" makes it sound like it's supposed to be obvious. 00:51, 28 March 2015 (UTC)
Logically the waffle cones are unrelated to the wine, it's a separate item. -Pennpenn 00:55, 18 May 2015 (UTC)
Using the principle of explosion, boxed wine and waffle cones are very much related, and are essentially the same thing. 01:29, 7 August 2015 (UTC)
Gah, unpaired parentheses... 05:48, 17 August 2015 (UTC)
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