704: Principle of Explosion
|Principle of Explosion|
Title text: 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 propositions (axioms) that contradict each other, it is possible to derive (prove) any statement you want 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, such as the fact that some numbers must be both even and odd. Consequently, you can draw the conclusion that √2 must be an irrational number (provided such a thing exists at all! - luckily, it does and obeys the same calculation rules as for rational numbers; this is how proof by contradiction works.)
This can be seen in a Truth Table:
|P||¬P||P ∧ ¬P||P ∧ ¬P ⇒ Q|
The formula P ∧ ¬P ⇒ Q is true in every possible interpretation. No matter what propositions are substituted for P and Q the implication is true. So if a single example of a contradiction were found, then every proposition would be true, (and simultaneously false).
Cueball's friend then proceeds to misinterpret (perhaps intentionally) that you can derive any fact about the physical world. His formula of propositional logic in the third panel reads "P and not P", where ∧ is the formal logic symbol for "and" and ¬ is the symbol for "not". P stands for a proposition. As "P and not P" is shorthand for "P is both true and false", this forms a contradiction from which the principle of explosion can begin. Humorously and to Cueball's bewilderment he then successfully manages to 'derive' 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.
Waffle cones are a variety of ice cream cone. The rest of the title text is just more of the main comic's derivation joke, since Cueball's "friend" is apparently a cheap bastard who can't spare five bucks to buy his own ice cream cones. (Unless he is smart enough to exploit the system of universe.)
- [Cueball is talking to his friend.]
- Cueball: If you assume contradictory axioms, you can derive anything. It's called the principle of explosion.
- Friend: Anything? Lemme try.
- [Cueball's friend is writing on a piece of paper on a desk.]
- [Cueball's friend is holding up a piece of paper to Cueball, while holding a phone.]
- Friend: Hey, you're right! I started with P∧¬P and derived your mom's phone number!
- Cueball: That's not how that works.
- [Cueball is looking at the piece of paper, while his friend is talking to someone on a phone.]
- Friend: Mrs. Lenhart?
- 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!
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