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 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!
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