Thursday, December 28, 2006

Proving it

I had a comment to an old post last night. It started with the words " prove? true, you probably can't prove it. as many people have pointed out, you can't PROVE anything. "

I got somewhat frustrated with that statement, and so I replied "what are you trying to say - "you can't prove anything"? Have you taken a highschool geometry class?", but really, I missed the point as much as I think the commenter did.

Donald Knuth (for those of you who are computer scientists) once put a warning in one of his programs - "Beware of bugs in the above code; I have only proved it correct, not tried it."

Using predicate calculus or some other formal system is really operating in a made up universe which may or may not correspond to reality, although most of the time it does. But we don't rely on proof to live our lives, because if we did our lives would spiral into some kind of absurdity. Holocaust deniers say there's no proof that the Holocaust happened! Lucky for us, humans be default favor more of a "fuzzy logic" model. This is why courts don't require absolute proof, but introduce the notion of reasonable doubt, essentially an error tolerance.


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