caravelair

i haven't actually read this, but i plan on it. i've heard a bit about it, and it seems interesting.

if anyone doesn't know what i'm talking about, my understanding is that he proved that it's impossible to prove that any axiomatic system does not contradict itself in some way. math, or logic, for example.

one thing i about it i find quite bizarre is that if he's right, then we can't know for sure that he's right, since the system of logic he used in this proof might be self contradicting.

does that make sense, or did i miss the point? anyone know a little more about this than i do? seems like an epistomological issue.

Philosoft

Godot? I'd bet dollars to doughnuts you're talking about Gödel's Incompleteness Theorem.

ex-xian

Actually, it Godel's proof. And the "o" should have two little dots over it. And unless you have studied symbolic logic extensively, you won't be able to understand his proof. I suggest you look for the book "Godel, Escher, Bach: an Eternal Golden Thread." There's another book about the incompleness theorem written for the popular audience, but I can't recall the name of it now. The philosophy or mathematics section of you local book super-store should carry them both. A university library may have "Godel, Escher, Bach."

As far as the theorem, it states something like this. In any formal system powerful enough to include number theory, it is possible to generate statemens of the form, or analogous to, "This statement is not a theorem of the system." If the statement is true, then it can't be proven based on the axioms of the formal system. If it is false, then the system breaks down. What is all boils down to is that no formal system can be both complete and consistent.

As for logic and mathemtics go, yes, they cannot be known for absolute certainty, but as long as you choose good axioms, everything should be okay.

caravelair

ah crap. sorry about the mistake in the name! how terribly embarrasing.

Godot

and for a second, I thought someone started a thread about me (or my namesake). Oh bother.

Neilium

I was waiting for this.
-n

John Page

No, we were just waiting for you.

mac_philo

The subject of this thread is one of the funniest malapropisms I've ever seen!

Wiploc

I'll bet this locution dates from way back. You can probably find donuts that cost over a dollar these days.
crc

Clutch

Perhaps you mean Godel's Proof , by Ernest Nagel and James Newman, now reissued in a Hofstadter-edited version.