Truth and Justification in light of Godel

[matt grime]

This doesn't have anything to do with Godel's theorum

None of this thread has anything to do with Goedel (apart from those bits explaining why it has nothing to do with his theorem).

 

[Dichter]

None of this thread has anything to do with Goedel (apart from those bits explaining why it has nothing to do with his theorem).

Sure but the critics are not helping much. There is a struggle from non-mathematicians, like myself, to understand what all the hoopla about Gödel is about, and all we get in response is pedantry. Come on, enlighten us instead of simply keep saying we're in the dark!

For anyone interested in a better understanding of "Truth and Justification in light of Godel" and skip the pendatry, I've found a very interesting link:

http://www.edge.org/3rd_culture/goldstein05/goldstein05_index.html

 

[matt grime]

And most mathematicians are completely unmoved by Goedel's theorem, most of them won't even know what it is; heck I don't even know the precise statement of the theorem and end up guessing most of the time. The fascination amongst lay audiences the amazing thing.

Maths in some sense 'is' pedantry, or at least the application of rules and formal reasoning. Goedel's theorem is explained all over the web, and in the forums. I think it states that in a finite recursively axiomatized system that is strong enough to define the natural numbers (ie in which we can do induction) then there is a statement such that neither it nor its negation is derivable from the axioms.

Examples: System is the standard Zermelo Frankel set theory axioms, then the continuum hypothesis, the generalized continuum hypothesis and (I believe) the axiom of choice are all consistent with the axioms (ie there is a model of ZF where they are true) as are their negations.It is a statement about mathematics, finite recursive axioms, and induction. Nothing to do with language, or real life, or anything. It also has practically no bearing on 'doing' almost all mathematics. In fact outside of this forum I have never had any reason to talk about it, but then I'm not a set theorist, or logician. If I want the axiom of choice I use it, I don't care whether it is or isn't independent of ZF.

Everything from post 7 pretty onwards has just not been about mathematics, if that observation is pedantry that annoys you then so be it.

 

[Dichter]

And most mathematicians are completely unmoved by Goedel's theorem

So much so they don't even know how to spell his name...

(even if you can't type Gödel, with the umlaut, you still don't have to add an extra 'e'...)

 

[matt grime]

I do know how to spell his name, I do not know how to typeset umlauts in html, and nor do I care to learn since adding an extra e is perfectly acceptable (in my opinion) as a workaround (nb, see your own post 10, if we're being picky) just as it is acceptable (even preferred, these days I believe) to use ss and not the 'beta' like symbol in German (it annoys me I can't remember its name) as well as ascii-tex for maths. I would much rather offend your sensibilities on that, than misapply his theorem. Now, do you have a valid mathematical point, or would you like to spell Tchebyshev (aka Chebyshev, Chebytchev or God knows how many variations; there is supposedly some book with 22 different spellings of the one name (all for one person) in the index).

 

[Hurkyl]

Since we've strayed from talking about Gödel's theorem, and are beginning to degenerate into personal attacks () I think it's time that this was closed.

 

[HallsofIvy]

Actually "oe" in place of "ö" is fairly common even in Germany.