Fairy tales for adults (long)

Rob Park rbpark-NOSPAM at ualberta.ca
Thu Feb 13 15:26:36 PST 2003


Alas! Richard Lightman spake thus:
> Not quite right:
> Mathematicians chose a set of axioms - normally ones that are
> not contradictory, and attempt to prove things to be consistent
> (or in consistent) with the axioms.

Well, this is more or less what I was referring to:

http://www.miskatonic.org/godel.html

But at the time I made that statement, I was going off of a poorly
explained statement from a book...

> That 'not inherently self-consistent...' needs a bit of explaining.
> Are you refering to the proof that in a system of axioms sufficiently
> complex to describe arithmetic, there are some propositions that
> cannot be proved?

Sure. Any system of axioms is incapable of proving itself to be
self-consistent.

At least, that's the gist that I got.

> So far examples of such propositions are all things like:
> "this statement cannot be proven."

A more elaborate example is on that website ;)

-- 
Rob Park
http://www.ualberta.ca/~rbpark
--
I am two with nature.
		-- Woody Allen
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