Fairy tales for adults (long)
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:
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
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 ;)
I am two with nature.
-- Woody Allen
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