Re: [sl4] foundationalism

From: Stuart Armstrong (
Date: Wed Feb 25 2009 - 02:53:28 MST

> Godel demonstrated that there must be arithmetic statements which
> cannot be proven algorithmically, but just "happen to be" true for all
> natural numbers. I have used the Goldbach conjecture (which may be
> unprovable in the Godel sense) as an example.
> If something is true but cannot be proven true, the only thing we can
> say is that it is "experimentally true".

Ah, I see what you mean. In that sense I agree - Godel did not create
these "experimentally true" statements, but did show that it might be
the best you can get.

> I am very intrigued by he suggestion that maths is really the physics
> of bottlecaps, which seems to me a very pragmatic and sane way to look
> at it.

As a mathmatician, it seems to be a very poor way of looking at
things, and bearing little relationship to what I know. I'd say that
maths is the task of axiomatising basic intuitve concepts (counting
bottle-caps, drawing figures on the sand, watching the planets move)
and then pushing the axioms out as far as they can go, well beyond the
original intuitve concepts.

But that's from an insider - what is your intution for the "physics of


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