Re: RE: RE: Premises, Circularities etc was Re: His tor ical Materialism

["Justin Schwartz" <jkschw@xxxxxxxxxxx>]

> Martin Brown writes:
> > Re geometry.  I think Goedel's paradox tends to refute your [Justin's??]
> statement. ...<
>
> which statement? and how does Goedel do so?
>
> I'm not great mathematician, but I think that Goedel says that geometry and
> many other sub-fields of mathematics, are, in some sense, circular, because
> they are not reducible to a set of primitive fundamentals that are in some
> sense self evidently true.

That's not what logicians means by circularity. G's theorem is as I have
explained here before) that for any formal system that is powerful enough to
state simple arithemaetic, there is at least one true proposition in that
system that is not provable within it. E.g., for arithemetric, you need set
theory, etc. There is no implication of circularity, which is a matter of
defining term A in terms of term B and vice versa.

I met G and spoke to him when he was at the Institute and I was a Tigertown
undergrad . . . .

jks

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