From: Marc Geddes (m_j_geddes@yahoo.com.au)
Date: Thu Jan 26 2006 - 20:48:04 MST
--- Daniel Radetsky <daniel@radray.us> wrote:
> On Thu, 26 Jan 2006 12:23:48 +1100 (EST)
> Marc Geddes <m_j_geddes@yahoo.com.au> wrote:
>
> > But the explanation as to *why* this system of
> mathematics
> > existed could never be explained. It would just
> have
> > to be accepted as a brute fact.
>
> The explanation for why and how math exists is the
> province of philosophy, not
> mathematics. So it would be a 'brute fact' in the
> sense that math would have no
> explanation for it. But that's not the same thing as
> saying that no explanation
> existed.
>
> > Now this to me seems to run contrary to the
> scientific
> > method, which by its very nature assumes that
> there
> > are no unexplained supernatural brute facts of
> > reality. And mathematics itself is a part of
> reality.
>
> This is controversial. Platonists such as Godel do
> not think that math is part
> of reality, and thus that science need not explain
> mathematics. So we do not
> have the endless tower of turtles you refer to.
If we define 'reality' to mean 'everything that
exists' and mathematical entities are objectively real
things as Platonists say (though of course they are
not physical things), then math *is* part of reality.
>
> > Now if, however, we adopt my superficially
> > 'unappealing' suggestion that reality as a whole
> is
> > inconsistent
>
> What on earth does that mean? Are you saying that
> there are two facts of
> reality in contradiction with each other? It sure
> sounds like it. If so, I can
> show that everthing you say is wrong via an
> elementary exercise in logic.
>
> Marc, I'm trying to give you the benefit of the
> doubt here, but you aren't
> helping me. If you claim that math is a part of
> reality, and that some true
> theories are inconsistent with one another, then you
> are saying that there are
> inconsistent facts in reality, right? It's not just
> the beer talking? Doesn't
> this mean that by the principle of explosion,
> everything is simultaneously
> true and false and everything I know is wrong, but
> also right?
Read 'Impossibility' by professional mathematician
John Barrow. Also read some math papers. The idea
that reality is best described by several different
formal systems which are not completely consistent
with each other is a perfectly valid concept.
By the way, Ben, John Barrow talks the universe being
a formal system quite blithely in his book. Barrow
also specifically (albeit briefly) looks at the
possibility that reality as a whole may be
inconsistent.
Book link:
http://www.amazon.com/gp/product/0195130820/sr=1-1/qid=1138333532/
"Till shade is gone, till water is gone, into the shadow with teeth bared, screaming defiance with the last breath, to spit in Sightblinder’s eye on the last day”
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