From: Daniel Radetsky (firstname.lastname@example.org)
Date: Thu Jan 26 2006 - 01:36:06 MST
On Thu, 26 Jan 2006 12:23:48 +1100 (EST)
Marc Geddes <email@example.com> 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
> 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.
> Now if, however, we adopt my superficially
> 'unappealing' suggestion that reality as a whole is
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?
> the situation changes. There would then
> be several different over-lapping formal systems
> needed to fully describe reality. *And each formal
> system could be used to provide an explanation of the
> others* Thus mathematics could 'explain itself' and
> there need be no endless unexplained tower of Godelian
> turtles. So you see, my suggestion is not so
> unappealing after all.
I don't find an explanation like "'Why A?' 'Because B.' 'Why B?' 'Because A.'"
appealing, and I don't see why what you're suggesting is different, except
for maybe having more variables.
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