Re: Platonism
From: J.E. (troubled6man_at_yahoo.com)
Date: 11/28/04
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Date: 28 Nov 2004 07:12:56 -0800
Neil W Rickert <rickert+nn@cs.niu.edu> wrote in message news:<cob5mj$fbr$2@usenet.cso.niu.edu>...
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> troubled6man@yahoo.com (J.E.) writes:
> >examachine@gmail.com (Eray Ozkural exa) wrote in message news:<320e992a.0411261232.41252e2e@posting.google.com>...
>
> >You did ask earlier about *most* mathematicians, so I'd like to add my
> >two cents. Most mathematicians when they say "exist" have an
> >axiomatic system (like ZFC) in mind, and mean that they are
> >considering a formla with the symbol E flipped backwords in it. I
> >believe it might be called formalism, and it is fairly common IMO.
>
> I would have to disagree with that.
>
> Most mathematicians (myself included) could not state the axioms of
> ZFC even if their career depended on it. Sure, they probably have a
> copy of ZFC in a book somewhere on their shelves. But that book is
> gathering dust.
I think you are confusing practise and belief. There are many
professed Chrsitians who could not recite the ten commandments if
their life depended on it, and may act like jerks (not following the
golden rule) but if you pushed them about their beliefs, then they'd
run and hide behind their bible. Most mathematicians will retreat to
ZFC if you press them either (1) hard for the basis for their claims
or (2) really hard about the meaning of their claims. Just because in
informal practise you consciously ignore the alleged basis for your
beliefs doesn't mean they are not the basis.
> Mathematical foundations, built on axiom systems such as ZFC, were
> constructed underneath an already thriving mathematics.
I would agree the pre-ZFC mathematicians believed something else. But
with the huge growth in mathematicians in the modern world, I'd feel
confident saying that ZFC has no been around longer than MOST
mathematicians have been around.
> This gives
> the illusion that mathematics is built on such foundations. But it
> is only an illusion. If, by chance, the foundations should crumble,
> most of mathematics would continue to thrive without them.
I doubt it, seriously. I agree it depends on how it crumbles, but
your claim that it would always survive is simply baseless. And the
whole word thrive seems to indicate that set theory was useless for
mathematics developement and just made for "skeptics". Human
intuition goes astray and formalism is there to keep people in line,
without it nonsense would appear again IMO.
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