Re: Platonism
From: Acid Pooh (poopdeville_at_gmail.com)
Date: 11/30/04
- Next message: Neil W Rickert: "Re: mathematics"
- Previous message: Stephen Harris: "Re: Platonism"
- In reply to: J.E.: "Re: Platonism"
- Next in thread: tchow_at_lsa.umich.edu: "Re: Platonism"
- Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]
Date: 29 Nov 2004 17:02:19 -0800
troubled6man@yahoo.com (J.E.) wrote in message news:<39d6e584.0411290901.4cbd77b4@posting.google.com>...
> Neil W Rickert <rickert+nn@cs.niu.edu> wrote in message news:<cod2hh$er0$1@usenet.cso.niu.edu>...
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
> >
> > troubled6man@yahoo.com (J.E.) writes:
> > >Neil W Rickert <rickert+nn@cs.niu.edu> wrote in message news:<cob5mj$fbr$2@usenet.cso.niu.edu>...
> > >> troubled6man@yahoo.com (J.E.) writes:
>
> > >> 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.
> >
> > It is interesting that you used the word "hide".
> >
> > > 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.
> >
> > I'm not so sure that is correct.
>
> Any thoughts on a better replacement? Just saying you disagree isn't
> saying much. I still respect your opinion, but just saying you
> disagree isn't as useful as saying either why you disagree or what you
> believe instead.
>
> > >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 doesn't seem particularly relevant.
> >
> > A new up and coming mathematician has already done a lot of
> > mathematics before being exposed to ZFC. In many graduate schools, a
> > class in mathematical foundations is still not a requirement for a
> > doctoral degree.
>
> Interesting, you actually think many people could study mathematics in
> depth without studying set theory?
Set theory is not ZFC. ZFC is a formalization of what is called
"Naive Set theory" that avoids some of it's paradoxes through
judicious axiomatization. The idea is that if one can formulate a
"naive" argument without using the axiom that leads to Russell's
paradox, then one can in principal formulate a ZFC argument also.
When one actually *does* need to use a comprehension axiom, ZFC is
always there anyway. I would imagine that every student in a modern
collegiate mathematics program would *have* to study some or another
form of naive set theory and Russell's paradox (to learn how to
intuitively avoid comprehension fallacies), if not actually studying
the first order language FOL+ZFC.
'cid 'ooh
- Next message: Neil W Rickert: "Re: mathematics"
- Previous message: Stephen Harris: "Re: Platonism"
- In reply to: J.E.: "Re: Platonism"
- Next in thread: tchow_at_lsa.umich.edu: "Re: Platonism"
- Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]
Relevant Pages
|
