Re: Platonism

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 11/29/04 

Date: Mon, 29 Nov 2004 17:47:07 GMT

On 29 Nov 2004 09:01:25 -0800, troubled6man@yahoo.com (J.E.) in
comp.ai.philosophy wrote:

>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 isn't the mathematical foundation except in Euler's mind.
 
>> >> 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".
>>
>> I readily grant that set theory has proved useful. Indeed, it is
>> surely one of the parts of mathematics that would continue to thrive,
>> even if the foundations should crumble. It might survive in a
>> slightly different form, but it would still survive. As Hilbert
>> wrote, "No one shall expel us from the Paradise that Cantor has
>> created."
>
>You seem to idicate that mathematicians are "doing something else"
>that isn't ZFC most of the time, without being clear what you think
>they are doing. If you want to disagree, it's helpful to disagree
>positively. And quotes and opinions about the future are just as good
>as my predictions about the future, which is to say, they are next to
>nothing.
>
>> > Human
>> >intuition goes astray and formalism is there to keep people in line,
>> >without it nonsense would appear again IMO.
>>
>> I'm not knocking formalism. I am only suggesting that it is not the
>> source nor the basis for *all* of mathematics.
>
>Mathematicians can say what they say as parroting all they want, but
>if you push them they almost always say that they rely on the work of
>"previous mathematicians". And for most mathematicians today for most
>of the work they do, that foundational previous work of previous
>mathematicians that itself doesn't go back for it's basis to someone
>yet earlier mathematician's work is ZFC, an axiom system that by
>definition just asserts the axioms without saying that "a previous
>mathematician proven the axioms". Even theorems "older than ZFC"
>require ZFC-based definitions to be turned into modern theorems. So
>to me it seems the basis for the majority of mathematical claims by
>the majority of mathematicians. If you disagree please either state
>why I am wrong or at least give a competiting view. Thank you.
>
>P.S. We are discussing most, not all, surely you can understand the
>distinction if you want to, right?

Regards - Lester

Relevant Pages

  • Re: Platonism
    ... Just saying you disagree isn't ... >> mathematics before being exposed to ZFC. ...
    (sci.math)
  • Re: Platonism
    ... Just saying you disagree isn't ... >> mathematics before being exposed to ZFC. ... Set theory is not ZFC. ...
    (comp.theory)
  • Re: Platonism
    ... Just saying you disagree isn't ... >> mathematics before being exposed to ZFC. ... Set theory is not ZFC. ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... >> If TO can't hack math, nobody is forcing him into it. ... > upon close strutiny are inherently inconsistent, ... As to the reality of mathematics, I take a moderately Platonic view. ... I do not disagree. ...
    (sci.math)
  • Re: Is Nob Really Dr. Joseph Goebbels?
    ... >> And even the people you quote disagree with you. ... I note that you do not provide links to show them saying what you claim ... If you want a better analogy, how about this one: most scientists agree ...
    (rec.audio.opinion)
Loading