Re: Cantor Confusion

On Fri, 08 Dec 2006 09:19:01 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Lester Zick wrote:

On Thu, 7 Dec 2006 03:00:21 -0500, David Marcus
<DavidMarcus@xxxxxxxxxxxxxx> wrote:

If you use ZFC (or something similar) as your foundation for
mathematics, then everything is a set. Of course, while solid
foundations are good to have, if you are living on an upper floor, you
may prefer to ignore what is going on in the basement.

So you're saying that set "theory" is all of mathematics? Of course
since what you say isn't necessarily true that's not exactly a ringing
endorsement of set "theory".

It's quite simple. Set Theory can not be the foundation for mathematics,
because NOT EVERYTHING IS A SET. E.g. a calculation is mathematics, but
it's not a set. Set theory may be of limited use, but it's supremacy is
complete nonsense, and will be overruled in time.

Well you know there is a sense in which every "thing" may in some
sense represent a set of predicates. However it is pretentious in the
extreme to suggest that those predicates are in any sense points. I
can see set analysis as a valuable tool just not to the exclusion of
general analytical techniques.

~v~~
.

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