Re: Cantor Confusion

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.

Han de Bruijn

But everything can be modelled as a set. You simply do not understand
what "foundation" means in this context. Any calculation can
be rewritten as a set theory problem. It would be long, cumbersome,
and impractical, but it could be done. Just as an computer program
can be transformed into a Turing machine.

I do not know what you mean by "supremacy". Do you think 486
assembly language is the "supreme" programming language? It
currently is sort of a de facto candidate for a foundational
programming language.

Stephen
.

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