Re: Cantor Confusion

stephen@xxxxxxxxxx schreef:

Han.deBruijn@xxxxxxxxxxxxxx wrote:
David Marcus schreef:

Han.deBruijn@xxxxxxxxxxxxxx wrote:

To those who are unable to see it, there is no evidence that there is
any sort of mathematics not describable by set theory. But this is a
vicious circle. Mainstream mathematics simply DOES NOT ALLOW any sort
of mathematics that violates set theory.

Quite a silly thing to say. Do you have any evidence for such an absurd
statement? [ ... snipped "counter evidence" with Category Theory ... ]

Ah, now don't act as if you didn't have those heated debates with some
manifest opponents of set theory, i.e. Wolfgang Mueckenheim. I'm not
talking about any possibilities to replace set theory by look-alikes.

I'm talking about rejecting any monolithic foundation for mathematics,
any "foundation" that narrows down my freedom of thinking. I hate any
form of NewSpeak, whether it is called Set Theory, Category Theory or
Object Oriented Programming. I've seen too many of these.

Han de Bruijn

You are the one who is trying to restrict peoples' freedoms. You
cannot name a single piece of mathematics that is "forbidden"
by set theory.

Oh yes, I can:

Let P(a) be the probability that an arbitrary natural is divisible by
a fixed natural a. Then P(a) = 1/a . Forbidden by set theory.

http://groups.google.nl/group/sci.math/msg/b686cb8d04d44962

You on the other hand want to abolish any mathematics
that involves infinity, which is a severe restriction on others
freedom of thinking. In short, you are a hypocrite.

No. I am a truth seeker, against all odds.

I would imagine your understanding of Object Oriented Programming
is as woefully garbled as you understanding of set theory.

I've done quite some of it for a living. And I'm still alive and well.

Han de Bruijn

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