Re: Cantor Confusion

David Marcus schreef:

Han.deBruijn@xxxxxxxxxxxxxx wrote:

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.

If you've been reading the threads, then you should know that WM has so
far failed to present any mathematics at all. All he does is present
incorrect arguments that he insists follow from the standard axioms and
then proclaim: "Behold, standard mathematics is inconsistent." Big deal.

Nonsense. The arguments presented by WM are quite reasonable.

Anyone can prove 2 = 1, if they bend a rule here and there.

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.

Fine. Give some evidence that it "narrows your thinking". I.e., present
some mathematics that can't be done using ZFC as a foundation.

Í'm pretty sure you can twist and bend any thought in such a way that
it fits into your set theoretical paradigm. And as soon it doesn't fit,
you'd simply say that it is not mathematics. Wolfgang Mueckenheim has
come up with several of such examples. You'd not be better off with me.
See e.g. the "Probability XOR Calculus" thread, which was initiated by
this author:

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

Han de Bruijn

.

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