Re: Cantorian pseudomathematics


Han.deBruijn@xxxxxxxxxxxxxx wrote:
> Randy Poe wrote:
> > Han.deBruijn@xxxxxxxxxxxxxx wrote:
> > >
> > > Who the hell has decided that "there is no uniform distribution on N" !?
> >
> > It isn't "decided". It is "proven". The fact that people like you,
> > Ross, and Tony think theorems are arbitrary "decisions" and
> > alternate decisions could be made from the same axioms,
> > does not make those theorems false.
>
> There you say it ! But *I* don't think that "alternate decisions
> could be made from the same axioms". And *I* dont think
> that those theorems are "false", in the sense that they do
> not follow from the axioms. What *I* think is that the axioms
> themselves are false.

What does it mean for an axiom to be false?

> Worse, what *I* think is that the whole
> of mathematics cannot be founded on just axioms and logic.

Well, you can feel free to build up illogical systems, but
don't use the word "mathematics" for it.

> > A probability distribution must satisfy the condition
> > that the total probability over all events is 1. There is
> > no way to do that with a countable set of discrete
> > points.
>
> I have repeatedly pointed out that there _is_ a way.

I suppose what that means (I haven't seen it) is that
you have repeatedly *claimed* there is a way. But when
I ask you to actually that way, you decline, saying that
to do so would be to lower yourself in some way.

So pardon me if I don't believe you.

> > Feel free to prove us wrong. Define the uniform
> > distribution over N. Show us a procedure to generate
> > a random integer.
>
> I cannot "prove" that you are wrong

You can "prove" me wrong about the non-existence of the
uniform distribution over N by showing me the existence
of the uniform distribution over N.

> because that would
> imply that I should step into your vicious circle

Backing up your claims is not "stepping into a vicious
circle". Unbackable claims are just hot air.

- Randy

.

Loading