Re: Han's startling new set theory.

On 18 Aug 2005 14:25:10 -0700, Han.deBruijn@xxxxxxxxxxxxxx wrote:

>Jiri Lebl wrote:
>
>> Han.deBruijn@xxxxxxxxxxxxxx wrote:
>
>> Firstly, it is a proof that any sufficiently complicated system is
>> unable to produce a proof of it's own consistency. You will NEVER have
>> a ZF proof that ZF is consistent. You will NEVER produce a set of
>> axioms that allows the use of arithmetic with natural numbers that will
>> be able to prove itself consistent.
>
>But there IS a proof that Euclidian Geometry is consistent. Right?

I believe he proved the relative consistancy of it. (I've read that
he assumed that the reals and the arithmatic on it was consistent to
prove that Euclidean Geometry was consistant).

>And for the rest: if Nature can prove its Consistency, so can we.

I've never seen nature prove its own consistancy. Care to show me
this proof?

> A little bit of Physics would be NO Idleness in Mathematics.

>I keep repeating this mantra, in the somewhat desperate hope that it
>will sink into your stubborn brains within a century or so. Physics
>has _everything_ to do with a _provable consistency_ of mathematics.

Physics has very little to do with consistancy.

>Yes, you need arguments _from outside_ to prove consistency, because
>most theories cannot prove their consistency from within, as you have
>said. Why don't you see then that my mantra offers a key to success?

Because it doesn't. It leads instead to confusion such as your Ax
x={x}. Or WM's amorphous "set" of naturals. Etc.

>> Tell me that you are NOT as ignorant as you seem to be.
>
>I'm playing a game. But it's a serious game. And I don't care about
>what people think.
>
>> You are obviously starting with a preconcieved notion that
>> set theory is all wrong.
>
>It's wrong to use it as a foundation for the whole of mathematics.
>
>> You take a problem with NAIVE SET THEORY (as practiced by early
>> set theorists) and generalize it to a theory with does not have
>> this problem (namely ZF).
>
>Denied. ZF has the same problems as naive set theory, in disguise.
>Hiding them behind a far more complicated formalism will not help
>in the end, though.

One of the most famous problems of naive set theory is Russel's
paradox. Since you are claiming that ZF suffers from Russel's
paradox, please derive it for us.

Martin
.

Relevant Pages

  • Re: Russells Paradox
    ... There is no paradox here. ... genuine problem for naive set theory. ... realm of sex would certainly include publicly shared sex at a sex ...
    (sci.math)
  • Re: Hans startling new set theory.
    ... >Martin Shobe wrote: ... ZF has the same problems as naive set theory, ... Since you are claiming that ZF suffers from Russel's ... >> paradox, ...
    (sci.math)
  • Re: Hans startling new set theory.
    ... ZF has the same problems as naive set theory, ... >>Hiding them behind a far more complicated formalism will not help ... > paradox, ...
    (sci.math)