Re: Cantorian pseudomathematics

Han de Bruijn wrote:
> MoeBlee wrote:
>
> > Han de Bruijn wrote:
> >
> >>No. I do _not_ consider "intuitionistic" systems with primitives and
> >>axioms to be a foundation for constructive mathematics. I consider them
> >>as a _perversion_ of constructivism. Brouwer would turn in his grave
> >>if he heard about these things.
> >
> > He was alive when such things were under way.
>
> Yes. But I know for sure he was against it.

Perhaps so. But would you provide a cite, especially one
contemporaneous with work in intutionism as it had developed through
the decades?

> >> > How do you conclude that a constructive mathematics cannot be
> >> > axiomatized in a logistic system?
> >>
> >>I didn't conclude that. It's from L.E.J. Brouwer's original program
> >>and I just wholeheartedly agree with his views concerning this.
> >
> > Would you point me to a Brouwer reference on this point? Anyway, unless
> > you think my question is answered by saying, "Because Brouwer said it,"
> > I'm asking why YOU believe it.
>
> The basic reference is his thesis. Unfortunate for you it's in Dutch.
> Now, what's wrong in finding someone's arguments convincing? And no, I'm
> not going to copy and translate everything that's in Brouwer's thesis
> for the sake of 'sci.math'.

I don't fault finding someone's arguments to be convincing. I just
wouldn't mind knowing at least the gist of the arguments as you
understand them. But if you don't want to convey even an outline of the
arguments, then so be it.

> >> > And, 'logistic', 'primitive' and
> >> > 'axiom' are well understand words; I don't what you mean to indicate
> >> > by using them with irony quote marks.
> >>
> >>Standards of rigour are social standards. Absolute rigour is a phantom.
> >
> > I don't know what is social about Church's thesis, but even if rigor
> > were socially relative, I still don't know why that would prompt
> > putting 'logistic', 'primitive' and 'axiom' in irony quote marks.
>
> Quoting again from the book by E.T. Jaynes:
>
> > those who lay the greatest stress on mathematical rigor are just
> > the ones who, lacking a sure sense of the real world, tie their
> > arguments to unrealistic premises and thus destroy their relevance.
>
> > Secondly, we have to recognize that there are no really trustworthy
> > standards of rigor in a mathematics that has embraced the theory of
> > infinite sets.

I don't see how those opinions show that Church's thesis is socially
relative.

MoeBlee

.

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