Re: Cantorian pseudomathematics

Tony Orlow wrote:
> MoeBlee said:
> > Tony Orlow wrote:
> > > Randy Poe said:
> > > > > 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?
> > > >
> > >
> > > It means that they contradict other axioms. Now, you have some small set of
> > > axioms that don't contradict each other, but in the larger scope of mathemtics
> > > at large, the conclusions drawn from those axioms contradict conclusions drawn
> > > from other axioms of mathematics regarding sets such as Han is discussing. In
> > > the context of those other areas of math and their axioms, the axioms of set
> > > theory are flawed, as conflicts arise between them and the more solid
> > > computational axioms of the rest of mathemtics, and reality in general. The
> > > conclusions derived from the axioms are not correct.
> >
> > What axioms is Han discussing? Whatever his exact position, he just
> > posted his aversion to axiomatics in at least one sense.
> >
> > MoeBlee
> >
> >
>
> Yes, well, Han didn't say that axioms are wrong in general.

Right, he didn't. But my question is what axioms AT ALL do you claim
that he is talking about.

> I believe what he said was, not that
> axiomatic systems are bad or wrong, but that they are not sufficient in
> themselves to ensure their own correctness, which is basically what Goedel
> proved, isn't it, in a sense?

1. I don't know that that is what Hans means. Without, so far, giving a
reason (other than that he says that Brouwer said so), he just said a
logistic system is not good for a constructive foundation.

2. What you said is not what Godel proved. The second incompleteness
theorem, roughly, says that a consistent, recursive axiomatization
strong enough to express arithmetic cannot prove its own consistency.
That is not a basis to reject the axiomatic method.

MoeBlee

.

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