|
|
In article <45478bb7@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> MoeBlee wrote:
> > Tony Orlow wrote:
> >> I am beginning to realize just how much trouble the axiom of
> >> extensionality is causing here.
> >
> > Oh, now the axiom of extensionality.
> >
> > When you buy into Robinson's non-standard analysis you buy into the
> > axiom of extensionality, and all the other axioms of set theory, and
> > mathematical logic - the whole kit and kaboodle - including the axiom
> > of choice, ordinals, and uncountable cardinals, and all the
> > "transfinitology" (even if not with platonistic committments) you so
> > strenuously disclaim.
> >
> > MoeBlee
> >
>
> Dear Moe -
>
> When I say there are problems with the axiom of extensionality, I refer
> to the application of the fact that two sets, when viewed statically,
> contain the same elements.
When you deny that, you cannot then insist on anything that relies on
that, such as Robinson's non-standard analysis.
Such things as ZF set theory or Robinson's theories come all of a
piece, not as parts catalogues from which you can pick only what you
want and then go to someone else's catalog for other bits and pieces.
|
|