Re: Well Ordering the Reals

In article <MPG.1df925fe18aaead398a7de@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <1133427464.857888.284340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > albstorz@xxxxxx wrote:
> >
> > > David Kastrup wrote:
> > > > albstorz@xxxxxx writes:
> > > >
> > > > > David Kastrup wrote:
> > > > >> albstorz@xxxxxx writes:
> > > > >>
> > > > >> > David Kastrup wrote:
> > > > >> >> boink <boink@xxxxxxxxxx> writes:
> > > > >> >>
> > > > >> >> > On Mon, 21 Nov 2005 16:34:20 -0500, Tony Orlow wrote:
> > > > >> >>
> > > > >> >> >> How did the set become infinite, if you only added a finite
> > > > >> >> >> number
> > > > >> >> >> of elements to it? if you added elements an infinite number of
> > > > >> >> >> times, each one bigger than the last, how do you NOT have
> > > > >> >> >> elements
> > > > >> >> >> which are the result of an infinite number of successions, and
> > > > >> >> >> if
> > > > >> >> >> you do, how do they NOT have infinite values? If, asfter
> > > > >> >> >> infintiely
> > > > >> >> >> many steps you get an infinite set, then after infinitely many
> > > > >> >> >> increments, you get an infinite value.
> > > > >> >> >
> > > > >> >> > that's funny, because in some sense that's exactly what
> > > > >> >> > happens, but
> > > > >> >> > you don't get it. after omega many steps, you get the infinite
> > > > >> >> > ordinal omega which is the set of all finite ordinals. and
> > > > >> >> > omega is
> > > > >> >> > infinite and contains no infinite ordinal.
> > > > >> >>
> > > > >> >> Nonsense. With that kind of logic, with aleph_1 many steps, you
> > > > >> >> get the infinite ordinal omega_1, but there is no such thing.
> > > > >> >> Steps don't get you omega. Omega is an _inexhaustible_ supply of
> > > > >> >> sequential steps. Either you have it, or you don't. If you
> > > > >> >> don't,
> > > > >> >> you can't put it together using finite steps. A sentence like
> > > > >> >> "you
> > > > >> >> get omega, if you just exhaust an inexhaustible supply of finite
> > > > >> >> steps..." does not make sense.
> > > > >> >
> > > > >> >
> > > > >> > It's really funny. You have infinitely many natural numbers but
> > > > >> > you
> > > > >> > have not infinitely many steps (or you have it but you can't
> > > > >> > supply
> > > > >> > the natural numbers with it).
> > > > >>
> > > > >> You have an inexhaustible supply of steps. Since it is
> > > > >> inexhaustible,
> > > > >> you can't perform "all of those".
> > > > >
> > > > > This must hold in the exact same manner for the inexhaustible supply
> > > > > of
> > > > > natural numbers. Since it's inexhaustible you can't have all of
> > > > > those.
> > > >
> > > > Not one by one. Only as a supply. And N is exactly that.
> > >
> > > If N is a supply, its extent is exact this what is usually called
> > > potential infinity.
> > Then we only have a potential one and a potential two , etc., as these
> > have no more actuality than N does.
> >
> > > > This is not problematic: _all_ mathematical entities exist by virtue
> > > > of their definition and their properties.
> > > >
> > >
> > > That's arrogance. The natural numbers don't exist since you or someone
> > > else define them. The natural numbers exist, since men exists. 100.000
> > > years ago, nobody had defined N.
> > > Not math creates N. N creates math!
> >
> > Mankind creates both!
> >
> > Or does Storz wish to reserve that right of creativity to God?

> Kronecker seemed to think that way. God creates N and man creates math out of
> N. That was his perspective.

Well, Knonecker has had his chance to propose that thesis face to face
to God by now, and might have had occasion to change his mind.

And if God created N, he certainly did not do so in either TO's image or
Storz' image.
.

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