Re: Well Ordering the Reals


William Hughes wrote:
> albstorz@xxxxxx wrote:
> > 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.
> > The set N doesn't exist. That's what I'm talking about the whole time.
>
> No, you cannot get all the numbers from the inexaustible supply.
> But what about the entity "the inexaustible supply". Does this
> entity not exist?

It's no entity in any useful sense of the word. So it exists, but it is
no entity and it is no set. Maybe it's a potential.

"Infintum actu non datur."
Infinity is just a "facon de parler".


Regards
Albrecht Storz

.

Quantcast