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Topic: Cantor's argument and the Potential Infinite.
Replies: 17   Last Post: Nov 17, 2012 10:59 PM

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Posts: 185
Registered: 4/18/12
Re: Cantor's argument and the Potential Infinite.
Posted: Nov 16, 2012 4:54 PM
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In article <k856vb$b40$>,
"LudovicoVan" <> wrote:

> "Zuhair" <> wrote in message

> > On Nov 16, 11:36 am, "LudovicoVan" <> wrote:
> >> "Zuhair" <> wrote in message
> >>
> >>

> >> > We still can characterize Cardinality in this setting.
> >>
> >> And you keep missing the point, as the various objections of course
> >> involve
> >> that the standard definition of cardinality for infinite sets is wrong!
> >>

> >> > So Cantor's diagonal is applicable to potential infinity context!
> >>
> >> Cantor's arguments are *only* applied to potentially infinite sets, in
> >> fact
> >> in standard set theory there is no such thing as actual infinity at all.
> >>
> >> Please get your head out of your ass and read and try to understand what
> >> you
> >> are rebutting before you actually get to do it.

> >
> > Good advice for you actually, since you don't know what you are
> > speaking about. So just try to read what is written here, and if you
> > don't understand what is written, or you have some problem with it,
> > then just try to ask politely about it, so that I or others who are
> > more informed that you can explain matters to you. Anyhow standard set
> > theory "ZFC" is of course not limiting itself to the potential
> > scenario, not even to the one I've presented here, that's why it
> > accepts Impredicative definitions, as well as non well founded
> > versions of it, the reason is that it doesn't have a problem with
> > considering the possibility that all sets in the universe of discourse
> > are GIVEN beforehand, and Godel's have stated that there is nothing
> > wrong with this assumption, so there is no problem with considering
> > that the set N is already Given, i.e. it is there beforehand with all
> > its elements, i.e. N is a completed actual infinite set, in standard
> > set theory understanding of N is not limited to the potential of
> > becoming that I've presented here. However here I showed that even if
> > we assume potential infinity in the sense I've presented, which is as
> > I showed here the most faithful to that concept itself, then still
> > Cantor's diagonal argument applies to it. All of what I'm saying here
> > is that standard set theory as customarily understood doesn't not
> > restrict itself to a potential infinity context, but even if so then
> > if we faithfully represent that concept of potentiality then Cantor's
> > argument can be still carried on.

> As usual, you are not even wrong.

The response of someone who can't find any actual errors but still

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