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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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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: Cantor's argument and the Potential Infinite.
Posted: Nov 16, 2012 5:34 AM
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On Nov 16, 11:36 am, "LudovicoVan" <ju...@diegidio.name> wrote:
> "Zuhair" <zaljo...@gmail.com> wrote in message
>
> news:5e28971d-adb1-49ae-878f-db9ebaf2621c@o8g2000yqh.googlegroups.com...
>

> > 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.
>
> -LV


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.

Zuhair



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