Date: Nov 16, 2012 5:34 AM
Author: Zaljohar@gmail.com
Subject: Re: Cantor's argument and the Potential Infinite.
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