Date: Mar 22, 2013 10:19 PM
Author: Virgil
Subject: Re: Matheology � 224
In article <f6mdnWDVEcc1eNHMnZ2dnUVZ_oSdnZ2d@giganews.com>,

fom <fomJUNK@nyms.net> wrote:

> On 3/22/2013 5:11 PM, William Hughes wrote:

> > On Mar 22, 10:49 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> > <snip>

> >

> >> All sets are finite, but not fixed.

> >

> > I did not claim that all sets in

> > Potential infinity are fixed.

> > They are finite and thus not

> > different from finite sets.

> >

> > WH: Infinite sets are different from finite sets

> > WH: but they do not contain anything

> > WH: "beyond any finite set".

> >

> > WM: Of course.

> >

> >> There is no upper threshold,

> >> contrary to every finite set.

> >

> > More Wolkenmuekenheim logic

> >

> > Every finite set has an upper threshold.

False, since not all finite sets are ordered.

> >

> > A potentially infinite set

> > does not have an upper threshold

In order for something to be a set is any standard set theory, its

membership cannot be ambiguous, each object must be unambiguously a

member of the set or unambiguously not a member of that set.

Thus what WM calls his sets "with no upper threshold" are not sets at

all, at least not anywhere outside of Wolkenmuekenheim.

> >

> > A potentially infinite set is finite.

So what WM claimes as his " potentially infinite sets" are not sets at

all anywhere outside Wolkenmuekenheim.

> >

>

> And, when properly developed in a constructive

> framework, the objects to which that statement

> might apply are clearly understood as such.

They are all non-sets.

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