Date: Mar 22, 2013 10:19 PM
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.