Date: Mar 25, 2013 6:30 PM
Author: Virgil
Subject: Re:Wolkenmuekenheim 224

In article 
WM <> wrote:

> On 24 Mrz., 23:10, Virgil <> wrote:
> > In article
> > <>,
> >
> >  WM <> wrote:

> > > On 24 Mrz., 16:13, William Hughes <> wrote:
> > > > On Mar 24, 4:03 pm, WM <> wrote:

> >
> > > So you do no longer adhere to ZFC+FOPL?
> >
> > ZFC+FOPL? does no support WM's alleged proofs, whether by induction or
> > any other method.

> What axioms are mis-applied? You can find the axioms here:
> M%C3%BCckenheim%26any&currentPosition=4

The axioms of ZFC+FOPL, require the existence of actually infinite sets.

SO that as long as WMytheology rejects actually infinite sets,
WM is misapplying those axioms.

Note that the inductive principle requires at least one actually
infinite set also, so that WM cannot appeal to it without first
accepting the existence of actually infinite sets!

Or proving that his WMytheology is corrupt and self-contradictory!

Or both!

One acceptable form of the inductive principle is:

There exists a set of objects, N, and a zero object, Zero, such that
1. Zero is one of the objects in N.
2. Every object in N has a successor object.
3. Zero is not the successor object of any object in N.
4. If the successors of two objects in N are the same,
then the two original objects are the same.
5. If a set contains Zero and the successor object of every
object in N, then that set contains N as a subset.

Such a set as that inductive N is a not-finite, therefore infinite, set.
and WM can't do inductive arguments without it.

So, apparently, in Wolkenmuekenheim one can, or at least WM can, switch
existence of infinite sets on and off at will, or at need.