Date: Mar 3, 2013 4:10 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 2 Mrz., 23:55, Virgil <> wrote:

> > Create the list of von Neumann naturals taken in order, so that each
> > line is both a member of and a FIS of the next line, then the set of all
> > FISs is just the set of all such naturals, which cannot, by definition,
> > be contained in any one line.

> So not all naturals are finite?

Maybe not inside WMytheology,
but they are all finite outside WMytheology.

> Every finite natural is in a single finite line together with all its
> companions.

With all its predecessors, yes, but with all of its successors NO!
There is at least one natural in each such line for which no successor
exists in that line.

> If you don't believe it, then find some naturals that you can
> individually identify and that are not within a finite subset of
> naturals.

That is not at all the same thing. Since one "companion" of any natural
is its successor, and every natural has a successor (and all naturals
have successors) for every natural there is a "line" which contains it
but not its successor.

Thus WM is WRONG
> > Note that WM violently dislikes the von Neumann naturals because
> > they are so useful in poking holes in WM's phony arguments.

> I dislike only mathelogical dogmas like "the set of all prime numbers"
> that does not allow for constructing another prime number.

WM dislike common sense with regard to set theories.

If we can distinguish between prime numbers and things which are not
prime numbers, it makes sense, at last outside Wolkenmuekenheim, to
speak collectively of those things which are prime numbers as
distinguished from those things that are not.

The number of things which are or which are not prime numbers is
irrelevant in any such distinguishing.

Thus WM's whining about infiniteness is an irrelevancy to mathematics,
and to common sense, of which WM has little to none.