Date: Jan 17, 2013 12:30 PM
Author: fom
Subject: Re: WMatheology § 191

On 1/17/2013 10:44 AM, WM wrote:
> On 17 Jan., 17:38, fom <> wrote:
>> On 1/17/2013 4:52 AM, WM wrote:

>>> On 17 Jan., 08:42, Ralf Bader <> wrote:
>>>> In a similar way it seems to be
>>>> impossible for M ckenheim to grasp something actually (not in the
>>>> always-growing sense) countably infinite without a boundary at the far end.

>>> Not at all! I consider and vivdly imagine the actually infinite set of
>>> all terminating decimal representations of the reals containg all
>>> natural numbers as indices. Alas I cannot imagine that there is
>>> another decimal representations of the reals which deviates from all
>>> of them. Can you?

>> Then, do irrational numbers exist
>> transiently on a problem by problem
>> basis? (Vacuum energy numbers)

> They exist in many forms but certainly not as never ending decimal
> representations that somehow manage to end or at least to be complete
> nevertheless.

This is where I generally have a
problem with what you are doing.

No question about the fact that the
history of realism regarding the foundation
of mathematics makes most of it comparable
to Descartes' proof of the existence of
God. But, in failing to provide reasonable
alternatives (that is the hard part), you
do nothing constructive. Thus Virgil
is correct in referring to WMytheology.

You do bring up certain legitimate
issues. For example, it it clear
that the quantifiers are ambiguated.
This probably comes from the structure
of finite projective geometries,



Where the reversed order of non-zero entries
on the first line is evident. It is not
so difficult to imagine a "march to infinity"
in terms of such geometries since one exists
for every prime.

Moreover, if one treats the basic boolean
functions as a "system," then truth-functional
negation is nothing more than a certain
projectivities of the 21-point plane with
the boolean functions comprising the points
of the associated affine geometry.

The ambiguation of the quantifiers is
related to duality with respect to
DeMorgan conjugation (negate the arguments...,
then negate the connective. It works with the
quantifiers viewed as unary truth functions.)
and this too, can be modeled using finite
projective geometry.

You, however, simply whine.