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 <fomJ...@nyms.net> wrote:

>> On 1/17/2013 4:52 AM, WM wrote:

>>

>>> On 17 Jan., 08:42, Ralf Bader <ba...@nefkom.net> 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,

..6..|..5..|..4..|..3..|..2..|..1..|..0..

-----|-----|-----|-----|-----|-----|-----

..1..|..2..|..3..|..4..|..5..|..6..|..0..

..2..|..3..|..4..|..5..|..6..|..0..|..1..

..4..|..5..|..6..|..0..|..1..|..2..|..3..

.12..|.11..|.10..|..9..|..8..|..7..|..6..|..5..|..4..|..3..|..2..|..1..|..0..

-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----

..1..|..2..|..3..|..4..|..5..|..6..|..7..|..8..|..9..|.10..|.11..|.12..|..0..

..2..|..3..|..4..|..5..|..6..|..7..|..8..|..9..|.10..|.11..|.12..|..0..|..1..

..4..|..5..|..6..|..7..|..8..|..9..|.10..|.11..|.12..|..0..|..1..|..2..|..3..

.10..|.11..|.12..|..0..|..1..|..2..|..3..|..4..|..5..|..6..|..7..|..8..|..9..

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.