Date: Mar 12, 2013 11:13 AM
Subject: Re: Matheology § 222 Back to the roots

On 12 Mrz., 12:40, William Hughes <> wrote:
> On Mar 12, 11:44 am, WM <> wrote:

> > On 12 Mrz., 11:08, William Hughes <> wrote:> On Mar 12, 10:19 am, WM <> wrote:
> > > > On 12 Mrz., 00:51, William Hughes <> wrote:
> > > <snip>
> > > > > There is a fixed column, C_1, which is coFIS to
> > > > > |N.   There is no fixed line which is coFIS to |N

> > > > There is no |N in potential infinity.
> > > |N is the potentially infinite set of natural numbers.
> > The "potentially infinite set" is already a contradictio in adjecto,
> > because the notion of set always requires completenes.

> OK, let |N  be the potentially infinite sequence
> of natural numbers.
> <snip>

> > Actual infinity requires that *all* natural numbers are in the list
> > but not in a single line. That is a contradiction.

> OK, your position is that the equivalent
> statement in potential infinity
> Every natural number is in the list but not in a
> single findable line.

Note: "Every natural number"! This sentence means about the same as
every man or every Chinese character, namely a collection that is
finite but capable of growing (or shrinking). The only problem here is
that this collection or better these collections exist only in the
heads - but in very many heads, memories, books and whatever is able
to store ideas.
> is not a contradiction.

This is not a contradiction, since everything that exists at a time in
a memory can be there. It is a finite collection and can exist in a
finite line.

The list

1, 2
1, 2, 3

has only *finite* lines!

> Even if I accept this
> all it means is that I am incorrectly talking
> about numbers in infinite sets,
> rather than findable numbers in
> finite sets with unfindable last
> elements.

Why is the last element unfindable? Because it is not fixed. Therefore
we cannot prove that it is the last element. If we find that a memory
contains n as the last element, we easily can double it. Well, then 2n
is the last element, for a moment. We are not limited to invent new
abbreviations to increase the maximum. But we will never have more
numbers than 10^100 or so. This is because mathematics is not with God
but with reality.

> My results do not change.

That is deplorable. Your results are a contradiction. You argue that
an actually infinite set or sequence can violate the rules of logic
of finite elements. But even an infinite sequence of finite elements
does not contain an infinite element.

Why don't you believe in an actually infinite natural number? Why do
you think that it differs from an actually infinite FISON?

> All you have is a teddy bear that says
> "An infinite set of natural numbers
> does not exist".

And so I am well off the dilemma with an infinite FISON. And I live in
the real world. Mathematics is the last science that lives in a pre-
Darwin state, believing everthing rotates around it (pre-Copernicus-
state), everything is influenced by mathematics, but mathematics is
not acted upon by reality (actio without reactio, pre-Newton state).

Regards, WM