Re: The modern mathematical concept of infinity is ...

Jesse F. Hughes wrote:

lwalke3@xxxxxxxxx writes:

On Feb 19, 8:51 pm, Ralf Bader <ba...@xxxxxxxxxx> wrote:
lwal...@xxxxxxxxx wrote:
One can only imagine how many more mathematicians
WM must find having similar or even identical
ideas as himself, before Bader, Chandler, and the
others finally accept that WM can have a theory
that isn't the "Most Stupid Philosophy" ever.
That is now getting completely ridiculous.
The point is that Isles' or Nelson's work has mathematical content, and
Mueckenheim's has not.

Yet WM implies that he agrees with Isles. Therefore
WM has mathematical content if and only if Isles has
mathematical content.

That's just nonsense.

First, of course, persons do not have mathematical content. Second,
just saying "I agree with Einstein" does not make me a physicist.

We already know that WM makes many inferences that
are invalid in ZFC, but are apparently invalid in
the WM-Isles theory. So WM is wrong to say that ZFC
proves the existence of only finitely many naturals,
but right to say that WM-Isles proves the existence
of only finitely many naturals.

What the *** is "WM-Isles"?

A phantasy of lwalke3.

Perhaps Isles has a mathematical theory
(I wouldn't know),

I wouldn't call it a theory (theories, for my feeling, are book-size, not
paper-size). The first point to consider is that Isles means "natural
number notations" when he writes "natural numbers", and he considers
"natural number notations" to be linguistic entities. Contrary to
Mueckenheim, he is explicit about that. And when he writes that the natural
numbers of today are different from those of yesterday then this is to be
understood in the sense just explained. Mueckenheim likes to quote that
sentence about the numbers of yesterday, because he assumes that it
supports his crazy view that naturals can go in and out of existence, or,
formimg a potential infinity, some new naturals can emerge. Whatever Isles
is thinking about potential infinity, that quotation is intended to say
something very different from what Mueckenheim believes.

Neither does that whole paper of Isles speak in favour of Mueckenheim; of
course he finds its title appealing, but there is a big contradiction
between Isles' position in that paper and Mueckenheim's mad moonshine
theory expounded in his "Physical constraints of numbers". Isles in a sense
_refutes_ Mueckenheim's "theory", but Mueckenheim is way too stupid to note
that. Namely, Mueckenheim asserts that by using exponentials and similar
notation, it follows that arbitrarily large naturals can be denoted and
made to exist. This implies first that Mueckenheim is not an ultrafinitist
and secondly if one uses different notations for natural numbers one needs
procedures to transform between these notations and Isles just explains
that those transformations can get unwieldy.

However, the only originality of Mueckenheim's "theory" lies in that stupid
idea to get arbitrarily large numbers by using abbreviative notations - and
thereby also getting gaps in the natural number sequence. If he gives that
up, what remains is (besides misconceptions about set theory) indeed plain
ultrafinitism, and that is nothing new, ridden with difficulties and sticky
points like the usage of paraconsistent logics and anyway better served by
other people who contrary to Mueckenheim know what they are doing.


Ralf
.

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