Re: Review of Mueckenheims book.

On Fri, 9 Mar 2007 12:57:31 -0500, David Marcus
<DavidMarcus@xxxxxxxxxxxxxx> wrote:


It's funny: Reading your proposal I get the impression that you didn't
see (or appreciate) the very point of my argument (what I'm after, what
I wanted to address with it).

I saw it. If by "appreciate", you mean like, then I guess I didn't.

I see. :-)


Let me try again: If you start with:

IN contains ALL the natural numbers (and ONLY the natural
numbers).

then it is NOT immediately clear that there are no infinite natural number
in IN. (Not even to me! ;-)

I've no idea what an infinite natural number is.

Same with me!

Quote from my argument:

"Assume (for the sake of the argument) that in the set of _all_
natural numbers, denoted by IN*, there were infinite natural
numbers (though I don't have the slightest idea how such numbers
would look like)."


It seems to me that as soon as we start talking about such (mythical)
things, we plant the idea that such things [might] exist.

Well, not really. We just _assume_ that such "mythical things" exist. It
turns out that even if such strange things would exist, the claim

"Unless there is an infinite [natural] number the number of
[natural] numbers [...] cannot be infinite." (W. Mückenheim)

can be refuted. With other words, if it weren't meaningless ("What are
infinite natural numbers?") it would be false. :-)


It is like talking about green unicorns.

Sure. Why not?! (Ever heard of A. Meinong, btw?)


The more we talk about them, the more I start looking over my shoulder to
see if one is there.

Oh, come on. If you didn't put it in your room yourself, there shouldn't be
one of these beasts in it.


Hence the "construction" of IN the way described above. This _ensures_ that

IN contains ALL and ONLY finite natural numbers.
~~~~~~

The rest of the arguments are (more or less) identical, of course. It's
just that MY argument would lead to the conclusion that there is no
largest number in IN, even though all the numbers in IN are finite (since
we "constructed" it this way).

I think 99.8% of people are incapable of logical thought. If you want to
reason with such people, you have to be very careful.

I see.

On the other hand, logic (or rather valid arguments) and consistency are
the cornerstones of mathematics (once the axioms are given).


F.

--

E-mail: info<at>simple-line<dot>de
.

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