Re: Reactions to/against the Binary Tree

Herbert Newman wrote:

On Wed, 03 Jun 2009 04:09:11 +0200 Ralf Bader wrote:

If a person comes up with such nonsense once, one would say it is a silly
joke. If a person does this over years, and a 5-digit number of postings
one would have to conclude that this person is nuts.

Agree. On the other hand, "arguing" with WM _for years_ about such
important things like the exact meaning of "path" (or rather: WM's
understanding of "path" and whatnot) is a sign of craziness too, imho.

I don't deny that, but I wanted to make a point about the way in which
Mueckenheim is crazy. For example, look at this:
"By the way, here lies the reason why Cantor's diagonal argument must fail,
nevertheless. Every number
smaller than ω is a finite number, and it is surpassed by other finite
numbers [Cantor, p. 406]. Hence, if the
list contains "every number smaller than ω", then there are other numbers,
not contained in the list."
http://arxiv.org/pdf/math/0408089, note 8.

This is utter nonsense with the common understanding of the phrase "every
number". But it becomes understandable if you suppose that "every number"
is a name of a certain number, like Avogadro's number or my niece's
favourite number. Or even if "every number" is understood to be something
like a variable in the programmer's sense, i.e. a name for a memory cell
which can hold a value of the type of natural number. Then, every_number is
of course surpassed by every_number + 1 (mixing up a variable and its value
in the usual way). Now, someone who comprehends the phrase "every number"
in one of these ways (and calls this "potential infinity") - what
understanding will he have about infinite sets, or assertions about
infinite sets?


Ralf
.

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