Re: Ultimate debunking of Cantor's Theory


Virgil schrieb:
In article <1184404361.053421.146760@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 14 Jul., 07:11, Virgil <vir...@xxxxxxxxxxx> wrote:

While I can see numerals (names of numbers) I have never seen a number.
While I have seen the names of sets, I have never seen a set itself.

But this evidence does not convince you that what you suspect to be
numbers and sets does not at all exist?

I have never seen a triangle, only "pictures" representing them, but I
do not doubt their mathematical existence.


Geometrical objects are ideals. That fact is well known at least since
Platon. But this doesn't hold for numbers and there is no connection
between the one and the other fact at all.

Any realisation of geometrical objects has little discrepancies to
their ideal. But two objects are _exact_ two objects, not a little
more than two nor a little less than two.

Triangles and numbers are both mathematical objects, yes. But this
fact provides no cause that for both objects must hold the same
properties as you suggest.







The collections of names and representations *are* the
numbers. The ghosts are imagined nonsense.

Regards, WM

As there is no finite limit to the set of 'names' for any single number,
and there are 'names' for which no umber exists I do not identify names
with things named. "The map is not the territory".


But the properties "being twice", "being threefold", ... are matters
of fact. There is nothing fictional around that facts. Being twice is
not more or less real than being hard, being red-colored or being
gaseous.
Mathematics provides a lot of names for "being twice" but the fact of
twofoldness isn't touched by this circumstance. The moon has much
names in the different languages of the world. Does this fact imply
that the moon doesn't really exist?


Regards
Albrecht

.

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