Re: Cantor's Theory sucks

The Ghost In The Machine wrote:
> In sci.math, oðin
> <oðin@xxxxxxxxxxxx>
> wrote
> on Wed, 18 May 2005 13:27:45 -0700
> <R7WdndolwMjcOBbfRVn-oQ@xxxxxxxxxxxxxx>:
> >> The problem with Cantor's Theory is that it is not
> >> grounded in reality. In contrast, mathematics very
> >> definitely is grounded in reality.
> >
> > Right... and there is no such thing as zero...
> >
>
> Zero does not exist, except as a thought-process. Ditto
> for 1, 2, 3, ... ; bear in mind that 2 means that there
> are two elements that are sufficiently indistinguishable
> to be considered a pair, but one can't catch the "2" of
> that pair with a butterfly-net.

This is a somewhat shallow reasoning. Let me show you why.

You emphasize that numbers are abstractions, and as abstractions
they really exist only in our minds, and therefore mathematics
is not empirical.

Now, look at the language of any scientific discipline. You will
find that its terms are quite often abstract. It couldn't really
be otherwise. However, the theories can be experimentally verified.
So, we see your above conclusion doesn't follow.

However, there is a more drastic mistake.

You say zero does not exist. But I will tell you that if you
say so, I will tell you that lists do not exist in the world,
they are just an abstraction. Then, however, I can point out
to any object that may be conceived of a list, such as a list
of symbols on a paper. And then I tell you that this is in
fact a list, and the mathematical theory of lists would be a
theory of lists in the real world. It doesn't matter how much
I abstract lists, the concept is still derived from our
physical reality.

Then, I show you an empty bucket, and I tell you that I have
zero marbles in it. There, the meaning of "zero marbles"
corresponds to the reality of the bucket. Now, is there such
a thing as zero in the world? If it did not correspond to
the *lack* of a quantity, in delineating what is true of
a container and what is not, then it would mean nothing.

Zero isn't zero because it's some arbitrary mind-trick in
some mathematician's mind. Zero is zero because it has a meaning.

And yes, *every* word you use is abstract, that doesn't make
their referents non-existent, non-physical or what. The criteria
for that is something else.

What I mean is that if by a number you do not understand a
definite physical property in a description of a physical
situation, then I think you have forgotten the origin of a number.

Of course "zero" as some Platonic entity doesn't exist. But
having zero elements, having zero quantity, etc. are well grounded
in our experience.

Regards,

--
Eray

.

Quantcast