Re: Is continuum completely filled up?

On 1 Feb., 20:04, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1170329251.895028.224...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





"Albrecht" <albst...@xxxxxx> wrote:
Dave Seaman schrieb:

On 30 Jan 2007 00:15:24 -0800, Albrecht wrote:

Dave Seaman schrieb:

On Tue, 30 Jan 2007 02:55:55 +0900, toshiaki wrote:

"Dave Seaman" <dsea...@xxxxxxxxxxxx> wrote in message
news:epiuer$4j5$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Do you really believe the existence of N, or is it only a matter of
difinition?

Do you really believe the existence of 3, or is it only a matter of
definition?

I believe the existence of 3 as three pieces of pebble, line as drawed
line,
and infinite space. But as for the latter two cases, even though they
are
consisted of infinitely many points, we can not know all of them. If 0
line
up infinitely, then there is a 1 acompanying infinite 0 too.

I wasn't asking about the existence of three objects. I was asking
about
the existence of an abstract concept, the natural number 3. My point is
that this number does not have physical existence at all, and therefore
its existence is just as much a matter of "belief" as is an infinite
cardinal such as aleph_0.

That's really a poor view. What do you see here in the brackets:( # #
# )? You see objects of the form "#"? Maybe you see three of them? You
are unable to comprehend that you only can see three if you see three?

Let's make it even simpler. Do you believe that the empty set has
physical existence? I don't. It's an abstract object. The empty set is
not the same thing as an empty sack.

Your point of view was, that all things which have no physical
existence are a matter of believe. That's wrong.

If you see a red colour there is red (light with 400 nm wavelength).
If you see three things, there is three (multiples of same types of
the amount three). Three is. Three is the equivalent class of all
three objects as red is the equivalence class of all red objects.
What do you think about this view?
You say, the existence of abstract objects is a matter of believe. Do
you really think like this? Is the existence of the univers a matter
of believe? Is the existence of the colour red a matter of believe? Is
the existence of humanity a matter of believe?

The existence of humanity can be verified in the physical world. The
existence of a natural number cannot. We can only see instances of the
number, not the number itself.

If there are no numbers, all is one. You can't distinuish anything
from anything other. The concept of multiples exists. Since we exist
(cogito ergo sum).
Do you think trees exists? But "tree" is just an abstract concept.
There is no object "trees". There is only one (concret) tree here, one
tree there, another one on the left, another on the right, .... But
there is nowhere a "trees".

We can verify the existence of natural numbers since if they are not,
we are not.

Maybe you are not but the rest of us are.

If there are no numbers in concrete existence, you are me and we all
are one. Since if there are no numbers there is only one or nothing
(but consider: cogito ergo sum).


There is a qualitative difference between the sort of existence enjoyed
by physical objects and that enjoyed by mental images like numbers.



You see different sorts of existences? I do so too. A natural number
has very much more existence than e.g. aleph_0.#

Best regards
Albrecht S. Storz

.

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