Re: A consideration concerning the diagonal argument of G. Cantor
Klaus Cammin
> How would you think without a physical pattern in your brain?
So what? I have no objections to the notion, that numbers - and ideas in
general - depend on physical processes in our brains. The important issue
here is, whether these inner-brain images have brain-external counterparts.
And I believe, that the physical representation of numbers *at most* exist
in brains - and nowhere else. We have an image of "one chair" in mind, and
our sensory tells us, that the chair actually is not only in our brain. The
sensory apparatus doesn't tell us anything about the "one".
Here we have one of the many possible ways to tell apart numbers and
things. I almost can't believe, that Albrecht apparently denies, that
internal and external objects can't be distinguished.
If these two types of objects are all the same, then you're either doomed
to assume, that numbers exist materially, or you wind up assuming, that
things don't exist materially, which makes a pretty solipsistic point of
view. And both positions are very contradictory to physics.
> Why do you use physical means to express numbers?
From that follows, that numbers are physical?
We do so in order to give our images a material form. However we know, that
the material of the "number" only is used to *symbolize* the number. As
Virgil said, Santa Claus actually doesn't exist, although a company has
given him a material form.
(It occurs to me just now, that the clip with Lefty and Ernie really is
very good. Lefty tries to muck Ernie about the 8, however Ernie knows darn
well, that he hasn't anything of value to sell. How so, because nobody, not
even Lefty, would loose the 8 with the purchase. Consequently he offers
something of the same value - some 9s, which let Lefty realize, that Ernie
is smarter than him.)
> Try to answer for yourself
> the question, what you think when you think a number like 3. Does an
> unphysical feeling cross your brain? No, you think of a physical
> entity. Without being in possesion of physical images you could not
> think at all.
Yeah, I might think of the 3 written with ink on paper, or with chalk on a
table. But mostly I think just of the form, i.e. HOW it's written, and not
where and with what material, because that's simply unimportant in many
contexts. And all those numbers are just symbols. So no, I don't
necessarily think of numbers as physical entities. It just depends,
whichever is more convenient in the proper situation.
> Numbers are simply represented by a multitude of
> different images,
But those images are not the same type of images, which we make from
material objects. The mere fact, that numbers are represented by a
multitude of different images, IS a difference to material objects. We
can't imagine my chair simultaneously made of ink and chalk, because
actually my chair is made of leather, metal and plastic, and this isn't
likely to change in any other image of it.
> as are other abstractions like screw or car or human
> or abstraction.
We can touch a screw, a car or a human, we can't touch the number, only the
material, which we chose to symbolize the number with. We can't touch an
abstraction, can we? Another of the many means to distinguish ideas from
things ...
> But they do not exist without and independent of physics.
I never said that.
Viele Grüße
Klaus