Re: Cantor's Theory sucks
- From: "James Hess" <mysidia@xxxxxxxxx>
- Date: 18 May 2005 14:47:04 -0700
david petry wrote:
> George Orwell wrote, "some ideas are so stupid that only
> intellectuals can believe them." Cantor's Theory is an
> example of such an idea.
I take issue with this unsubstantiated claim that Cantor's Theory
is a stupid idea.
> The problem with Cantor's Theory is that it is not
> grounded in reality. In contrast, mathematics very
> definitely is grounded in reality.
I take issue with this unsubstantiated claim that Cantor's Theory
is not grounded in reality.
> The reality underlying mathematics is computation. That
> is something which everyone accepts as a reality.
I take issue with this unsupported claim that the reality
of mathematics is just computation: this idea seems to deny
so many elements, so depending on what you mean by computation.
These words are not very precise: in general I think 'computation'
is broad enough to include all the ideas from Cantor's Theory
and the many other very generalized abstract notions in their
respective worlds...
Re-defining mathematics as a more narrow thing does not lend
credence to the idea that Cantor's Theory is stupid.
Are you suggesting Cantor's theories are only relevant to some
broader area like Philosophy, because they don't have to do with
mathematics?
> The computer revolution gives us an enlightened way of
> looking at mathematics. We can think of the computer as
> a microscope into the world of computation, and mathematics
> is the science which studies that world.
The computer revolution is irrelevent as to the validity of
Cantor's theory. Technology offers many tools that are useful
in a variety of contexts, and could provide powerful means to
establish or refute theory, but that's about it.
Mere physical contraptions do not effect the validity of such
general theory.
There's no guarantee that electronic computer technology today
offers all or any significant portion of the variety and nature
of tools that will be available in the next few centuries.
> Mathematics is about truth. Truth necessarily has
> observable implications. It must be grounded in reality.
> The theorems of Cantor's Theory are not truths.
False. Some but not all truths can be observed by direct
implications in the world. Just because some theory cannot
be observed concretely does not mean it has no value.
The question of ultimate truth is one philosophy and science
but not mathematics or idealisms can answer really.
I think of mathematics as a system that can postulate
worlds very different from the one in which we live.
> Formal systems, such as Cantor's Theory, are objects that
> live in the world of computation, and hence, they are
> things to be studied in mathematics. But that doesn't
> justify the special status that Cantor's Theory is
> currently given in the mathematics community.
The acclaim of Cantor's Theory is irrelevent, the only thing
important is it is one established theory way of thinking
and apparently preferred widely enough to matter.
A theory that is useful is not stupid unless it is wrong or has
been superceded.
If you expect any credence from anywhere, you need to justify
your opinion by posing what you think of the theory is
inconsistent with itself, with other well-grounded theory,
with reality.
If you go out and claim "1 = 0", for instance, you need to
provide further explanation: changes are greater that you made
a mistake, than that you are right and anyone who understands
and accepts Cantor's Theory is wrong.
Or a more appropriate cause of action would be to pose or
point to (if already existing) what you believe is a better theory,
only then can you legitimately contend that Cantor's theory is stupid
in any way.
The justification being that you have a better substantiated
alternative that will suit the needs.
When something is stupid, it's because there's something more
rational than it in existence. If there is no better alternative, then
the best that legitimately can be said is "in need of improvement",
a claim which still begs for justification.
> Contrary to what some mathematicians seem to believe,
> consistency does not favor Cantor's Theory. We can be
> perfectly consistent defining mathematics to be the
> science of phenomena observable in the world of
> computation.
I take issue with this unsubstantiated claim that consistency
does not favor Cantor's Theory.
What do you mean by phenomena observable in the world of
computation?
In particular, what are phenomena?
What is the "world of 'computation'" ?
How is Cantor's Theory inconsistent with something?
> So why are intellectuals attracted to such stupid ideas
> as Cantor's Theory? Due to the structure of our society,
> intellectuals tend to value cleverness, consistency,
> complexity, and even sensationalism, more highly than
> truth. We live in a sick society.
Why is society so full of people who like tossing around random
careless criticisms of any thing that doesn't suit
fanciful ideas so often that whenever a real criticism ever pops up,
it is in danger of just being ignored?
Why do people point to some "problem in society", for not
accepting their unconvincing suggestions and rhetoric as
the great truth they think it is?
-Mysid
.
- References:
- Cantor's Theory sucks
- From: david petry
- Cantor's Theory sucks
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