Re: OT (sets and stuff)

On Feb 6, 10:40 am, "Neo" <neo55..._at_hotmail.com> wrote:
> > That's not empiricism.
>
> I probably misunderstand and misused the word empiricism. According to
> wiki, In the philosophy of science, empiricism is a theory of
> knowledge which emphasizes those aspects of scientific knowledge that
> are closely related to experience, specially as formed through
> deliberate experimental arrangements. It is a fundamental requirement
> of scientific method that all hypotheses and theories must be tested
> against observations of the natural world, rather than resting solely
> on a priori reasoning, intuition, or revelation. Hence, science is
> considered to be methodologically empirical in nature."
>
> I think you are saying I can't question the validity of a set theory's
> definition of a construct such as {{}}.

Correct. It exists if we say it exists.

> I am saying I can question the validity of such definitions,

Yes

> if it can't be verified against observations in the real world,

No. This is where you're hung up. But:

> leads to exceptions,

Yes

> contradictions,

Yes

> ambiguities,

Yes

> unsystematicness,

(I don't know what this one means, but let's leave that be for now.)

The point being, if you can find some problem, any problem, *within* the formal system, such as a contradiction, you've really demonstrated something, and the system itself will have to be revised or dropped.

However, if you want to try to use observations of the natural world to find a flaw in the formal system, you're on the wrong track. If there exists even *one* useful mapping from the formalism to natural phenomena, then the formalism is useful. Finding a mapping with a flaw in it doesn't do anything at all. To say something significant about the usefulness of a formalism relative to the natural world, you have to show that *every* *possible* mapping from the formalism to the natural world is broken. Just finding one such doesn't do squat; anyone can do that.

Example:
I will map 1 to unicorns, 2 to horses, and 3 to donkeys. Unicorns don't exist, therefore the concept of 1 is flawed and all of arithmetic is useless.

Do you see why that doesn't matter?

So I'm allowed to show utility by talking about a bag of potatoes. But you're *not* allowed to show problems by talking about bags of potatoes, or elephants. If you want to demonstrate a problem, you have to show that the problem holds for every possible way that I could think about the formalism in real world terms. In essence, this means you've got to show a contradiction, ambiguity, etc. Which in turn means that nothing you can say about the real world matters. So let us hear no more talk about elephants being a problem with set theory. Elephants (or any other thing in the natural world) are only able to demonstrate the value of set theory, not the lack of value.

It may be unfair, but them's the rules.

Marshall Received on Tue Feb 06 2007 - 20:26:59 CET