Re: Axiomatic ontology
Rob,
There are many different issues about knowledge representation
that are worth discussing. I was just commenting on a few
that I felt required some further clarifications:
1. There is an open-ended number of different knowledge
representations that are useful for many different purposes.
2. Any attempt to restrict the number to just a few is likely
to ignore, omit, or overlook others that may be just as
useful or even more useful for other purposes.
3. But the fact that the same thing (or many related things) can
be described in different ways for different purposes does
not imply that the things that are being described embody
some kind of internal "contradictions".
4. It merely means that our choice of representation of x
for one purpose may be an approximation that is inconsistent
with a different approximation made for a different purpose.
For example, the equations of fluid mechanics are so complicated
that it is common to use special-case approximations that are easier
to use for to certain kinds of applications. One such approximation
is to assume that all movements are much slower than the speed of
sound. That simplifies the equations for some purposes, but those
equations are inconsistent with different approximations that are
designed for speeds greater than the speed of sound.
The fact that such contradictions arise in our theories does not
imply that the world itself or any part of it is contradictory.
It merely means that some of our descriptions are approximations
that may contradict different approximations.
> I think the discovery of fundamental indeterminacy in mathematics
> deserves recognition as more than a mere "interesting historical
> note".
But what I was trying to say is that any particular mathematical
theory can be very definite. However, there is an infinite number
of different mathematical theories. What is indeterminate is our
choice of which theory to apply to any particular problem.
The world itself is quite determinate. But we may not be able
to determine the exact theory that determines how it actually is.
John