Re: SUO: Theory Query
Pat,
As ontologists, our primary concern is to develop theories
about actual things that exist in the real world. But we
use mathematics to express those theories and computers
to implement them.
Patrick Cassidy wrote:
>The way I am using "theory" is in
>the sense of an ontological theory, which is
>a "theory of the real world" -- one which
>addresses the question of which formally
>expressed concepts and relations
>best represent the objects and processes of the
>real world for the purpose of automated reasoning.
True. But we must distinguish form (its syntax) and
content (what it is talking about in the real world).
From the computer's point of view, it's all mathematical,
and the computer can't tell what the terms refer to.
>In order to be such a "theory", an ontology
>must have specific widely recognized real-world
>objects and processes and events which are
>**instances** of some concept in the "theory".
True -- but irrelevant from the computer's point of view.
> This definition specifically excludes mathematical
>theories which do not purport to represent objects
>or events on the real world.
Irrelevant. Your definition merely expresses your
intentions, but there is nothing in the axioms and
definitions that can in any distinguish terms that refer
to the real world from those that are purely mathematical.
> For the definition you propose:
>
> > | A '(first-order) theory' T of $L$ is a collection of sentences of $L$.
> > |
> I would view this as a mathematical theory, unless
>some of those sentences describe real-world objects
>as instances of some concepts in the theory.
All theories are mathematical objects. As I said above,
there is no way for the computer (or even a human being
who looks at the axioms) to determine whether they are
true about the world.
Bottom line: The lattice of all possible theories will
include all those that are true of the real world and
all those that aren't. Distinguishing one from the other
is a job for science and engineering. It can't be done
by the computer by itself.
John Sowa