Re: SUO: Vote 2001-02: IFF Foundation Ontology
Chris,
I am sympathetic to the use of category theory as a framework for
supporting the multiple mappings between various theories in the
infinite lattice. However, I agree with you that the terminology
of category theory is unfamiliar even to most mathematicians and
logicians, and it generally strikes terror in the hearts of everyone
else.
> Me, I don't care. I'm all for using whatever framework is most powerful
> and appropriate. But can you, or anyone, provide us with one concrete
> example of a shortcoming in the traditional framework of first-order
> syntax, proof theory, and model theory that would necessitate moving to
> a framework as abstract and (to most) unfamiliar as category theory?
I believe that the appropriate place for category theory is under
the rug where no one will ever see it. It would be useful to have
a white paper that shows how all the mappings from theory to theory
can be untangled in category land, but then present the results
without using any of the terminology of category theory. No one
who uses the ontology (even with the lattice of theories is shown
right up front) should ever see any of the terminology or machinery
of category theory.
John Sowa