Re: SUO: RE: Criteria that an ontology must satisfy
Jay,
Those criteria define the target that was established as the
primary goal by the ontology workshops that were sponsored by
the NCITS T2 committee from 1996 to 1997. I certainly admit
that it will take us some time to meet them satisfactorily.
> As we well know, some terminology is not directly formally
>first-order definable (e.g., the general concept of finiteness). What do you
>mean by 'define'? Definability is a notion (I will argue) which has a
>precise meaning only relative to the logical system in which it is embedded.
>The notion of finiteness is definable, for example, within an first-order
>version of set theory. Or within a 2nd-order version. Have we yet been
>sufficiently exact about the nature of the logic contemplated by the SUO? Or
>about the nature of the set theory, e.g.? Is SUO-KIF, for instance,
>sufficient for SUO's logical purposes as it stands at the moment? Such
>concerns are also relevant to a discussion of definitions of identity.
The language of core KIF is pure first-order. But we have been
talking about extending KIF to a sorted language, which can be
used as a metalanguage for arbitrary many metalevels. A sorted
first-order language can indeed support true HOL, if you allow
sorts that have uncountably many members.
But in any case, defining all the terms of mathematics is
almost trivial in comparison to defining all the words of
English. Following is a quotation from C. S. Peirce, which
I quote at the top of the ontology page on my web site:
The task of classifying all the words of language, or
what's the same thing, all the ideas that seek expression,
is the most stupendous of logical tasks. Anybody but the
most accomplished logician must break down in it utterly;
and even for the strongest man, it is the severest possible
tax on the logical equipment and faculty.
And Peirce certainly knew both logic and lexicography. He
invented both the modern notation for predicate calculus and
the graph notation, which I use for conceptual graphs.
And for lexicography, he was an associate editor of the
Century Dictionary, for which he either wrote, edited, or
reviewed 16,000 definitions -- more than any other editor.
And I agree with the following point:
>P.S. There is often a tension, perhaps direct conflict, between scientific
>discourse and ordinary language discourse. I expect that there will be cases
>in which this tension is irresolvable, save by discriminating judgements.
John Sowa