Pat and Chris M,
I have read the following slides, which make some interesting points
and cite some useful references:http://www.micra.com/COSMO/TheFoundationOntologyForInteroperability.ppt
First of all, I have a very high regard for the work by Anna Wierzbicka
which I have been following for nearly 30 years. (I cited her early
_Lingua Mentalis_ in my 1984 book.) I also agree with Cliff Goddard
that the arguments against that kind of research are *bad*.
But I must emphasize that the so-called "primitives" that Anna W. and
others have proposed are most definitely *not* primitives in the sense
that mathematicians use.
Anna W's primitives and the Longman's primitives may be useful as
rough guidelines in a methodology for designing good
representations. I suspect that they could support a better basis
for pedagogy than set theory, which turned out to be a disaster
when it was inflicted upon innocent children by inept teachers.
I would encourage such research.
But Anna W's "primitives" are extremely vague and squishy. She manages
to use them to "define" lots of different terms across many different
languages and cultures. I find those exercises intriguing. But her
definitions are so vague that they would be totally worthless for
formal ontology. The give *ZERO* evidence in support of Pat's claim
that a precise FO is possible or that it would have the slightest
value for interoperability.
Furthermore, the FO that Pat has suggested is a closed system.
Following is the point I made, which Pat did not address in the
more recent note:
JFS> I suspect that what you have in mind is a closed
> finite set of relations (i.e. primitives) that are fully specified
> by necessary and sufficient conditions...
> Then all possible terms that could be defined in your system would
> consist of closed-form definitions of the following kind:
> Every term T is either a primitive or it is defined as synonymous
> to an _expression_ that is composed only of primitives.
A closed system is a dead end. It rules out most of mathematics,
including systems that are important for physics and engineering.
Since it is very difficult to analyze a system with 2148 "primitives",
I used the many versions of set theory as an example. Chris raised
the following point, which I agree with:
JFS>> But Chris M. used the example of set theory, all versions of
>> which have the same two "primitives" -- subsetOf and
CM> elementOf, i.e., ∈, is the only primitive you need (and the only
> one you'll find in most modern texts).
I agree. I should have added a qualification to avoid that objection,
but I'd like to generalize the issue in a way that makes my argument
The reason why I claimed two "primitives" for set theory is that
I was thinking of a broader range of theories, which would include
the many versions of mereology and set theory as special cases.
Some versions of mereology deal with continuous stuff, which is
infinitely divisible (no atoms). Other versions have atoms, but
no continuous stuff (sometimes called 'gunk'). And other versions
of mereology contain both atoms and gunk.
It is possible to treat set theories as special cases of mereology
in which there is no gunk. In that case, the subsetOf operator of
set theory is a relabeling of the
partOf operator of mereology,
and there is the more basic elementOf operator, which can be used
to define subsetOf.
When you consider the many versions of *both* mereology and set
theory, you get a huge number of ways of formalizing the vague
notions of parts, wholes, and collections -- and all of them are
based on just one or two "primitives".
You can also look at all the many axiomatizations of the notions
of possibility, necessity, and other modal operators. Those are
further examples of the open-ended number of ways of formalizing
the vague modal terms that are common in NLs.
I'm sure that every one of Anna W's "primitives" and any others
that might be proposed by Goddard and others can be similarly
formalized in an open-ended number of ways. Picking just one
of those formalizations over any others would be purely
Conclusion: Pat has not shown any credible
evidence for the
claim that an FO based on such primitives would help support
interoperability among practical computer systems. On the
contrary, its closed nature would probably create more
obstacles than it could eliminate.
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