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.pptFirst 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
human-factored

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
system: a

> 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
elementOf.

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

stronger.

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

arbitrary.

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.

John

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