SUO: 22 May 2002 -- Still Unanswered Questions About SUMO Set Theory
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SUO Working Group Members,
I continue to ask the SUMO Team a modest set of basic questions:
| 1. What is the exact formulation of set theory used in SUMO?
|
| The extended family of SUMO documentation contains the
| remark that the set theory supposedly "built into KIF"
| is "a version of Von Neumann/Bernays/Godel set theory".
|
| 2. Can you provide a reference and a justification for this assertion?
|
| If the SUMO proposal no longer depends on this built-in set theory,
| it remains to specify what variety of set theory it does depend on.
| And it still remains to provide arguments, explanation, references.
|
| 3. Can you provide a detailed account and a justification of
| the differences, if any, between the SUMO set theory and
| standard versions of Von Neumann/Bernays/Godel set theory?
|
| A similar request would of course attach to departures of SUMO
| from any other standard versions of set theory that it invokes.
I have yet to receive anything approaching a responsible answer.
Instead I have received, all without even so much as a simple
acknowledgement of my questions, a host of evasions, a slurry
of indirections, and a spate of red herring in muddied waters.
This has, of course, been the pattern every other time that I
renewed my efforts to take the SUMO Team's proposal seriously.
But is it really so "hopelessly naive" of me to expect fellow
human beings to be capable of learning from their experiences?
Maybe it will serve to back up a bit and review the situation:
None of us wants to go through the kind of a cliff-hanger vote
on the matter of SUMO that we went through before, with all of
the time, energy, and good will that got wasted in the process.
That does not mean that I can just set aside my better judgment
with respect to what I consider to be very critical issues, not
responsibly, anyway, just to get along and be easy going, since
that would not be nice, to everybody concerned, in the long run.
The purpose of this working community is to make all of the
group proposals, in fact, all of the personal contributions,
better and better over time.
Criticism is permitted, indeed, it is necessary to the process.
I do not think that we can afford to pull our punches, not and
still do the work. And I don't think that it has gone too far.
I have been through poetry workshops far more brutal than this.
By way of putting one of those red herrings in the freezer for
another occasion, my present serving of questions concerns the
content of SUMO, not form. There are axioms there that invoke
words like "class", "collection", "instance", "member", "set".
I am asking how the SUMO Team intends the collection of axioms
that bear on these terms, and others like them, to be compared
with any one of several established formulations of set theory.
It is, all in all, a basic question, a crucial question to answer.
Members of this working group, along with the prospective users
of its envisioned results, have a critical need to know whether
such words are likely to have any meaning at all, in the formal
way of meaning something, that resembles the meanings they know
from their former education and experience within their several
schools of thought and work.
It is unreasonable to expect people to redo this basic material
from scratch, to go through the work of decades or centuries that
it would take to check out its usability and to validate all of it
from the get-go, not without a good reason and a lot of discussion.
Unless there is a demonstrable reason for a radical novelty in this
domain, it would be better to stick with one of the tried and maybe
true enough formal systems for set theory that are already in place,
even if just for a start.
As to the status of set theory, it is nothing all that sacred to me,
but since we cannot possibly fathom ahead of time all of the divers
sorts of customers to which we might be forced to become accustomed
at some future date, I regard it as yet another a benchmark, one in
a minimally adequate validation suite, a "New York Modus Tollens",
if you catch my drift -- "if you can't make it there, you can't
make it anywhere".
I am interested in a lot more than set theory here.
If I were only interested in set theory, or graphs,
or groups, or something like that, I would just go
out and get one of the specialized theorem-proving
environments for negotiating these domains. I did
not start with questions about set theory for that
reason, but because sets are just one of the basic
varieties of formal structure that give a backbone
to the species of ontology that we need to address.
When it comes to the main versions of formal set theory,
it may be true that they do not differ all that much in
the long run, or that we do not care all that much what
lies at their outer limits, but they do differ a lot in
the methods and the perspectives that they accord us in
the meantime frame of work, and the following fact just
cannot be dismissed: All of the formal theories differ
in radical ways from our informal theories of sets, and
it is the formal theories, and their controlled proxies,
that we are forced to recur to for engineering purposes.
I just wish that the SUMO Team would understand that
I am trying to give them information that is intended
to be useful. Some day they will encounter critics of
a sufficient authority that their critiques cannot be
refused, and I think that I am asking at least some of
the same questions that any such reviewers would ask.
Most anybody who has been through the wringer of any
formal set theory or even much math at all would ask
these same questions, I believe. I could be wrong.
None of us has perfect information about anything,
that we know of, but this is just the information
that I have, and it is my responsibility to ask
these questions and to give this information.
The volume here is not being generated by me.
All of it could be reduced if the SUMO Team
would simply answer these simple questions.
There will be more questions to come, but
folks who cannot or will not answer basic
questions about their initial proposal do
not inspire much confidence for the future.
Jon Awbrey
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