On Sep 18, 2008, at 9:21 AM, John F. Sowa wrote: Pat,
The major differences between us result from several related
assumptions about how a formal system can be related to the
world.
I don't think they do (arise from this), as I agree with most of your observations. However, I draw slightly different conclusions from some of them. I'll expand on the points in-line. You may take it that anything I do not comment upon, I wholeheartedly agree with.
Following are the points I would emphasize:
1. The immense size and complexity of the universe and its
continuous variability in time and space make it impossible
for any discrete, finite set of labels (words or predicates)
to have a perfect, one-to-one mapping to all aspects of the
universe or even to some small chunk we are familiar with.
Of course it will not be one-to-one. No semantic theory I have ever read, by anyone, of any kind, makes such a claim. So this kind of trite but deep-sounding remark is misleading and tendentious. It seems to imply a distinction between your views and those of others, but in this case there are no others.
However, if one were to infer from this that it is impossible to make a true assertion about the real world using a finite number of labels, that would be a very much stronger, and much more radical, claim. It would mean that all of human language was necessarily false: that it was in fact impossible to express a truth in any possible language. Perhaps so: but if so, then we might as well all stop talking and writing altogether. I prefer to work on the assumption, which seems to be borne out by practical everyday experience and justified by semantic theory, that it is possible to express true assertions about the real, actual, world (in all its overwhelming complexity.)
2. Human systems for perception, action, and mental imagery
enable us to interact with the world more accurately than
we can characterize it in discrete words or predicates.
Well, that all depends on what you mean by 'accurate'. We can all do things using our senses that we have trouble describing in language, of course: no doubt that is what your shoestring example is meant to convey. As Im sure you know, I have been saying things like this for the past 30 years, and indeed it was the basis for the whole 'naive physics' enterprise. (My own epiphany example was flicking a folded sheet to make it settle over a bed, a skill I realized one day I had acquired entirely non-linguistically and was unable to describe.)
However, I would not characterize this in terms of accuracy. I don't think seeing is necessarily more accurate than description: in many cases, surely, the reverse is true.
Moreover, In many cases, when dealing with practical skills (I have thought a lot about carpentry, one of my hobbies) one finds that in fact, contrary to first impressions, greater accuracy often comes from people having taken the trouble to describe the 'indescribable' skills, and thus revealed sources of inaccuracy which, once understood, can be eliminated, for example by improved tool design. I know of no case where the rich sensory interaction is in fact necessarily opaque to description. Even such deeply haptic skills as dancing and playing music can be described in language, though it remains the case that access to such descriptions is not sufficient to acquire the skills they describe.
A simple example is tying a shoestring. Another example
is the high-speed interactions of basketball players who
can successfully get the ball through the hoop despite the
active interference of the opposing team.
3. Therefore, anything we can express in a discrete string of
symbols (in logic or natural language) will inevitably be
an approximation to some limited part of the universe for
the purpose of fulfilling some particular narrow goal.
That simply does not follow from what you said earlier. First, nothing has been said about 'narrow goals", which is a complete red herring. But leaving that aside, it does not follow that anything we can say must be an "approximation". It is not a question of accuracy, as previously noted. If I say Chris is an American, that is indeed (and necessarily) partial - it leaves out a lot of important truths about Chris - but it is not approximate. It is in fact specifically and literally and precisely and accurately true, with no room for imprecision: it is true and not false, and that 's it. No amount of seeing or smelling or tasting is going to make it more true, or more accurately true. So a discrete description need not be an 'approximation'.
The finiteness of a description does not mean that it can only describe or refer to finite things, by the way. It is easy to write finite FO axioms which are satisfiable only in infinite models; that is, for any resolutely un-mathematical readers, its easy to give a finite description of infinity.
4. Natural languages have evolved under those constraints for
thousands of years, and they have proved to be amazingly
successful and flexible in adapting to an open-ended variety
of situations while enabling us to communicate enough of our
thoughts with sufficient accuracy to achieve specific goals.
You missed out one - perhaps the most - important fact about language: that it is used to convey information a bout the real world we all inhabit. This is almost certainly why it evolved. Just sharing thoughts isn't very much use: sharing information about the world is extremely useful. And this 'aboutness' is exactly what semantics sets out to analyze. 5. In the past few centuries, mathematics has developed from
a level that could be mastered by a single individual to a
rapidly expanding family of extremely powerful systems that
support the even more rapidly expanding branches of science
and engineering. But it is so rich that no single person
or even a single math department at a university can master
in its totality.
That is probably true, though I fail to see why it is relevant. And if you restrict it to applied mathematics, there is a much narrower field to encompass. (And please spare me, in response, anecdotes about how any pure math might have an application, Einstein and matrix algebra, etc.. I've read all those books too. The fact remains that at any one time, the vast majority of pure mathematics has no direct application in engineering or science.) 6. By contrast, formal logic is still a relatively compact
subject (especially if some of the complexities, such as
set theory are considered part of mathematics). And that
subset whose semantics is completely defined by a model
theory along the lines of Tarski or Kripke is even smaller.
Again, true, but I fail to see the relevance. 7. Montague tried to expand that core to accommodate natural
languages, but even many logicians were skeptical (e.g.,
Peter Geach, who called it "Hollywood semantics"). After
40 years of development, no NLP system can translate one
article from a typical newspaper to any version of logic
(except for a short stylized paragraph, such as a weather
report on a calm day). Even pioneers in the field such as
Hans Kamp have admitted that "something more is necessary."
I believe that these observations have strong implications for
the development of logics and ontologies that can support the goals
of interoperable systems, the Semantic Web, and many related problems.
Point #5 about mathematics is significant: any large engineering
project, such as designing a bridge or an airplane, has an enormous
number of related subproblems that require specially tailored
formalisms based on distinct branches of science with very different
mathematical techniques.
I doubt if it is an enormous number. Maybe ten or so for a large civil engineering project, including the software needed for the administrative and managerial work. All the calculations for the NASA planetary probes was done using classical Newtonian gravitational theory and basic calculus.
There is no such thing as a single, unified
ontology that can support every aspect of just one such project under
the management of a single prime contractor.
True. Did anyone imply that there was? How is this relevant to what we were talking about? It is inconceivable
that a single unified ontology could be developed for just one
large company, much less for an entire industry, and certainly not
for all the major industrial companies in any large country.
I tend to agree, though one should give a passing nod in the direction of efforts towards industry-wide ontological frameworks, such as those that Matthew West has worked on for many years, and the ambitions of the BOF approach to biological ontologies. These do seem to have met with some success.
Points #4 and #7 about natural languages imply that we are not
likely to solve the problem of NL understanding with a single
logic and ontology.
Again, I agree but find this wholly unrelated to the topic we were originally talking about in this thread. Even if we were to edict a single logic and
ontology for some important domain, say medicine, it is extremely
unlikely that we could teach all the formal definitions to all
the practitioners (physicians, nurses, pharmacists, technicians,
programmers, administrators, etc.). We might be able to teach
them to use a fixed vocabulary, but each person will continue
to use and interpret those words as though they were part of
their ordinary natural language.
My conclusion is that we will continue to have an open-ended
family of specialized terminologies and ontologies for a long
time to come.
I also think this is likely. The links among those ontologies will not be
supported by a detailed formal ontology.
I'm less pessimistic here. I think such connections will get made and systematized, maybe on an ad-hoc basis, but they will get made. This seems to be main focus of effort in bioinformatics at present, for example.
But again, I fail to see what this has got to do with what the debate between us (if it is a debate) was about.
Pat Some comments:
...
JFS>> What group of "we" are you talking about and for what purpose? PH> People doing semantics of the formal languages used to write ontologies.
But what training will the people who write those ontologies get?
Im sure there will be courses on 'principles of ontology construction 101' offered which will be prerequisites for later courses which explain semantic principles in enough detail. This is a matter for the designers of university curricula, not longer (thank God) a concern of mine. Again, I fail to see what this has to do with the topic.
You scoffed at my list of Google counts, but just note the numbers
15,400,000 for "ontology", 785,000 for "model theory", and only
34,000 for both "ontology" and "model theory". I seriously doubt
that the people who will be hired to write those ontologies by
businesses will have any more logical training than those who did
"systems analysis". They will just put up a different shingle
on their front door (or home page).
And even if by the rarest of good fortune you could recruit super
intelligent logicians to define those ontologies, the people who use
them will interpret the terms with their old background knowledge.
So, your conclusion is that the world is run by uneducated morons? Of course. How could it be otherwise? They have to have something to do. ... PH> [The developers] find themselves obliged to pay close attention to one another. I know, because I was often the guy who had to do
the mutual translations of terminology.
Great. So how are we going to make your services available to the millions of people who write/use those ontologies if and when those languages become widely used?
I have quite reasonable consultancy rates.
JFS>> That kind of very precise talk is done by the academics who publish papers about model theory.
PH> It is done, perhaps implicitly, by anyone who uses mathematics to talk about the real world. Which is a lot of people.
Wait. Practicing mathematicians, as Chris M. concurred, do not care about the foundations of math or logic. They don't use models in Tarski's sense, but in George Box's sense: "All models are wrong, but some are useful." PH> In fact, this concern with vagueness or blurriness of boundaries is itself a purely academic issue, verging at all times on the
philosophical.
Practicing DB analysts are extremely sensitive to those issues, which constantly plague their systems. For a good source of examples and anecdotes, see the book _Data and Reality_ by Bill Kent, who was not an academic, but a DB guy who had to work with actual data. He discussed "philosophical" problems like the oil company that had different departments with different definitions of 'oil well'.
I agree that these kind of issues are important and central. But it is a terrible mistake to say that these examples show that model theory s wrong or inadequate. On the contrary, model-theoretic thinking is exactly what one needs to bring to bear, in order to properly analyze such issues. Those different definitions of "oil well' differ precisely because one of them allows interpretations which the other excludes. A very good way to tackle problems like this is to take the two definitions and ask yourself, can I construct a model of this which makes that false? Then ask: How? What would such an example be like? What can I say that would rule out things like this? All of these are model-theoretic questions. PH> ... the people who know most about boundary-line issues are, of course, the people who specialize in this topic, which includes
surveyors, lawyers (of a certain specialization), cartographers
and others. I've worked with some of these people, and its quite
possible to ontologize their expertise, just as it with other experts.
I was using the term 'borderline' in a metaphorical sense, which includes physical borders as a special case. But since you mention lawyers, essentially every case they address is a metaphorically borderline problem -- primarily because the ones that are not on the border are settled out of court. PH> Previously we were talking about individuation criteria (this cabbage vs. that cabbage), now you are talking about how to
distinguish among genera (cabbage vs. broccoli).
Chris is the one who brought up cabbages. And I pointed out that there are no clear identity criteria for distinguishing a cabbage. You need such criteria if you want to count cabbages or oil wells.
And I said, and repeat, that for purposes of counting, there are such criteria. PH> My own view on questions like this is, consult an expert: for Brassica Oleracea, a botanist or gardener, and so on.
The oil company had no shortage of experts on oil wells, but different experts looked at the same question from different points of view.
Because there wasn't an agreed-upon body of expertise to produce terminological agreement. In fact, the company didn't have any experts on oil wells per se, probably because there aren't any. What it had were experts on aspects of oil wells, or other topics relevant to oil wells. I agree, this is a big issue in knowledge management. It is however not a critique of Tarskian semantics. Knowledge management isn't the same as semantics. If its done well, however, it ought to USE semantics. JFS>> Even for the 3% who know model theory, the task of ensuring that those models reflect reality won't get done by itself.
PH> What is this 'task' that you keep worrying about? Please read Bill Kent's book or George Box's book or many others written by people who map reality to actual databases.
Ive read many such books, and work closely with people who do 'knowledge capture' and solve its attendant problems. I've never seen or heard anything which suggests to me that anything in this area even hints at the idea that model-theoretic semantics is somehow semantically inadequate. Almost all of these 'practical' issues can be cast as confusions about ontology mappings. Does this person's use of the symbol "OilWell' correspond to that person's usage? That is not a question about how Tarskian models relate to the real world, it is a question about how formal ontologies relate to the real world. And Tarskian semantics is a vital part of the process of answering such questions. Without such a 'formal' semantics (perhaps not expressed formally, but that is a matter of pedagogy), questions like this cannot even begin to be answered. ... I agree that Carnap's book is a classic of its kind. But just look
at all the hand waving at every difficult problem. I blame that book
for leading Doug Lenat (directly or indirectly) to an attempt to carry
out the details. The entire AI field (and the US taxpayers) learned
a lot from that exercise: it doesn't work.
Well, lets get the facts straight. Cyc was developed by CyCorp, using largely non-government funding. And while I agree that Cyc isn't going to wake up one day and say "hello Daddy" to Doug, I don't think its fair to say that it 'doesn't work'. In fact, Cyc does work and is effective at many tasks, and the Cyc knowledge base has even wider application. Its just inaccurate to characterize it as a tax-wasting failure.
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