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Re: [ontolog-forum] Reality and semantics. [Was: Thing and Class]

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 17 Sep 2008 14:49:55 -0400
Message-id: <48D15153.5000906@xxxxxxxxxxx>
Pat,    (01)

As an "academic" myself, I certainly do not want to belittle the
importance of academic work.  But I do *not* consider the academic
work to be intellectually superior to good engineering work that
is forced to get "down and dirty".  There is always a tension
between theorists and practitioners, and the best work is usually
done by people who have a solid appreciation for both sides.    (02)

I have a very high regard for formal logic and model theory.  But
the number of people who study and use those subjects is a tiny
fraction of the number who use languages that are logic-like,
but much less formal, such as SQL or UML.  For a very rough
estimate of relative interest, look at the Google hits:    (03)

    MYSQL                257,000,000
    SQL                  222,000,000
    UML                   21,500,000
    ontology              15,400,000
    "semantic web"        11,000,000
    "systems analysis"     4,620,000
    "business rules"       3,410,000
    logic prolog           1,810,000
    Tarski                   755,000
    "model theory"           532,000
    "modal logic"            365,000
    RDFS schema              346,000
    "description logic"      296,000
    "predicate calculus"     198,000
    OWL & (RDF | RDFS)       162,000
    "conceptual graphs"      150,000
    "common logic"           105,000    (04)

Note:  Google hits are often distorted by "heuristics", so these
counts are not completely reliable.  But by any measure, the top
few terms overwhelm any of the academic logics.  The term RDFS
by itself counts files that have "rdfs" inside XML tags, but are
about some other subject.  The terms HTML and PHP, for example,
each get over 11 billion hits, while 'the' gets 16 billion.    (05)

There are three major areas in which logic has been successful.
Outside those three areas, there is little use of formal logic,
except in academic publications (see the Google counts):    (06)

  1. Set theory, where the subject matter is, by definition,
     a set of discrete entities and sets of sets of sets of ...    (07)

  2. Relational databases, for which the SQL language has become
     the most successful and most widely used logic-based notation
     every invented.  The SemWeb languages of RDF and OWL have
     insignificant usage compared to SQL.    (08)

  3. Computer science and applications, where everything expressible
     is reducible to bits or organized structures of bits.    (09)

The 19th century goal was to use set theory as the foundation for
mathematics and thereby extend logic to all of science.  But in
practice, working mathematicians *ignore* the foundational work.
It may be a required course, but it doesn't help them solve problems.    (010)

PH> In fact, we all manage extremely well with a single-layered
 > semantics called model theory.  This two-level idea is a
 > chimera, and an intellectual dead end.    (011)

What group of "we" are you talking about and for what purpose?
People were using integers for thousands of years before Frege
defined them in terms of sets, so you can't count a child who
learns to count as using logic, set theory, or model theory.    (012)

An academic publication that uses model theory to analyze the
foundations of OWL or SQL has little or no influence on the
people who use those languages for any practical application.    (013)

PH> You have argued for the idea, but do you have even an outline
 > or a sketch of what the second, model-to-reality, semantic theory
 > looks like?    (014)

Yes, indeed.  For categories #2 and #3, it is called systems analysis,
database administration, and various fad terms.  Compare the Google
counts for "systems analysis" to "Tarski" or "model theory".    (015)

PH> [Model theory] is the foundation of ontology engineering, for
 > a start, as well as such topics as decidable logics (such as DLs).    (016)

I agree that academics who design formal logics (as well as SQL)
know model theory.  But just look at the Google counts:  for
"ontology", 15,400,000 hits; for "model theory", 532,000 hits.    (017)

That ratio of 30 to 1 is a clue about the percentage of people
who do "ontology engineering" and also know model theory.  In
practice, the labels on those ontologies are English words and
phrases with no semantics other than informal English.    (018)

JFS>> How are you going to form n-tuples of such things [people,
 >> tables, and cabbages] when you can't even state clear criteria
 >> for identifying individuals of those types?    (019)

PH> Easily. You don't NEED to give such individuation criteria in
 > order to talk clearly and precisely about n-tuples.    (020)

That kind of very precise talk is done by the academics who publish
papers about model theory.  But when they ignore the model-to-reality
stage, the people in the trenches who use SQL, RDFS, etc., are left
with no guidelines for relating those neat n-tuples to the very
messy world in which borderlines are often vague or invisible.    (021)

PH> But in any case, its fairly easy to state individuation criteria
 > for people, tables and cabbages: you can do it using spatiotemporal
 > contiguity in all three cases.    (022)

That is inadequate for distinguishing an egg from a person or
cabbage from cauliflower, broccoli, wild mustard, and many other
variations of the species Brassica oleracea.    (023)

JFS>> And those are the simplest "real world" examples you can find.
 >> Everything else is immensely more difficult.    (024)

PH> Well, in fact it often isn't all that difficult, which is why
 > ontology-writing is possible at all.    (025)

The writing is easy.  Most of it is done by the 97% who heard the
word "ontology", but know nothing about model theory.  Even for the
3% who know model theory, the task of ensuring that those models
reflect reality won't get done by itself.    (026)

PH> By and large, its the people who build the best robots or the
 > best NL-comprehension software who also tend to write the best
 > academic papers.    (027)

I agree.  But that is because the people who build the best robots
and NLP systems are forced to understand the distinctions and
*synthesize* them.  The ones who compartmentalize those topics
(logic, ontology, and epistemology) in separate academic fields
are rarely the ones who make significant breakthroughs.    (028)

PH> But in any case, building ontologies and building robots are two
 > different activities.  And understanding natural language is yet
 > a third.    (029)

I agree that they are different.  But note that, in practice, the
labels used on those ontologies are nothing more than slightly
disguised English words and phrases.  Even if an RDFS+OWL spec
is proved consistent, the dirty little secret is that the people
who write tags on web pages or choose them from menus will still
be thinking in terms of informal English semantics.  That means
that their usage will be unrelated to the formal definitions.    (030)

JFS>> But their attitudes [of Frege, Russell, & Carnap] toward
 >> language, logic, and their interrelationships have polished
 >> formal semantics to an elegant system that ignores problems
 >> instead of solving them.    (031)

PH> This is such rubbish that I won't even try to sketch a response.    (032)

That is my summary of points made by Hao Wang (1986), a student
of Quine's who implemented the first theorem prover (in 1959) that
proved all 378 theorems in propositional and first-order logic in
the _Principia Mathematica_.  Wang also worked as an assistant
to Kurt Gödel and published many books and papers on logic.    (033)

PH> Which *semantic* problems are being ignored?    (034)

 From Hao Wang, _Beyond Analytic Philosophy: Doing Justice to What
We Know_, MIT Press, Cambridge, MA, 1986:    (035)

     Quine merrily reduces mind to body, physical objects to (some
     of) the place-times, place-times to sets of sets of numbers,
     and numbers to sets.  Hence, we arrive at a purified ontology
     which consists of sets only.... I believe I am not alone in
     feeling uncomfortable about these reductions. What common and
     garden consequences can we draw from such grand reductions?
     What hitherto concealed information do we get from them?
     Rather than being overwhelmed by the result, one is inclined
     to question the significance of the enterprise itself.    (036)

In support of this view, Wang quoted a personal letter from another
of his former teachers, Clarence Irving Lewis, about the state of
philosophy in 1960:    (037)

     It is so easy... to get impressive 'results' by replacing the
     vaguer concepts which convey real meaning by virtue of common
     usage by pseudo precise concepts which are manipulable by
     'exact' methods -- the trouble being that nobody any longer
     knows whether anything actual or of practical import is being
     discussed. (p. 116)    (038)

Wang also observed that Carnap was "willing to exclude an
exceptionally large range of things on the grounds that they are
'not clear,' or sometimes that 'everything he says is poetry.'"
And he traced the sources of the problem back to the very
negative attitudes toward language by Frege and Russell.    (039)

If you don't believe Wang or me, just look at Carnap's famous
"Logische Aufbau der Welt".  It starts off with very precise and
formal definitions and axioms, but it get sketchier and less
detailed in each chapter.  By the end, it's all hand waving for
all the serious problems.  One of the terms he admits is "very
difficult" to define by his methodology is 'sign'.  That makes
it hard to define 'word' or 'language' etc.    (040)

PH> In fact I would go so far as to say that the whole idea of
 > treating NL as similar to a logic, which reached an apogee
 > with Montague, is now dead in the water.  But that is NL
 > comprehension, and this forum about ontologies.  Different
 > topics.    (041)

I agree that Montague's project is dead.  But just look at what
all those "ontological engineers" are doing:  using English
words and phrases for their tags.  Pretending that there is
anything other than informal English semantics to support 97%
of those tags is wishful thinking.    (042)

John    (043)

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