[Top] [All Lists]

Re: [ontolog-forum] Model or Reality

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Cassidy, Patrick J." <pcassidy@xxxxxxxxx>
Date: Wed, 8 Aug 2007 15:58:57 -0400
Message-id: <6ACD6742E291AF459206FFF2897764BE01B80C8C@xxxxxxxxxxxxxxxxx>
   The issue I am concerned with is whether there are multiple
situations that *require* the use different models of reality that are
truly *logically* inconsistent, as an asserted *true* part of the
ontology itself, not merely as one of multiple theoretical
approximations.  The scientific models that are known to be only
approximations to reality can be represented as theoretical
approximations in an ontology without generating such a logical
inconsistency.  The issue is whether we can have a single
self-consistent foundation ontology that can be used to define all
other ontologies.  Scientific theories such as Newtonian and
Einsteinian mechanics can both be represented as theories of motion,
and will not be logically inconsistent, since different theories are
not asserted to be equivalent.  Of course, if one attempts to represent
both models as *exact* models, there will be an inconsistency but it is
not necessary to represent such models as *exact* models of reality,
and in practical use no one actually thinks that way.  Each is used to
good effect under different circumstances, knowing that we are dealing
with approximations.  I do not have any concern with contradictory
models used in scientific theories, because as you note, we all know
that these are approximations and should therefore be represented in an
ontology as theories useful in particular circumstances, not as the
**final and only** model of reality.  An ontology can have both Newton
and Einstein in it as alternative theories, each useful in different
situations, and the ontology will not be internally inconsistent.  The
ontology should also know that Einstein is the better approximation,
but a lot harder to calculate.  Whether such a set of models conforms
to the "lattice of theories" view, I don't know.
   The issue of automatically deciding which theory, context,
microtheory, script, etc, is applicable in a particular situation
appears to be quite difficult, but that is not the issue I was
concerned with in the question I sent.  I was responding to a comment
about a need for "contradictory" models.  What I am curious about is
whether, in trying to get to agreement on the content of a common
foundation ontology, we will run into true logical inconsistencies that
are not merely different theoretical models that can be resolved, at
least in theory, by appeal to experiment.  With scientific models, any
two that are logically inconsistent in the sense of giving different
predictions for specific situations should be resolvable by experiment.
One or both will be wrong, but both may be useful in different
situations.  Representing them as theoretical approximations will
present no problem.  Representing them as the ultimate structure of
reality would be a problem, but would be unnecessary.
   The various practical models or rules of thumb that people use in
different situations to solve problems may well be logically
inconsistent.  They should not be represented in a foundation ontology
as asserted to be true in all situations in the real world, but as
models useful in specific situations.  When one needs a simplified
ontology for use only in specific situations, those theories can be
extracted from the foundation (or consistent extensions) and used as
though they are true.  That does not require them to be represented as
true in the common foundation ontology.
    In general, a foundation ontology should be able to contain a rich
set of structures of types, attributes, relations, instances, functions
and axioms, with mappings to linguistic terms where appropriate,
without making any (or few) commitments as to quantitative relations
among the objects and processes.  The theories making quantitative
predictions can be represented as different theories with different
models, with known or unknown accuracy, useful or not for making
predictions in specific situations.  I don't think of that as requiring
any logical inconsistencies.
   The question that concerns me is whether, in building up a
"conceptual defining vocabulary" to specify the meanings of complex
concepts, we will run into a need for different primitive elements that
are in fact logically contradictory.  I expect the different theories
of the physical world to be constructible from agreed primitives, but
am concerned about the logical consistency of the inventory of
primitives.  That is where I have not yet seen a need for inconsistent
elements in the foundation ontology.  If anyone has any candidates, I
would appreciate learning about them.
    (Thus far 3-D versus 4-D appear to be consistent in the sense of
translatable into each other, at least when sufficient axiomatization
is provided so that ambiguities can be resolved.)
   The goal of a common foundation ontology does not require "perfect
knowledge" of anything.  It just requires an agreed vocabulary for use
among consenting adults.    (01)

Pat    (02)

-----Original Message-----
From: John F. Sowa [mailto:sowa@xxxxxxxxxxx] 
Sent: Wednesday, August 08, 2007 11:17 AM
To: Cassidy, Patrick J.
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Model or Reality    (03)

Pat,    (04)

There are many, many examples in *every* branch of science and
engineering:    (05)

AT>> The problem is: two contradicting conceptualization can both
 >> be right ...    (06)

PC> Can you provide one or more examples of that phenomenon?  I've
 > been looking for "contradictory" models that both conform to
 > reality for some time.    (07)

First of all, no models ever conform to reality *exactly*, since
every theory of science is at best an approximation that conforms
within the limits of experimental error and within the range of
reality on which it has been tested.    (08)

Therefore, we are frequently faced with different approximations
derived for different purposes under different circumstances.    (09)

The likelihood that any two such approximations will be consistent
with one another is high under certain conditions:    (010)

  1. They refer to separable domains and have no common terms
     or predicates that could create a contradiction.    (011)

  2. Or if they do have common terms or predicates, the definitions
     of those terms are so vague and underspecified that they
     don't impose constraints that could cause contradictions.    (012)

But if those approximations have a large overlap that is described
in any detail, then the likelihood of contradiction is extremely high.    (013)

One of my favorite examples was the proof that nothing could travel
through the air faster than the speed of sound.  It turned out that
the scientist who "proved" this theorem had started with a commonly
used approximation, which was widely assumed in the early days of
aeronautics:  that all velocities are very small compared to the
speed of sound.    (014)

Of course, that incompatibility has since been ironed out, but similar
problems arise constantly.  All the detailed equations of physics are
so difficult to solve in general (even by a supercomputer) that
simplifying assumptions are always necessary.    (015)

For example, Newton's equations are always used for the motion
of an automobile and its major mechanical parts.  However, quantum
mechanical effects are used in designing new kinds of fuel for
the engine, the computer circuitry in the chips that control the
engine, etc.    (016)

Since those systems are separable, in most cases, they can be
treated as case #1 above when the detailed problems are being
analyzed.  When the fuel is pumped into the car, case #2 comes
into play, and the details of the fuel are ignored when computing
how its mass would affect the acceleration.    (017)

Summary:  Physics, the hardest of the "hard" sciences, has some
very general equations that are known to be false in detail, no
general equations that are known to be absolutely true, and an
enormous collection of inconsistent approximations for every
type of practical problem that anyone really needs to deal with.    (018)

Compared to physics, every other field of science is a nightmare
of special cases.  And the social sciences haven't even reached
the stage where any degree of precision is conceivable.  As they
say, economists are great in explaining why something occurred
but hopeless in predicting it.    (019)

John    (020)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (021)

<Prev in Thread] Current Thread [Next in Thread>