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Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 12 Mar 2010 00:23:55 -0500
Message-id: <4B99CFEB.2040307@xxxxxxxxxxx>
Chris,    (01)

CM> As you note, a 3D ontology is in fact fully 4D -- "3+1 D" as
 > you put it -- in the sense that time is not ignored (the way the
 > "z-axis" of R3 is ignored in R2, say).  Rather, the difference
 > between the two ontologies concerns how they conceive the relation
 > between individuals and time.    (02)

Yes.  The difference between a 3D and a 4D ontology is not in the
geometry, because every point in a 3+1 D ontology can be mapped
to and from every point in a 4D ontology by an isomorphism.    (03)

The critical issues for ontology arise with the nature of individuals,
the question of temporal "parts" of individuals, and the nature of
changes to individuals.  Those go beyond the geometry of space-time
to the issues of how to represent physical things that reside, move
around, and change in that geometry    (04)

CM> ... the endurantist ontology doesn't "embed" isomorphically in any
 > obvious way into the perdurantist ontology (unless, perhaps, you also
 > introduce temporal parts into the endurantist ontology, which seems
 > sort of self-defeating).    (05)

I agree.    (06)

CM? So what, exactly, are you proposing?    (07)

I am definitely *not* proposing any kind of embedding of a 3+1 D
theory into a 4D theory or vice-versa.    (08)

As many people who use a 4D approach have observed, it is possible
to exchange data among different computer systems based on different
ontologies.  But then we have to ask:  "How can they exchange names
of people and their addresses, dates of birth, etc., and use that
data successfully in systems that have different and inconsistent
theories about the nature of the individuals?"    (09)

What I am proposing, as I have said many times, is a lattice of
theories -- or at least a finite subset (hierarchy) of theories
that have actually been defined and stored in a repository).    (010)

To illustrate the issues, let me consider a particular individual
named Kermit.  Somebody who talks in ordinary English with a
3+1 D ontology might make the following observations:    (011)

  1. At time t1, Kermit was an egg.    (012)

  2. Later, at time t2, Kermit was a tadpole.    (013)

  3. Later, at time t3, Kermit was a frog.    (014)

Another person who uses a 4D ontology might say that the individual
named Kermit has temporal parts.  His egg part has a range of times
that includes t1, his tadpole part includes t2, and his frog part
includes t3.    (015)

This example shows that the problem arises with talk about parts.
There is a simple way to avoid that problem:  don't talk about
parts.  Just talk in simple observation terms:    (016)

    at t1, Kermit egg.
    at t2, Kermit tadpole.
    at t3, Kermit frog.    (017)

A theory that can express just these observations would be
very underspecified.  It couldn't express or reason about
the many things one might want to say about frogs and their
spatial and/or temporal parts.  But any data that can be
expressed in simple, observational terms can be shared among
more detailed theories that do detailed reasoning about
those observations.    (018)

But somebody might ask, "How can you explain your detailed
reasoning in therms of that simple observation theory?"    (019)

The answer is that you can't.  You don't even try.    (020)

Another person might object, "But what if two incompatible
theories do different kinds of reasoning that cannot be
expressed in terms of each others terminology?"    (021)

The answer is that you don't attempt to explain one theory
in terms of the other.  You only share data in simple
observational terms.    (022)

But someone might object, "How can you be sure that their
theories are consistent."    (023)

The answer is that the world itself is consistent.  Any
theory that reasons correctly about the world must make
predictions in terms of observation statements.    (024)

The basic test of any physical theory is consistency with
observations.  If two different theories are both consistent
with observations, they can share data about those observations.
Any differences in their detailed axioms and terminology are
irrelevant, as long as their predictions are accurate.    (025)

John    (026)

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