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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: Wed, 24 Mar 2010 01:01:19 -0500
Message-id: <4BA9AAAF.4000102@xxxxxxxxxxx>
Christopher,    (01)

CS> My point was not a scientific or empirical one.  I did not
> have illusions versus "reality" in mind.  My point is an
> Ontological one.    (02)

I was trying to make the ontological point that observation alone
is not sufficiently informative to determine how the images or
other sensations must be interpreted.  For example, it cannot
convince a solipsist that anything exists outside the mind.    (03)

Similarity of patterns is observable.  But the existence of anything
that causes those patterns is always an assumption.  Most of us
are firmly convinced that the evidence for that assumption is
overwhelming, but a confirmed solipsist could deny it all.    (04)

CS> But there is an absolutely inescapable assumption in "a" anything -
> which my simple mind can only call Ontological as it's *so* basic to
> our conceptualized knowledge itself - that it can make sense to
> abstract individuals out from the raw flux of our otherwise
> unconceptualized or unformed physical or mental experience.    (05)

I certainly agree.  Most people who are not locked up for their
own safety would also agree.    (06)

CS> So I am not talking of that glib and much-abused notion of
> "theory-laden observations" either.  I am finding it impossible
> to conceive of "a" anything without a notion of Individual.    (07)

Yes, but as soon as we agree on that point, we have to face
nontrivial questions about ways of characterizing those
individuals.    (08)

If we want an ontology that is consistent with modern physics,
we must admit that Heraclitus was right:  everything is in flux.
Our most solid "objects" are slowly changing processes. In fact,
Whitehead had a very reasonable ontology in which events are
fundamental, and objects are processes for which the change
is slow enough that we can recognize similar patterns at
different encounters.    (09)

But identity is always an inference.  For example, suppose that
Tom and Dick are identical twins.  An observer who sees Tom and
Dick separately might believe that they were the same person.
But someone who knew Tom at age 4 might find it difficult to
recognize him at age 24 or 44.    (010)

CS> So perhaps my point is that one must not go overboard in
> "lattice-ifying" our most basic ontologies?  Perhaps there is
> no harm in assuming a wider and still universally-acceptable
> degree of commonality?    (011)

But note that the participants in this forum have very different
preferences for the basic ways of talking about individuals
and representing them in a 3-D or a 4-D ontology:    (012)

  4-D:  An individual corresponds to a volume in a 4 dimensional
        space. Different *temporal parts* of the individual named
        Kermit correspond to an egg stage, a tadpole stage, or
        a frog-stage.    (013)

  3-D;  There are no such things as "temporal parts".  For any
        time at which a human, animal, or rock exists, all its
        parts are present at the same time.  From one moment to
        the next, the individual might gain or lose some molecules
        or even major parts, but all of that individual exists
        at each point in time from birth to death (or from
        formation to dissolution).    (014)

Pat Hayes claimed that these two ways of talking are so
diametrically opposed that there can be no common generalization
that is consistent with both.  But I claimed that my primitive
ontology, which avoids all talk about individuals, is consistent
with both.    (015)

Doug Foxvog suggested an "entity variable" e, which could be used
as a URI for identifying an individual, to serve as a link between
different observations of that individual.  But Matthew objected
that some further claims by Doug were not compatible with a 4D
ontology.    (016)

I was trying to make the following points:    (017)

  1. All the participants in this conversation have made reasonable
     claims, but they're not consistent with one another.    (018)

  2. If we need to share data among systems that use a 3D vs a 4D
     ontology, we need to find some common ground (i.e., a very
     general theory) that is compatible with each system.    (019)

  3. I believe that a simple ontology that is suitable for stating
     observations (but very little reasoning) would be consistent
     with all the theories.    (020)

  4. But I admit that one would like to have some way of referring
     to individuals that is compatible with different ontologies
     and with simple observations.    (021)

Following are three ontologies.  Please comment on any preferences,
objections, or variations.    (022)

__________________________________________________________________    (023)

Simple theory with no recognition of individuals:    (024)

    (exists (p t1) (and (tag p "Kermit") (egg p) (coord p 4 t1)))    (025)

    (exists (p t2) (and (tag p "Kermit") (tadpole p) (coord p 4 t2)))    (026)

    (exists (p t3) (and (tag p "Kermit") (frog p) (coord p 4 t3)))    (027)

An extension of the above with a variable e that refers to something
called an "individual":    (028)

    (exists (e) (and (individual e) (name e "Kermit")    (029)

       (exists (p t1) (and (tag p "Kermit") (egg p) (coord p 4 t1)))    (030)

       (exists (p t2) (and (tag p "Kermit") (tadpole p) (coord p 4 t2)))    (031)

       (exists (p t3) (and (tag p "Kermit") (frog p) (coord p 4 t3))) ))    (032)

Another variation with the variable e in some of the relations:    (033)

    (exists (e) (and (individual e) (name e "Kermit")    (034)

       (exists (p t1) (and (tag p e) (egg e) (coord p 4 t1)))    (035)

       (exists (p t2) (and (tag p e) (tadpole e) (coord p 4 t2)))    (036)

       (exists (p t3) (and (tag p e) (frog e) (coord p 4 t3))) ))    (037)

Note that just introducing a monadic predicate (individual e),
by itself, does nothing to specify what it means to be an
individual.  Any model that satisfies the first theory could
satisfy the second theory just by saying that any predicate that
takes the string "Kermit" as a valid argument could take the
variable e.    (038)

Similarly, any model that satisfies either of the first two
theories could be modified to satisfy the third.  The converses
are also true:  any model that satisfies any of the above three
theories could be modified to produce a model that satisfied
the other two.    (039)

This point implies that the notion of individual, as expressed by
the relation (individual e), is meaningless.  If it is to have
any meaning, further axioms about that relation are required.
One selection of axioms would restrict the theory to 4D, and
a different selection could restrict it to 3D.    (040)

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