John F. Sowa wrote:
> 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.
> 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.
> 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
> 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).
> I agree.
> CM? So what, exactly, are you proposing?
> I am definitely *not* proposing any kind of embedding of a 3+1 D
> theory into a 4D theory or vice-versa.
> 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?"
> 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).
Are these ideas sufficiently well-formed that we could start to talk
about the metadata required to support the lattice? (02)
> 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:
> 1. At time t1, Kermit was an egg.
> 2. Later, at time t2, Kermit was a tadpole.
> 3. Later, at time t3, Kermit was a frog.
> 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.
> 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:
> at t1, Kermit egg.
> at t2, Kermit tadpole.
> at t3, Kermit frog.
> 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.
> But somebody might ask, "How can you explain your detailed
> reasoning in therms of that simple observation theory?"
> The answer is that you can't. You don't even try.
> 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?"
> 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.
> But someone might object, "How can you be sure that their
> theories are consistent."
> 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.
> 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.
Does this imply that a reasoning engine can read the metadata from both
theories and automatically map data from one to another to actually
implement the sharing process? (03)
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