On Mar 11, 2010, at 11:23 PM, John F. Sowa wrote: (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.
> 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).
> 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,... (02)
But the question I would ask is, how can you write that in FOL in such
a way that you don't fall into one or the other of the 4D/(3+1)D
frameworks? Put another way, how can one formalize this 'minimalist/
neutral' way of talking? This isn't at all obvious. One way would seem
be to have a temporally indexed hybrid logic, where entire sentences
(tenseless and timeless) are associated with times, with the meaning
'this is true then'. But then the sentences themselves have to be
understood as written in 'presentist' language, so they quantify over
entities which exist **at a time**, and there is no way to quantify
over entities which, um, endure over several times, such as Kermit in
the example. In fact, this whole "sequence-of-presentist-views" idea
is, I strongly suspect, what gives rise to the whole warped idea of a
'continuant' in the first place. OR, you can give the same formalism a
rather different semantics, in which the successive sentences are
considered to be about 3-d slices of a 4-d world, but then... you see
where this is going. It really is extremely hard to come up with a
single semantic picture or account which is neutral towards these two
views of time. They are profoundly irreconcileable. (Your reassuring
talk of 'frogs' begs the question, because the 4d view of what 'frog'
means is fundamentally different from the continuant view of what
'frog' means. The two world-views are not talking about the same kind
of frogs. Continuants are *logically impossible* in a 4-D world. )
What we can do is give a single formal account which can be
interpreted in either way, and I think this is the best we can do. (03)
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