Pat Hayes wrote:
> On Mar 11, 2010, at 11:23 PM, John F. Sowa wrote:
>> Chris M 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). (01)
>> I agree. (02)
>> 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. (03)
The issue is how to phrase "at t0". In broader terms, a basic issue
is how to state the context for various statements using an FO. The
temporal specification can be interpreted as a context wrapper. (04)
A 4D theory can interpret a temporal context in one way, while a 3+1 D
theory can interpret it differently. (05)
For expressing statements using an FO, there seems to be a need for
specifying contexts -- not everything asserted in every knowledge base
using any ontology is consistent with everything else asserted in every
other knowlege base. Contexts could be defined as distinct models; in
Cyc terms, they would be "data microtheories". (06)
>> 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. (07)
>> But somebody might ask,... (08)
> 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. (09)
> 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'. (010)
They need only be associated with contexts. The interpretation of
what it means to be associated with a temporal context would be
different in 4D & 3+1 D theories. (011)
> 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, (012)
No single semantics can be given to such a context syntax (imho). The
semantics would depend on the theory (3D or 4D) used. Different semantics
would apply for different dimentionality. Without assigning a syntax at
the FO level, the following issues should not come up. In order to reason
about statements, instead of merely translating them, a dimentionality
would have to be selected. (013)
> 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. ) (014)
> 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. (015)
I agree. Does someone dispute this? (016)
-- doug f (017)
> Pat (018)
=============================================================
doug foxvog doug@xxxxxxxxxx (019)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
============================================================= (020)
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