|From:||Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>|
|Date:||Wed, 11 Mar 2009 11:32:02 -0400|
@Chris, you are right, I'm not sure what I was thinking. :D|
Thank you for your insightful response. I will respond holistically.
One of the purposes of this email is to show(? or explore the idea) that there is not a fundamental incompatibility between the perdurantist and endurantist points of view - at least at the pragmatic level.
I should clarify some terms right now. I lifted "ontological equivalence" from Gibson's phd thesis. I imagine it to mean exactly what it says, an equivalence on the level of things that exist. IMO this is too strong for the 3D-4D debate, since they each offer a fundamentally different perspective on how things exist.
I used the term logical equivalence only in response to the preceding phrase. Admittedly it is a broad term, so let me delimit it by instead using Definably Interpretable. We can say that ontology A is definably interpretable in ontology B, if the concepts of A may be defined using B's lexicon. For a more thorough exposition of this type of "equivalence" people might want to refer to:
Now on some specific points:
Could you posit some things that appear to be untranslatable into the other formulation? I haven't had time to go through Hawley's book (you would think in this day and age, access to information wouldn't be the limiter...) in detail yet, except through excerpts on google books. Without actual axioms, it's difficult to show that perdurance theories are definably interpretable in endurance theories, but I am fairly confident it is doable. I haven't come across anything that would suggest that it isn't. We would do well to recall that most 3Dists also admit events, which are 4D entities with temporal parts.
[AH]some cl axioms
What I was trying to do in the above is to place a restriction on the types of relations a 4Dist would want to enforce.
The first snippet was stating that a particular relation was a relation ranging over 4D objects. The second was to enforce that such a relation requires a time argument.
I also neglected to include axioms for what "temporal_part" might mean in such a perspective, which is absolutely essential.
For the record, i'm neither a 3Dist nor a 4Dist, i think each perspective has advantages depending on the types of questions and problems we're trying to answer.
Hehe. I was hoping to see how the 3D-4D debate has practical implications for ontology interoperability. I have difficulty pinning down these problems. Maybe it's still too early to be asking these questions...
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