On Aug 11, 2009, at 5:19 AM, David Leal wrote: (01)
> Dear Pat,
>
> You wrote:
>> I will try to sketch the argument, though I would hesitate to call it
>> a proof. It amounts to defining a syntactic transformation from one
>> ontological formalism style to another, and then observing that one
>> of
>> these can reasonably be seen as a formalism of the 4D picture, and
>> the
>> other of the 3D one. The basic point is that there are only two ways
>> to insert a time parameter into a 'static' description: it either
>> gets
>> attached to a relation name as an argument, or to an individual name,
>> converting them to a term. One writes either (R a b t) or (R (a t)(b
>> t)). The first is naturally read as a continuant-style description,
>> using time-dependent fluents to talk of things whose identity is
>> considered to be timeless, the latter as a 4D one, in which
>> assertions
>> are made timelessly about 'slices' of a 4D entity. (There are other
>> ways, but they all involve changing the logic in some way, eg by
>> adding temporal contexts or tenses.) Basically, and oversimplifying
>> things greatly, one can convert from 3D to 4D and back by 'moving'
>> the
>> temporal parameter between these two positions. This is an
>> observation
>> about the formal notation, of course, but the philosophy is basically
>> irrelevant until it gets cashed out in a formal expression of some
>> kind. Whatever your views are on property instances, in particular,
>> can (if they are relevant to the final ontology) be ultimately
>> expressed in one of these ways, and when it is so expressed, can be
>> almost mechanically transliterated into the other, and from there
>> 'read back' as being about the other kind of temporal entities. I
>> realize that this hardly constitutes a philosophically valid form of
>> argumentation, but then of course we are not here doing philosophy,
>> but rather ontology engineering: right?
>
> This is how I see it too. Some further thoughts are:
>
> 1) Consider a test to determine material properties. During the
> test, the
> test machine - test specimen assembly goes through a succession of
> states.
> For these states, time (since the beginning of the test), crosshead
> displacement, extensometer displacement and force are measured.
>
> - The 4D approach defines the states as different objects, and
> records time,
> crosshead displacement, extensometer displacement and force for each.
> - The 3D approach records crosshead displacement, extensometer
> displacement
> and force as time varying relationships with the whole life of the
> test
> machine - test specimen assembly. (02)
Right. And of course we can have both, provided we agree to not pay
too much attention to the philosophers :-)
>
> The 3D approach would be convenient if we were principally
> interested in the
> variation of these measurements with time. However, we are principally
> interested in the variation of force with extensometer displacement.
> The
> variation of force with time or extensometer displacement with time is
> secondary, but both need to be kept within limits. The 4D approach
> has been
> adopted by the test machine manufacturers for their output format.
>
> 2) There is a problem with "slices" - both temporal and spatial. Naive
> models assume that relationships exist for a material object at an
> instants
> in its life and for a point within it. Consider the variation of
> density
> with time and space within a fluid - something that fluid
> dynamicists worry
> about.
>
> But density is not defined at a point. (03)
Well, it can be defined as a limit. There isn't anything
**conceptually** hard about this any more, though the details can get
hairy. (04)
> A description of the variation of
> density from point to point within a body requires a specification
> of scale. (05)
Right. That is because real stuff isn't smooth all the way to the
mathematical limit, of course. (06)
> This is not an academic issue when describing complicated composite
> materials. There are similar problems with properties which purport
> to be
> defined for an instant. (07)
Oh sure. This issue has been done to death in early temporal ontology
work. See (08)
www.ihmc.us/users/phayes/Pub/timeCatalog.pdf (09)
for an overview. (010)
Pat (011)
>
> Future ontologies which recognise scale when considering instants in
> time or
> points in space, may shed some light on the 3D/4D issue.
>
> Best regards,
> David
>
> ============================================================
> David Leal
> CAESAR Systems Limited
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> ============================================================
>
>
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> (012)
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