Ali,
Rather than point to a long thread, I will summarize: The
incompatibilities of 3D and 4D arise solely at the philosophical level.
Perdurantists don’t believe that 3D objects exist; endurantists don’t
believe that 4D objects exist. These are contradictory **belief systems**. But
when one wants to make an assertion about an object’s properties, it can be
done equivalently in either form and translated accurately to the other form.
Pat Hayes has one way of executing the translations, I have a different way.
My own preferred way for the simple case of translating assertions about properties
of an object is, to wit:
Assume
{Obj123 isanInstanceOf Object3D}
{Obj456 isanInstanceOf Object4D}
{Obj456-200901-200902 isaTimeSliceOf Obj456}
{Obj456-200901-200902 beginsOn Date20090101}
{Obj456-200901-200902 endsOn Date20090201}
And also assume a bridging relation between the two views of
that object:
{ Obj123 isThe3DcorrelateOf Obj456}
Now given the above, an assertion about that object in 4D “Time
slice Obj456-200901-200902 of Obj456 is Red”
{Obj456-200901-200902 hasAttributeValue Red}
Is equivalent to an analogous assertion in 3D “Obj123 was
Red from Date20090101 to Date20090201”
{Obj123 hasAttributeValue Red from Date20090101 to Date20090201}
Or, in general, given the assumptions:
(ó
(?rel Obj456-200901-200902
@args)
(?rel Obj123 @args from Date20090101
to Date20090201))
In summary, models that are incompatible on the philosophical level
can be represented as different *theories*, but when practical
assertions about real-world things are made in the *notation* adopted by either
camp, those assertions can be translated accurately into equivalent assertions,
having the same meaning, in the notation of the other camp. Having different
philosophies about the fundamental nature of the universe doesn’t mean
that we can’t *understand* each other when we talk about the
universe. Whenever there are different preferred representations, the task of
the FO will be to provide the translations that allow assertions from one
viewpoint to the other.
Pat
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
From:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ali Hashemi
Sent: Saturday, February 21, 2009 8:24 AM
To: [ontolog-forum]
Subject: [ontolog-forum] Incompatibilities in 3D to 4D
Hello again,
Can someone point me to discussion / papers which outline
the irreconcilable(?) differences between these two paradigms.
My (semi)naive
impression is that each approach considers a set of information as a given,
while another requires that it be explicated. It seems like a relatively
straightforward affair to keep track of what is needed to facilitate adequate,
two-way translation between each approach.
Am i missing something? Why is this such a thorn? Where do
the problems arise?
Ali
--
(•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,.,