Re: SUO: Re: Ballot Comment - 3D versus 4D.
>Chris and Adam,
>
>This is another of the very many reasons why the goal of a monolithic
>ontology is hopeless:
>
> > I never suggested - or hoped I did not - that there was a simple single
> > answer to this question. Philosophers will be arguing about this for
> > decades - they have a vested interest in doing so - and one of the standard
> > arguments will be that the distinction is misguided. My point is that the
> > issue is well enough understood to recognize some of its important
> > features - one of which is that there are serious problems in having a
> > single consistent way of talking about 3D and 4D - along with a variety of
> > other metaphysical positions. And that deciding on these points is a
> > particularly important aspect of any top ontology.
>
>I believe that there are strong arguments for both sides (and maybe
>there are even more than just 2 options on this and many related
>issues). The lattice of all theories very nicely accommodates
>all of these views; it can show exactly what axioms are common
>to both, and what axioms are contradictory.
>
>All the effort spent in arguing over these issues could have been
>much more profitably spent in making a clean division of the
>axioms for both approaches and giving developers a choice.
Right. Let me try to summarise the two approaches in a slightly more
'formal' way. Consider the place in the upper ontology where one
first encounters things that exist in time and are subject to change.
(I think this is Physical Object in the SUMO)
Assume for example we know that:
(instance Joe PhysicalObject)
(instance JoesArm PhysicalObject)
Now, there are two ways to understand what these things are and how
to talk about them.
First Way (Endurantist)
POs are n-dimensional entities where n<=3. They exist in space, have
spatial parts and endure through time, but have no temporal parts.
Any property (more generally, any predication) which is liable to
change, ie which may be true of a PO at one time but not at another,
has to be understood(in an extensional logic) as a relation between
the PO and a time or time-interval. More generally, any fact that is
liable to change (a fluent) has to stated relative to a time or
interval.
Some properties of Joe and his arm might be stated this way:
(equal (length JoesArm (YearFn 1990)) (inches 10))
(equal (age Joe (YearFn 1990)) 10)
(PartOf JoesArm Joe)
Notice that the last one has no temporal reference since it applies
to the enduring entities themselves.
There is no notion here of 'spatiotemporal part' or things like
'JoesArmAtAge10', which would be meaningless. Beginning and endings
of enduring things are considered to be significant events in this
ontology, like births and deaths; they are not arbitrary boundaries.
Second Way (Perdurantist)
POs are n-dimensional entities where n<=4. They exist in spacetime,
and can have spatiotemporal parts. All properties are asserted
timelessly, and what is ordinarily thought of as 'change' is simply
the assertion of a property to one temporal part but not to another
temporal part. There are no fluents.
The same properties of Joe:
(equal (length JoesArmAtAge10) (inches 10))
(equal (BeginFn JoeAtAge10) (beginFn (YearFn 1990)))
(forall (?x ?y)(implies (and (TemporalPart ?x Joe)
(TemporalPart ?y JoesArm)
(contemporary ?x ?y))
(SpatialPart ?y ?x)))
where
(forall (?x ?y)(iff (contemporary ?x ?y)
(and (= (BeginFn ?x)(BeginFn ?y)) (=
(EndFn ?x)(EndFn ?y)))))
Temporal 'boundaries' are merely geometric, in general, and have no
special significance, so that one can chop up POs into temporal
slices quite causally. If one had a 'temporal slicing' function then
this last one could be restated much more compactly like this:
(forall (?i) (SpatialPart (at JoesArm ?i)(at Joe ?i)))
but nothing in this Way can recapture the elegant simplicity of the
third axiom in the First Way.
One would also need things like the following, none of which needs to
be said in the First Way (and most of which would be incoherent
there, in any case):
(instance JoesArmAtAge10 OrganicObject)
(instance JoesArmAtAge20 OrganicObject)
(spatioTemporalPart JoesArmAtAge10 JoesArm)
(spatioTemporalPart JoesArmAtAge20 JoesArm)
or, better:
(forall (?i)(spatioTemporalPart (at JoesArm ?i) JoesArm)
(equal (BeginFn JoesArmAtAge10) (BeginFn (YearFn 1990)))
(equal (EndFn JoesArmAtAge10) (EndFn (YearFn 1990)))
(equal (BeginFn JoesArmAtAge20) (BeginFn (YearFn 2000)))
(equal (EndFn JoesArmAtAge20) (EndFn (YearFn 2000)))
Mappings between the two Ways can be defined as follows (assuming
temporal slicing):
First-->Second:
Map every simple PO term t into a term (at t ?i), using the same
?i within each top-level assertion. If t occurs in an atom with a
temporal argument S, then bind ?i to S and erase the temporal
argument from the atom. (If there are any 'present tense' assertions,
bind their ?i's to 'NOW'.) Universally quantify all free temporal
variables at the assertion level.
Second--> First:
In general, this is impossible since one can assert relationships
between things at different times in the Second Way, but this cannot
be expressed in the First Way. However, for the subcase which is
translateable, do this: Replace every term of the form (R....(at t
I)...) by (R...t...., I), where R has an extra argument.
This would map
(forall (?i) (SpatialPart (at JoesArm ?i)(at Joe ?i)))
into
(forall (?i) (SpatialPart JoesArm Joe ?i))
rather than
(Part JoesArm Joe)
The last stage in the translation would need to be done by something
which 'knew' that certain relations were to be understood as
themselves enduring, a notion which isnt available in the Second Way.
Hope this helps.
Pat
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