RE: SUO: Metaphysics: a book report (long message)
Dear Pat,
Some thoughtful observations.
See my comments below.
Matthew West
Principal Consultant
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> -----Original Message-----
> From: Patrick Cassidy [mailto:pcassidy@bellatlantic.net]
> Sent: 06 September 2001 15:58
> To: Adam Pease
> Cc: standard-upper-ontology@ieee.org
> Subject: Re: SUO: Metaphysics: a book report (long message)
>
>
>
> Adam -
> I have also been reading chapter 6 of Loux's Metaphysics, and
> re-reading Pat Hayes's paper on Liquids, and also Chris
> Partridge's book
> chapters 7 and 8, to try to get a good grasp of exactly what the
> properties of a 4-D object are. There are questions I haven't yet
> resolved, so I can't be sure there is a way to relate 4-D and 3-D
> comprehensively.
MW: Relating them is something I am confident we can do. Merging them is
something else.
> It does seem that the kind of treatment you give, for
> predicates
> on 3-D objects that specifically mention the time interval
> during which
> the predicates are held to be true, can be related directly to
> predicates on temporal parts of a corresponding 4-D object.
MW: Yes, provided you time index everything to do with individuals.
However, much of what I have seen from 3D uses a "current state"
approach that looses history. This meets some needs, but is hardly
comprehensive. 4D forces you to consider the wider context.
> However,
> there may be more than one 4-D object that has a 3-D object as a
> temporal part in some time interval.
MW: Well strictly 3D objects (continuants) do not perdure through
time, so they can't be temporal parts of anything.
MW: 3D objects are wholes, and I would expect a mapping between
the intent of a 3D object and a 4D spatio-temporal extent that
was a temporal whole (the maximum temporal extent of an instance
of a class).
> We can say there is at
> least one
> such 4-D object.
MW: More than one 3D object may map to the same 4D object. The 4D
object will then be a member of the classes of both the 3D objects.
> The main problem seems to be in going in the other
> direction, specifically how to interpret predicates on 4-D objects.
MW: It works just the same the other way round. If I have an object
that is a temporal whole 4D car, it maps to a continuant that is a
3D car.
> My initial impression of 4-D axioms is that a predicate relating
> temporal parts of two different 4-D objects holds at every time point
> in the time interval those temporal parts exist.
MW: Ordinarily yes, and this means ordinarily that the temporal parts
exist for the same period.
> In Pat Hayes's
> "Liquids" paper there is an axiom 42a, which indicates that
> predicates
> on histories of objects (I think this is the same as a
> temporal part of
> a 4-D object) are only meaningful for temporal parts that
> have the same
> beginning and ending time points, and in addition that such a
> predicate
> holds at every time point in that interval (the time interval is
> expressed as when(x) for temporal part x and <=> is the "identically
> equal" sign [subscript symbols are not subscripted in this ASCII
> transliteration]):
>
> <Axiom 42a:>
> R(h1, . . . hn) <=> when(h1) = . . . = when(hn)
> AND forall t in when(h1), R(h1@t, . . . hn@t).
>
> This accords with what can be represented with 3-D objects
> and explicit
> time intervals, much as you indicated in your note.
MW: Well yes ordinarily. But for example if I today talk about
Winston Churchill, then you have two spatio-temporal extents
that are related, but not contemporaneous. So I might have a bone
to pick with Pat.
>
> But when a perdurantist asserts something about a *whole* 4-D
> object, I am very uncertain what that is intended to mean for the
> temporal parts. It seems from Chris's book that a unary
> predicate on a
> 4-D object will hold in every time interval within the
> lifetime of that
> object.
MW: My working hypothesis is that what ever is true for a temporal
whole is true for any/all temporal parts. The only exception I am
aware of is that a temporal part of a car is not a temporal whole car
(the one that is equivalent to the continuant). But each temporal
part of a car is for example a car.
> But I can't find the interpretation for how
> relations between
> two 4-D objects relate to their temporal parts, and especially
> troublesome are relations between 4-D objects that have unequal
> lifetimes. Clarification with specific examples from
> perdurantists will
> be immensely helpful in deciding whether and how such
> predicates can be
> related to predicates on 3-D objects.
MW: In general relations to a temporal super-part are relations to
any/all sub-parts, just like properties. For overlapping temporal
parts there are intersection temporal parts for which all the
"inherited" relations and properties apply. It is really very
like set theory.
>
> Loux makes much of the "mathematical identity" of 3-D
> objects at
> different times, as presenting a big problem for
> endurantists. I think
> the most consistent view is that the "identity" of a 3-D object at
> different times is not a mathematical or logical identity of
> the whole
> 3-D object at different times, but only the identity of the
> "identifying
> tag" that is attached to the object.
MW: I think I would hope there was a bette basis for identity
than that we made a tag!
> I don't know if anyone can say
> for sure whether a physical object actually has some
> "essential element"
> other than its properties, or whether it is only a "bundle" of
> properties. In either case, the "identity" is the tag we give to the
> object, whether the object has some essential core *or* whether it is
> only a bundle of properties. The tag labels *whatever* it is
> that moves
> with its properties together in space and time, or *whatever* has
> properties which change over time. The tag remains constant
> as long as
> the essential identity conditions for the object are
> satisfied.
MW: I think an endurantist should respond to this. But your description
here is uses at least some perdurantist language.
> As best
> I can tell this is not really different from the "identity" for a 4-D
> object. Calling an object 4-D doesn't make it any easier to
> specify the
> identity properties, which in the 4-D case means specifying precisely
> the region of space-time that constitutes a 4-D object; the
> problem of
> actually identifying a 4-D object in the flesh is the same as
> for 3-D,
> though it may be convenient for some purposes to *talk* about
> the whole
> 4-D object, rather than instantaneous instantiations of it.
MW: There are some key differences. If 4D objects coincide, they are the
same object. However, for 3D objects coincidence is at a point in time
only, and so different objects can coincide.
MW: The other key difference is that for 4D objects, the object over its
whole life and the object at a point in time are different objects. For
3D objects these are the same.
>
> Given that all of the predicates on 3-D objects that relate to
> time-varying properties will have to be asserted for some
> time point or
> interval, the question remains as to whether *timeless*
> predicates can
> be asserted and what they mean. I would prefer to adopt the
> convention
> that any atemporal predicate with some PhysicalObject as domain is
> intended to be true throughout the lifetime of the
> PhysicalObject. Thus
> a predicate of the form:
>
> (hasPart Car Motor)
>
> . . . would mean that as long as a car exists, it has a motor; if the
> motor is removed, it no longer is a car, and when the motor
> is replaced,
> it is a car again. Such predicates in effect are necessary and
> definitional - they form part of the identity criteria for
> the objects
> we are discussing. (Of course, we might prefer *not* to
> insist that all
> cars must have a motor, but to say that an "OperationalCar"
> must . . .
> it is at the ontologist's discretion how to define the
> objects.) But I
> would expect most assertions about real-world objects to be
> time-dependent as well as having a contextual wrapper with other
> information. The terminological definitions such as teh one
> above can
> be timeless.
MW: It certainly works like that in 4D.
>
> Accordingly, if ?PO is a PhysicalObject and ?TS a
> time-slice of the
> corresponding 4-D object ?PEROBJ (which I call a
> PersistentObject in
> my ontology) which exists only in some time interval ?TI within the
> lifetime of ?PEROBJ (hasTemporalPart ?PEROBJ ?TS ?TI), then to assert
> that the object is blue in some time interval ?TI within
> ?LIFETIME, we
> could use either the Predicate hasProperty for the time-slice or the
> equivalent assertion wrapper holdsIn for the PhysicalObject:
> (hasProperty ?TS blue)
MW: This is a 4D stsement.
> (holdsIn hasProperty ?PO blue ?TI).
MW: This is an equivalent 3D statement (although I don't know why you
need "holdsin").
>
> The relation between the 3-D object and the 4-D object could be
> expressed explicitly:
> (hasTemporalExtension ?PO ?PEROBJ)
MW: This gives precedence to the 3D object - to which I object.
?PO and ?PEROBJ seem to me to be equivalent, not that one has the
other.
>
> In this representation, since a PersistentObject has
> some time interval
> during which it exists, it can be considered as the maximal temporal
> part of itself, and any predicate using the entire object
> would have to
> hold true of all time points within the lifetime of the
> PersistentObject. Thus for the same instance variables above
> (using the
> predicates beginning and ending for the endpoints of temporal
> parts and
> startPoint and endPoint for time intervals):
>
> (forall (?PEROBJ ?TI ?t1 ?t2)
> (implies
> (and
> (PersistentObject ?PEROBJ)
> (beginning ?PEROBJ ?t1)
> (ending ?PEROBJ ?t2)
MW: I would say this in a different way. See some of my notes to
Adam.
> (TimeInterval ?TI)
> (startPoint ?TI ?t1)
> (endPoint ?TI ?t2)
MW: This is an abstract view of time.
> (hasProperty ?PEROBJ blue))
> (exists ?PO
> (and
> (PhysicalObject ?PO)
> (hasTemporalExtension ?PO ?PEROBJ)
MW: See above.
> (holdsIn hasProperty ?PO blue ?TI)))))
>
>
> But it is not clear to me from what I have seen thus
> far that this
> is the proper interpretation of what a predicate on a whole
> 4-D object
> means. Also, it is unclear whether such relations would hold
> for *all*
> predicates, or whether there would be exceptions.
MW: I only know of the one exception, that of being the temporal
whole.
>
> As for predicates relating 4-D objects to each other, they might
> be interpreted as meaning that the relation holds only during the time
> interval when both exist.
MW: No. It means the relation is between those two objects. If the
relation holds between the interval when they both exist, then it is
between those temporal parts of the two related objects. This is the
normal case.
> Since causal relations hold between non-
> contemporary entities, causal relations might have to be restricted
> to processes and events, rather than to objects, which I
> would prefer in
> any case.
MW: Me too. Though again see my note to Adam about temporal boundaries
being what is caused rather than spatio-temporal wholes.
>
> I hope one of the perdurantists can explain what the
> relation is
> between a predicate on a whole 4-D object and the same
> predicate on its
> temporal parts.
MW: The relationship is redundancy. If something was true for the whole
4D object, then (generally) it is true for any temporal part, so you do
not need to say it for them since it is inherited.
>
>
> Pat Cassidy
>
> =============================================
> Patrick Cassidy
>
> MICRA, Inc. || (908) 561-3416
> 735 Belvidere Ave. || (908) 668-5252 (if no answer)
> Plainfield, NJ 07062-2054 || (908) 668-5904 (fax)
>
> internet: cassidy@micra.com
> =============================================
>
> ============================================================
> Adam Pease wrote:
>
> >
> > Folks,
> > I thought I'd present a "book report" of Metaphysics by
> Michael Loux
> > and recommended on this list by Chris Partridge. I found
> this a very
> > clear and helpful book. I hope that its discussion of
> endurantism vs.
> > perdurantism will be enlightening since on this and several other
> > topics, Loux outlines the relevant arguments but does not,
> for the most
> > part, take a particular position.
> >
> > INTRODUCTION
> >
> > Loux explains metaphysics as
> >
> > "...its aim is to identify the nature and structure of all
> there is.
> > Central to this project is the delineation of categories of being."
> >
> > He also notes that
> >
> > "...metaphysicians have disagreed about the categorical
> structure of
> > reality."
> >
> > An editorial comment that I would make is that any account
> of the world
> > must be consistent and stand up to scrutiny on the merits
> of its own
> > arguments, not simply because it is a widely held position.
> Nor do I
> > think we should be compelled to accept any one account in
> its entirety.
> > We are at liberty to create other accounts of the world and should
> > choose them to the extent that they provide greater
> descriptive power,
> > even if they do not accord with some previously held and
> labelled position.
> > I find the strongest arguments that Loux explains are those which
> > present examples or thought experiments that versions of
> the positions
> > he describes fail to capture adequately. Those examples or
> experiments
> > motivate modifications of the positions. Merely to say
> that "X who is a
> > Y won't accept this." is too weak an argument.
> >
> > In Chapter Six Loux's Overview states that
> >
> > "The endurantist claims that for a concrete particular to persist
> > through time is for it to exist wholly and completely at different
> > times. The perdurantist, by contrast, denies that it is
> possible for
> > numerically one and the same concrete particular to exist
> at different
> > times...the concrete particular is an aggregate ... made up
> of different
> > temporal parts."
> >
> >
> > CHAPTER SIX
> >
> > In the body of the chapter (my editorials within quoted
> passages are in
> > []):
> >
> > "...[Both theories assert that] concrete particulars
> [(instances)] are
> > entities with temporally bounded careers."
> >
> > "...perdurantists insist that ... spatial parts and ...
> temporal parts
> > are, in one and the same sense, parts of a concrete
> particular. ...at
> > any time I am a spatial whole made up of spatial parts at
> that time, so
> > am I a temporal whole made up of all my temporal parts...
> [considerable
> > elision] ...many of those parts overlap."
> >
> > Loux then has some descriptions of the two positions which
> I find either
> > too difficult or more likely, take an account of a
> correspondence of the
> > positions with natural language rather than an account of
> the underlying
> > structures of the positions.
> >
> > "Typical endurantists are what we might call
> presentists...only what
> > exists in the present really exists."
> >
> > "Perdurantists [assert that] ... all times, all things
> existing at those
> > time...are equally real."
> >
> > The former seems practically incoherent to me and can be
> addressed just
> > by a matter of modeling convention in which every statement
> is wrapped
> > in an implicit (holdsIn Now (...)) unless otherwise specified.
> >
> > Loux also gives some nice analogies between 3d vs 4d as a
> debate similar
> > to possibilism vs actualism.
> >
> > Loux goes on to discuss an odd position of some perdurantists that
> > assert that groups of entities that seems disconnected in a
> common sense
> > view of the world such as "Big Ben from ... noon to ...
> midnight...and
> > Wmbley stadium from 2pm to 3pm..." are just as real as the
> group "...the
> > Loux of yesterday and the Loux of today".
> >
> > He continued to say "...Perdurantists insist that there are
> insupperable
> > logical difficulties in the assumption that we have
> numerical identity
> > where we have persistence through change." However this is
> unsupported.
> >
> > Endurantists argue that the solution is to "...describe [a] ...
> > situation by time indexed properties..." Perdurantists
> them claim that
> > endurantists are committed to time indexing all properties.
> > Endurantists reply that they are not.
> >
> > Perdurantists then argue that only their theory properly supports
> > modeling changes in parts of entities. This seems related
> however to
> > another dogma of Indiscernibility of Identicals (the notion
> that "if a
> > is identical with b then, for any property p, p is a
> property of a if
> > and only if p is a property of b") rather than a genuine criticism.
> >
> > A stronger claim for a defect in the endurantist position is in the
> > following example. Say we have our friend Joe again and he
> loses an arm
> > at a point in time which we'll call "t". Endurantists acknowledge
> > spatial parts and so would allow the notion of a spatial
> part of Joe
> > minus his arm, so we have
> >
> > JoeBeforeT, JoeAfterT, JoePartOtherThanHisArmBeforeT,
> >
> > Before amputation we have both Joe and the part of Joe
> without his arm.
> > Endurantists also believe that Joe survives the loss of his
> arm with his
> > identity intact. After the amputation we have only a Joe
> without his
> > arm. This leaves us with the assertions that Joe is the
> same as both
> > Joe before the amputation as well as the more clearly true
> statement
> > that Joe after the amputation is the same as the spatial
> part of Joe
> > minus his arm before the amputation. Thanks to the
> Indiscernibility of
> > Identicals though, they can't both be true.
> >
> > The Endurantist responds however in several ways
> >
> > 1. There are different notions of identity. One notion is
> strict and
> > requires all parts to be present. The other is informal.
> So the two
> > problematic statements are actually using incomparable identity
> > relations. This position is attributed to Roderick Chisholm
> >
> > 2. Peter Geach also asserts that there should be different
> notions of
> > identity but says instead of just two as in (1) that they
> should be with
> > respect to a particular class.
> >
> > 3. Peter Van Inwagen offers that there is no such thing as
> arbitrary
> > undetatched parts an so JoePartOtherThanHisArmBeforeT is not a
> > legitimate instance.
> >
> > This is not the end of the argument since there are responses and
> > counter-responses to each of these points.
> >
> >
> > JOE'S ARM REVISITED
> >
> > Let's consider an example again of Joe and his arm. Joe
> existed from
> > the year 1980 to 2000. So did his arm. Many aspects of Joe were
> > constant. Some were not.
> >
> > Both 3d and 4d might assert the existence of Joe.
> >
> > (instance Joe Human)
> >
> > ...and that he had an arm
> >
> > (part Joe JoesArm)
> >
> > A strict presentist would be unconcerned about the temporal
> > characteristics of Joe but would have no concrete objection to the
> > inclusion of such information other than an extreme adherence to
> > Ockham's razor.
> >
> > (start Joe Year1980) etc
> >
> > It seems to me that the first concrete point of divergence in these
> > positions (with respect to practical modeling in a logical
> language)
> > would be once we want to talk about a change in properties
> of Joe during
> > his lifetime. For a perdurantist, properties are
> unchanging. An entity
> > may only have different spatio-temporal parts, each with different
> > properties. For an endurantist, properties of an entity
> may in fact
> > change. So, if Joe tragically loses his arm at age 10, the
> perdurantist
> > would state
> >
> > (instance Joe Human)
> > (part Joe JoeFrom0to10)
> > (part Joe JoeFrom10to20)
> > (part JoeFrom0to10 JoesLeftArm)
> > (not
> > (exists (?X)
> > (instance ?X LeftArm)
> > (part JoeFrom10to20 ?X)))
> >
> > whereas the endurantist would state
> >
> > (instance Joe Human)
> > (holdsIn (IntervalFn (Year 1980) (Year 1990))
> > (part Joe JoesLeftArm)
> > (holdsIn (IntervalFn (Year 1990) (Year 2000))
> > (not
> > (exists (?X)
> > (instance ?X LeftArm)
> > (part Joe ?X))))
> >
> > But why not simply allow both options when nothing prevents
> this other
> > than the dogma of each particular position? We only get
> into trouble
> > when we adopt the conventions of the perdurantist and
> expect endurantist
> > notions of identity to apply.
> >
> >
>
>
> --
>