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.
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. However,
there may be more than one 4-D object that has a 3-D object as a
temporal part in some time interval. We can say there is at least one
such 4-D object. The main problem seems to be in going in the other
direction, specifically how to interpret predicates on 4-D objects.
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. 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.
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. 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.
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. 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. 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.
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.
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)
(holdsIn hasProperty ?PO blue ?TI).
The relation between the 3-D object and the 4-D object could be
expressed explicitly:
(hasTemporalExtension ?PO ?PEROBJ)
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)
(TimeInterval ?TI)
(startPoint ?TI ?t1)
(endPoint ?TI ?t2)
(hasProperty ?PEROBJ blue))
(exists ?PO
(and
(PhysicalObject ?PO)
(hasTemporalExtension ?PO ?PEROBJ)
(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.
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. 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.
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.
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.
>
>
--