Wiggins:
Wiggins begins by drawing our attention to our Commonsense Truism (6), or what he
calls S.
S:
two things cannot completely occupy
exactly the same place or exactly the same volume (or exactly the same
subvolumes within exactly the same volume) for exactly the same period
of time.
He discusses two examples that would not count as counterexamples to
S:
(i) A man and his forearm.
(ii) A sponge saturated with water.
(i) does not count as a counterexample to
S because a man and his forearm do
not
completely occupy
exactly
the same place at the same time. (ii) does not count as a
counterexample because the water molecules that saturate a sponge do
not occupy the small subvolumes within the volume that the sponge
occupies; anywhere a bit of sponge is, water isn't, and anywhere water
is, the sponge isn't.
However, Wiggins continues, perhaps the following is a counterexample
to
S:
The
Tree and the Cellulose: Imagine that there is a tree, T, that occupies a certain volume, v1, at a certain time, t1.
However, at t1, v1 is also occupied by
an aggregate of cellulose molecules, W.
Thus, T and W are completely occupying the same
place at the same time. Moreover, we know that T is not identical to W because of Leibniz's Law. We
could imagine that the tree is thrown into the wood chipper, but none
of the cellulose molecules are destroyed. In this way, W has the property of being able to survive if thrown in a wood
chipper, while T does
not. Moreover, the tree could undergo a pruning, and have some of its
branches removed, and yet still survive, whereas the aggregate of
cellulose molecules would be destroyed. Thus, T has the property of being able to survive a pruning,
while W does not. Thus, since
there is at least one property that W
and T don't share, by
Leibniz's Law, W is not
identical to T. But then this
will violate principle S.
Wiggins thinks that there is still something right about principle
S, even if the tree and cellulose
example seem to be a definitive counterexample to it. He thinks that we
can amend
S to accommodate
purported counterexamples if we relativize
S to kinds or types (or sortals),
yielding what he calls
S*:
S*:
No two things of the same kind (that is, no two things which satisfy
the same sortal or substance concept) can occupy exactly the same
volume at exactly the same time.
Wiggins thinks that
S* is "a
sort of necessary truth"--that is, he thinks that is cannot fail to be
true. Notice that
S* allows
for two things to be in he same place at the same time, provided these
two things are two different kinds (or sortals or substance concepts).
Hence, Wiggins' view is one that endorses
coincident entities. He also thinks
that adopting
S*, or replacing
our principle (6) with
S*,
will provide us with solutions to our four Puzzles of Objects. In
particular, he thinks that
S*
helps solve the case of
Tib and Tibbles.
Questions: How, exactly, is
S* supposed to help solve the puzzle
of Tib and Tibbles? Is this a satisfying solution? Why or why not? How
does this solve the other puzzles--e.g., the Debtor's Paradox, Goliath
and Lumpl, and the Ship of Theseus? Do you think that embrace
S* is as counterintuitive as giving
up
S, our our principle (6)?
Can you think of any counterexamples to
S*? Discussion in class.
Doepke:
Like Wiggins, Doepke also thinks that the source of our trouble when we
are considering puzzles of material objects such as Tib and Tibbles,
Goliath and Lumpl, etc., is our commonsense principle (6). His project
in his article "Spatially Coinciding Objects" is to take some of the
bite out of rejecting principle (6) and maintaining that two objects
(of two different kinds)
can occupy
the same place at the same time.
Doepke first canvasses several examples--e.g., a man and his body, a
ship and the wooden planks that make up the ship, a statue and the lump
of clay that constitutes the statue, etc.--and demonstrates how
Leibniz's Law will easily show us that in each case, the the two
entities under consideration are distinct. Hence, in each case we are
dealing with (at least)
two objects,
not one.
However, Doepke realizes that there are at least four different ways
someone might try to block the conclusion that, in the puzzles under
consideration, there really are two distinct objects occupying the same
place at the same time. In other words, there are four ways someone
might argue that our principle (6)
is
true, and that resorting to coincident entities is
unnecessary and avoidable. These ways are as follows:
1. The One-Many View: claims that in
each of the puzzle cases, there is only one singular object in question, not
two.
2. The Relative Identity View (both the Temporal Version and the Sortal
Version): modifies Leibniz's Law.
3. The Diachronic View: denies that the two objects exist at the same
time.
4. The Reductivist View: revises the commitments of ordinary talk about
material objects.
Since we will be discussing each of (1)-(4) in more detail in the
following weeks, I will only mention the positions here. Doepke's
strategy is one of elimination: he goes through each of these positions
one by one and shows how he thinks that each can be refuted. In the
process, he thinks it is revealed how it could be the there are
coincident entities--i.e., how it could be that two things are in the
same place at the same time, by looking at how such collocated,
distinct things might be related. His aim is that in looking at his
(and
Wiggins' view) in contrast to the alternatives will show how the
coincident entity view is less
unintuitive than may have first been supposed.
A couple of points to highlight, and questions to consider:
(a)
In discussing the One-Many view,
the distinction is made between
singular
referring expressions and
plural
referring expressions. We will talk about this in class and it
will be explained briefly on the Useful Terms and Concepts page
here.
(b) Doepke discusses two
Relative Identity Views: a temporal version and a sortal version. We
will be discussing both of these views in more detail, but Doepke gives
a nice, quick summary of each if you were looking for a preliminary
look at some of the material we will be covering in the next couple of
weeks.
(c) In his discussion of the
sortal relativity view, Doepke claims that certain pairs of
objects--like you and your body, or a ship and the wood that
constitutes the ship--might share parts, but that they do not share
all of their parts. He claims, for
instance, that you might be made up of molecules, and it might seem as
if you and your molecules have all of the same parts--after all, where
you are, there some molecules are, etc. But he thinks that you have
some parts that the molecules constituting you don't have: you have a
heart as a part, whereas the molecules constituting you do not have a
heart as a part. Similarly, he thinks that a ship may have some boards
as parts, but he doesn't think that the wood that constitutes the ship
has boards as parts. "Though every part of the collection of
[molecules] is a part of you and every part of the wood is a part of
the ship, you and the ship have 'additional' parts not shared by the
collection of [molecules] and the wood." p. 16 (MC) Think about this
line of reasoning. Can you see any problem with it? Suppose, for
example, that unlike Wiggins and Doepke (and Johnston) you disagree
that constitution is not identity. That is, suppose that you disagree
that in the various Puzzles of Objects we have been considering that
there are always two distinct objects occupying the same place at the
same time. What might be your response to Doepke's little argument
above?
Note: Doepke uses the above argument to prove a different point than
the one I am highlighting, but I wanted to draw your attention to the
fact that constitution puzzles--e.g., ones about you and your body, or
a ship and the wood that constitutes the ship, etc.--can often repeat
themselves at the 'part' level.
(d) Notice that the Diachronic
view is one way of denying our commonsense principle (3): an object can
gain and lose parts and still remain the same object. For insofar as
our principle (3) allows that an object can change a
little bit, the Diachronic view (as
describe by Doepke) denies this. Can you see why?
Also, Doepke charges that the Diachronic view lacks explanatory power.
Why is this?
(e) Transitivity,
Symmetry, and
Reflexivity. Doepke claims (almost
uncontroversially) that the identity relation is
transitive and
symmetrical. Also, while Doepke
does not explicitly discuss it, identity is traditionally assumed to be
reflexive. These relations can
be defined as follows:
Transitive:
A relation, R, is transitive when: if xRy & yRz, then xRz
Symmetrical: A relation, R, is
symmetrical when: if xRy, then yRx
Reflexive: A relation R is
reflexive when: if xRy, then xRx
Notice that the identity relation is
transitive, symmetrical, and reflexive. If x = y, and y = z, then x = z
(transitive). If x = y, then y = x (symmetric). If x = y, then x = x
(reflexive).
Doepke claims that the constitution relation is asymmetrical. Do you
think he is right here? Why? What view of constitution does he rule out
here if he is correct in thinking that constitution is asymmetrical?
Again, Doepke does not discuss reflexivity. Do you think the
constitution relation is reflexive? Why or why not?
(f) Doepke makes the
distinction between the "is" of identity and the "is" of constitution.
How will this affect the set-up of the puzzles? How will it (if it
indeed does) affect our commonsense "truisms"?
Also, notice how this distinction saddles nicely with one of our
intuitive tests for sortal-hood: an answer to the question "what is it?"
(g) Notice that the
Reductivist View (as Doepke describes it) is one way of denying our
commonsense principle (1) and (2). Can you see why?
Johnston:
Johnston begins with one of our Puzzles of Objects, Goliath and Lumpl:
Imagine
that Sam the sculptor has decided to make a statue of Goliath.
However, due to an odd superstition, Sam prefers to sculpt one half of
the statue, and then the other, and then he puts them together after
the halves are complete. So, on Day 1, he sculpts both the top half and
the bottom half of Goliath. On Day 2, he sticks the two halves together
and lets the statue harden. On Day 3, he realizes the endeavor was a
complete failure, and takes a sledgehammer to the statue, smashing it
to smithereens.
Let us call this the
First Case.
Johnston claims that in the First Case, Goliath and Lumpl are entirely
coincident entities: they "came into being at the same time and ceased
to be at the same time." (p. 44 (MC))
Yet clearly the following situation is possible:
Imagine the First
Case. Only this time, Sam takes Goliath and rips off his arms and the
bottom part of his legs, and dissolves them in acid. Then reshapes arms
and lower legs with new bits of clay and adds them to Goliath, so that
now Goliath has arms and lower legs.
Let us call this the
Second Case.
Johnston thinks it is clear that in the Second Case, Goliath and Lumpl
are not entirely coincident entities since Lumpl did not survive parts
of it being dissolved in acid, while Goliath did survive the
replacement of its arms with new arms.
But if the Second Case is possible, then we know that in the First
Case, Goliath is not identical to Lumpl since the second case shows us
that Goliath has the
modal property
of
could survive replacement of arms
and legs, whereas Lumpl does not. In other words, Goliath and
Lumpl have different
persistence
conditions.
Johnston claims that there are many who want to endorse the following
two claims:
(1) In case of complete coincidence,
Lumpl is identical to Goliath
(2) Lumpl could not have survived the loss of those of its parts which
made up the arms and calves of Goliath. Goliath could have.
But deny this third claim:
(3) Lumpl could not have survived the
loss of those of its parts which made up the arms and calves of
Goliath. Lumpl could have.
Yet, Johnston claims, (3) follows directly from (2). Consider: by (1),
Lumpl = Goliath. By (2),
Goliath could
have survived the loss of those of its parts which made up the arms and
calves of Goliath. So by Leibniz's Law, since L = G,
Lumpl could have survived the loss
of those of its parts which made up the arms and calves of Goliath. But
this directly contradicts the first part of claim (3).
(Note: the ability to substitute co-referential terms without change in
truth value is called
The Law of
Substitutivity of Co-Referential Terms. It will be discussed in
class and summarized briefly on the
Terms
and Concepts page.)
Johnston explains that one way people (e.g., David Lewis) have tried to
get out of inferring the contradictory (3) from the intuitively correct
(1) and (2) is by appealing to opaque contexts. An opaque context is
one in which the Law of Substitutivity of Coreferrential Terms cannot
be applied. Lewis claims that "Goliath" is not merely a directly
referring term. Rather, it carries with it "a particular counterpart
relation or set of necessary and sufficient qualitative conditions for
tracing Goliath across worlds..." (45) We will discuss Lewis' view in
more detail when we cover
Contingent
Identity.
Another way that people have tried to get out of being committed to (3)
yet granted (1) and (2) is to appeal to a four-dimensional view, where
objects are four-dimensional sums of temporal stages. We will be
discussing this view later in the semester.
Johnston thinks that neither of the above to ways of denying that (3)
follows from (1) and (2) are plausible (just why he thinks this is
something we can discuss in more detail in class, and as we discuss the
alternative views in more detail).
Rather than try to wriggle out of the inference, Johnston argues, we
should reexamine the truth of the claims (1) and (2)--in particular, we
should see whether (1) is in fact true. He discusses two arguments for
(1), both of which concern issues of mereology and our intuitions
concern part-whole relations and identity, and neither of which he
thinks stands up to scrutiny. The details of his view and his arguments
will be discussed in class, time permitting.
In short: Johnston
argues that
constitution or
the
made up of relation is
not identity, and so Goliath can be
made
up of Lump, and yet Goliath is not identical to Lumpl. So he
rejects our commonsense principle 6.
Page Last Updated: Feb.
12, 2008