TIME CHANGE AND IDENTITY
We often say something like the following:
“That ship is the same ship we met on
ten years ago,”
meaning:
“That 3-dimensional object is the same
thing as the 3-D object we met on ten
years ago”
Or, more abstractly:
Y at T2 is identical to X at T1
Reasons we might give:





The ship has the same name
Is docked at the same port
Looks the same
Is run by the same company
Etc.
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Leibniz’s Law
Moreover: most of us feel that an object can
remain one and the same thing even if it
changes a little bit:
 The foghorn is replaced on the ship.
 Still, it is the same ship.
But consider the following:
Leibniz’s Law: If x = y, then every property
of x is a property of y and vice versa.
This seems obvious: if x and y have
different properties, they must be different
objects.
 E.g., two indistinguishable balls except
one is heavier than the other.
 Clearly they are different objects.
But: it leads to a problem…
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Imagine the ship’s planks are replaced until
we have all new parts.
T1:
T2:
T3:
T4:
T5:
ABCD (ship 1)
ABCE
ABEF
AEFG
EFGH (ship 2)
Two options:
1. Ship 2  ship1.
Rationale: Leibniz’s Law:
 Ship 2 has properties that Ship 1 lacks
(and vice versa).
Consequence: By the same reasoning,
ABCE is not identical to Ship 1.
Conclusion: loss of a single part destroys
identity.
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Second option
2. Ship 2 = ship 1.
Rationale: Forget Leibniz’s Law!
 Let ship at T1 = X.
 X-1 plank is a very small change.
 So, X-1=X.
 But: X-2 = (X-1)-1 = X-1 = X.
 And so on…
So, the ship we see today is identical to the
one we saw 10 years ago.
 Similarly, each object along the way is
identical to the original ship.
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Problem: Ship of Theseus case.
T1:
ABCD (ship 1)
T2
ABCE
D
T3:
ABEF
CD
T4:
AEFG
BCD
T5: EFGH
ABCD
(ship 2)
(ship 3)
 Which is identical to ship 1?
Sub-options:
I. Ship 3 = Ship 1
Rationale: Only Ship 3 has all the properties
of Ship 1(back to Leibniz’s Law?).
Result: ABCE is not identical to ship 1.
Conclusion: Loss of one part destroys
identity.
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II. Ship 2 = Ship 1
Rationale: Forget Leibniz’s Law (again)!
 As above: X-1=X.
Problem: Ship 3 has all the parts of the
original ship.
 It might even continue to be used to
transport people on the same body of
water.
 To favour ship 2 over ship 3 simply
seems arbitrary.
Conclusion: this position is arbitrary—it has
no rational basis.
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Further problem: Sorites paradox:
 We know it is possible to destroy a ship
by removing planks
 So it must be false that for all n, X-n
equals X.
 But there is no rational way to determine
which n destroys identity—we can’t
draw the line at how many planks
destroy the ship.
Conclusion: Since we know ships can be
destroyed, and we know there is no way to
determine how many planks will do this, the
only rational position is to admit that loss of
one plank destroys identity.
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Grand Conclusion
All the rational options lead to the same
conclusion: the loss of a single part destroys
identity.
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A solution?
“Intactly persisting temporal objects” (IPTO).
 X is an IPTO if and only if at all times
during its existence it has exactly the
same parts.
 So, ABCD, ABCE, etc. are all IPTO’s.
 They are all distinct: none is identical to
any other (still have Leibniz’s Law).
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How does this help?
 There is no IPTO that is identical to the
original ship.
So if we ask: is ship 2 or ship 3 identical to
ship 1, the answer is “no”.
 But there is a non-IPTO that consists of
ABCD-EFGH.
If we ask: Is EFGH part of the same (nonIPTO) object as ABCD”, the answer is “yes”.
Once we make this distinction, all our
questions have definite answers.
Problem solved?
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Chisholm
 We can combine the IPTO’s into at least
10 “objects”
 Before we thought there were only two.
 So, which of these “objects” is the
original ship—what were we originally
referring to?
 This is an ontological “explosion”!
Important questions still can’t be answered.
Two positions:
Identity realist: there is a definite fact of the
matter. One of the two ships is the
original.
Conventionalist: There is no objective fact
of the matter as to which is the original.
It depends on the conventions we adopt.
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Chisholm’s Identity conventionalism
X at T1 is identical to Y at T2 if:
 Y evolved from X = at each step,
common parts; not too much change.
 Every object that evolved from X and
into Y was used for the same purpose
as X (sailing).
 If other objects evolved from X, their
function was different from those that
became Y. I.e., only one “chain”
continued along the same way – nonbranching clause.
So:
 Strictly speaking, an object (ship) never
retains its identity when it loses a part.
 What we call a particular ship, X, is
really a collection of non-identical
objects.
 We pragmatically decide to group them
together into “X”.
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Vagueness
There may be borderline cases where it is
not clear whether X and Y are identical.
 E.g.: two ships, Y and Z, evolve from X,
i.e. at each stage, some parts overlap.
 Y and Z are each used to sail the same
route on similar schedules.
 There is no clear answer as to which is
the same ship: we must adopt a useful
convention.
T1
T2
T3
ABCD
ABEF
AIEF
GHCD
GHJD
If both AIEF and GHJD have the same
function, it is a matter of choice which to
identify with ABCD.
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Summary of Chisholm’s view
 X can be the same as Y even if strictly
speaking X and Y aren’t identical.
 Strictly speaking, nothing remains
identical when it loses a part.
 Identity over time is a matter of
convention and overlapping of some
parts.
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Problem
What defines a “good” rule? There is no
philosophical ground for calling one good
and another not good.
Alternate conceptions have equal
philosophical justification.
E.g. tomorrow someone tries to steal your
car.
 Your say, hey that’s my car.
 Reply: no, it’s not identical to the object
you purchased.
If Chisholm is right, this is just as correct as
the view that it is your car.
He favours the view that would call it your
car, but there is no metaphysical ground for
this.
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Moreover, Chisholm’s view presupposes
something, namely:
 That some things retain their strict
identity across time, i.e. some things are
IPTO’s
In order to say one object is the same ship
as another, we had to assume the parts of
the ship remained the same across time.
 Otherwise, there could be no overlap
and wouldn’t make sense to say one
evolved from the other.
So some things must retain their strict
identity if conventionalism is going to work.
 Perhaps things without parts, such as
elementary particles?
 Everything else, built out of them, is only
“loosely” identical, i.e. by convention?
Do you agree with this?
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An Alternate Solution: 4-Dimensionalism
Common view:
Objects undergo changes in time, but
remain self-identical:
T1
T2
T3
T4
T5
 Objects are three-dimensional
 They endure through time: i.e., the
object is permanent from T1-T5 (so it
retains its identity) but it also changes
Smart, Quine and Lewis all reject this view.
What’s the problem?
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The problem with 3-dimensionalism
Objects gain/lose properties all the time.
 So, only IPTO’s retain their identity.
 But things like wooden planks, metal
bars aren’t actually IPTO’s – they can
gain or lose atoms, molecules, etc.
It seems that only elementary particles
retain their identity over time.
 But that seems unnecessarily harsh.
Why not alter our concept of objects instead
of our concept of identity?
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Four-dimensionalism
Objects are spread out in time: they occupy
four dimensions; they don’t endure through
them (they perdure)
 Change isn’t remaining identical yet
changing
 Change = time-slices of a 4-D object
differing from each other
Space
Time
T0
Birth
T1
T2
T3
T4
P1
(x’ tall)
P2
(y’)
P3
(z’)
Death
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A solution?
On this view, the ship at T1 is simply a
(temporal) part of a 4-D object that stretches
out over time.
 So, the ship at T2 is a different temporal
part of a 4-D object.
 Such objects may even have
“branching” structures such as the boat
whose planks are replaced.
 So, what retains its identity is a 4-D
object spread out in space and time.
This entity never changes. Different parts
have different properties.
But this doesn’t violate Leibniz’s Law (no
more a change than a plank being green at
one end, red at the other).
 The whole 4-D structure never changes
(no gain/loss of properties).
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Problems
1. There are no objects in this room, only
(temporal) parts of objects.
2. There is no “you” that survives one
moment to the next.
 You are the collection of parts from birth
to death.
 We’ll look at this more in the case of
personal identity.
3. The parts of a 4-D object may reach
back and forward in time infinitely. Are
“objects” eternal?
Quine: where you decide to draw the line
and call something an “object” is simply the
result of pragmatic considerations.
 There is no fact of the matter.
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