METAPHYSICS
CHANGE: DEVIANT ID APPROACHES
LECTURE
PROFESSOR JULIE YOO
(under construction)
Classical ID Is An Equivalence Relation
Classical ID Is Absolute, Determinate, Necessary, and Permanent
Relative Identity
Comparing Relative and Absolute Identity
Applications of Relative Identity to Puzzle Cases
Problems for Relative Identity
Vague Identity
Comparing Indeterminate and Determinate Identity
Applications of Vague Identity to Puzzle Cases
Problems for Vague Identity
Contingent Identity
Comparing Contingent and Necessary Identity
Logical Contingency
Semantics of Referential Terms (Rigid Designation)
Applications of Contingent Identity to Puzzle Cases
Problems for Contingent Identity
Occasional Identity
Comparing Occasional and Permanent Identity
Applications of Occasional Identity to Puzzle Cases
Problems for Occasional Identity
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CLASSICAL ID IS AN EQUIVALENCE RELATION
An equivalence relation is a relation that satisfies three logical relations: reflexivity, symmetry,
and transitivity:
x=x
ii. it is symmetric: (x = y) ↔ (y = x)
iii. it is transitive: [(x = y) and (y = z)] → (x = z)
i. it is reflexive:
A reflexive relation is a relation that something can bear to itself:
x
For instance, being as tall as, is a property you can bear to yourself, but being taller than, is not,
because you cannot be taller than yourself. Self-admiration is another reflexive relation, since it
is a relation that one bears to one’s self (an extreme self-admirer would be narcissist), but mere
admiration is not reflexive, since someone can admire everyone else except themselves (some
poor guy will bad self-esteem). A symmetric relation is a relation that if x bears a certain
relation to y, y must bear that same relationship to x:
x
y
For instance, being a sibling is a property that you and your brother/sister bear to each other
equally, but being a sister is not symmetrical, because while you may be a sister to your brother,
if your brother cannot be a sister to you. Another symmetrical relationship is the property of
being married to your spouse. If Mo and Jo are married, then Mo bears the property of being
married to Jo, just as Jo bears the property of being married to Mo. A non-symmetrical property
or relationship is loving (unfortunately). Just because Mo loves Jo doesn’t mean that Jo also
loves Mo. A transitive relation is a relation that if x bears a certain relation to y, and y that same
relationship to z, then x must also bear that same relationship to z.
[x y and y z] → [x
z]
For instance, being taller than, is a transitive relation: if Mo is taller than Jo and Jo is taller than
Bo, then Mo is taller than Jo. Also, being a descendent of is a transitive relation: if Mo is a
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descendent of Jo and Jo is a descendent of Bo, then Mo is a descendent of Bo. However, being
the child of, is not a transitive relation: if Mo is a child of Jo and Jo is a child of Bo, then Mo is
NOT a child of Bo – instead, Mo would be the grandchild of Bo.
To sum up, to say that strict identity is an equivalence relation is to say that the following three
claims hold:
Reflexive: Rxx
Symmetric: Rxy → Ryx
Transitive: [Rxy & Ryz] → Rxz
Adherence to classical identity requires that one also adheres to these three relations that make
up the equivalence relation. Any relation that violates any one of these relations is not classical
(or standard) strict identity.
CLASSICAL ID IS ALSO ABSOLUTE, DETERMINATE, NECESSARY, PERMANENT
Further logical work on identity has led philosophers and logicians to adhere to these other
principles of identity:
Classical ID is Absolute, Not Relative
Absolute: If x = y, then for all F, x is the same F as y.
Identity is absolute in that every feature of x ALSO equally applies to y. This means that it is not
possible for x and y to be the same F, yet differ when it comes to being G.
The denial of absolute identity, i.e., the Relative Identity Theory, allows for this possibility,
namely, where x and y are the same F, but x is G whereas y is not.
Classical ID is Determinate, Not Vague
Determinate: If x = y, then it is determinate that (x = y).
Identity is a determinate fact, like being an even number, or being an odd number, or being
pregnant. Things that are not determinate are things like being young (when is a person still
young – 1 day to 16, 21, 28 years old?) or being on Earth (a grounded plane is on Earth, while
the Moon is not, but a plane in flight is more or less on Earth). If identity is determinate, it is not
possible for x to be more or less identical to y.
Yet this is what the Vague Identity Theorist maintains: it is possible for x and y to be more or
less identical, the way a plane in flight is more or less on Earth.
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Classical ID Is Necessary, Not Contingent
Necessary: If x = y, then  (x = y).1
This means that if x really is y (if the strict identity holds), then it is impossible for x and y to
come apart. We can express this idea in terms of possible worlds talk. If you really are
___________ (put your name here), then there is no world where you are someone else or where
someone else is you. This doesn’t mean that you exist in every world, since your existence is
contingent (there is a world where your parents never met), but in any world where you DO
exist, you cannot come apart from yourself. This idea, of course, applies not only to people, but
to every object.
According to the Contingent Identity Theorist, x = y in the actual world, there is a possibility
where x ≠ y. A certain lump of clay is a statue in this world, but that lump is a vase in a different
world.
Classical ID Is Permanent, Not Intermittent
Permanent: If x = y, then for all times during which x exists, x = y.
This is a temporal variant of the necessity of identity. Basically, the idea is that if x = y, then the
extinction of x automatically means the extinction of y. One cannot survive the destruction of
the other, which makes sense if x and y really are one and the same thing.
But the Intermittent or Occasional Identity Theorist claims that it is possible for x to survive even
though y gets destroyed, despite the fact that x = y. On Tuesday, maybe a lump of clay gets
sculpted into Goliath. But if on Thursday the artist turns the lump into a vase, then the lump
remains, but Goliath is destroyed.
RELATIVE IDENTITY (GEACH)
The positions we are about to see take on each of these claims and reject them to accommodate
the phenomena of compositional, qualitative, and substantial change.
Comparing Relative and Absolute Identity
According to the standard view of identity, identity is an absolute relation. If x = y, then that is
true simpliciter (in other words, it is true period). If 007 is numerically the same individual as
James Bond, then ‘007 = James Bond,’ period. The relative identity theorist, however, claims
1
Boxes and diamonds are used to symbolize the ideas about the necessity or possibility of some situation.
Necessity is symbolized with a box: . Possibility is symbolized with a diamond: ◊. The principle could equally
be expressed this way: If x = y, then ~ ◊ (x ≠ y).
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that absolute identity claims are incomplete, and that they are always tacitly relativized to some
sortal, like BEING THE SAME SPY or BEING THE SAME COLLECTION OF MOLECULES.
James Bond = SPY 007
James Bond on Thursday ≠ MOLECULES James Bond on Tuesday
In these identity statements, the identity sign is qualified by some sortal (in all capital letters,
subscript) relative to which the identity claim is made. For the relative identity theorist, saying,
‘x and y are the same,’ makes little sense. One needs to say HOW they are the same, or in what
respect they are the same. Every meaningful strict identity claim must be qualified relative to a
sortal: e.g. TREE, TIGER, STATUE).
Absolute Identity
Relative Identity
x = y → ∀F(Fx → Fy)
∀F(Fx = Fy) → ∀G(Gx → Gy)
If O and O* are numerically the same under
sortal F, then for any different sortal G, O and
O* are MUST ALSO BE the same under G.
If O and O* may be the same under sortal F,
but for any different sortal G, it is possible that
O and O* are NOT the same under sortal G.
(a =F b) → it is NOT possible that (a ≠G b)
(a =F b) → it IS possible that (a ≠G b)
In short, for the relative identity theorist, it is not the case that x = y simpliciter. That is, x and y
can be identical relative to one sortal but not relative to a different sortal: x and y can both be F,
and x may be G, but that doesn’t mean that y must also be y. Under classical identity, whatever
applies to x – F and G – must equally apply to y in order for the strict identity to hold.
Applications of Relative Identity
The Statue and the Clay
Lumpl = CLAY Goliath
Lumpl ≠ STATUE Goliath
The Ship of Theseus
Renovated = ARTIFACT Original
Renovated ≠ PLANKS Original
Reconstructed ≠ ARTIFACT Original
Reconstructed = PLANKS Original
The 1001 Cats
Tibbles = CAT Tibbles-minus hair n
Tibbles ≠ CAT-PARTS Tibbles-minus hair n
Tibbles and Tibs
Tibbles = CAT Tibs
Tibbles ≠ CAT-PARTS Tibs
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Problems for Relative Identity
Under regular absolute identity (identity not relativized), the formula for identity does not
relativize the antecedent of the condition to a sortal. This maintains the logical properties of
symmetry, reflexivity as well as transitivity. But under a relativist view, these properties have to
get rejected. Let’s just look at symmetry:
Non-Symmetry: Rxy →? Ryx: Even though x = y, it is not always y = x.
And this loss of symmetry in the relativized identity notion leads to some odd results. Let’s
consider again the case of another piece of clay and a new statue, David, made out of it. Under
the Relativized Identity view, David is numerically identical as Lumpl, relative to the sortal
CLAY, but not identical relative to the sortal STATUE. In other words:
Lumpl = CLAY David (Lumpl is the same piece of clay as David)
Lumpl ≠ STATUE David (Lumpl is not the same statue as David)
Problems for relative identity are many and varied. Most problematically, identity and existence
are intimately related – lose the identity of an object, the object goes out of existence. If you
relativize identity to sortals, then you relativize existence to sortals as well. But this has an odd
implication: suppose the clay statue is mushed but the piece continues to exist as a mere lump.
Clearly, there exists a lump; Lumpl has survived. But so has David! A relativist would have to
say that there is still a statue, even though the statue-ish shape is no longer there. But this seems
like an extravagant claim. Most would say that the statue no longer exists. It has undergone
substantial change when the shape went from being statue-shaped to being a mere blobby lump.
VAGUE IDENTITY
Comparing Indeterminate/Vague and Determinate Identity
According to this view, it is possible that if y1 and y2 are fission products of x, then it is
indeterminate which of them are identical with x. According to the Vague Identity view, each
are vaguely identical with the original. We can use the squiggly equal sign to designate vague
identity:
V(x = y1)
V(x ≠ y1)
V(x = y2)
V(x ≠ y2)
In other words, there is no fact of the matter about which one is numerically the same with that
original one in the harbor. To appreciate this view, we need to observe a crucial distinction
between the vagueness of the INDIVIDUALS being identified, on the one hand, and the
vagueness of the IDENTITY QUA RELATION, regardless of the vagueness or the
determinateness of the individuals identified. That is, it may be a vague matter whether there is a
heap of sand on the table, but it does not follow from this alone that the heap that goes by “x”
and the very same heap that goes by “y” are indeterminately identical.
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?a
?
VAGUE OBJECTS
=
?b
?
VAGUE RELATIONS
a ? =? b
van Ruisdael (1629 - 1682)
What is at stake is whether the very notion of BEING NUMERICALLY THE SAME is vague.
It is not about whether the relata (the objects identified) are vague.
Applications of Vague ID to Puzzle Cases
The Statue and the Clay
V(Lumpl = Goliath)
The Ship of Theseus
V(Renovated = Original)
V(Reconstructed = Original)
The 1001 Cats
V(Tibbles = Tibbles-minus hair n)
Tibbles and Tibs
V(Tibbles = CAT Tibs)
Problems for Vague Identity
This view, however, has been criticized by Evans (1978), which proceeds as a reductio:
1. Suppose that it is indeterminate whether x = y: I (x = y)
2. Surely it is determinate whether x = x: D (x = x)
3. By Leibniz’s Law, however, it follows that if something is true
of x but not of y, then it is determinate that they are not
identical: D (x ≠ y).
4. But this result contradicts our original assumption: if it is
determinate whether x is not identical with y, then it is not
indeterminate whether x is identical with y.
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A defender of vague identity (see Cook 1986) might want to reject the use of Leibniz’s law,
since the law imposes the condition of determinateness on the identity relation, and thus begs the
question against the vague identity theorist. The defender may also want to reject Premise (2):
If it can be vague that (a = b), perhaps it can also be vague that (a = a). These are variables, after
all, and the question is not about our modes of designation when pinning down cases of vague
identity; rather, the question is about the stability of the INDIVIDUAL itself under conditions of
compositional, qualitative, or substantial change. Perhaps the ripe banana on Thursday is
identical with the green banana on Tuesday, but only vaguely so, and no determinately so.
CONTINGENT IDENTITY (Gibbard) - STILL UNDER CONSTRUCTION
According to this view, the numeric identity of x and y can be a logically contingent matter. To
get a sense of what this means, we need to cover two things: the notion of logical contingency
and a little bit of terminology in philosophy of language pertaining to how terms refer to objects.
Comparing Contingent and Necessary Identity
Logical Contingency
A statement or a situation is logically contingent if it is coherently conceivable that it could be
otherwise. Here are some examples of logically contingent things:
•
•
•
•
your place of birth
GW was the first president of the US
the temperature at which water freezes at 1 atm
the existence of mammals on earth
Here are some things that are logically necessary and hence not contingent:
•
•
•
•
the number of sides in a triangle
the fact that bachelors are unmarried
the fact that 2+3 = 5
if p → q, and p is the case, then q (modus ponens)
Some philosophers further explicate contingency and necessity in terms of “possible worlds,”
where a possible world is all the ways the world could be, in addition to the way it actually is. A
contingent claim holds in some possible worlds but not others; a necessary claim holds in all
possible worlds or none (2 + 3 = 5 holds is all worlds whereas 2 + 3 = 4 holds in none).
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The Semantics of Referential Terms
Most philosophers reject the notion of contingent identity because they accept the proofs for the
necessity of identity given by Kripke and Marcus. In a nutshell, Kripke argues that claims of
numeric identity framed in terms of “rigid designators” hold with logical necessity.
A rigid designators is a term that attaches to its object no matter where that object goes, whether
it is in this world or in some other possible world. Most proper names, like “George
Washington,” function as rigid designators, whereas definite descriptions, like “the first president
of the US” function as non-rigid designators. All this means that that a term like “George
Washington” picks out that individual who was given that name from birth; had GW not gone
into the military or in politics and just remain a farmer, “George Washington” would still
designate that man that did something other than what he ended up doing.
Desfinite descriptions, like “the tallest person in this room right now,” or the “youngest person in
this room right now” function as non-rigid designators, which means that they can pick out
different individuals depending on the situation.
According to Kripke, identity claims formed in terms of rigid designators are true in all possible
worlds. That means that there is no world in which the identity could come apart. If indeed
Muhammad Ali IS Cassius Clay, then there is no way where that individual could come apart
from itself in any situation.
Applications of Contingent Identity
The proponent of contingent identity denies the view proposed by Kripke. She argues that it
makes perfect sense to say things like:
•
The Statue and the Clay: these are contingently identical, and when they are, there is
only one object on the table, but when the statue gets smushed, the identity no longer
holds.
•
The Ship of Theseus:
– Before any changes are made to the Ship, the renovated ship is
contingently identical with the original, but once the planks start to get
replaced, the identity no longer holds.
•
The 1001 Cats: each of the possible 1001 cats are contingently identical with Tibbles
prior to the shedding.
•
Tibbles and Tibs: Tibs and Tibbles are contingently identical prior to the accident.
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Occasional Identity (Gallois) – STILL UNDER CONSTRUCTION
It is possible that x and y are identical at a time (over s stretch of time) but not identical at a later
time. If x = y at t, then for all times tm – tn during which x exists, x = y. Does this view entail
intermittent existence? Can an object come into existence, then go out of existence, then come
into existence again? Consider tents. When we think of something coming into existence, we
implicitly think that it comes into existence for the first time. But surely this cannot be what
happens with intermittent existence. (For Lowe, artifacts can survive disassembly so that it
never goes out of existence even in its disassembled state, as long as the parts have not been
appropriate by other complete objects. But it is not true of organisms; they cannot survive
disassembly. Lowe’s view, however, is problematic, as it makes identity extrinsic.)
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