Identity and Becoming*
Robert Allen
Dust
you are and unto dust you shall return.
Genesis 3:19
A material object is
constituted by a sum of parts all of which are essential to the sum but some of
which seem inessential to the object itself. Such object/sum of parts pairs
include my body/its torso and appendages and my desk/its top, drawers, and legs.
In these instances, we are dealing with objects and their components. But,
fundamentally, we may also speak, as Locke does, of an object and its
constitutive matter—a “mass of particles”—or even of that aggregate and
the sum of subatomic particles ‘making it up’. The “problem of material
constitution” (henceforth, PMC) is generated by assuming inter alia that the
members of any such pair are numerically identical, that is, that the
constituted and the constituting are one and the same thing.1 This
assumption—that constitution entails identity (henceforth, CA)—makes for
cases in which supposedly identical things differ as to their essential
features: for example, it seems that my desk could have one of its parts
replaced without ceasing to exist, unlike the sum of its components or its
constitutive matter.2
I shall attempt here to
preserve CA, which underlies the way in which we count, as well as an ontology
consisting of “commonsense” continuants: objects capable of surviving
mereological modification (such as, tables, trees, and tigers). I, therefore,
not only defend CA, but also provide an account of how it is possible for an
object to change the sum/aggregate of parts to which it is identical. The
resulting dualistic conception of identity ultimately requires me to refine the
principle of the Transitivity of Identity (TI).
The concept formed when
“considering anything as existing at another time,” as Locke characterizes
judgments of diachronic identity, is to be regarded as our “popular”
under-standing of identity, defining the relationship holding between (e.g.) the
present author and a certain boy but not between that boy and Winston Churchill.
It is this notion that entails the existence of the mereologically alterable,
such as the boy who was to be the present author. In contrast with it, there is
the “strict” sense in which things may be identical, CA, which makes for
ontological parsimoniousness and, thus, entails our standard counting procedure:
we do not tally as two a sum or aggregate of parts and that which it
constitutes. To abdicate one of these concepts, we would have to countenance
either expanded inventories or the loss of the belief in commonsense
continuants.3
I use Roderick Chisolm’s
terms here only because, being familiar to identity theorists, they readily call
to mind the notions under discussion. They are not intended to indicate a
preference towards the strict sense of identity. On the contrary, I hope to show
how a conceptual scheme can accommodate both, as ours seems to have awkwardly
done. Unlike other current CA-preserving treatments, the solution to PMC that
emerges violates neither our commonsense beliefs regarding relational and
mereological change nor the spirit of ontological parsi-moniousness behind CA.
Its cost, if you can call it that, is the acceptance of our hitherto
unacknowledged reliance upon a dualistic conception of identity. The adjustments
to TI thereby required make for a conceptually tolerable situation, that is, one
in which the PMC does not arise.
1.
Consider the following
version of the PMC taken from the writings of the Stoic Chrysippus. A man named
Dion undergoes the amputation of his left-foot. Assuming that he is identical to
his body, we may then ask: what is the relationship between Dion, the amputee,
whom we shall call “Leon,” and “Theon,” the erstwhile aggregate of all
of Dion’s body parts minus his left foot?4 Shall
we say that it is Dion who is (has become) the amputee Leon, Theon having
perished? Or is it Theon to whom Leon is identical, Dion having perished? A
third option is that both survive the operation as the amputee. I believe that
the third answer is the correct one. Before developing it, let us consider the
problems attendant upon the alternatives.
Assume that Dion survives the
operation. He is, thus, constituted by Theon, assuming that it survives as well.
CA entails that he is identical to Theon. But, given the Necessity of Identity
(NI), CA also entails that Dion is identical to that aggregate of bodily parts
of which he was constituted before the
operation, of which Theon was only proper part. Given TI, it follows that Theon
is identical to that of which he was once a proper part—something from which
he was once distinct, which seems to
violate the Necessity of Nonidentity.
To preserve CA, it may be
responded here that Dion is not
constituted by what was formerly a proper part of himself, that is, Theon.
Strictly speaking, it is a new torso/appendages sans left foot (Theon2 as it were) that emerges from the
operation, since had Theon survived it, he would have become a person, into
which a proper part of a person could not develop. A non-person, on this line,
is essentially one. Moreover, the proper parts of a person, such as Theon, are
not themselves persons: otherwise each person would be ‘made up of’ many
other individuals of the same sort as himself.5
A “Cambridge” or
relational change, thus, causes Theon to cease to exist. It is not possible for
him to go from being a part of a person to being that person himself. He exists
only so long as he remains a proper part of Dion. But what explains this
inability on the part of Theon? Having lost none of his parts, why would Theon
not survive the operation?
Suppose Dion himself had
failed to survive the operation. Would we not want to say that Theon would have
become Dion’s corpse? And if so,
shouldn’t be accept that Theon can become Dion himself? What could explain his
having the prospect of being the former while lacking the possibility of
existing as the latter? Moreover, it seems uncontroversial that in some cases a
proper part of thing does survive as
long as the thing itself. We have the depleted military unit, the rump state,
the eroded dune, and the maimed limb. Why, then, would Theon’s ceasing to be a
proper part of a whole drive him out of existence? There does not appear to be a
relevant dissimilarity between the cases.
The assumption here, it
should be emphasized, is that the property of belonging to the sort
‘non-person’, is inessential to its bearers: that a non-person may survive
as a person (and vice versa, making ‘person’ a “phase” sort).6
But this assumption is born out by our experience with persons/animals who, even
in the normal course of things, appear to have non-persons/non-animals as stages
of their life histories (viz., zygotes). And if what became Dion at some point before
his operation was a non-person, why wouldn’t the same hold true of him after
the procedure?
The defenders of the above
proposal may reply that there are other substance sorts to which Dion belongs
but Theon doesn’t, such as ‘human’, ‘human body’, ‘animal’,
‘animal body’, and ‘organism’ (so that, given the essentiality of these
sorts, Theon could not exist as one of their members, not having always
been so).7
But these sorts, I would maintain, must also be phase sorts otherwise it would
not be possible that things not of them should become their instances, which, as in the case of persons, seems
embryologically false. Reclassifying them as such seems preferable to abandoning
the idea that it is a zygote that once emerged as the person/human/human
body—whatever sort to which Dion belongs. That Theon’s existence, like a
zygote’s, predates its becoming a person/human is explained by the fact that
substantially it is a sum of subatomic particles, existing just as long as they
do (though not necessarily being a torso/appendages minus left foot). Citing
this fact is the metaphysically best way to answer the question “What is Theon?”
though, given the principles of composition associated with various phase
sortals typically used in individuating, it is not the most popular
characterization. (As explained below, continuants, the “articulated”
objects of everyday experience, which supervene upon the arrangement of certain
sums of subatomic particles, would be diachronically “linked” phases of such
sums, having the same ontological status as the supervenient entities of other
types, for example, moral and economic values.)8
These considerations, it must
be conceded, are not decisive; those under attack may reject the above paring
down of the list of substance sortals and dismiss the above examples as question
begging. But, as defenders of CA, (ontological “neat freaks,” if you will)
they cannot disregard Ockham’s Razor. And across time their account does
“multiply entities beyond necessity”: witness Theon and Theon2, no less an increase in objects
than that entailed by CA’s denial. Thus, the idea that Dion alone survives the
amputation is not an option to those who would not violate the spirit, if not
the letter, of CA.
Perhaps Dion doesn’t
survive. Is it Theon alone who is the amputee? This would be the case if
“mereological essentialism” (ME) were true: if an object could not survive
the loss of any of its parts.9
But this doctrine entails a wholesale revision of the ordinary way of viewing
mereological change and, in the above case, would make amputation tantamount to
homicide. Moreover, as with the just considered view, it defeats the purpose of
preserving CA: whereas abdicating CA multiplies “beyond necessity” the
objects one must synchronically judge to exist, ME allows things to ‘pile
up’ needlessly over time. (“And you thought we’d been living in the same
house all these years.”) Thus, it too is a non-starter for those concerned
with ontological parsimoniousness.
In sum, the first two
solutions to the PMC exaggerate the ramifications of, respectively, relational
and mereological change. Moreover, both are in need of trimming by Ockham’s
Razor, something a view put forth by a defender of CA should not require.
2.
Defending the view that Dion
and Theon both survive as the amputee involves delimiting the sense of numerical
identity that allows for the possibility of a proper part of an object,
something that is at one time distinct from it, becoming that object itself.
Theon, I propose realizes, as the result of the amputation, his potential of
becoming Dion. Both survive the operation by becoming one, since it is in the
nature of a person to become, under circumstances such as those following an
amputation, one of his proper parts. Theon, for his part, is the same entity as
before the operation in the way that a regiment’s only battle surviving
battalion is still itself even though now being (what is left of) its unit.
Alternatively: Theon survives the amputation in the manner of a hand minus its
thumb, which, following the latter’s amputation, is all that its owner has
left of his hand. All of these are true judgments of “popular” or
“diachronic” identity as that concept is explicated below.
But if Theon survives as Dion,
is it not true, as noted above, that Dion’s former aggregate of parts is (now)
identical to a part of itself? In one sense yes in another no, as the following
definitions should make clear.
CA, which makes up our strict
sense of identity, pertains only to (judgments of) “synchronic” identity,
identity at a single time (henceforth
S-identity). Thus, we have the following Aristotelian principle of
“individuation”:
(SI)(x) (y) (t) {@t, x =s y <—> ($m) [@t, (Cmx & Cmy)]} (where t is a time, ‘m’ is either a mass term or the name of a sum or aggregate of parts, and ‘C’ denotes the relationship of “constitution,” as defined below, that holds between a material object and the sum/aggregate of parts of which it is ‘made up’.10
In words: Necessarily, at any time t, x and y are synchronically identical just in case at t they are constituted by the same sum/aggregate of parts.
Cmx is explicated as follows.
Constitution is generally treated as a one-to-one relationship. Thus, in the
case of something being constituted by a sum (e.g., a sum of stones constituting
a fence) rather than an aggregate, the sum needs to be taken as a singularity:
an x such that.…
In the case of ultimate
constituents or mereological atoms—the parts that do not “decompose” into
“smaller” parts (the fermions of contemporary physics)—we should have to
say that a collection thereof constitutes itself. (A demonstration: Everything
is made of something. A thing’s atomic parts are not constituted by other
parts. Therefore, they make up themselves.) Otherwise, it would not be possible
for such an aggregate to be S-identical to anything else that it constitutes,
there being then no sum of parts of which each is made up. Since in the case of
non-atomic parts we need not make this assumption, consti-tuting is being
treated here as non-reflexive. Further, it is obvious that an entity may be made
up of more than one sum of parts: the top, drawers, and legs constitute the
table but since they are made up of parts themselves…, making Cmx transitive.
Finally, I assume that constituting is asymmetrical.
Thus:
(C) Cmx iff m and x spatially coincide and m can survive mereologically unaltered without being x.11
SI defines the identity of
constituted entities in terms of sameness of constitution, that is, identity of
constituting entities, which can, of course, be constituted themselves. To avoid
circularity here, the identity of constituting entities, thus, must be defined,
à la Locke, in terms of something unconstituted, viz., (a sum of) subatomic
particles. Thus:
(SM)($m) @t, (Cmx & Cmy) <—> ($S) (z) @t, [(zÎS & z >> m) . (z >> x & z >>y)] (where S is a set of fermions, ‘Î’ denotes the membership relationship of standard set theory, and ‘>>’ stands for the parthood relationship of standard mereology).
In words: Necessarily, x and y are constituted by the same thing iff they share all of their subatomic parts.
Numerical identity may,
therefore, be explicated mereologically: it ‘comes down to’ the sharing of
subatomic particles by a constituting entity and that which it constitutes.
Being an equivalence
relation, SI meets the minimal standard for being the relation of identity. If x
is constituted by the same sum/aggregate as y, then y is constituted by the same
sum/ aggregate as x, making SI symmetrical. If there is some sum/aggregate
constituting at a time t x and y and that same sum/ aggregate constitutes at t y
and z, then x and z are then constituted by the same thing, making SI
straightforwardly transitive. If, on the other hand, the time at which that
sum/aggregate constitutes x and y is not the same as the time at which it
constitutes y and z, the transitivity for SI is established by one of the
unconventional transitivity principles discussed below. Finally, if x and y are
constituted by the same sum/aggregate, then x is constituted by the same
sum/aggregate as itself, making SI reflexive. SI is not, however,
straightforwardly one-to-one, as identity is supposed to be; an object can be
constituted simultaneously by more than one thing. This defect may be remedied,
however, by pointing out that, assuming the existence of mereological atoms,
there is only one sum of which an object (and each one of its “intermediate”
constitutions) is “ultimately” constituted. (CA entails that this sum is
that to which “they” are ultimately identical.)
A familiar objection to such
an account of identity, however, is that it fails to meet another requirement
for being the identity relation, viz., obeying Leibniz’s Law (a.k.a. the
Indiscernibility of Identicals). How could a sum/aggregate of parts be identical
to that which it constitutes when its essential features or “persistence
conditions”—how it would come into/go out of existence—are different from
those of the latter? As noted above, a sum/aggregate of parts cannot survive the
loss of one of its members; ME is not thought to apply to the composite objects
of everyday experience. On the other hand, the constituting could survive
mereologically unaltered the complete destruction of the constituted while the
latter could fail to exist without losing any of its parts. Again, how could
this difference exist if they are the same thing?
Here it is necessary to
remind ourselves that a sort’s persistence conditions have only to do with
judgments of identity across time. Our understanding thereof enables us to
determine whether or not one of its instances, existing at a given time, is
identical to something extant at another
time. Therefore, it would be inappropriate to apply such knowledge in situations
in which our concern is only with what is presently the case: a sort of
“category mistake.” Leibniz’s Law, as a standard for judgments of
S-identity is thus applicable sans consideration of a thing’s modal
properties.12 Properly under-stood the concept
of essence belongs only to our so-called loose and popular concept of identity.
A fuller explanation of just how it facilitates judgments of diachronic identity
awaits exposition of that notion.
The PMC arises from applying
the above principle of individuation to judgments of “diachronic” identity
or identity across time (identity in
the “loose and popular” sense, henceforth ‘D-identity).13 Unless one is willing to embrace
ME or “temporal parts theory”—both of which are at odds with our ordinary
way of viewing change—one must define D-identity as holding between objects
constituted by distinct sums of parts, that is, entities that were at one time
not S-identical (such as Dion and Theon).14 We should abdicate the
commonsense notion that the objects of everyday experience can survive gain or
loss of parts only if this relation proves indefinable. I propose the following
definition:15
(DI)(x) (y) {x =d y <—> ($t) ($t’) ($m) ($n) [(@t, Cmx & @t’, Cny) & (Pmn v Pnm)]} (where ‘t’ and ‘t’’ denote times, m and n are sums of parts, ‘C’ denotes the relationship of constitution as defined above, and ‘P’ denotes the relationship of “perpetuation” that holds, as specified below between sums of parts.
In words: Necessarily, x and y are diachronically identical just in case that of which either one is constituted is the “perpetuation,” as defined below, of that of which the other is ‘made up’.
The sums/aggregates of parts
of which a persisting object is successively composed make up the same thing,
that is, each sum/aggregate is D-identical to every other, though there may be
elements of one not shared by some of the others. Minimally, what we expect of a
temporally ordered series of such sums is that each member becomes its
“successor” by either adding to, subtracting from, or retaining its parts.
Further, it is supposed that each “descendent” has undergone mereological
alterations and/or reconfigurations that are consistent with the persistence
conditions of the sortal under which it may be subsumed along with all of its
“ancestors” (assuming a sortal to specify the persistence conditions of its
instances, the types of changes they can undergo without ceasing to fall under
it).
Thus the relation of the
perpetuation is defined as follows:
(P) (x) (y) {Pxy <—> ($t) ($t’) [(y@t & x@t’) & (xey v yex) & ($F) (@t’, Fx & @t, Fy)] v {($S) (xÎS & yÎS) & (w) (u) [(wÎS & uÎS) & w/u] —> [weu v uew) & ($F) (@t’, Fw & @t, Fu)]} (where x, y, w, and u are aggregates or sums of parts, F is a sort, and ‘e’ denotes the inclusion relationship of Lesniewskian mereology, ‘@’ denotes the exists at relationship that holds between a sum of parts and an instant of time, S is a set of sums of parts, ‘e’ denotes the membership relationship of standard set theory and ‘/’ denotes the relationship that holds between a pair of sums/aggregates of parts w & u iff ($t) ($t’)(w @ t’ & u @ t) & t’ is t’s “immediate successor,” i.e., t precedes t’ & between t and t’ an arbitrarily short amount of time elapses, assuming here that time is a dense continuum).16
In words: Necessarily, x is the perpetuation of y just in case y antedates (or exists simultaneous to) x and both belong to a temporally ordered series of aggregates or sums of parts each member of which belongs to the same sort and either includes or is included in its immediate predecessor.
D-identical entities are one
and the same thing in the sense that one is a “perpetuation” of the other.
(Think of the Olympic flame being passed from torch to torch. Cf. below for a
discussion of the awkwardness of using ‘the other’ in this context.) This
relation holds in cases such as that of Theon becoming Dion, where an aggregate
of parts retains its members and configuration while coming to meet the criteria
of a new phase sortal as the result of a relational change, cases where a sum of
parts retains its members while it is subsumed under a new phase sortal due to a
reconfiguring of the same (such as when a piece of clay is molded into a vase)
or cases where a series of distinct sums of parts, some of which may not overlap
with others, are the stages of a single “perpetualization-series”
(P-series). (The life of an organism may be seen as such.)
Like SI, DI also qualifies as
an equivalence relation. It is obviously symmetrical. And since the time at
which a perpetuation of x exists need not be distinct from the time at which x
exists, we allow that everything is (trivially) the perpetuation of itself,
making DI reflexive. This feature of P also makes for DI’s transitivity: in
fission cases (which are not straightforwardly transitive, being covered by the
left disjunct of B’s consequent below) where an S-identical x and y ‘go
their separate ways’, becoming S-distinct, P dictates that x and y are
D-identical (each belongs to the other’s P-series; in effect, S-identity
entails D-identity). Like SI, DI is also not straightforwardly one-to-one; an
object may be D-identical to more than one thing, as in fission cases. But, as
with SI, there exists a remedy for this defect, since there will be only one
P-series every member of which a
continuant is going to be D-identical and S-identical
to: the series of which it is the sole “full-timer,” which is determined by
its essence. (More on this below.) To count what has existed during a period of
time, we should tally the P-series that have had stages extant therein, not
reducing the result by subtracting from it the number of instances of
D-identity.
DI can hold “transtemporally,”
that is, between entities separated by an interval of time. André Gallois
argues, however that this feature disqualifies it from being an identity
relation. Transtemporal relations, such as ‘being the same height as’,
according to Gallois, need not hold at any specific time, unlike the identity
relation.17 But
if there is no transtemporal identity relation, if SI is the only legitimate
identity relation, as Gallois maintains, then there is no “principle of
unity” to generate mereologically alterable persistents, the existence of
which he endorses by eschewing ME. The PMC, to which Gallois takes himself to be
providing a solution, would not even arise were there not some reason for
thinking that temporally separated entities, such as Dion before his amputation
and (what seems to be) Theon after it, though not related by SI, are nonetheless
identical: stages of the same person despite having once been distinct. Without
something like DI, we would have no reason to maintain the problematic view that
distinct sums of parts can be identical. Our position would, thus, be tantamount
to ME.
If two distinct sums are
linked across time by DI, they are as identical as those connected at a time by
SI: the former is not to be taken as identity only in a “loose” sense.
Moreover, the suppression of reference to a time in typical statements/judgments
of diachronic identity should not be mistaken for the absence of a temporal
element therein. Dion comes to be identical with Theon at the time at which the
amputation is performed. Thereafter, it is true at every time that they are
D-identical, which is why that goes without saying.
Armed with the above
distinction between DI and SI we return to the PMC. Consider the following
argument based on Chrysippus’s puzzle:
(1) At t1, Dion = S (the aggregate of parts of which Dion is constituted at t1) (CA)
(2) At t2, Dion = Theon (the aggregate of parts of which Dion is constituted at t2) (CA)
(3) \ (Dion = S) & (Dion = Theon) (Adjunction, 1 and 2, NI)
(4) \ Theon = S (TI, 3)
Taken as a statement of
S-identity, (4) is false, since there is no time at which Theon is constituted
by S, prompting a search for a fallacy or a false premise. But it need not be so
construed. Understood diachronically, (4) is true: at t2, Dion, that is, what was
at t1 S-identical
to S, has become Theon in virtue of being that as which S/Dion has perpetuated
itself. (At t2, the same may be said of 3’s
left conjunct.) The moral here is that identity is not unqualifiedly transitive:
inference principles involving the concept of identity must reflect the
difference between SI and DI.
Thus we have as valid
transitivity principles:
(A) (x)(y)(z)[($t)
(@t, x =s y) & y =d z] —> (x =d z)
(B) (x)(y)(z)(x =d y
& y =d z) —> [($t)
(@t, x =s z) v (x =d z)]
(C) (x)(y)(z)[($t)
($t')
(@t, x =s y & @t',
y =s z) —> (@t (i.e.,
t'),
x =s z v x =d z)]
Since 1 and 2 are statements
of S-identity, the appropriate principle to apply in the above argument is C,
which together with Theon =s S @ t1
or t2
yields the (true) conclusion that Theon is D-identical to S. The (false)
conclusion that Theon is S-identical to S, which is what might prompt a
rejection of CA, is arrived at when the following invalid principle is applied
instead:
(D) ($t) ($t’) (@t, x =s y & @t’, y =s z) —> (@t/t’, x =s z)
D comes out true only in
those cases in which the time at which x =s y is the same as the time at which y
=s z. There:
($m) ($t) @t, [(Cmx & Cmy) & Cmz].
C reflects the fact that this
possibility may not be realized: that z may instead be that as which x has
perpetuated itself or vice versa, eliminating a reason to abdicate CA.
A and B may be understood as
follows.
A is appropriate to cases in which:
($m) ($t) [@t, (Cmx & Cmy)] & (Pyz v Pzy)
which
entails:
Pxz v Pzx.
B applies to situations, such
as those involving fissioning or fussioning objects (the Ship of Theseus comes
to mind) in which:
(Pxy v Pyx) & (Pyz v Pzy)
which
entails:
($m) ($t) [@t, (Cmx & Cmz)] v (Pxz v Pzx).
A’s
invalid counterpart is:
(E) ($t) [(@t, x =s y) & (y =d z)] —> (@t, x=s z)
E’s
consequent is false unless:
($m) ($t) @t, (Cmx & Cmz)
which
is not guaranteed by the truth of its antecedent’s conjuncts.
It has been argued that the
PMC may be generated without assuming TI.18
The nub of Chrysippus’s puzzle, on this view, is that Dion seems capable of
surviving the loss of one of his parts while S (to which, according to CA, he is
identical) appears incapable of undergoing mereological alteration. But the
question of whether or not identity is transitive is implicit therein, since it
raises the issue of the nature of Dion’s survival: following the amputation of
one of his members, does he live on as
the remaining proper part or not? A negative answer to this question entails, as
we have seen, counterintuitive results. An affirmative one, as we have also
seen, raises the question of whether or not a whole has become one of its proper
parts and thus the issue of TI. Alternatively, the claim that S cannot survive
mereological alteration seems based upon the notion that, given
TI and CA, were S to survive as Theon, the latter would be identical to Dion,
contradicting the initial assumption of their distinctness. Solving the PMC,
thus, necessarily involves taking a stand on this issue.
Reflecting upon the
difference between SI and DI also leads to a clarification of NI. If, at any
time t, x =d y, then at any other time t’, x =d y:
each having become a member of a P-series, they will always belong to it. But
if, at any time t, x =s y, then at any other time t’,
possibly, x =s y. Constitution can be a “fleeting” relationship:
it may hold only for an instant. Perpetuation, on the other hand, links its
relata as long as they (it) exist(s). Thus any conceptual scheme, such as our
own, that entails the existence of the mereologically alterable and
“Ockhamistic” counting must allow that two things can become one and
what is one two, as Dion becomes D-identical to that from which he was
S-distinct and S-distinct from that to which he was S-identical.
The SI/DI distinction exposes
the limited role CA plays in our judgments of identity. CA allows for the
individuation at a specified time of any object existing thereat. Chrysippus’s
puzzle arises from overextending this role. We should not expect D-identical
objects to be constituted of the same portion of matter or sum of parts. It is
the assumption that they must be that leads one to reject the notion that at t2 Theon—that is, Dion at t2—is identical to S—that is,
Dion at t1. Dion is at t2 D-identical to that from which he
was once S-distinct. Theon, for its part, has become (D-identical to) that which
it was not, which is only to say that it has realized one of its
possibilities—being Dion.
It is in the nature of a
commonsense continuant to remain identical to itself while changing that to
which it is S-identical. Such is the process of becoming. Our understanding of
D-identity reflects this fact. The career under a sortal of a single object is a
series of perpetuations of that to which it was initially S-identical. (Think
again of the Olympic flame’s journey.) In that sense, its identity does not
change over time: it remains D-identical to each one of the things to which it
is ever S-identical (Cf. B above). At the same time, the possible fleetingness
of S-identity is implicit in our understanding thereof: it is taken to hold, in
contrast to D-identity, at a single time. To acknowledge as much is not to
disavow NI, since, as shown above, DI provides us with a sense in which an
entity in surviving mereological alteration remains identical to that of which
it was formerly constituted. It is rather to divorce CA from the notion of a
persisting thing, which is what requires the elaboration of a concept of
identity that provides for an ontology of commonsense continuants.
The present position is,
thus, importantly different from that of George Myro’s, in that it allows for
a sense in which NI is true.19 Whereas Myro would want to deny (given what he says regarding a
similar case discussed below) that Theon is in
any sense identical to Dion unless the former constitutes the latter, it is
maintained below that Theon prior to the
amputation is D-identical to Dion after it, the former having perpetuated
itself as the latter (having, because of the operation, ceased to exist as an
arbitrary undetached part of a person and become a person itself, all the while
continuing to be the same sum of parts). That is why we are not forced to
restrict Leibniz’s Law to what Myro calls “time-free” properties. In his
case of a vase-shaped piece of wax that is to be reformed as a bust, the vase,
just as much as the piece of wax (after all, according to CA, they are one and
the same thing) will, say, be on the mantle following
the reshaping. That is so because the vase is S-identical to something—the
piece of wax—that, following the reforming, will be D-identical to
something—again the piece of wax—that is going to be S-identical to the
bust, making vase and bust D-identical—the vase will become a bust. (Cf. A
above.) Again, by accommodating distinct notions of identity, we can allow that
there is a sense in which the vase is not identical to the bust, since the wax
never simultaneously constitutes both items, but that across time they are, in
another sense, identical—as ‘stages’ in the ‘career’ of that which
each is at some time constituted, the piece of wax. We have a parallel here to
the case discussed above of the zygote becoming a person, presupposing in this
case that the substance sort is ‘piece of wax’ (‘vase’ and ‘bust’
designating phases thereof).
What role, then, does the
notion of essence play in our understanding of identity? As noted above, the
essence of a sort allows for the counting of its instances across time. Here we
must distinguish between the questions “Are x and y the same S?” and “Is x
D-identical to y?” An affirmative answer to the former entails that x and y
belong to the same S P-series; the
latter does not: here each must only be constituted by something that belongs to
a P-series in which that which makes
up the other is also a ‘link’ (as with the just mentioned vase and bust).
Our understanding of S’s essence provides us with a way of determining of any
temporally separated x and y whether or not one has persisted as the S that the
other was, being a single instance of the sort. The proper use of such features
is in determining the co-members of the P-series to which an object belongs,
that is, the sums/aggregates of parts to which it has been or will be
S-identical. In other words, an object’s essence allows us to make “backward
or forward looking” judgments as to the extent of its P-series, giving us an
answer to a question such as “Will the bust be a member of the vase’s
P-series?” (A P-series extending itself to any time at which its full-timer is
constituted.) To say of an S that it is essentially E is to say that if it is to
be D-identical to any future S, it must retain its E-ness. It is not to say that
it will not be D-identical to any
existent to come unless it remains unchanged in this respect.
It may be objected at this
point: How could the vase and the piece of wax be modally distinct if they share
such time-bound properties as being on the mantle as a bust after the
reconfiguring of the latter? Let us say, following a suggestion of André
Gallois,20
that x will be F at t iff x is at some time before t S-identical to something
that will be F at t. By that criterion, the vase will be on the mantle following
the reconfiguring along with the piece of wax—whose reconfiguring makes for
the vase’s. Further, to account for the modal difference between them, allow
that x is “independently” essentially (I-essentially) F iff x is F in any
possible world in which it exists and that x is at t “dependently”
essentially (D-essentially) F iff x is at t S-identical to something that is
independently essentially F while not itself being I-essentially F. If it is
possible, as the believer in occasional identity insists, for the piece of wax
and the vase to be temporarily identical, then it is also possible for the
latter to be essentially a piece of wax only
for a time—that is, for the piece of wax to “lend” the vase its
essence. In “borrowing” it, the vase also acquires the above time-bound
property.
To make this point employing
the conceptual resources of my own view, we should say that, having become a
member of the P-series that is the piece of wax’s career, the vase becomes
D-identical to any of its future stages—including the bust—thus its sharing
of the piece’s time-bound properties. For its part, the piece of wax is going
to be S-identical to every member of that series; it is its sole full-timer, the
vase being only a part time member thereof, which establishes their being
modally distinguishable. But, to repeat myself, this fact does not make them
S-distinct. To draw such an inference is to misuse the notion of an essence,
employing it to compare things existing simultaneously.
There is a problem, as Hume
and others noted, of speaking of diachronically identical objects, as if a plurality of things could really be one and the
same.21 The need for
identifying seems otiose if we are dealing with only one thing; it should be
resisted if we are not. What sort of thing could be the subject of a true
D-identity statement that was not pointless? It seems that either any instance
of the D-identity relationship does not (really) have relata, in which case a statement thereof is uninformative, or no
such relationship exists.
A solution to this problem
was indicated above. The relata of a true D-identity statement can be a
plurality in the sense that they may be distinct sums/aggregates of parts. They
are yet united in the sense that one is a perpetuation of the other: it is that
by which its “ancestor” has temporally extended itself. That is not to say that each is a distinct temporal
part or “stage” of a “perduring” object, an entity that is wholly
present at no single moment of its existence.22
Rather, each perpetuation is the object itself, being D-identical to every other
one of its stages, despite their being (in some cases) mereologically distinct.
Transitivity principle B captures the sense in which it is possible for an
object to “endure,” that is, be wholly present at each moment of its
existence. The temporal parts that make up a unified particular, on the other
hand, are generally thought of as being only “nomically linked,” each
‘giving way’ to its successor—something from which it is distinct. Thus,
they would not constitute a perpetuation chain, where a relation of identity
holds between temporally contiguous sums of parts.
DI is thus meant to do for
“endurantists” what David Lewis’s “I-relation,” that is, the “R-relatation,”
(assuming these are necessarily coextensive, as Lewis maintains) does for “perdurantists,”
viz., provide a principle of unity for objects existing at distinct times.23 They
share the same formal characteristics—both being symmetrical and reflexive,
neither being (straightforwardly) transitive—differing only in their relata.
(And Lewis could even help himself to the following perdurantistic version of B:
“If A is I-related to B and B is I-related to C, then either A is I-related to
C or there is some time at which A and B share a stage, as in cases of fission
or fussion.”) But, insofar as the relata of those “objects” standing in
(an instance of) the DI-relation better accord with our commonsense ontology, DI
is to be preferred as an explication of diachronic identity (with the foregoing
having obviated the need to fall back upon the perdurantist’s ontology).
In sum, the above solution to
Chrysippus’s puzzle preserves CA, NI, and TI, the latter albeit as a set of
fine-grained principles rather than a single dictum. DI, for its part,
establishes a sense in which the idea of a whole becoming one of its proper
parts is unproblematic, providing for commonsense continuants. Our concept of
identity has been seen as a package, containing both the notion of an object’s
dwelling and the idea of its ability to exchange its residence. It has been
further shown how it is possible to conceive of the world in terms of this
dualistic understanding of identity.
Notes
*I thank Karen Bennett, Greg Ray, David Sanford, and Robin Smith for the incisive comments and criticism they made regarding the version of this paper that I presented at the 1999 APA Central Division Meeting. I am also grateful for the helpful correspondence of Lynne Rudder Baker, Michael Burke, Frederick Doepke, Trenton Merricks, and David Oderberg.
1 See Rea (1995a) for a discussion of the various forms the PMC takes and the assumptions behind each.
2 A sum of parts exists iff the parts do, whereas the aggregate thereof exists just in case they remain connected one to another and only one to another: between any two of the parts there being a series of spatially contiguous parts with no part being thereby joined to anything else. For the most part, we may ignore this distinction and speak of the sum and/or aggregate (sum/aggregate) of parts of which an entity is constituted. See Sharvey (1969) for a defense of the principle that a sum (what he calls a “class”) is mereologically unalterable. Myro (1985, 405–407) presents a dissenting view. Regarding aggregates, we follow Locke who writes of them (under the terms “mass or body”): “and whilst (its atoms) exist united together the mass … must be the same mass or body, let the parts be ever so differently jumbled. But if one of these atoms be taken away, or one new one added, it is no longer the same mass or body” (1975, ch. 27, sec. 3). Olson (1996b, 376), in rejecting CA, bypasses the issues addressed below, pursuing instead the question of how materially coincident sums (as with a lump of clay and the bust it constitutes, both of which are made up of the same subatomic particles) could differ in terms of their respective persistence conditions. But one might think that “things can compose two different material objects with different persistence conditions” because one of the compositions is a sum having its parts essentially and thus to be distinguished in kind from the mereologically alterable object which it (in turn) composes (as in atoms composing a collection of stones composing a wall). Thus, there does not appear to be a non-question begging way of avoiding a discussion of the relationship between those things which can and those things which cannot survive a change in parts.
3 Here we have the makings of a transcendental argument spelling out the conceptual requirements of our “folk ontology,” establishing the conditional necessity that if the commonsense view of what exists is correct, there must be two disparate ways in which things can be one and the same—an obvious point in favor of the view of identity developed below. Arda Denkel (1996, 89–90) denies CA without rejecting standard inventories by positing a distinction between being non-identical and being distinct. A vase and the glass constituting it are not going to count as two things, on his view, because, though non-identical objects in virtue of the differences in their essential properties, they are not distinct individuals, since only the vase has the status of being an individual. In drawing such distinctions, he sees conceptual space where I can make none out. Thus, I pursue an alternative defense of a sparse ontology.
4 Substance dualists or those favoring a Lockean approach to personal identity may thus reformulate the question asked as “Does Dion’s body survive to become the body of the amputee?” (leaving aside the question of whether or not Dion is the amputee) or “Is the amputee’s body Theon?” taking the ensuing discussion as one concerning bodily rather than personal identity. Entities such as Theon are often referred to as “arbitrary undetached parts.” The term ‘arbitrary’ refers to the fact that such things are rarely the objects of our attention, unlike members such as a hand. Cf. Van Inwagen (1981) for an argument opposing their existence. To generate the version of the PMC presented here, I assume that this argument fails of its purpose. But even if it does not, there still remains the general problem of how the mereologically stable—Dion’s original aggregate of parts—can be identical to the mereologically alterable—Dion himself: whether Theon existed before the operation or not, Dion has become identical to something from which he was distinct (it is just that if Van Inwagen is correct Dion has become identical to something that did not even exist before the operation rather than a proper part of himself).
5 Burke (1994, 134–139) advances this novel thesis. Geach (1980, 215–216) challenges the argument’s “maximality” assumption.
6 CF. Burke (1994, 135–136) and Carter (1990, 104–105) for a discussion of how to classify ‘person’ as a sortal. A phase sortal would be one such as ‘adolescent’ that denotes a period out of which a thing may pass without ceasing to exist. Carter (1999), Baker (1999), and Olson (1999) debate the implications of treating ‘person’ as a phase sort.
7 In response to Burke (1994, 136). The alternative sortals that Burke lists appear to meet the definition of a phase sortal as well as ‘person’ does. If so, he may be forced to engage the question of how to classify it after all.
8 See Olson (1997a) and Denkel (1996, 87–89) for additional argumentation against Burke’s position. Cf. Sosa (1993) and Allen (1998) for a discussion of the ontological status of the supervenient.
9 The classical proponents of ME are Peter Abelard in D. P. Henry, Medieval Logic and Metaphysics (London: Hutchinson University Library, 1972); G. W. Leibniz, in New Essays Concerning Human Understanding, book 2, ch. 27 (Cambridge: Cambridge University Press, 1996); Thomas Reid, “On the Intellectual Powers of Man,” Essay 3, ch. 14, in The Works of Thomas Reid, edited by Sir William Hamilton (Bristol UK: Thoemmes, 1994); and G. E. Moore, “External Relations,” Philosophical Studies (Paterson, N.J.: Littlefield, Adams, and Co., 1959), 287–289. Amongst contemporary philosophers, Roderick Chisolm is its best-known defender in Person and Object (LaSalle: Open Court Publishing Company, 1976), 145–158.
10 Oderberg (1996, 147) speaks of “individuation conditions”—ways of ‘picking out’ the members of a sort and differentiating them from each other and the instances of other kinds—as being “synchronic identity conditions.” Lowe (1998, 33, 74–75) distinguishes between a “criterion of identity” for a sort—what makes for the differentiation of its instances—and its individuation conditions: a “principle of unity” that makes its instances countable. The distinction is not important insofar as objects designated by count nouns (‘table’, ‘horse’, and ‘person’) are concerned. Where things designated by mass terms (such as ‘piece/portion/quantity/part of gold’ or ‘hunk of clay’) are concerned, it does have significance, since they can be differentiated one from another but not counted: it makes no sense even to ask ‘how many pieces of gold are there in Fort Knox?’ since a piece of gold cannot be individuated as such but only as the piece of gold that constitutes or occupies something that can itself be individuated in its own right (e.g., a certain ring or a space-time position). Further, quantum theory has demonstrated the existence of entities (the “super-positioned” electrons contained in the shell of a neutral helium atom) that cannot be differentiated one from another—there is nothing in which their identity consists—although they can be counted. Lowe (1998, 70–71) calls these entities “quasi-objects.” I intend SI to be taken as a principle of individuation in Lowe’s sense.
Rea (1995, 528) calls SI the “identity assumption” while Simons refers to it as the thesis of “mereological extensionality.” Van Inwagen (1990) calls into question the existence of principles of composition for all but organisms. Refuting his skeptical arguments against principles that would allow for the existence of other natural objects and artifacts is beyond the scope of the present work. Those convinced that such an undertaking would prove unsuccessful may take the present essay as examining CA/SI as applied to the case of organisms. See Rosenkranz and Hoffman for a description of a set of such principles. See Noonan and Johnson for an exchange over the question of whether or not constitution entails identity.
11 Burke (1997, 15), Simons (1987, 232–233), and Lowe (1989, 81) all regard Cmx as asymmetrical. Burke and Simons take it to be irreflexive as well. C’s right conjunct is my emendation of Simons’ definition of Cmx: “(m) could survive (x’s) complete destruction,” (Simons 1987, 239) which is itself an emendation of Doepke’s analysis (1982, 54). Sans the change, constituting fails to be asymmetrical: a ship whose planks are replaced over time while the latter are destroyed survives, making it that which constitutes the planks (which obviously could survive the ship’s complete destruction). Without the addition of the left conjunct, moreover, this definition is still too broad, since a substance can survive the destruction of another substance without constituting it, as with the Statue of Liberty and St. Patrick’s Cathedral. Thomson (1998, 157) agrees that the constituted and the constituting are spatially coincident. Interestingly, though, she marks the “ontological difference” between them not by reference to the former’s being more “strong[ly] attached” to its form than is the latter (as in C) but, rather, by the latter’s being more strongly attached to its parts than is the former. I can think of no reason to prefer my approach to hers and the thought occurs that they may both be correct: perhaps a’s being less strongly attached to its parts than b entails its being more strongly attached to form than b and vice versa?
12 This charge appeared most recently in Baker (1998, 599–602). I take myself to be providing here a rationale behind the position of Myro (1986, 335), who excludes consideration of a thing’s essential properties in applications of LL. Note further that S-identity is not “identity relative to a sortal,” à la Geach (1980, 215–218), Griffin (1977, 177–185), and Chandler (1971). A vase and the piece of wax constituting it are S-identical simpliciter, not merely relative to a sortal (thing?) under which each falls. Cf. Rea (1995, 547). Denkel, in arguing against an Aristotelian principle of individuation, says that it conflicts with LL, allowing identical things to differ as to even their nonessential properties (1996, 59–60). But that a constituting entity has at one time (in one possible world) features that it lacks at another (in another) does not tell against LL. Moreover, “super-positioned” things are going to be indiscernible. Thus, the only way in which the “possibility” Denkel has in mind could be realized is if, per impossible, a thing could be at a distance from itself: the discernible things would have to be constituted by the same entity yet not spatially coincident. I conclude that there can be no conflict between (an individuation principle such as) SI and LL.
13 This is to say, having dismissed the above objection to SI (as well as the first two solutions to Chrysippus’s puzzle), the PMC is still in the offing unless it can be shown how it is that Theon can be identical to Dion without a sum of parts being constituted by a subset thereof. DI, as explicated below, is meant to address this concern.
14 See Heller (1990), Lewis (1983), and Oderberg (1993, chs. 3 & 4) for discussions of the doctrine of temporal parts: the view that an entity’s existence at any moment during its “career” is distinct from its being at all other times. An entity then is diachronically the sum of its temporal stages just as synchronically it is composed of its spatial parts. I would cite DI’s utility in solving the PMC as a “positive reason” for maintaining that, pace Merricks (1998), there are criteria of identity over time.
15 Merricks (1998), following Lewis (1986, 202), defines an “enduring” object as one that is “wholly present” at each moment of its existence. Such an entity lacks temporal parts. By contrast, a “perduring” object is said to ‘persist’ (a neutral term) in virtue of having temporal parts, the aggregate of which is said object. Since DI is meant to capture the sense in which things endure, I am committing myself here to “presentism”—the view that the present is the only time that exists—as Merricks (1995) has shown that the opposing view, “indexicalism”—according to which there exists times besides whatever happens to be the present time—is incompatible with the existence of enduring objects.
16 See Simons (1987, 18–24, 60–75) for a discussion of Lesniewskian mereology. I take it that P entails the “spatiotemporal continuity under a sortal” criterion of identity favored by some identity theorists. Cf. Hirsch (1982, 34–71). P is not meant to apply to masses, bodies, (in Locke’s sense) hunks, pieces/portions/quantities of stuff, sums, aggregates—entities of any type whose instances have their parts essentially. It is intended only to cover the mereologically alterable: complex objects whose persistence depends upon the persistence of the elements of masses, hunks, etc. If Zimmerman (1995, 82–85) is correct, homogenous instances of such things do not have informative diachronic identity criteria. Cf. Hirsch (1982, 133–137) for a less skeptical view of this matter. I am inclined to agree with Lowe (1998, 121–127, 154–173) that diachronic identity conditions for the complex objects of everyday experience entails the existence of “simples” whose diachronic identity is primitive or unanalyzable.
17 Gallois, 1998, 116–117. Gallois candidate for a pseudoidentity relation that is transtemporal is (TTI): (x) (y) [x =t y <—> ($t) ($t’)(z)(@t: z = x —> @t’: z = y)]. Not being symmetrical, TTI fails to be an equivalence relation and, thus, cannot be an identity relation either. But why the insistence on everything being identical with x being identical with y? Is it not enough that there is something that is identical with x at one time that is also identical with y at another? Such is the case with any continuant that is constituted at different times by distinct sums of parts. DI allows such sums to be one and the same thing and thus generates the folk ontology for which TTI does not provide.
18 See Rea (1995, 540–410) for an argument to this effect.
19 Myro, 1985, 391–393. Myro’s case of the vase and the bust parallels one presented in Thomson (1998, 152–153) as a counter-example to CA, except that in the latter it is the constituting entity’s persistence conditions that are seemingly violated, one of its parts being replaced. But, since the new set of parts is S-identical to something (the statue that endures the above replacement), we can use A here as well: the (portion of) clay that lately constituted the statue is D-identical to that of which the statue comes to be made up, the statue, having perpetuated itself, à la Dion, as one of its proper parts (plus an additional portion of clay).
20 Gallois, 1998, 79–100, 168–172.
21 Cf. Oderberg, 1993, 43–44.
22 Cf. Oderberg (1993, ch. 3) for a fuller discussion of the connection between the notion of a persistent and the doctrine of temporal parts. See also Lowe (1989, 78–83) and Mellor (1981, 127 ff).
23 Lewis, 1983, 58–61.
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