Master's Culminating Examination Papers:
- Continuously Recognizable Self-Perpetuation and Identity Paradoxes
- & Mādhyamaka Ontology and the Problem of Ultimate Analysis
- & Daoism and Computation
#
Prepared at the University of Hawai‘i at Mānoa, 2006–2008.
"For with much wisdom comes much sorrow;
the more knowledge, the more grief."
— Ecclesiastes 1:18
⁂
『識得本心本性
正是宗門大病』
"To know the original Mind, the essential Nature,
This is the great disease of our religion."
— 佛祖綱目卷第三十八
⁂
『古人の跡を求めず、
古人の求めしところを求めよ。』
"Seek not after the footsteps of the ancients;
seek what they sought!"
— Bashō
Table of contents:
Continuously Recognizable Self-Perpetuation and Identity Paradoxes
Introduction
In the discussion of vague objects in his Paradoxes,1 R. M. Sainsbury presents a modified version of the sorites paradox directed at the human being: A human being still exists even if he or she loses one molecule from his or her body. Losing one molecule cannot make the difference between existence and non-existence for a human being. Therefore, even if all your molecules are taken away one at a time, you will still exist even if none of your molecules do. However, it is absurd to suppose there could be a human being without a body; therefore, human beings do not exist.
In this same section, Sainsbury presents the familiar example of the ship of Theseus which is slowly replaced plank by plank. The reader is asked, "Did Theseus' ship survive?" If one had made a new ship of the discarded planks, "Does this have a better claim to be the original ship of Theseus?"2
In this paper I will show that both paradoxes can be defanged by creating more precise definitions of "human being," "ship," and other relevantly similar composite objects that are based on continuous self-perpetuating processes rather than static substances. The use of a more precise definition for these types of objects does not rely on any particular exotic ontology being the correct underlying metaphysical reality and is quite independent of whatever the particulars that underlie our world turn out to be. Once this more precise definition is in place, I will compare my solution to the problem with similar proposals about the nature of diachronic identity from the perspective of ontology and personal identity. Finally, I will show that paradoxes of the sort given by Sainsbury can be safely sidestepped by denying their assumptions.
Essential features of commonsensical notions of identity over time
The problem with using formal identity
Underlying the two paradoxes presented so far is the central question, How can there be things which are not the same as their material composition yet which nevertheless rely on their material composition for their existence? Another pertinent example in this regard is the river. Since at least the time of Heraclitus,3 philosophers have been familiar with the problem with supposing the material identity of rivers. A river cannot be just what makes it up at a particular time, since if we say that a river is the matter that makes it up, then we must agree with Heraclitus that one cannot step in the same river twice, because a river's material composition is in constant flux. At the same time, we commonly speak of rivers as though they were things that persist for years and years.
To begin, we should note that "same" by itself is an ambiguous term. In our most typical usage of "same," we only mean "same in certain respects." For to say that a river at one time is not the exact same in all its properties as the river at another time is tautological. Obviously, a river that exists at a later time has at least one different property than the first river--namely, the property of existing at a different time. Even if one were to discount existing at a particular time as a relevant or meaningful property, there is still the issue that if anything else in the universe has moved between the two times, then the first and second rivers are different with respect to their distance from the objects in the universe that have moved. Of course, such properties as the distance between one river and everything else in the universe are clearly not essential, intrinsic properties for the identity of a river, but the problem at hand is to determine which properties of the river are those that are essential for its being considered the same according to our common usage of the term. Thus, the "sameness" of being the same river (or the same anything else) at two different times must not mean "same in all respects" but only "same in certain relevant respects," and our task now is to discover what those relevant respects are.
One way to resolve this ambiguity and solve the problem brought up by Heraclitus is to say that ordinary references to sameness in rivers refers to sameness with respect to one of the river's formal physical properties even if its material make up varies. However this quickly runs into difficulties. Imagine that there existed perfect teleporting machines that could duplicate objects down to their most minute physical properties and that we used such a machine to make a perfect physical duplicate of the Earth's Colorado River on Mars. Each water molecule in the teleported duplicate would be positioned as the exact analog of our terrestrial river, and the banks as well would be perfectly copied. Nevertheless, in spite of being in every way like the Colorado River, our duplicate river would not be the Colorado River for the simple fact that it is located on Mars and not on Earth, which is commonsensically essential to the identity of the Colorado River.
Accordingly, we might next propose that geography or physical location is essential to the identity of the river. Unfortunately, this will just as quickly run into problems, since a particular river's banks are constantly changing and being eroded. Returning to our example, the Colorado River's banks were at one time on the surface of a plain, but now they are the bottom of a canyon. Thus, the formal characteristic shared by a river over time cannot be just the shape of its banks, since they are not the same over time. Nor can it be the generalized path of the river, since this is also subject to radical change, as when a river breaks through and finds a new course or when a river alternates between meandering and bypassing oxbow lakes.
One might protest that membership in certain classes allows some flexibility. For example, something can be considered "triangular" for everyday purposes even if it is not precisely composed of three straight lines, but instead it is composed of atoms lined up within a certain degree of tolerance. The river problem though does not allow recourse to geographic formalism by means of increased tolerances. Consider a case in which two rivers happen to run parallel to one another from source to the sea while separated by only a few meters. In this case, we would say there are two rivers, not one. On the other hand, if there were just one river and it were to shift over by a few meters such that its new course is parallel to its old course, it would still be one river, not two, in spite of having moved over by a distance as large as the distance that separated the other two rivers. Thus, merely adding tolerances is not sufficient to resolve the problems with regarding geography as the essential formal property of rivers. Tolerances are sometimes useful as means of defining classes of objects but insufficient when distinguishing between individual objects like rivers.
A river also cannot even be any such continuous stream of water that shares a common origin, since it is not uncommon for one source of a river to dry up, but for the river to continue its existence by drawing on water from other sources. Even if the Mississippi were to lose the contribution of its own headwaters or of the Ohio or Missouri rivers, we would still call the remaining waters that empty into the Gulf of Mexico the Mississippi River so long as it maintained its integrity as a stream. So long as the main stream continues to flow, a river can still be the same river even if fed by different waters.
Thus, none of the formal properties listed so far--particle properties, geographic location, or head water source--can fully account for our understanding of rivers.
The problem with radical nominalism
One response to these many difficulties is to abandon all hope of coming up with a precise definition of river or ship or human being and to switch to a form of radical nominalism about the issue. One might say that a river is whatever people say it is (or worse, whatever people in power say it is) and there's nothing more to it than that. If we cannot come up with a precise definition of river, then the problem is with the natural imprecision of human languages and nothing can be done to fix it.
This pessimistic account does contain some correct observations, but on the whole it sacrifices too much. Yes, it is difficult to come up with a precise definition of river, and natural language is optimized for properties other than precision, but nevertheless there are cases where it is necessary to provide precise definitions. Even ignoring the paradox that began this discussion, suppose that a river runs through two states and that the two states form a contract that each is allowed to use a certain amount of water from the river. Then suppose that a flood causes a shift in the course of the river, and afterwards one state suddenly begins to take much more than its share of water while arguing, "Who is to say we are in the wrong? The contract we formed was about a certain river, but that river is gone now. The contract can no longer bind us since its object does not exist now if it ever did." Certainly, we would like to have recourse to a precise means by which to settle such a legal dispute. On what grounds can the wronged state claim that the river still exists?
However, even this does not capture the full problem of pure nominalism. Of course words naturally mean just what we as a society want them to mean. Thus the nominalist is correct that it may be the case that our use of some terms is so jumbled that their contradictions and ambiguities cannot be removed. Accordingly, if we wanted to define a river as being the same only if it had the same atoms or the same particle properties or the same banks or same general location or whatever else, we would be entitled to stipulate the use of such a definition. The goal here, however, is to produce a definition that allows us to preserve our commonsensical understanding of terms while still being able to reason rigorously using these terms. The river example is just a test case for a broader class of similar objects that exist as sets without fixed membership. If we cannot define river, then it is likely that we will be even harder pressed to define a number of other terms. The end result will be the inability to make more than suggestive claims about individual objects in the world. For this reason, it is worth making every effort at capturing an appropriate definition for a term before resigning ourselves to linguistic chaos.
The problem with simple co-material identity
One way to solve the river problem might be to propose a theory of co-material identity. In this theory, as long as a certain arbitrarily defined percentage of material from the original composite object at time 1 remains in the object at time 2 then the reconstituted object is the same. Thus for the ship of Theseus example in which there is a "modified ship" that was in continuous service and a "reconstructed ship" made of cast off parts, the modified ship is the same ship so long as at least a particular number of original planks remain. It will then be up to the users of the word "same" to determine whether for their purposes "same" requires just one original plank or at least half of the original ship or some other specified percentage of the ship's composition be preserved. The difference is arbitrary and can be disambiguated as needed, eg. for legal purposes connected to the ship's docking rights one plank might be sufficient, but for the purposes of a museum the "same" ship should be composed of at least three quarters original material.
There are two obvious problems with co-material identity. First, it is not clear whether a ship constructed out of discarded planks would have the same right to the title "ship of Theseus" as the modified ship. It is possible that our definition of sameness will sometimes allow splitting (see below), but we want to avoid this possibility where possible. Another difficulty would come if the modified ship and discarded parts ship both contained fifty percent of the original material. It might seem in this case that which of the two is called the ship of Theseus can be changed by taking a single plank from one ship and putting it on the other and thus changing the balance of parts. However, the exchange of one plank seems like too small of a change for identity to be passed with it.
If the ship of Theseus example is a difficult one for the co-material theory of identity, then the river example is deadly. It should be clear enough that the Colorado River is rapidly emptying into the ocean. Whenever it would be that we designate the reference set of material in the Colorado River by which to make later comparisons, after a certain amount of time, more of the original river would be in the ocean than contained in what we take to be its banks, and after a little more time none of the original river would be left. Thus simple co-materiality is not enough to give a rigorous definition of commonsensical identity.
Continuous recognizability
Organ donation example
Before proposing a new model to solve the various problems listed so far, it might be useful to give some examples that demonstrate what our common sense's requirements for identity are.
Consider for the sake of example a case in which one person, Alice, donates her kidney to her friend, Berta. After the operation, we will naturally want to say that legally the kidney is now Berta's even though historically we can recognize that it was once Alice's. That is we can say that Berta's new kidney is the same as Alice's old kidney. (Also we will say Berta is still Berta in spite of her now containing a new organ. Thus, she is, in one sense of the term, the same person after the operation.) Furthermore the one kidney will continue to have the same two properties (legally being Berta's and historically being Alice's) even if after years of being in Berta's body all of the atoms within the kidney just happen to be replaced by new atoms from the food that Berta eats. Much as Berta retained her identity even with a new kidney, the kidney retains its identity even after its molecular parts are replaced. Thus, we can say that neither property is strictly based on material identity. Perhaps we might then propose that the identity of the kidney is based on one of its particular formal properties--in this case that it has Alice's DNA patterns even if the atoms making up that pattern are different.
However, as was the case with the river example, formal properties are not a reliable carrier of identity. Suppose that Alice and Berta had been identical twins with identical genomes. In this case the formal property that we are using to distinguish the kidney as being historically Alice's is no longer sufficient to distinguish parts of Berta's body that have the property of being historically hers from those that do not. Thus, if we wanted to say that a person is the same over time because they have the same DNA patterns, we would be unable to distinguish between identical twins and would have to hold that cells within a person with minor DNA mutations are not a part of the same person.
To give a slightly macabre example of the difficulties of formal properties, suppose after removing Charlie's kidney instead of just implanting the organ in Derek mad scientists feed Charlie's kidney to Derek and these atoms from Charlie's kidney just so happened to replace all the atoms in Derek's kidney by moving to places in Derek's body analogous to their former place in Charlie's. Unlike the case of Alice and Berta, we would not say that Derek's new kidney is the same as Charlie's old kidney even if it contains the same material and happens to take on a shape similar to its old shape, because we would hold that at the time of digestion Charlie's kidney was destroyed and any new kidneys that come about cannot inherit the identity of the destroyed kidney. We would only say that the atoms in Derek's new kidney are the same as the atoms in Charlie's old kidney. When those atoms are replaced by Derek's ongoing metabolic processes, we will no longer be able to accurately speak of Derek's current kidney having historically been Charlie's. Thus, the sameness of a kidney over time is not merely its physical shape just as it was not its DNA.
The difference between Berta's new kidney and Derek's new kidney is illustrative of the operant properties that underlie commonsensical identity. Berta's kidney is the kidney that was Alice's in part just because we could have theoretically watched the kidney continuously existing as the same kidney even after it was moved into place, whereas Charlie's kidney is visually destroyed during digestion. So at least partially, our commonsensical notions of identity fall out of the particular visual object recognition heuristics that are present in the human brain. Accordingly, one model of sameness that we might employ is continuous recognizability. If we could (at least in theory) watch something throughout its transformation and recognize its identity the whole time then it is the same as the original thing. The problem with continuous recognizability as a theory of identity is that it is just a reification of our prejudices. That is, if the question is, "Is this the same object as the one that was here before?" the only advice that continuous recognizability gives is, "Yes, if you continuously thought so. No if not." Thus, it is only useful in the cases where we can already recognize sameness, but it does not tell us how the recognition process actually works. Recognition itself is a black box function, and identity is just the sameness of the function's output over time. What it is that we are recognizing is unknown.
The problem of splitting
The difficult with leaving recognition as a black box is that there are cases where our intuitions seem to clash, and continuous recognizability does little to resolve the problem. Consider an acorn and the oak it becomes. We will say that the acorn is the same as the oak, in part because we could theoretically watch the acorn become the oak, as is done in time lapse photography videos. If we watch further, we might see the oak cut down and turned into a plank of lumber. However, we might be reluctant to say that a desk made from the plank is the "same" as the acorn in a manner analogous to the way that an oak is the "same" as its originating acorn. The sameness of the oak to the desk is purely a material sameness, but the sameness of the oak to the acorn is a different sort of sameness, such that transitivity does not hold between the plank and the acorn. Thus, although continuous recognizability holds from the acorn to the oak to the plank, "sameness" can be broken into two different sorts, one type of which holds from the acorn to the oak, the other type of which holds from the oak to the desk. Without understanding what it is that we are recognizing, it will not be possible to differentiate these two kinds of sameness.
Similarly, consider a variation on the river example. The river that is the Missouri River in Montana is the same river as the Mississippi River in Louisiana, and the river that is the Ohio River in Pennsylvania is the same as the Mississippi River in Louisiana, but the Missouri River is not the same as the Ohio River in certain relevant respects. If possible, we want our definition to allow for the non-transitive sameness of rivers and tributaries, but doing so on the basis of just continuous recognizability is impossible, since someone walking down from the Missouri River's banks along the Mississippi and on to the Ohio River will recognize what is being seen as the same river throughout the journey. The changes that make the difference between the Missouri and the Ohio (the fact that the streams flow into a common outlet but not each other) will not be picked out by continuous recognizability alone.
Self-perpetuating identity
One way to fill in the recognition gap is to say that what is recognized is the self-perpetuation of a particular pattern. Consider the river example. If we define a river as a process by which the gravitationally influenced motion of certain water molecules causes other water molecules to follow them in a similar manner then we can solve many of the problems concerning the sameness of rivers. If we have a river where molecule A is replaced by molecule B, we can recognize the two of them as participating in the same river if we see that it was the gravitationally compelled motion of molecule A that caused the motion of B, which in turn will allow the motion of its successor C. This sameness will hold even if the river changes its shape, so long as the changes do not interfere with the process by which the void left by water molecules moving due to gravity is filled by other molecules of water that are also gravitationally compelled. Similarly, the river's source changing is fine as long as the water that enters the river from the new source is similarly compelled to run downhill by the opening of space left by the vacancy of its predecessors. The identity of the river does rely partially on co-materiality, but only from moment to moment within the self-perpetuation of the process. Even if all of the river's present molecules are someday gone the river will remain if there is an unbroken chain of causality connecting the current molecules to the molecules that will someday inherit the title of "the same river."
Next consider the ship of Theseus. In this case, we can define a "ship" as the material that inherits the process of being treated as a seagoing vessel by a crew or holding a certain form. Note that the ship need not always be at sea or have a crew, just that it must be either treated as a ship by some community or be a collection of materials that base their shape on the prior shape of the ship. That is, as long as the ship is at sea and being used by its crew, it is the same vessel even if the crew replaces some of its parts, so long as they continue to use the new set of parts as a ship, and when it is uncrewed, it is fine for some of its material to be replaced by new material (eg. through planks rotting), so long as the new material bases its shape on the old within a certain degree of tolerance. Thus, so long as the process by which the parts of the ship are replaced is slow and continuously a part of the process of using the ship as a ship or the ship be weathered by the elements, it is the same ship. Hence taking a plank off the back of a ship and nailing it to a different ship does not make the other ship "the same ship" as the first, since the plank was not being used as a ship during the time between its removal from the first ship and its addition to the second. Similarly, constructing a ship out of junkyard scraps is not sufficient to inherit the title of the same ship.
One consequence of the proposed definition of identity in ships is that if a ship is dry docked, taken completely apart, and left for scrap, but then reassembled using all of and only its original parts by an unaffiliated crew, then it is no longer the same ship, whereas it may be necessary in the normal service life of a ship to take it apart and reassemble it in a similar manner, but because of the continuity of treatment by its crew, this second ship will be considered the same despite the superficial similarity of its treatment. A crew can reassemble the same ship, but archeologists cannot. This consequence holds whenever the ship is dismantled to the point that it is no longer called a "ship," but rather "a collection of ship parts." It may seem counterintuitive, but I hold that this result is actually a useful feature of my proposed sharpening of the definition of identity for certain composite objects. While it may be somewhat controversial, common sense will not totally reject our saying that a newly constructed ship is a new ship, even if old parts were used. This is clearly a case where our intuitions are weak. Part of the continuity of sameness in retrofitted ships is that they have a continuous treatment as a ship by some community. Lacking that treatment, the identity of the ship parts as parts of a particular ship, rather than parts in general, evaporates. That the sharpening of our definition lets us make a meaningful decision about this potentially controversial choice is a benefit of our proposed definition, not a shortcoming, since we can now make definitive pronouncements about questionable cases.
Consider again the example of the kidneys. Our proposal is that a kidney is the same kidney so long as the biological processes that cause an organism to sustain its existence are still in effect. As with the reassembled ship, we hold that kidney that just so happens to be reconstituted is not the same kidney. Here our intuition more closely aligns with the result of the proposed definition, giving more confidence to the reassembled ship example. Similarly, we allow that the kidney is the same kidney that used to be in someone else even now that it is implanted in its new host. Similarly, the patients can be considered the same people after their surgeries, even if they receive new organs with different atoms, different DNA, etc., so long as their life processes as human beings continue without interruption.
With the example of the oak, we may now distinguish clearly between the biological sameness of the acorn and the tree and the material sameness of the oak and the plank by defining biological sameness according to the self-perpetuating properties of cells, and material sameness as the self-perpetuation of atoms. (Note that since quantum mechanics tells us that atoms contain numerous "virtual particles" that pop in and out of existence every second and help give the nucleus its shape, it is not practical for us to require the material sameness of the plank to hold down to the subatomic level. Instead it must merely hold to it down to the atomic level.)
Finally, we can at last pick out the difference between the Missouri River and the Ohio River. When the water in the lower Mississippi River flows out, it leaves a void that water from both of the rivers rushes in to fill. However, there is no unidirectional causal chain between the Missouri River and the Ohio. Water evacuating from the one river in no way contributes to the evacuation of water in the other river. Thus, we can distinguish between the two rivers, even though they become a part of the same river further downstream.
Note the interesting result that the stipulative definition of identity provided here explicitly does not have the properties of transitivity and symmetrically as the normal definition does.
Comparison of proposal to other accounts
The account of commonsensical sameness given here is original but by no means unprecedented. There are two broad categories of antecedent descriptions: those that deal with the ontology of flux and those that deal with the status of personhood in a world of flux. Of course, it is impossible to do full justice to the vast number of prior accounts of identity over time in the space provided here, but giving a few representative explanations will be useful for demonstrating through contrast the strengths and weaknesses of the account I have provided. Of the many accounts dealing with the ontology of flux, I will restrict myself to Aristotle's theory of substance and the contemporary theory of genidentity. Of the many possible accounts of personhood that could be contrasted here, I will restrict myself to those of Derek Parfit and Mādhyamaka Buddhism. Using these accounts will allow us to challenge the plausibility of the account so far, and in doing so, create a final version which is not only better able to defuse the paradox that initiated our inquiry, but also more suitable for general usage when describing the sameness of changing objects.
Aristotle
According to Aristotle in Metaphysics, "a substance… is a principle and a cause…"4 When one inquires about why something is what it is, we are really seeking to learn its cause, "and this cause is the substance of the thing."5 When one examines a composite thing, it "exists in such a way as to be a totality, not like a heap…."6 To take the example of flesh, it is "not only fire and earth or the hot and the cold but something else besides."7 The "something else" which gives unity to flesh is the cause of its being flesh. For objects that are substances "formed according to nature or by nature, the substance of these would appear to be this nature, which is not an element but a principle."8 Hence, over and above the material (elemental) make up of composites there are non-elemental principles that serve as causes of unity.
Traditionally, commentators have linked the "causes" mentioned the Metaphysics to the causes listed in Physics, which they have labeled the formal, the material, the efficient, and the final.9 Clearly, Aristotle would be in agreement with the part of the analysis at the start of this paper in which it was shown that neither material nor formal definitions of identity are sufficient to track our commonsensical understanding of sameness for certain kinds of objects. In the cases given above, a substance must take its unity from the conjunction of all four causes. Under Aristotle's scheme, the proposed criteria of continuously recognizable self-perpetuation might be classified as either an efficient cause or final cause depending on where the emphasis placed in self-perpetuation. If self-perpetuation is taken as meaning that the prior form gives rise to the later form, then self-perpetuation would be called an efficient cause. If self-perpetuation is taken as meaning that the arising form will be recognizable as a perpetuation of the prior substance, it might be called the final cause. (This is particularly relevant in the case of biological life, in which the organism may be anthropomorphically conceived of as "wanting" to survive, prosper, and reproduce, which is the "for what?" of the organism's existence.)
However, while continuously recognizable self-perpetuation might be seen as fitting either cause, it is a precise match with neither. It is not enough that to say that one thing acts as the efficient cause of the other for it to count as a part of the thing. For example, in addition to being a cause of its later self, a river is also a cause of erosion, but the silt in the bottom of a river is not a part of the river. At best, it is a part of the riverbed. Mere causal connection is not enough to count as proof of sameness or else everything that gravitationally influences anything else would be indistinguishable from the universe around it. We may metaphorically remark that a person has put something of herself in the house she builds, but we do not mean the house is the same as the person. Efficient causation is not identity.
Similarly, we cannot say that continuously recognizable self-perpetuation is the same as Aristotle's final cause. For Aristotle, the final cause of a biological organism is the prosperity of its soul, but since modern materialists will reject this, we do not wish to include such a requirement in our own account, as doing so would severely limit its usefulness for public discourse. Worse, the hypothesizing of a soul for a river or a ship would limit our account's acceptance to committed animists, whereas our intention is to gain universal assent to our scheme in order to remove the applicability of the sorites paradoxes from a broad class of objects. Thus, we wish to give a naturalistic account of what it is that self-perpetuation entails without ruling out the possibility of non-naturalistic elements to reality. One might try to do this by simply describing the final causes seen in nature. However, as Roger Ames has quipped, most acorns end up becoming squirrels, not oaks! Hence, any naturalistic account of what it means for something to be the same cannot simply point to final causes in nature as if they were there to be seen on the surface of the thing. Final causes are imputed by interpretation rather than revealed by investigation. As such, there is no guaranty that various individuals will see the same final causes at work in a particular object.
This difference hints at a fundamental difference between the Aristotelian project and the proposal offered in this paper. Aristotle sought to describe the physical nature of reality as it is. The continuously recognizable self-perpetuation model of identity does not attempt to describe the physical nature of reality as it is, but rather seeks to come up with a coherent way of thinking about nature as it is described to us by science and ordinary experience. It aims to be a useful interpretation of the world that provides us with a usefully concrete heuristic for talking about our ordinary intuitions without in any way assuming that the world is obliged to exist at its fundamental level in a manner similar to what we describe.
Thus, both to the problem of distinguishing relevant casual connections from irrelevant ones and to the problem of describing self-perpetuation without presuming the existence of a substantive self-identity, what is proposed here is to defer to the existing recognitional capacities of social situated interpretive communities. In other words, society can already tell that us that though both the empty shell of a chrysalis and the butterfly have direct causal links to the pupa, it is the butterfly not the shell that inherits the mantle of "sameness" with the caterpillar. We do not need a theory to tell us that we think this already. The examples given during the exploratory phase of this paper would have been meaningless if we did not already possess intuitions about the "correct" meaning of sameness in those cases.
Does this mean then that the theory of sameness presented here is already superfluous? If we have a social capacity to identify what we mean by the "same river" or the "same human being" already, does the use of "continuously recognizable self-perpuation" as a definition of sameness add to our understanding? Yes, it does, because definition given here is meant to sharpen the pre-existing ways of thinking about the world and in so doing aid us in 1) making concrete judgments in situations where we would otherwise be reluctant to make pronouncements (as seen in the dismantling of the ship argument earlier) and 2) removing absurdities that seem to result from trying to interpret the world naïvely as though material identity were the only sort of sameness, namely the paradox presented by Sainsbury.
Genidentity
The term "genidentity" was coined by Kurt Lewin in 1922, and since has received broader usage in the field of physics thanks in part to popularization by logical positivists like Rudolph Carnap10 and logical empiricists like Hans Reichenbach. Reichenbach adopted the term in the posthumously published The Direction of Time after espousing similar views in earlier works, such as Elements of Symbolic Logic where he writes that Heraclitus
is right if he intends to say that a river is not a thing in the sense of an enduring substance but an event sequence in which matter does not remain the same; he is wrong, however, if he wants to infer that it is not permissible to consider a river as a thing. The meaning of the phrase 'the same river' is a matter of definition; and with the definition of the word 'river' as denoting a thing that consists in an event sequence it is possible to step twice into the same river.11
In The Direction of Time, Reichenbach adopts the term "genidentity" to describe identity of this sort. As he explains a "thing is series of events succeeding one another in time; any two events of this series are genidentical. The concept of physical identity, of an individual thing that remains the same throughout a stretch of time is based on the properties of this relation."12 Furthermore,
[P]hysical identity of a thing, also called genidentity, must be distinguished from logical identity. An event is logically identical with itself; but when we say that events are states of the same thing, we employ a relation of genidentity holding between these events. A physical thing is thus a series of events; any two events belonging to this series are called genidentical. The relation of genidentity is therefore a two-place propositional function which is symmetrical, transitive, and reflexive.13
Thus, for events identity is maintained forwards and backwards throughout time as a consequence of their having a single linear chain of existential causation between them. In addition, the relationship of genidentity is applicable to composite, organic entities, such as rivers and human beings. Hence, Reichenbach urges us to discard the dichotomy between things and events and see rather that the two "represent merely different modes of speech," such that the phrase "this tree is old" is translated with equal facility to the phrase, "The first events of the series constituting this tree are separated by a long stretch of time from the present event."14
Like the present account, Reichenbach acknowledges that due to the multiplicity of casual connections between events, it is not sufficient to speak of genidentity on the basis of casual connection alone. Accordingly, he defines two kinds of genidentity. "Material genidentity" has three necessary conditions: continuity of change, spatial exclusion, and discernibility of spatial interchange.15 However, if we examine the world at the quantum level, we find that all of these properties are lacking of subatomic particles, hence "there is no material genidentity at all in the physical world,"16 though we may continue to speak conventionally as though there were. The only true genidentity in quantum world is "functional genidentity." Unfortunately however, as Bas van Fraassen and Isabelle Peschard note in their paper "Identity Over Time," Reichenbach "does not offer an explicit definition" for functional genidentity.17 Rather, Reichenbach obliquely remarks that functional genidentity is "a genidentity in a wider sense," in which the latter two qualities of genidentity are jettisoned, "whereas the first is usually adhered to."18
Reichenbach is admirably frank about the fact that there is no "true" definition of genidentity, since we "can define genidentity to suit our purposes."19 However, by defining genidentity as transitive and symmetric, he has made his concept less useful in the case of branching identities. Again, the Ohio and Missouri rivers are distinct from one another in spite of their not being distinct from the lower Mississippi. Similarly, the sameness of the acorn and the oak does not entail the sameness of the acorn and the desk. Thus, the concept of genidentity as defined by Reichenbach is not sufficient to map all of our commonsensical sameness relations.
In their exploration of the salience of identity and genidentity, van Fraassen and Peschard further argue that since there are quantum superpositions in which a pair of particles have no differentiating characteristics the Leibnizian "Principle of the Indiscernibility of Identicals" must be discarded. "[C]onceptual discernibility cannot, even logically, be a foundation for knowledge of numerical distinctness, but is a further stage of knowledge which has to involve a cognitive procedure, of individuation, which requires particular conditions of possibility."20 Thus, while for Reichenbach functional genidentity is lost in certain interactions, van Fraassen and Peschard insist that there is a distinct concept of identity which is preserved even during entanglement. Hence Reichenbach's genidentity is not the same as the kind of identity over time which subatomic particles have. As for my own proposal, the principle of continuous recognizability is not sufficient to speak about the instantaneous self-sameness of particles in super-position, let alone to speak about their sameness before and after entanglement, so it too must be abandoned as an adequate description of the quantum world.
The upshot of this is that neither the concept of genidentity nor the concept of continuously recognizable self-perpetuation are adequate to describe the world in certain quantum configurations. For the purposes of my proposal however, this is not a damning difficulty, since continuously recognizable self-perpetuation is not meant to describe all possible kinds of sameness relations. Rather, it is heuristic that lies over top of whatever ontology an individual may hypothesize for the ultimate or pen-ultimate constituents of reality, be it perdurantism, endurantism, or something wholly different. As for Reichenbach's three necessary marks of material genidentity (continuity of change, spatial exclusion, and discernibility of spatial interchange), while these can serve as a useful formalization of continuous recognizability and self-perpetuation in certain contexts, I believe that ultimately more useful criteria are those that evolve organically from an interpretive community rather than any completely fixed, formal description of what it is to be recognizable or self-perpetuating. Attempting to define these terms prematurely is sure to lead to unintended inclusions and exclusions. If the need arises for a sharpened definition of either term, then we can use Reichenbach's criteria as the starting point for further refinement together with the embodied instincts of the society of inquiry.
Parfit
One area in which there is a surfeit of pre-existing communal dialogue about the nature of sameness is that of personal identity. However, as Derek Parfit writes in his paper "Personal Identity," notwithstanding this dialogue,
We can… describe cases in which, though we know the answer to every other question, we have no idea how to answer a question about personal identity. These cases are not covered by the criteria of personal identity that we actually use.21
That is, an abundance of dialogue need not produce consensus, even when the facts are completely established. Part of the problem, according to Parfit, is that our intuitions about personal identity are held unusually strongly and in conjunction with another belief about the general decidability of such questions.
No one thinks this about, say, nations or machines. Our criteria for the identity of these do not cover certain cases. No one thinks that in these cases the questions "Is it the same nation?" or "Is it the same machine?" must have answers.22
Thus, our expectation that "personal identity" is a solid relationship leads us to disappointment when we discover that it is no more robust than other conventionally stipulated, provisional definitions. The reason that this expectation is so deeply ingrained in us is that we all experience the world from the viewpoint of our own consciousnesses. Hence the "I" and the question of what I am become deeply familiar to us. This would not be so bad except that we go on from this instinctive attachment to the self to confound other important questions with a presumption that personal identity is always circumscribable. Fortunately, these questions, "can be freed of this presupposition. And when they are, the question about identity has no importance."23 Thus Parfit's expository purpose is to provide examples that help us to shed our intuitions concerning the solidity of the self.
Considering the possibility of brain transplants and the temporary division and recombination of brain hemispheres, Parfit concludes that, "a person's mental history need not be like a canal, with only one channel. It could be like a river, with islands, and with separate streams."24 On the basis of this, he argues that we should separate out the concepts of "personal survival" and "identity." One can survive the splitting of one's personality, even if one's numerical identity cannot be maintained. In fact, the reason that we place such great emphasis on personal identity is that maintaining one's identity is indicative of survival, and it is survival that is the real crux of such inquiries. For Parfit, survival is a matter of degrees of psychological continuity rather than an absolute dichotomy. Parfit argues for this conclusion on two grounds. First, through a series of thought experiments about beings that split and fuse their identity at different times and ways, he shows that a gradated definition of personal identity better accords with our intuitions, and second, he argues that from an experiential point of view, seeing one's life from the point of view that identity is a matter of continuity and degree allows one a better outlook on life:
Egoism, the fear not of near but of distant death, the regret that so much of one's only life should have gone by-these are not, I think, wholly natural or instinctive. They are all strengthened by the beliefs about personal identity which I have been attacking. If we give up these beliefs, they should be weakened.25
There are two distinctions between Parfit's account of identity and the account offered in this paper so far. First, for the most part Parfit emphasizes the importance of psychological continuity to the exclusion of bodily continuity. One exception is a footnote in which he explains that psychological continuity is a sufficient condition for survival rather than a necessary condition, since "in the absence of psychological continuity bodily identity might be sufficient."26 My own inclination is to emphasize the interrelated nature of somatic and psychological survival, since failure to do so can lead to difficulties in characterizing cases of amnesia, etc.
The second and more significant divergence between the accounts is that as described so far continuously recognizable self-perpetuation has been treated as a bivalent truth function. Two things either share the relation of being the same, or they do not. Clearly, however, there are advantages to replacing the concept of "sameness" with "degrees of similarity" as Parfit has done. One would expect it to be easier in general to resolve disputes about whether things are somewhat similar than to resolve disputes about whether two things are different manifestations of the same thing. However, part of the reason that these questions are more easily resolved is that much less hangs on them. Saying, for example, that a person is the same person even after entering a persistent vegetative state is controversial precisely because it brings along with it questions about whether the vegetative individual should be considered to have the same sorts of rights as before their brain was damaged. To just say that one is radically psychologically dissimilar after such brain damage is less controversial precisely because it is less useful of a judgment. While there is not sufficient space to explore the issue here, needless to say, for legal and moral purposes, it is not sufficient to leave the matter behind after resolving that the individual is dissimilar to their past self by whatever percentage. If the next of kin wish to pursue euthanasia, a judgment must be rendered about whether the body that remains counts as the same person or not. Thus, to give an account about "degrees of psychological continuity" is just to restate the issues that are not in dispute, rather than to address other issues that seen to bear on the matter of dispute. Hence, the chief objection that can be leveled at Parfit's account is precisely that there is nothing objectionable in it. What is objected to is what Parfit's account leaves out: a definitive judgment about the matter of survival and identity.
Mādhyamaka Buddhism
Parfit's account of personal identity as survival has (like the account given here) many precedents, among them Hume's "bundle of sensations" and the Buddhist notion of self. Since there are many different kinds of Buddhism with different doctrinal emphases, this paper will restrict itself to Mādhyamaka. The conventional level outlook of the Buddhist is that human consciousness is a stream of disconnected mental events arising due to previous mental events. As Paul Williams summarizes, "We are each of us an ever-changing composite of various radically impermanent psycho-physical components extended over space and time."27 With this background in place, the Buddhist concludes that the self is an illusion, as for example in Bodhicaryāvatāra 8:101, where Śantideva says,
The continuum of consciousness, like a series, and the aggregation of constituents, like an army and such, are unreal. Since one who experiences suffering does not exist, to who will that suffering belong?28
The basic groundwork behind this argument seems to be remarkably similar to one made by Kant in a footnote to the first edition of the Critique of Pure Reason. He writes,
An elastic ball striking another such ball in a straight direction communicates to that ball (if we take account merely of the positions in space) its entire motion and hence its entire state. Now let us--by analogy with such bodies--assume substances one which imbues the other with presentations along with the consciousness of these. We shall then be able to think an entire series of such substances: the first would communicate its state, along with the consciousness thereof, to the second substance; the second would communicate its own state, along with the state of the previous substance, to the third; and the third substance would similarly communicate to yet another the states of all previous substances, along with its own state and the consciousness of all of them. Hence the last substance would be conscious of all the states of the substances that had changed before it as being its own states, because these states would have been transfered to it together with the consciousness of all of them. Despite this, however, that substance would not have been the same person in all these states. [Emphasis mine]29
Thus, for both Kant and Śantideva, merely causal continuation of a consciousness from moment to moment is not enough to speak of a true existence. Interestingly, for Kant, this shows that the self is more real than the person, whereas the Mādhyamika draw the opposite conclusion. For Kant, this serves merely as a theoretical argument against certainty that the self is one with the subject. For Buddhists, however, this serves to show that there cannot be such a thing as a self at all. Both conclusions seem to rest on the supposition that identity of the sort I have been calling "continuously recognizable self-perpetuation" is insufficient to uphold a robust concept of existence. Furthermore, like Parfit, the Buddhists claim that seeing things as mere imputations and aggregates is useful for building virtue and taming the passions. For the Mādhyamika, my attempt to piece back together a meaningful sense of identity for an aggregate being is not just entertaining a pragmatic fiction--it is a pernicious reinforcement of those mindsets which have hampered our enlightenment for uncountable ages! This is not to say that Buddhists must make themselves ignorant of our commonsensical judgments about composite entities. As Williams writes,
[T]ables, chairs, and mountains seen by cognitions which in everyday life are held to be valid (there is no disfunction in the means of cognition), are correct conventionalities, but still 'fictions.' … [A] great many things (probably all) which we would normally consider to be genuine realities, the 'furniture of our world,' are going to be fictions for Śantideva since they are wholes, composites made out of parts. This includes, of course, the cosmos--the 'totality of things'--itself.30
Thus, the basic position of the Mādhyamika is to assent analyses like that of Sainsbury which opened this paper: if no constituent part of a human being is sufficient to give or take away totality from the whole of the human being, then the conclusion is that the totality itself is an illusion. As in Bodhicaryāvatāra 9:56–59, the Mādhyamika regularly draw conclusions about the possibility of enlightenment from the fact we find nothing that can withstand repeated analysis,
If there were something called "I," fear could come from anywhere. If there is not "I," whose fear will there be? Teeth, hair, and nails are not I, nor am I bone, blood, mucus, phlegm, pus, or lymph. Bodily oil is not I, nor are sweat, fat, or entrails. The cavity of the entrails is not I, nor is excrement or urine. Flesh is not I, nor are sinews, heat, or wind. Bodily apertures are not I, nor in any way, are the six consciousnesses.31
The Mādhyamika do not restrict these sorts of analyses to human beings, but by means of repeated application of the reductio-like prasaṅgika argument attempt to show that all phenomena are mṛṣā, fiction, since there is nothing substantial in them that can be identified with a self-existing phenomenon. This is not to say that conventionally perceived objects are utterly non-existent. The Mādhyamika are not nihilists. Rather, as their name suggests, they seek a "middle way" between substantialism and nihilism. As Williams explains a conventional object such as a table,
will be a fiction because it will not exist the way it appears (it will appear as if it is existing from its own side, as independently self-subsistent, 'inherently' existent, while actually it exists as a conceptual imputation superimposed upon its 'bases of imputation'), but that fiction will nevertheless exist. It will enter perfectly adequately into pragmatic transactional usage and therefore will not be the same as a completely non-existent thing.32
It is clear then that the Mādhyamika will permit the use a theory of description such as this paper's continuously recognizable self-perpetuation only so long as the individual using this method of identification is intimately aware that there is nothing independently existing which supports its use. Rather, the use of such a method is possible because of the codependent arising of illusions born of ignorance from the fathomless past. From the perspective of this paper, such a caveat is acceptable if not obligatory.
Result of comparison
So far, the proposal presented in this paper has shown itself able to coexist with philosophical systems as diverse as Aristotle's theory of substance, Reichenbach's logical empiricism, Parfit's analytic Anglo philosophy, and Mādhyamaka's non-dualism. If time and space permitted, it might be possible to compare the current proposal to any number of other schools of thought from process philosophy to Daoism. The literature on the Heraclitean problem is quite deep. While the results of such comparisons cannot be known in advance, the evidence suggests the theory here would show itself to be compatible with many such systems. The reason for this wide-ranging compatibility is precisely because it attempts only to describe the surface level of reality, and even that only provisionally and subject to refinement. While it might seem that attempting only to make a surface level description of sameness should result in a "shallow" theory, quite to the contrary, by proposing a relatively modest theory, we are better able to conform our theory to our intuitions where we are sure of those intuitions and to provide guidance where our intuitions leave us without clear guidance. The principle at work here is analogous in the field of ontology to the semi-compatibilist view of determinism that John Fischer endorses in a review article for Ethics,
I want to end by sketching what I take to be a very powerful motivation for embracing "semicompatiblism"—the doctrine that causal determinism is consistent with moral responsibility, even if causal determinism rules out alternative possibilities. I believe that we-you and I and most adult human beings-are morally responsible (at least much of the time) for our behavior. Further, I do not think that this very important and basic belief should be "held hostage" to esoteric scientific doctrines. For example, if I were to wake up tomorrow and read in the Los Angeles Times that scientists have decisively proved that causal determinism is true, I would not have any inclination to stop thinking of myself, my family and friends, and human beings in general as morally responsible. The precise form of the equations that describe the universe, and whether or not they are or correspond to universal generalizations, are not the sorts of thing that should be relevant to our most basic views of ourselves (as morally responsible agents and thus apt targets of the reactive attitudes).33
In the same way that our moral intuitions should not be subject to the vagaries of scientific research, so too our basic intuitions about the sameness over time of composite entities such as human beings, ships, and rivers should not be subject to complete rejection when a new ontology presents itself, though they may, of course, be shown to be merely provisional designations and not reflective of ultimate reality. Any new ontology must show us how to refine the basis of understanding that we already have, but it is impossible for it to completely overturn our existing intuitions, because these intuitions have already shown themselves to be so pragmatically useful for ordinary life.
By comparing to Aristotle, we see that efficient causes are too numerous to reflect our intuitions about identity and final causes are too interpretative to consider as a point of agreement for all observers. From Reichenbach and genidentity, we gain a valuable starting point for further formalization of the concept presented here, and we see the limitations of both genidentity and this concept when dealing with the quantum realm. From Parfit, we see benefits and disadvantages of using degrees of similarity rather than bivalent predicate. From the Mādhyamika, we are warned of the potential dangers of reifying the concept of sameness given here into a self-sufficient mode of being.
Application to paradoxes
Returning to the paradox that opened the paper, we said that, "A human being still exists even if he or she loses one molecule from his or her body." However, in light of our newly refined definition, we cannot assent to that assumption without caveats. If the human being is thought of as a solid, unitary object, then clearly it disappears as soon as a single molecule changes. However, if we think of a human being as a recognizable continuum of self-perpetuation, then it may sometimes be the case that a person persists even after the loss of a molecule, but if this is the case, it is only the case in virtue of the fact that this molecular loss has not disrupted the larger self-sustaining processes within the body. These processes could indeed be disrupted by a too rapid loss of molecules. Thus, the premise must be changed to, "A human being still exists even if they lose one molecule from their body, so long as the loss of this molecule does not interrupt the biological self-perpetuation of the person as an organism," since certainly we can imagine cases where the loss of each additional molecule adds ever so slightly to the probability of near term death. With that clause added to the assertion, the paradox collapses, since it no longer allows itself indefinitely repeated application but only strictly limited application, such that the rate of molecular loss is never significantly greater than the rate of molecular replacement. As our intuitions suggest, a person can withstand the loss of any one atom, but not the loss of all or even too many of them.
Similarly, we can answer the question, "Does [the ship built from discarded parts] have a better claim to be the original ship of Theseus?" with a resounding "no," given the stipulation that when the ambiguous term "original ship" is used it refers to sameness according to the criterion of continuous recognizability as described above rather than sameness according to a naïve materialistic criterion. Hence this paradox turns out to be a matter of the ambiguity of the term "same" rather than a matter of vague