Understanding personal identity is a problem which most philosophers reduce to that of finding an appropriate equivalence relation. However, even a shallow survey of the problem quickly demonstrates the subtleties of a relation which successfully withstands the challenges of the border line cases such as gradual change and teletransportation. Because a philosopher cannot afford to narrow an applicability of a concept through its definition, a luxury often relied on by a scientist, the equivalence relation of personal identity will necessary be of a complex and somewhat bizarre nature, with the problematic issues of psychological and physical changes accounted for within the attributes used for comparison. Nevertheless, I believe not only that such an equivalence relation can be found, but, more significantly, that the relation will prove to be a precise definition and an important insight into the problem of personal identity.
In mathematics, the concept of identity is expressed as an equivalence relation - a relation satisfying three simple axioms, reflexivity, symmetry and transitivity. Usually, although by no means always, satisfying these axioms amounts to what translates into plain language as “X is equivalent (identical) to Y iff for each relevant attribute A of X, Y also possesses A.”
For example, a physicist would differentiate between elementary particles based on half a dozen or so properties such as mass and atomic spin. For our physicist, all electrons are interchangeable and indeed identical, as if there was only one abstract electron occupying a multitude of locations spread across both space and time. This approach, bizarre as it may seem, is perfectly satisfactory from a purely experimental perspective, although, at the first sight, it cannot be extended to the more involved case of personal identity.
Sometimes, however, a physicist wants to differentiate between particular “instances” of that abstract conceptual electron. In that case, it is usually apparent that the straight-forward approach of adding the spatio-temporal location of the particle to the set of its attributes is not sufficient, as the experiment's context involves the troublesome concept of time which always implies some kind of continuity. It becomes evident that the special treatment required of time becomes the single most difficult aspect of defining equivalence relations, although in case of particles, one usually solves the problem by treating the spatio-temporal paths as a single attribute.
If the physicist happens to enjoy intellectual challenges, he will proceed to analyse more difficult cases which occur when a particle is destroyed and a different particle is created from its energy. Fortunately, Nature created out of its kindness well-defined boundaries between different types of elementary entities, and so I will content myself with recognising the contrived nature of the metaphysics involved in any such experiment, and will not treat the issue any further. It should be clear, however, that we may talk of an electron which occupies a certain orbit of a certain atom, or one that traces a particular path in the cloud chamber, but that assigning any more “magical” identity to an electron is more than slightly contrived.
Based on the above, rather lengthy, introduction, I will differentiate between two different senses of identity. In the first sense, each equivalence class may contain an arbitrary number of elements, as in the case of the abstract electron discussed above. I will refer to this approach as the weak identity. In another sense, each equivalence class contains at most one element, each object being identical only to itself. The later case, represents what I call a strict identity, and is the usual sense in which identity is understood in philosophy. Although, logically, the two concepts are not well defined and should be treated as a convenience rather than a formal classification - weak identity being reducible to the strict identity with a help of an abstraction similar to the above analysis of electron - the two concepts have very different metaphysical implications which must be recognised in order to understand the issues involved in personal identity.
In his essay titled What we Believe Ourselves to Be (Derek Parfit, Reasons and Persons, 1984), Parfit proposes a quite different classification of identities. He distinguishes between a qualitative and a numerical identity. Qualitative identity is based on the attribute calculus similar to that involved in the weak identity as defined below, although some attributes, namely spatial location and the object's history, have for some reason been taken a priori as inapplicable. Parfit does not provide any clear description of what exactly constitutes numerical identity, which, it is claimed, captures the common sense perception of personal identity. Parfit proceeds to define two criteria - psychological connectedness and physical continuity - which to me look suspiciously like reverting to a narrower version of qualitative identity. Because, it seems, the solution of the question of personal identity necessary involves a search for a suitable set of attributes necessary and sufficient for maintenance of identity, I will assume that such a set can be found, and that the solution consists of that, uniquely determined, set of attributes, even though, strictly speaking, I have no grounds for presuming its uniqueness. In other words, I take the Reductionists' approach to identity, assuming that the numerical identity is reducible to a qualitative identity when only a subset of the object's attributes are used for comparison.
We can now proceed to analyse the problem of teletransportation as raised by Parfit in the article mentioned above. In Parfit's example, a person is replicated to produce an exact copy indistinguishable, psychologically as much as physically, from the original. Neglecting the probabilities involved, the issue certainly challenges our understanding of the concept of personal identity. Parfit presents two cases; in the first one, the original person is destroyed before being recreated. Because many seem to regard this case as essentially equivalent to the more traditional methods of transportation, Parfit proceeds to describe a situation in which the original continues to exist alongside the replica. If, as most people hold, in the first case personal identity of the subject is transfered to the replica, the second “branch-line” case, being of no substantial difference to the “simple” one, must leave us with two people possessing the same personal identity.
Teletransportation is suspiciously similar to our physicist's treatment of electrons. In both cases, we are dealing with a number of entities qualitatively indistinguishable from each other provided we refrain from examining their spatio-temporal histories. While indistinguishable, the replica certainly is not strictly identical to the original, by the virtue of the definition of strict identity. To validate this claim, it is enough to note that any change to the teletransported person after she has left the teletransporter on Earth will not be automatically reflected by her replica on Mars. If the replica happens to cut herself or experiences trauma, none of these experiences is felt by the person on Earth. This feature is characteristic of naive qualitative equivalence relations, which are not transfered across changes. While some philosophers, including Parfit, approach this weakness by narrowing the choice of attributes, I believe that approach to be doomed when cases such as teletransportation are analysed. Specifically, it seems that the commonly understood identity allows for a spectrum of changes broad enough to render any such restriction too harsh.
For the sake of consistency, we must accept that teletransportation, even in its simple form when the original ceases to exist before the replica is created, does not transfer personal identity, but merely creates a person indistinguishable from the subject, in the same way as two siblings may be indistinguishable immediately after birth. To conclude my case against teletransportation, I do not see how someone who has underwent teletransportation should be the same person as before, any more than a carefully replicated artifact is the original.
Although teletransportation, as presented by Parfit and others, is relatively easy to analyse, it may be possible to introduce a variation which is by no means obvious. Imagine a case when the Teletransportation Agency runs out of the raw materials on Mars, and after destroying the poor passenger on Earth, sends a space ship with her remains. The passenger is reconstructed from her original matter, and, after waking up, issued with an apology similar to one of the clichés well know to all public transport authorities around the world. I will return to this case later when discussing various continuity principles proposed by Parfit.
Parfit distinguishes between the Reductionist and Non-Reductionist views of personal identity. Of the second view, he identifies two specialisations, namely that of the Cartesian Pure Ego and the Further Fact View (see: What We Believe Ourselves To Be - The Other Views). Neither of the Non-Reductionist views seems particularly plausible and, although there may be no clear evidence against their correctness, because there is remarkably little evidence for an existence of any “further fact” or a Cartesian Pure Ego, one may discard both as mere intellectual devices, hardly of any value to a realist. One could argue that postulating existence of an abstract substance of identity is redundant if the identity can be explained without reference to such substance. At any rate, regarding a “further fact” as anything but yet another attribute sounds strangely contrived. On the other hand, identifying the Cartesian Ego with the entity itself could be seen as reducing the problem to that of the identity of the Ego, thus hardly supplying a satisfactory answer.
Two popular variants of the Reductionist View are those identifying personal identity with the physical continuity and psychological connectedness. The two concepts have been explained by Parfit in the above mentioned essay, and try to capture the informal continuity which connects a person throughout their history, putting emphasis on the physical and mental continuity respectively.
The importance of the two continuity principles lies in their intuitive applicability to the concept of strict identity. Arguably, it is a peculiarity of the concept of time that identity through time is a continuity principle. Thus, to complete the picture of personal identity, it only remains to state precisely the subject of this continuity. In other word, we must find out what exactly is continuous.
Parfit, in Reasons and Persons argues against physical continuity based on the example of teletransportation. Because I have already stated my objections to his conclusions about the teletransported person's identity, this does not seem to be a valid objection to the principle, although arguably the physical continuity principle is not sufficient for the sought after relation.
The psychological continuity principle is an appealing one in that it allows for temporal gaps such as unconsciousness, provided these gaps may be bridged. The concept is not foreign to the mathematical definition of continuity, where it is represented by removable discontinuity, a discontinuity which may be avoided by adding a single mapping point. In philosophical terms, this is equivalent to “ignoring” a finite continuous amount of time for the purposes of maintaining overall continuity. In this way, various cases such as the Multiple Personality Disorder can be handled without impact on the meaningfulness of the psychological continuity principle, which intuitively seems to capture the essence of personal identity.
Here, I am not going to answer the issue of a person whose psychological continuity has been abruptly terminated, such as the case of the neuro-surgery example presented by Parfit, because, although I insist on the existence of the correct answer, I am unable to satisfactory argue my personal choice in the matter. For that reason, below I retain both continuity principles, which, supporting each other, will satisfy either alternative.
There is, however, a problem with the continuity principles. It is possible to analyse a spectrum of cases differing gradually in small physical or psychological details. The persons presented at the extremes of such spectrum would differ completely from each other, and thus it would seem artificial to identify them as one. Parfit is unable to avoid this difficulty, being left with a vague notion of identity, in which, he claims, various intermediate cases in the spectrum cannot be assigned to one of the identity classes at its extremes. Later in the essay, I will show how this issue is dismissed by abstracting Parfit's Reductionist View.
The interesting challenge is that of translating the continuity principles into qualitative terms, in the spirit of my above reduction of the numerical identity to a qualitative one. Because the property of a continuity does not exist within a spatio-temporally isolated entity, but rather between a pair of such entities, one can say that two entities, X and Y are identical iff the ordered entity pair (X, Y) has the property of a continuity. As stated above, this definition seems over-complicated. However, by introducing an important abstraction, a much more appealing concept of identity can be arrived at.
To see how the continuity principle can be abstracted, I will again refer to the calculus definition of continuity. In mathematics, continuity is a well-defined property, which, however, is applicable only to functions (or mappings), rather than static entities such as numbers. This is an important distinction which, it seems, has been neglected by Parfit, who insists on refering to the continuity of discrete entities. I believe that the correct way of viewing a person, at least from the point of view dictated by the problem of personal identity, is to see a person as a process beginning with conception or birth and proceeding through their personal history until death. Such a process may be called a dynamic entity in contrast to the traditional static entities. Although this is not an original idea (Roderick M. Chisholm mentions it in the third section of his essay The Loose and Popular and the Strict and Philosophical Senses of Identity, giving further references), unlike others, I would like to insist on this view as a necessary logical consequence of the acceptance of temporal continuity as an essential part of personal identity. While temporal continuity may not be sufficient for identity, it certainly is necessary for it given the underlying Realist View. Thus, one says that an abstract entity such as that formed from one's childhood, adolescence and adulthood through to death forms one person complete with their strict identity by the virtue of its physical and psychological continuity. On the other hand, the compositum of the childhood of Howard, adolescence of William Butler Yeats and the adulthood of John Paul II does not form a single person because it does not posses the necessary continuity attribute. a and b are the same and one person iff they are qualitatively and spatio-temporally identical dynamic entities poses-sing physical and psychological continuity.
Now, we are ready to attack the problem of vagueness introduced by Parfit's spectra once again. It should be clear that, when the changes are taken as properties rather than forces acting between temporally isolated entities, the spectra loose their meaning. In the light of my approach, a range of cases, each slightly different from the other, either represents a single person with a clear spatio-temporal continuity, or refer to completely different, alas strikingly similar people. By undergoing a neural surgery that converts the subject into Greta Garbo, the person does not become Greta Garbo, but rather is indistinguishable from her in the manner similar to the case of teletransportation. The maintenance of continuity suggests rather than the person may be described as one who underwent the change. The change, strange as it is, becomes an attribute of the person's history.
I have stated in the introduction that if an equivalence relation is to capture the concept of personal identity, in addition to definining a strict identity, it must remain compatible with the traditional common sense approach to personal identity. Thus, an appropriate equivalence relation must provide for a degree of modality. However, it may be argued that my above definition says little else than that two people are the same if they are identical in every aspect. Consequently, this, somewhat over-deterministic approach, must be reconciled with the concept of possibilities, in particular the possibilities of differences to one's personality. This can be acomplished by yet another level of abstraction to the concept of an attribute. An entity may be attributed a spectrum of contradicting properties, provided only one of these is actual, and all the others are mere possibilities. For example, I, at one particular time, may be said to have a property of being capable of speaking with a range of accents from the purest to the most horrible foreign one that I am doomed to use. However, only one of these accents is actually used by me, as should be evident to anyone after a short chat with me. Note that this approach, instead of discarding possibilities, attributes more metaphysical weight to them than traditionally has been done. The above approach properly handles the problem of identity across possible worlds and even encourages such interpretations.
To conclude my discussion of dynamic identity, I will compare it with the system of compositia introduced by Chisholm in his essay The Loose and Popular and the Strict and Philosophical Senses of Identity (Roderick M. Chisholm, 1969), Chisholm discards philosophical significance of most of the popular concept of identity of entities, replacing it with a somewhat rigid “mechanical system”, in which identity is preserved by sub-entity rearangements and destroyed by most inter-entity activities. Because such approach is hardly applicable to persons, Chisholm is forced to recognise the uniqueness of the “Strict and Philosophical” sense of identity such as the numerical personal identity. My belief is that the chief problem with Chisholm's approach was his insistence on the temporal separation of entities which are subsequentially grouped into equivalence classes defining distinct in time instances of the same object. This approach can be quickly recognized as an example of a weak identity, and thus unlikely to succeed when applied to persons. Once again, the necessity of a dynamic aproach is demonstrated.
As every kind of identity, numerical personal identity is an equivalence relation which may be reduced to a qualitative analysis of the subjects of the comparison. Although the uniqueness of each person may be worrying to anyone searching for this relation, once the strict nature of personal identity is recognised, it is evident that personal identity may not be used to equate separate entities, and, thus, it becomes necessary to recognize a person as a time-spanning entity. By searching for a formal description of personal identity, we have not only succeeded in solving the problem, but have constructed a model of reality, which, by retaining temporal integrity, provides a deeper insight into the nature of persons and objects with respect to time.
Patryk Zadarnowski, Sydney 1998