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Self is Personal Identity over Time

An Essay By Trevor Stone

November 1997, Senior Year of High School, University of Colorado

[Author's note: the following document contains a few characters which may not be correctly rendered by your browser. Any reference you see to x2 is supposed to be x squared. Other math symbols, in order, are not equal to (twice), plus/minus, and radical (square root).]

The law of identity states that two things are identical if and only if all properties held by one are held by the other and vice versa. By this law, I am not technically the same person I was yesterday because at least one property, age, is different. But it seems that I am the same, both from the outside and the inside. Surely I may be a little different, but even the language we use, "I am not technically the same person I was yesterday" implies that there is some underlying self. I seem to sense some identity with the person I was long ago, but what makes us the same or different from past selves? The answer to this long-standing problem is that I am never the same person, by the definition of "same," but that both people are an instantaneous value of me; they are person-stages of my self.

This tricky concept may best be viewed in terms of a graph of personal identity over time, that is, self = personalidentity(t). To know exactly who Trevor is, a graph must be made of all person-stages of Trevor, or his personal identity at each time t. Once all points are plotted, the resulting graph is a graph of Trevor, someone who exists from a specific time (birth) to another time (death) and assumes all values of the graph over time.

This begs some definitions -- specifically, what are persons, person-stages, and selves? First of all, I must explain what I mean when I talk about persons. This essay will only be concerned with human persons, but the argument can easily be extended to other types of things which could be "people" (dolphins, apes, spirits, computers, etc.). Insofar as human persons are concerned, the person must have or have had a body, or else it wouldn't be a human.

The other required part of a person is consciousness. Consciousness is any combination of perceptions, thoughts, and memories. Someone who is perceiving but not thinking has consciousness, someone who has withdrawn all sensory perception but is thinking and remembering has consciousness, someone who is asleep has a low level of consciousness, because things like alarm clocks are perceived. Self-awareness is not required for consciousness, that is, someone does not have to realize that he's conscious to be conscious. Thus, a sleeping woman is a person, since she has at least some level of consciousness; a dead woman is not a person, since she has absolutely no consciousness, assuming there isn't a "hovering consciousness" that people talk about from near-death experiences.

Sometimes, a body or consciousness at one time is said to be the same as a body or consciousness at a different time. What is, in fact, meant is that the two are part of the same continuum. If a body is continuously observed from one time to another and exhibits continuity (it may change, but at no point does it suddenly become a different body), one may say that the two body-stages are part of the same body continuum. They are not the "same" body, because they are not identical, but they are both parts of a continuum that lasts over time. The same can be said about consciousnesses.

Two body-stages or two consciousness-stages can be part of the same continuum even though they are not observed continuously. We can infer that a body-stage is part of the same continuum as a previous body-stage if the two have the same DNA, similar appearances, or many of the same cells, though we can't be absolutely certain. We can also infer that if this determination has been made at several intermediate times, the first and last body stages are part of the same continuum. The best measure to determine whether or not a consciousness-stage is part of the same continuum as a previous consciousness is if it remembers being the previous consciousness. Another way to determine this relationship of continuity is to find out if the consciousness perceives and thinks in the same way, but this is very difficult to do. Determinations about body continua are best carried out by external observers; determinations about consciousness continua are best made by the internal observer.

Another term to define is the person-stage. What I mean by person-stage is a self at a single instant. This is technically the same thing as a person, but will be used for clarity. The person who wrote this sentence is a person-stage, a person at a single instant. Both a body-stage and a consciousness-stage are necessary for a person stage to exist in this definition. Person-stages can be vastly different at different times. The Trevor of today is very different from the Trevor of age 2. They can also be quite similar. The only differences between Trevor at 12:01 and Trevor at 12:02 are that the second person-stage is a minute older, perhaps a few cells or strands of hair have been lost, and atoms have rearranged themselves.

Self is one of the hardest concepts to put into words, yet we have some deep understanding of it. Self is a function over time, self takes on various values for each input of time. The self of Sue Smith is made up of all of the instantaneous Sue Smiths over time. Sue Smith at any given time is the sum of the values at that time of the body assigned to Sue Smith and the consciousness assigned to Sue Smith. It can be expressed as a function of ssSelf(t) = ssBody(t) + ssConsciousness(t). With the proper system, self could be made into a graph with three dimensions (time, body, and consciousness) so that at any given time, a value is produced for the stage of Sue Smith at that time. The self of Sue Smith is the set of all of these values. The graph as a whole would be a visual description of Sue Smith the self.

The value of a self is usually a person-stage, but it doesn't have to be. A self is defined as a specific body/consciousness pair. If one of the two factors is lost (the body loses consciousness, for example), the value of the self is just the value of the body, because the zero value of consciousness contributes nothing. This body without consciousness is not a person-stage because it's not a person, it's merely a stage.

Some people may object to this definition of self as merely body and consciousness, saying that there is more to a person than these two factors. It is certainly possible that other aspects like spirit or soul make up a person. In this case, if Sue Smith is defined by body, mind, psyche, and spirit, her graph becomes five dimensional. Everything presented in this essay could be expanded to include further aspects of self, but shall be limited to body and consciousness to keep things clear.

Some might further object that they feel no identity as a graph, they feel identity as a person. This is, more or less, what I'm arguing. Sue Smith is not the graph, the graph is a visual representation of Sue Smith. Sue Smith is each of her person-stages, taken together. Most people sense this sort of identity -- they feel that they are more or less the same person of a previous time, and each stage in between.

A mathematical function is not a number; rather a function defines a set of values for various inputs. For example, the function F(x) = x2 is the set of all results when each possible x value is squared. The graph is F, while 9 is an instantaneous value taken at a specific x value, namely 3. In the same way, Sue Smith is the set of all person-stages of Sue Smith at every possible time, and when I say, "I see Sue Smith," I see a specific person-stage at a specific time.

As another example, the Mississippi River is all of its river-stages from its source in Minnesota to its mouth at the Gulf of Mexico. If you cross the river at St. Petersburg, Missouri, and at Memphis, Tennessee, you have crossed the same river, but at different places and different times. In the same way, if you met Sue Smith last year and today you would have met two different person-stages of the same Self.

It is tempting to say that if you met Sue Smith yesterday and today, you have met the same person, but this is not correct under my view. At x=1, F(x) = x2 has a value of 1; at x=4, F has a value of 16. Both 1 and 16 are numbers, but F is not a number, merely a function. Even though all values of F are non-negative numbers, F itself is not a non-negative number. Similarly, we can't say Sue Smith the self has brown hair because hair color is a property of person-stages, not of selves. Thus we must be careful to speak of persons only as single outputs of self, rather than as identical to a self.


What are the ramifications of this view of self? First, it involves some linguistic changes. Technically, we cannot say, "Trevor is sitting in a chair," we must say, "A person-stage of Trevor is sitting in a chair," because Trevor occupies a large number of places in space-time. This does not mean that we must change our language to embody philosophical correctness. In common usage it is understood that when we say, "Trevor is sitting in a chair," what is meant is that "The current person-stage of Trevor is sitting in a chair."

Further, there is a distinction between "I of now" and "I over time." If I state that "I am hungry," it is clearly a comment about my current person-self. If, however, I say that "I enjoy studying philosophy," it is a comment about more than just the current person-stage. Yet it is not describing my self, because enjoying isn't something selves do, but what people do. Rather, this statement is making a generalization about my person-stages as a whole. In a similar way, it can be said that most of the values of x2 are above 10, which is a generalization of values. A statement about the function x2 itself would be something like "It's graph is moderately steep."

This view of self allows a self to exist despite discontinuity of personhood. For instance, under the Lockean view that the self is defined by psychological continuity, if Sue Smith suffers amnesia, she is no longer Sue Smith, because she has no memory of being Sue Smith before the amnesia. Yet we are tempted to assign the same self, because the body is more or less the same. This problem is solved by my definition of self: the value of the graph of Sue Smith is quite different before and after amnesia, but both sections are part of the same graph.


The objection can be made that the graph of Sue Smith is discontinuous when she has amnesia, so how do we know Sue Smith afterwards is the same self as Sue Smith before?

First, the graph is not discontinuous. Sue Smith is defined as a specific body continuum along with a specific psychological continuum. The graph of Sue Smith is really a three dimensional graph, having axes of time, body, and consciousness. When she loses consciousness, the value on the consciousness axis drops to 0, so while she is unconscious, the graph is in only two dimensions (her body and time). The original equation of ssSelf(t) = ssBody(t) + ssConsciousness(t) reduces to ssSelf(t) = ssBody(t) + 0 temporarily. The values of Sue Smith are quite different after amnesia, but they remain part of the graph.

Suppose Sue Smith's person-stage suffers a severe injury and loses consciousness permanently and completely. Is the current human "vegetable" lying in the hospital a person-stage of Sue Smith? Well, first of all, the human is not a person because it lacks the capability of consciousness, which is required for personhood. However, since the value of the self of Sue Smith is the physical states plus the psychological states, the human in the hospital is a stage of Sue Smith, with the consciousness value reduced to zero. From the point of injury on, the graph of Sue Smith becomes merely body and time: ssSelf(t) = ssBody(t) After the injury, the values of Sue Smith are no longer persons, because they lack consciousness, but they are still stages of Sue Smith the self.

But suppose that, after a time in the hospital, the body lying in the bed regains consciousness, but can remember absolutely nothing about being Sue Smith before the injury, and the personality is very different. The two person-stages are completely psychologically discontinuous. We can now deduce that the post-amnesia body-consciousness pair is a new self, since the old self was defined as the old body continuum plus the old consciousness continuum and the body is now connected to a new consciousness continuum. Sue Smith would still exist, but during and after the amnesia, the graph of Sue Smith would again consist only of body and time, Sue Smith's consciousness having ceased. Sue Smith from the beginning of amnesia on is merely the body. When the new consciousness arises, the new self is the new consciousness coupled with Sue Smith's body. (It is, of course, possible that the original consciousness returns, in which case the person after the incident would still be a stage of Sue Smith, but we cannot verify this without memories.)

This situation can be symbolically expressed as:
ssSelf(t) = ssBody(t) + ssConsciousness(t)
after amnesia: ssSelf(t) = ssBody(t) + 0

ssBody(t) = jjBody(t)

ssConsciousness(t) ≠ jjConsciousness(t)

jjSelf(t) = jjBody(t) + jjConsciousness(t) = ssBody(t) + jjConsciousness(t)


In my theory, there are two possibilities regarding life after death. First, it's possible that at the death of the body, the consciousness dies as well, and since the value of the self is zero plus zero, the self ceases to exist. Alternatively, Sue Smith (the self) could quite possibly continue to exist after the death of the body, though the body value would remain constant at 0. In this case, Sue Smith the self continues to exist after the death of a person-stage. Sue Smith's graph after death would consist of consciousness and time (since the body associated with Sue Smith is dead). At this stage, Sue Smith the self is just the consciousness.

In the case of reincarnation, after some time, Sue Smith's consciousness becomes attached to a different body. The person, call her Jane Jones, which has Sue Smith's consciousness and a different body is a value of a different self than Sue Smith. A different body/consciousness pair is a different self. Thus, if Jane Jones remembers being Sue Smith, but has a different body, she is not Sue Smith (as John Locke would say), but rather shares the same consciousness.

Symbolically, this situation can be expressed as follows:
ssSelf(t) = ssBody(t) + ssConsciousness(t)
after death: ssSelf(t) = 0 + ssConsciousness(t)
ssBody(t) ≠ jjBody(t)
jjConsciousness(t) = ssConsciousness(t)
jjSelf(t) = jjBody(t) + jjConsciousness(t) = jjBody(t) + ssConsciousness(t)
We find similar results in the case of multiple personalities. If a body has multiple personalities which do not share psychological continuity, each body/personality pair is a different self, and when a specific personality is not active, the consciousness portion of that person is reduced to zero for the time being. So, a "person" diagnosed with four separate personalities is actually four selves sharing a body. A sort of psychological version of roommates.


With my view of self, interesting things happen in a "split-brain transplant" This is a situation in which a doctor takes one half of Sue Smith's brain and puts it into one body, call it Sue Jones, and the doctor then takes the other half of Sue Smith's brain and puts it into the body of Jane Smith. Both new people then awake and remember being Sue Smith. The question arises: "Which one is Sue Smith?"

According to Parfit, there are three possible answers: she is neither, she is both, or she is one of the two, and he then goes on to say that they are all absurd. My view of self lends itself nicely to another solution.

First, as was established above, statements that are about Sue Smith as a "person" are generalizations about the values of her graph. Sue Smith, however, is a self, so the above question is asking "What is the value of the graph of Sue Smith?" And the answer is "The value of the consciousness of both Jane Smith and Sue Jones plus the body of the old Sue Smith."

The obvious complaint about this answer is "How can she be two (or three) separate people?" The answer is that Sue Smith now consists of three main parts, the consciousnesses of Jane Smith and Sue Jones, and the body associated with Sue Smith, now deceased.

Sue Smith cannot be talked about as easily after such a transplant, since she can no longer be seen as a function. The answer to the question "Where is the instantaneous Sue Smith," is that "One part is here, one part is there." Similarly, the mathematical graph of ± √x has two different numerical values for a given x input.

These characteristics need not be connected to be considered the same self. When we talk about things, we often ignore the space between parts. Indonesia consists of several islands, but the answer to the question "Which one is Indonesia" is "All of them together." Even when we talk about the very small, we are combining two parts over distance. Just as Indonesia isn't a single island, a self at a given time is not necessarily a single person, though it usually is.


How does my view of self measure up to the views of other thinkers? For one, it is similar to the view that Parfit holds, that identity is a matter of degrees. Parfit states that personal identity is no more than psychological continuity in a one-one basis, and that psychological continuity (and thus personal identity) is only a matter of degree. This is true under my view of self, but it's not the whole picture. Someone's identity as a person changes; two person-stages which are close to each other in time are quite similar, while two far-apart stages will share much less in common. Yet they're all part of the same self. So Parfit is correct about personal identity, but not about the self, which is different from identity.

Hume states that there is no identity between two person-stages, merely resemblance. He is correct in stating that there is no identity of any two person-stages, but fails to recognize them as parts of an overall self, rather than self at an instantaneous person-stage. My view also allows for the fact that someone is aware of and can remember his past person-stages; he is aware of his past self. Under Hume's empirical view, when Sue Smith's person-stage looks inward, it can't sense a self, merely a bundle of perceptions, and so there is no self aside from a bundle of perceptions. Yet the body and awareness of Sue Smith are continuously present, not almost-exact persons flashed at rapid speed. So while no two Sue Smiths (as person-stages) are ever the same, taken together and continuously, they form Sue Smith (as a self).

Holders of a Humean view of self may object to my view of self by stating that it merely complicates things, that all I'm doing is drawing a graph so that I can talk about similar people as one. However, my view retains the fact that two person-stages are never the same, while holding to the intuitive idea that Trevor now is somehow the same as Trevor at age 3, since Trevor is defined to be a specific body plus a specific, psychologically continuous mental state. It lets us make generalizations about and take actions on a self. If a large number of person-stages of a self share certain traits, we can often make the assumption that most of the future person-stages will also share that trait, since it is characteristic of the self. My view also works where Hume's does not, in that it explains why we are aware of being past person-stages, and in that we are aware of self over time.

Some people might object to my view of self by saying that the value of a person-stage is somewhat vague. I have claimed that in a split-brain transplant the self consists of two main and separate parts, and that consciousness can be lost while the self remains. By this view, opponents might claim, if Sue Smith donates a kidney to someone, isn't the next person-stage of Sue Smith both the body, mind, and the transplanted kidney?

This is not, in fact, the case. Since both self and person-stage are defined as a certain body plus a certain consciousness, a piece extracted from a body is no longer part of either the person-stage or the self after the transplant. If a kidney is removed from Sue Smith's body, her body portion merely has one less kidney than before. If, however, Sue Smith is completely taken apart so that the body is no longer that of a human (or if it dies), the body portion of Sue Smith is reduced to zero. If Sue Smith's body was somehow split into two separate functional humans, a physical analogy to the mental split above, Sue Smith's body part would be the sum of both parts.


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