Completeness and Invariance in Science
Completeness and Invariance in Science
Introduction
In science there is a basic requirement that the laws of nature be the same for all people. We will call this the requirement of invariance. Furthermore, there is a goal in science that the laws of nature explain everything. We will call this the goal of completeness. I will show that, so long as invariance is maintained, completeness can never be achieved.
Truths About The Self
In order to avoid becoming confusing I will begin with a definition. The self is the person who is writing these words (the author). When I (the author) mention the self, I am talking about me (the author) because I believe that I (the author) am the self. But I expect that the reader will make appropriate translations so that he or she will be able to follow the same reasoning as me. For example, if Joe is reading this paper, it would benefit his understanding if he believes that the self is Joe.
The question we now ask is, "Is the self real?" By real I mean worthy of specification. If the self were not real then a question like, "Why am I hungry," would be nonsensical unless it were in a context where the reference to "I" was substantiated. For example, if Joe were the one asking this question, we could understand it as an abbreviation of the question, "Why is Joe hungry," thus making it valid.
On the other hand, if the self is real, the question, "Why am I hungry," could stand on its own. This question would have an answer even though its subject is nothing more than the self. And if the self is a valid subject of our questions, then there should be a scientific answer to these questions (if science is complete).
Clearly an invariant science cannot admit that the self is real. If it does, it must admit that the self has certain properties (such as hunger) that not all people have. If science agrees that the self is hungry, everyone who isn't hungry will disagree with science.
The problem here is that a scientific explanation of the self must admit a means of determining who the self is. It must answer the question, "Why am I me?" In doing so, it will alienate all but one person, thus violating the requirement of invariance.
There are two ways of solving this problem. The first, which I believe is best, is to abandon the goal of completeness. I will discuss this later. The second solution is to reject the reality of the self.
In order to believe that the self is not real, I must believe that I am in no way especially unique from other people. When I am hungry, I must believe that this fact is no more significant than the fact that anyone else is hungry. Indeed, my thoughts must not indicate any form of individuality. As an illustration, suppose that Joe believes that Joe is hungry. Suppose also that Joe decides to eat because of this belief. Now, obviously Joe wouldn't eat just because he though Dave was hungry, so he must believe that there is something special about Joe (he believes that Joe is the self).
I don't think it is possible for rational people to believe that the self is not real.
The Axiom of Self
If we accept the existence of the self, and we agree that science must be invariant, we must conclude that science cannot be complete. But how can we fill the gap? How can we answer all of the important questions about the self without becoming mystics?
We should introduce a pseudoscience. This pseudoscience is almost exactly the same as regular science except it has one additional axiom. I call it the axiom of self. It says, "I (the author) am the self." This axiom would be different for different people because, unlike science, a pseudoscience is not invariant. One has only to put their name in place of the subject of the axiom in order to create their own pseudoscience.
Once we have added the axiom of self, we can answer questions like, "Why is the self hungry?" The pseudoscientific answer is: "the self is hungry because my (the author's) brain is in a certain state." Our pseudoscience (of which biology and psychology are of course a part) has little trouble answering such questions, as long as it knows who the self is. In fact, a pseudoscience has more explanatory power than regular science because it is more complete.
The Personal Identity
Problem
What Future People Will Believe
Consider a replicating machine consisting of a replication chamber and two exit chambers. If someone enters the replication chamber, two identical people will soon appear in the exit chambers and the replication chamber will be empty. The machine may work by merely moving the person from the replication chamber to an exit chamber and creating a replica in the other chamber, or it may work some other way. Regardless, both people in the exit chambers will be indistinguishable with the one exception that one person will be labeled A and the other will be labeled B.
Now, if some person, N, is placed in the replication chamber, two people will emerge from the exit chambers, NA, and NB. If both NA and NB are subsequently returned to the replication chamber, four people will be produced: NAA, NAB, NBA, and NBB. If this process is continued many times, we will soon have a vast pool of people, all of whom will remember having been in the replication chamber the same number of times. Furthermore, they will all have different names, as shown below.
Unlike us, these people will have had first-hand experience with replication. So if we were to ask one of these people about personal identity, what would they say? For example, what if we asked NBAABBBABAAAB what happens when someone steps in the replication chamber? Most likely, he will believe that, each time a person steps into the chamber, this person has equal chances of becoming A or B. Indeed, if NBAABBBABAAAB looks back at his own experiences with the replication chamber, he will see that his becoming A or B was, as far as he can tell, completely random.
With the possible exception of a very small group of people (like NAAAAAAAA... for example) we will find a general agreement with this assessment of the machine's operation. This will be true regardless of how the machine actually works, as long as the two resultant people are indistinguishable in all except for trivial matters (like their names, fingerprints, hair color, clothing, etc.).
This will also be true in any society where replication (or a similar activity) is common. Because it derives from empirical experience, I call this the common sense view. And because human replication (or a similar activity) seems inevitable considering the rapid rate of technological advancement, I think this is what future people will believe about personal identity.
The Triviality of Personal Identity
The difference between my body and other people's bodies seems to be trivial. In other words, there is nothing about my body that differentiates it fundamentally from all other bodies. However, my body is very special because I am in it. Other people will not agree with this fact. They will say, "Your body is not special, mine is. I am in this body, not that body." Despite this lack of agreement, I still know that this body is special. To argue otherwise is to argue that I do not exist.
Thus, the answer to the question, "Why am I me?" or "Why am I in this body?" must be trivial. Indeed, the only answer that is plausible is that, of all possible bodies, this one was randomly selected to be mine. This is an example of a fundamental question about self that has a trivial answer. Why then should we believe that questions about personal identity cannot have trivial answers?
What Evolution Would Have Us Believe
Let us consider for a moment a hypothetical race of people that has had easy access to replication machines for millions of years. Let us also suppose that these machines require large amounts of fuel in order to operate, so the people can't just replicate as much as they want.
Now, since these people will have been exposed to replication for so long, presumably their species would have evolved so that they are naturally inclined to have beliefs about personal identity that would take account of the replication ability. These beliefs would be the beliefs that would be best for the species.
If one of these people had the opportunity to be replicated for free, what would he do? Remember that his beliefs about personal identity would coincide with what is best for his species, and it is of course better for a species to increase in strength. This would be the basic effect of replication: an increase in population. Replication would be means for reproduction, perhaps even psychologically equivalent to sex.
To be more explicit, to be replicated would be about twice as good as ordinary survival for one of these people. This is because it essentially doubles the amount that a person benefits the species. If we define the cumulative utility of a species as the overall likelihood of its members to raise children, fight in wars, make discoveries, build buildings, etc, then by being replicated, a person increases the cumulative utility by his current utility, which is twice as good (for him) as only providing his current utility.
This conclusion is certainly foreign to us, who do not live in a world where replication is yet plausible. I know of no philosopher who advocates (or even considers) the view that replication would be, by itself, better than ordinary survival. However, because replication (or a similar activity) seems inevitable considering the rapid rate of technological advancement, I think that this is what beings of the very distant future will believe.
Because this view derives from evolutionary principles, I call it the natural view.
Concern For Past Selves
Dave is a professional athlete. One day, he receives a letter asking him to come to a scanning facility to get his body scanned. This scanner can create a precise record of every atom in Dave's body. It is explained that, for the time being, the scan will only be used for research. Furthermore, Dave will have complete control over how it is used in the future.
This seems like a good idea to Dave. The medical applications seem endless and, who knows, maybe when he is old he could have his old body rebuilt. Besides, what does he have to lose?
When he gets to the scanning facility, Dave uncovers a shocking truth. The real reason for creating the scan is so that, at some point in the future, new Daves can be created for use as slaves on Mars.
Obviously, Dave is appalled by this idea and decides to leave. But his escape is thwarted and he is forced into the scanning chamber where the scan is made. Will Dave end up on Mars among a thousand copies of himself?
If the plan of using Dave for manual labor is followed through, and we accept the common sense view about personal identity (see above), that seems like at least a possible, if not highly probable result.
But either way, there will still be Dave 1. Dave 1 will walk out of the scanning facility with a stern warning to keep quiet. Dave 1 will obviously never end up on Mars (assuming he lives a normal life), but should he care about his Mars-clones? Specifically, should he take action to destroy the scan of Dave?
Assuming Dave 1 isn't a particularly principled man, there seems to be little reason for him to do so. Even if the copies are made, he will never be transported to Mars.
Clearly, however, this is the wrong answer. While Dave 1 has no self-interested reason to destroy the scan, he does have a reason. But this reason is retrospective; it is a concern for his past self.
It arises before the scan occurs. During the short time between his discovery of the scanners' treacherous intentions and the actual scanning procedure, Dave should try to instill in himself a conviction to destroy the scan once he is released. If Dave 1 has this conviction, he will overcome his self-interest and destroy the scan. If he does not, he will have no reason to destroy the scan. In other words, Dave can eliminate the possibility of ending up on Mars by merely developing the conviction to destroy the scan (the conviction to be concerned about past-selves). Indeed, if he fails to develop this conviction in the time he has, he will quite probably end up as one of the clones on Mars, without even any opportunity to destroy the scan.
Problems with the Common Sense View
The common sense view has some odd implications, some of which have been illustrated above. Probably the most evident of these implications is that what happens right now can depend upon what happens in the distant future. Normally we think in terms of the present being affected by the past, but the common sense view suggests that it can also be affected by the future. We will discuss some possible solutions to this problem later. For now, we will present an example to illustrate this and another problem with the common sense view.
Joe is terrified of death. He will do anything he possibly can to prevent or delay his own death. Indeed, his fear has led him to spend his life designing and building a life insurance machine.
Every morning, Joe steps into the machine and presses a 'scan' button. Then he steps out and continues with his day as usual. If, for some reason, Joe is killed during the day, the machine will notice that he does not scan himself the next morning. When this occurs, the machine will create a replica of Joe from when he last scanned himself. So long as the machine continues to work, this system supposedly ensures that Joe will never be dead for long.
According to the common sense view, this machine will only be somewhat effective. Assume for example that Joe is going to die tomorrow. When he steps into the machine tomorrow morning and presses the 'scan' button, he will have a 50% chance of becoming the replicated Joe of day-after-tomorrow. But there is also a 50% chance that nothing will happen; he will continue with the day and die as expected.
Of course, this is not what an outside observer would see. An outside observer would see the machine work as expected. Joe would step in, press 'scan', step out, die, and be re-created the next day. The 'new' Joe would claim that he had just stepped into the machine on the previous day.
But the common sense view is not about what outside observers see. It is about what replication is like for the person being replicated.
Notice that in this example, whether or not Joe has a chance of becoming a replica when he presses the 'scan' button depends upon whether or not he will die that day. It depends upon a future event. We will discuss this problem later.
Now, consider for a moment how the machine could be made more effective. That is, how can we increase the likelihood (above 50%) that the machine works as advertised? The common sense view provides a strange answer: increase the number of replicas that are made if Joe dies. For example, if the machine makes nine replicas, Joe will have a 90% chance of becoming one of them when he presses the 'scan' button on the day that he will (apparently) die. The chance that he will remain as the Joe that dies is reduced to 10%.
This is a very odd result. But notice that the added security does not come without a cost. For example, if Joe wants 90% life insurance, his 'death' will be extremely expensive. This is because there is no way to know in advance which of the nine replicas Joe will end up as (if any). Indeed, each replica will claim to be the original. Thus all of the original Joe's property must be divided up amongst the nine replicas. Thus with 90% life insurance, a death will cost 8/9 of one's total wealth.
There may also be other sacrifices. For example, Joe may have a harder time finding work due to increased competition. If he is an artist or scientist he will probably not receive sole credit for his work. If he was married he will have to either leave his wife or share her with his replicas (or replicate her too).
It is clear that, on the common sense view, the quality of one's life insurance is somewhat proportional to its cost in terms of quality of life. Because this is what we would expect, it helps to make the common sense view seem less profound.
We will now discuss what is probably the main problem with the common sense view: it implies that the present is affected by the future. To this end we will consider another example.
Dave is considering betting all his money on a single coin flip. But he is no reckless gambler. Indeed, he thinks he has found a way to use replication technology to ensure his winnings. This is his plan: Soon before making the bet, he will create a scan of himself. If he is not transported to a future replica, he will bet on heads. Then, when the coin is flipped, he will do nothing if it comes up heads. Otherwise, he will use a replicating machine to create a million replicas from the scan he made previously.
Dave knows that if he is not transported when he makes the scan, there is an extremely good chance that the million replicas would not be made. Therefore there is an extremely good chance that the coin will come up heads. That is why he will bet on heads and will almost certainly win. Is this a good strategy?
There is a 50% chance that the coin will come up heads and a 50% chance that it will come up tails. Therefore there is a 50% chance that Dave's plan will work as he hopes, ensuring his victory. But if the coin is destined to come up tails, Dave will almost certainly be transported when he makes the scan. And he will find that the coin has come up tails. But the one Dave that is not a replica will have bet on heads. Hence there is a 50% chance of losing. Furthermore, a loss is extremely expensive due to the large number of new Daves (for the reasons discussed above).
The point of this example is that even though the common sense view implies a dependence of the present on the future, it does not fundamentally contradict our sense of probability and uncertainty of future events. This makes the problem less troubling and, once again, it makes the common sense view seem less profound.
However, it also illustrates another strange implication of the common sense view. It shows that there is a link between mental and physical events. Once Dave has decided to go through with his plan, the act of creating the scan is essentially equivalent to flipping the coin. After the scan has been made, it is as if the coin has already been flipped. The 'original' Dave really does know (with near certainty) that the coin will come up heads. Unfortunately, he cannot obtain this knowledge without previously assuming the risk of being transported to a Dave that has just lost a coin flip, i.e. developing the conviction to create the replicas if the coin comes up tails.
As in "Concern for Past Selves," what happens depends very much on Dave's convictions- what he plans to do. This link between completely mental concepts such as convictions and the consequences of scanning is fascinating, but it makes the common sense view more difficult to believe.
In spite of the problems I have described, I think the common sense view remains the most plausible view on personal identity. Unlike other views, it can be shown to be somewhat consistent with common sense in a wide variety of situations, and it admits no devastating objections.
Epistemology
Introduction
Imagine a giant machine made up of millions of gears and shafts. When this machine is activated, all of the gears start turning at various speeds, and when it is deactivated, the gears quickly come to a halt.
Clearly, such a machine would never work without some source of power. If we were to try to discover this power source, we may find that a single gear is providing all the power for the machine, as is the case in many mechanical devices such as watches and clocks. However, we may also find that many different gears are providing power to the machine. Some sections could even be completely isolated from others. We could even discover that all of the gears have a certain power source of their own.
In the first case above, all we would have to do to shut down the machine is disconnect the single power-gear. In the second case, we would need to disconnect all of the various power-gears. In the third case, we would have to dismantle the entire machine before it would finally stop.
This machine, though not particularly plausible, provides an excellent analogy for epistemology. If each gear in the machine represents a single piece of knowledge, and the gears it provides power to are pieces of knowledge which it provides support for, where is the source (or sources) of power for human knowledge?
A Formal Argument
I have a great many beliefs. Some are beliefs about what is good and others are beliefs about what is true. If prompted, I can readily defend most of my beliefs. Because of this, we will say that I have a reason for believing these things. The beliefs which I have reason for believing will be called supported beliefs. If there are some beliefs that I do not have reason for believing (I cannot defend them) then they will be called unsupported beliefs.
Note that in order to defend a belief, I must be able to provide a reason (or reasons) for its validity. Obviously, these should be reasons that I would agree with. That is to say, they should be reasons which I believe to be valid. Thus, the reasons for my beliefs are beliefs in themselves, albeit perhaps a bit more deeply ingrained than the beliefs that they support.
Are these deeper beliefs supported? If so, they must likewise have beliefs that support them. And these new supporting beliefs must have other beliefs that support them. Eventually, in defending my beliefs, I will find myself left with some basic beliefs which I cannot support. Any belief that I use in their defense will lead to a circularity such that two (or more) beliefs "support" each other like several gears connected in a ring without any external source of power.
Why is this result important? Some would claim that the only source of support for knowledge must come from other knowledge. However, this claim is equivalent to saying that a giant machine can operate without any source of power. Obviously, if there is no power source, or in the case of epistemology, no knowledge source, then no knowledge has any validity.
If we are not absolute skeptics, we must admit that some knowledge is unsupported. This means that some knowledge is valid, but cannot be adequately defended (in the normal way). This knowledge takes the form of unbased presumptions; these presumptions must be unbased because any reason for their selection implies some knowledge that supports them.
The Source of Presumption
In order to philosophize, one must make presumptions. One cannot ask what presumptions he should make because any reason for making them would be a presumption itself. Nor can one ever argue for or against a certain set of presumptions because any such arguments must assume other presumptions.
Therefore, in reasoning, our arguments must be based on the presumptions that we do have, not the presumptions that, for any reason, we should have.
What is the nature of these presumptions? Clearly they follow evolutionary patterns. Some of them are self-interested and others are ethical. Some of them deal with inductive reasoning, and others with deductive reasoning. Some of them deal with memory, thought, and emotions, while others are purely utilititative, dealing with such things as pain, hunger, and itch. But at any rate we can readily see that their description is the domain of psychology.
Science and philosophy, then, are the study of phenomena and paradoxes among these presumptions and their consequent beliefs. The difference between science and philosophy is that in science, we can be assured that, after sufficient reasoning, we will arrive at truth, and that other scientists would be convinced by our reasoning. In philosophy, this is not the case.
Philosophical problems arise when a contradiction is deeply rooted in our presumptions. Because presumptions vary somewhat from person to person, resolutions to philosophical problems can also vary. Indeed, this is even true of some non-philosophical problems, but generally only in cases of stupidity, abnormality, or insanity.
Why the Personal Identity Problem Supports
This View
In the section on the personal identity problem, I described two different beliefs about personal identity. One is a belief that people of the (probably) near future will have. Because this is a view that derives from empirical experience, I call it the common sense view. The other is a belief that people of the very distant future will probably have (if they exist). Because this second view derives from evolutionary principles, I call it the natural view. There are also many other views about personal identity. Indeed, few people currently believe in either of the views I discussed.
If we accept that each of these views could be right for different people at different times, then there wouldn't be a problem. But that isn't something most people are willing to accept. Most people believe that there is a single correct view.
However, if there is a single correct view, then everyone who does not hold that view will be wrong. This would make either the common sense view or the natural view (or both) incorrect. Therefore, we would have an example of a view that is most logical to a certain group of people (people of the near or distant future) but is in fact not correct. If we admit that such views can exist, our current views suddenly become very susceptible to skepticism.
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