In philosophy there are (at least) two problems relating to the idea of the self. What is it, and how is it continuous?
You might think that the existence of a self is unquestionable. After all there is something unique about you that is the essence of your identity, right? The problem is pinning down exactly what that something could be. Maybe the self is a viewpoint within the inner world, but then what is that viewpoint itself made up of, if it is not a result of our inner world? Nor can the self be easily explained as a straightforward product of the operation of your brain, for I have yet to see a theory that correlated neural activity with a sense of self, such that when damaged the individuals acted in the same way, except for reporting no sense of self. Theories have been put forward that the self is “emergent” from the operation of the brain, but in a way this tells us little about what the self is, only a proposal of how it can come about.
The continuity of the self is no less confusing. How do I know that I am the same person that I was yesterday, or last year? The self does not seem to exist continuously (for example during unconsciousness), so how do we know that the self that exists after a period of unconsciousness is the same self as the one that existed before. Some might argue that our memories of our earlier sense of self is what creates the continuity, but what is so special about memories? Does the fact that I have forgotten the first years of my life imply that I am not the same person as I was then? What about someone who suffers from amnesia?
These kinds of problems with the idea of self have led some to argue that there is no self, that it is an illusion generated by the brain for the convenience of its operation. Evidence from psychology and cognitive science can be construed to support this view, for example the powers of hypnosis, alien hand syndrome, split brain syndrome, ect. In all of these cases it seems like parts of the mind outside of the conscious self have the ability to perform tasks and make decisions almost as capably as the self that we are aware of. This may lead us to wonder if the entire brain functions this way, and if the self is simply an unneeded artifact.
This is not necessarily the last word on the self, so don’t despair, you may really exist after all. Before we tackle the self and its continuity though let us consider the continuity of the simplest particles. It is impossible for a physicist to be continually observing a given particle, so why does he or she believe it to be the same particle when they observe it next? Since the fundamental constituents of matter are basically indistinguishable from each other how can the physicist be sure that the particle in question hasn’t been replaced by its indistinguishable copy? Physicists don’t worry about this however, because they know that the behavior of particles is governed by laws, and because they have sufficient information about the state of the system. Laws combined with knowledge of the system tell the physicist where the particle will be in the future, and when their observations do in fact place the particle where they expect it to be they conclude that it is the same particle. This principle, continuity through prediction, can be extended into the macroscopic realm, although with less precision. Consider a bike you have left in your garage. To the best of your knowledge the bike does not move itself, nor has anyone a reason to move the bike. Thus if, several years later, you find a very rusty bike in your garage you will conclude that it is your bike, slightly the worse for wear, not some other bike that has replaced yours. If on the other hand the bike is of a different construction, or in a different place within the garage you may be less sure that it is the same bike, since your predictions did not include these changes. However if you later found out that someone had moved your bike, or made alternations to it you would revise your predictions, and thus would again consider the bike you found to be the same as the one you had left.
We can apply this approach to solve the age old “ship of Theseus” problem if we wish. The problem is as follows: Theseus owns a ship, and as he sails around Greece he makes repairs to it. After a few years he has replaced every component of the ship with new ones. Can we consider this ship the same as the old one? Now consider a mischievous philosopher, who reassembles the original ship from the discarded original components. Which ship is really Theseus’ ship? If we want to use the same approach that we did with our bike we must first make some predictions about the behavior of ships, i.e. that they will move around, that they will maintain some of the same crew, that their contents, ownership, and parts will change only under certain circumstances. Now if you see Theseus’ ship return to port you may not be sure initially that it is the same ship, after all the repairs may have changed its appearance. However if you ask Theseus about it, and he explains how the ship was repaired you will revise your expectations about the ship’s appearance, and have every reason to believe that it is the same ship. If however the mischievous philosopher sails into port, and claims that he is sailing Theseus’ ship you will not believe his claim, since his story about how he came by the ship does not fit with any of your predictions about ship behavior. You have more reason to believe that it is a new ship that was constructed with cast-off parts, as this fits with your predictions about ships.
Now we can take our tool and apply it to the continuity of self. First we would have to creates some predictions about the changes that result in people in response to events that they have experienced, and I assume most readers can predict human behavior to some extent, and thus won’t need me to spell them out. If you examine your own life you can see how the experiences (that you remember) have shaped your older selves into your current self, in agreement with these kinds of predictions. If you ask other people who have known you they too will agree that your current self is the result of reasonable changes in response to experiences. Thus you have every reason to believe that your current self is continuous with any self that you can remember.
As to the problem of what exactly the self is, well I will leave that for another day.