In the philosophical field of metaphysics, the the problem of change is the question of how change can occur.
Let's begin with a definition of the word "change." First, notice that when an object changes, it always changes in some particular way. A baby grows up, and so changes in the respects of size and maturity; a snake sheds its skin, and so changes in the respect of the skin it has. So here's a definition of "change":
An object O changes with respect to property P iff O has P at one time and at a later time O does not have P.
That seems to be what it means for a thing to change: it has a property at one time and later it does not have that property. If a banana becomes brown we say: at one time the banana is yellow; several days later the banana is not yellow, but instead brown. This is all appears fairly straightforward at this point. No apparent problems yet.
But what about the sort of change after which a thing is destroyed? When a person dies, we don't say that the person's life has changed. We don't go around saying, "Harry just isn't the same sort of guy after he died." We say that Harry's life has ended. Or when a building is demolished, we don't say that the building changes; we say that it is destroyed. So what sort of events, on the one hand, result in a mere change, and what sort of events, on the other hand, result in a thing's destruction, in the end of its existence? Now that's one aspect of the problem considered here; we can call it the problem of change and identity.
There is one particular problem of identity that is generally explained with the story of the Ship of Theseus: One day in ancient times Theseus had a ship -- call the ship "the Theseus" for short -- and it was launched into the Aegean Sea. As the years wore on the Theseus started getting creaky and weak and otherwise less-than-perfect. So as boards started getting particularly creaky, they were removed and put into a warehouse, and replaced with new boards. Then masts started tottering, and so soon they were warehoused and replaced with new masts. And in this way, after fifty years, there is a ship moored in the harbor, but this ship now has all new boards, masts, everything. So is the ship in the harbor now -- call it S2 -- the same ship as the ship that was in the harbor fifty years ago -- call that original ship S1? In other words, is the ship we're looking at now really the Ship of Theseus?
There's one answer which is a little too easy and quick. You might say: "No, of course not. The Theseus has changed a lot, so it's not the same ship. At the end of your life you're not going to be the same person you were when you were a teenager. You're going to change a lot in the meantime." However, this is not quite answering the intended question. What is intended by the question is a sense of the word "same" in which an old woman is the same person at the end of her life as she is at the beginning of her life. Certainly, the word "same" has such a sense. After all, we implicitly depend on it when we say, for example, "She has changed a lot." In order for someone to change a lot, there has to be one person who underwent the change. (One could perhaps reject that sense, saying that objects do not change over time.)
Look at it this way. Go back to our definition of "change." I said an object changes with respect to a property if the object has that property at one time and at a later time the object does not have the property. What changes is the fact that an object has a particular property. The only way that that fact can change is if the object remains in existence. So you can think of a continuing object as the ground of change, or the arena where change occurs, as it were. So to get back to the Theseus, the question is: Has the Theseus merely changed a lot, or is the Theseus gone and a new ship now in its place?
Maybe you'll say, "Sure; it's just a refurbished Theseus, greatly changed to be sure, but still the Theseus." If you think that, then consider an addition to our story. Suppose someone buys all the planks and masts and whatnot that is stored in the warehouse, and out of all of those materials, and no other materials, he builds a ship according to the same plans that were used to build the ship christened the Theseus. And this ship, call it S3, is launched and sits on the other side of the harbor where we find S2. Might we not say that S3 is the same as S1 -- that this recently-constructed ship is the same ship as the ship originally called "the Theseus"? After all, S3 was built out of the same materials, and according to the same plans, as S1.
But then we have a problem. We can't say that both S2 and S3 are the same ship as S1, the original Theseus. Because if they were both the same as S1, then they would have to be the same as each other. There is a rule that states that if x=y, and x=z, then y=z. And S2 and S3 are clearly different ships: they are sitting on opposite sides of the harbor. So we have three choices: either, first, S2 is the same ship as S1; or, second, S3 is the same ship as S1; or, third, neither is the same ship as S1, and S1 has ceased to exist. How do we decide what is correct in this case?
It's hard to tell. Well, let's get some more theory on the table. Whenever we make an identity claim -- that is, a claim which states that two things are the same -- we almost always use two different descriptions. Not always -- sometimes we say "x=x," like "I am myself," but such claims are not particularly interesting or informative. The interesting identity claims are claims where we use two different descriptions for one and the same thing. For example, take these two descriptions: "the Morning Star" and "the Evening Star." Sometimes you can look in the sky just before dawn and see a very bright point of light in the sky -- that has been called "the Morning Star." And then also you can look in the sky just after sunset and see a very similar bright point of light -- that has been called "the Evening Star." In fact, the Morning Star is identical to the Evening Star -- both are the planet Venus. So they are "two" things only in description; in fact they are one and the same thing under two different descriptions.
Now it's a similar case with S1, S2, and S3: those are three different abbreviations, which stand for descriptions. "S1" means the ship which sat in the harbor fifty years ago, newly christened "the Theseus." "S2" means the ship which sits in the harbor now with the new planks. "S3" means the ship which sits in the harbor, recently constructed out of the old planks. So when we ask a question like "Is S2 the same as S1?" we can be understood to mean this: "Is the ship which sits in the harbor now, with the new planks, the same ship as the ship which sat in the harbor fifty years ago, newly christened 'the Theseus'?" Do those two descriptions pick out or refer to the same thing, or don't they?
Philosophers aren't interested in the Ship of Theseus problem simply because it's an interesting little puzzle. In fact, it's just an example of a more basic problem. The more basic problem is this: How do we decide that X is the same as Y, where "X" describes something at one time, and "Y" describes something at a later time? If you like we can call this the problem of identity over time, or alternatively, the problem of change.
The German philosopher Gottfried Leibniz came up with a law, called Leibniz's Law, which may have some bearing on the question. Leibniz's Law can be stated as follows:
X is the same as Y iff X and Y have all the same properties and relations; thus, whatever is true of X is also true of Y, and vice-versa.
So let's apply Leibniz's Law to the Ship of Theseus problem. S2 is the same as S1 if, and only if, S2 and S1 have all the same properties and relations. Well, does the ship now in the harbor have all the same properties and relations as the ship that was in the harbor fifty years ago? Here you might be tempted to say, "Clearly not! They have lots of different properties. So they can't be the same ship." Does that sound convincing? Well, suppose we consider the property: "contains mast #1." Mast #1 is one of the masts that the original Ship of Theseus had. So S1 definitely had this property. But S2 is not equipped with mast #1, but instead has, we'll say, mast #2 in its place. So S2 must be different from S1.
That's one argument. However, many philosophers strongly oppose this view. For if this argument works, then, for anything at all, any property that has changed from the last time we looked at a thing would mean that the thing doesn't exist anymore, and there's a new thing in its place. Every little change in every little property would mean the whole thing is destroyed. Suppose we look at S1 just a couple of years after it was built. Say just one plank has been replaced then. Will we say that the ship is a different ship just because one plank was replaced? Many philosophers would say surely not, as would common sense. But the ship that's floating on the ocean for a couple of years does have different properties, it appears, from the original Theseus. So it looks like Leibniz's Law would have us say that it's a different ship. Now you might see all this and conclude, "Well, Leibniz's Law must not be a law at all, but a false claim! X and Y do not need to have all the same properties to be the same thing." However, there are a number of other ways of dealing with this objection.
We can save Leibniz's Law, like this. We can say: properties are to be described as occurring at particular times, or as we will say, they are indexed to imes. A property that is described as at a particular time is, we'll say, "temporally-indexed." For example, we can say that S1 has mast #1 in 600BC. If we say what time the ship has the mast, then we have indexed the property of having the mast to that time. We say the ship has the mast then: but then we use the word "has" tenselessly. That means we don't say that it at present has the mast; rather, we say it "has" the mast at 600BC. We aren't claiming that the ship has the mast at any other time; just at that time. But if it were a later time, say 550BC, that very same ship could "have" -- remember, we're talking about a tenseless "have" -- it could, at that later time, "have" mast #1 in 600BC. That is, it always has the same properties, but the properties are of the form P-at-T. This gives us a way to save Leibniz's Law from the objection we gave, but at the same time brings up the issue of whether change rreally occurs. After all, we defined change as something having one property at one time and not at some later time. By this solution though, any given object always has all the properties throughout time, and the properties are merely temporally specific.
To make it more clear, put this in plain English: S1 now has the property that it will have mast #2; and S2 now has the property that it did have mast #1. Then we can say that S1 and S2 have all the same temporally indexed properties. Then according to Leibniz's Law, they would be the same ship.
One might also say, through the same sorts of contortions, that S1 and S3 might have the same temporally indexed properties. And then according to Leibniz's Law, they instead would be the same ship.
So can Leibniz's Law help us decide whether it's S2 or S3 that is the same as the original Theseus? Perhaps not by itself. Leibniz's Law says that some ships are the same just in case they have all the same properties and relations -- or, rather, the same temporally indexed properties and relations. And how is one to decide that they have all the same temporally indexed properties and relations? Leibniz's Law seems to be little or no help when it comes to that decision.
Well, here is one suggestion which has become a common thing to say about the Ship of Theseus. Whether we want to call S1 the same as S2, or the same as S3, or different from both, depends on what purpose we have in calling something the "same" or not. For example, if the owner of S2 wants to say that S2 is properly called "the Theseus," because that will increase its value, that's a legitimate purpose. Or if S2 is sold into different hands, then it might make practical sense to regard it as a new ship; then maybe we could let the owner of S3 call that ship "the Theseus." Or perhaps owner of S2 made all the changes on the old Theseus and wants credit for the result; it would make sense for him to rename the ship and consider it a new ship. So by this view whehter S2 or S3 is the same ship as S1 is a matter of convention and what purposes we have for considering things the same or different.
Now let us briefly consider the so-called problem of personal identity. Basically, the problem is the problem of change as applied to people. Usually, there's no trouble saying that, for example, a little girl in 1920 is the same as an old woman in 1998. The same person is just described two different ways, first as a little girl and second as an old woman. In fact, we are confident enough of our ability to reidentify people over time that we are given Social Security numbers that are supposed to last us from when we get them until we die many years later. So it's not likely to seem mysterious just exactly why we call the old woman in 1998 the same person as that little girl in 1920.
So to see any problem about personal identity, we have to think up some rather contrived science fiction cases. Aune gives a typical sort of example of such a case -- in fact, his example is less contrived than most, which usually seem to involve brain or mind transplants. Anyway, Aune's case goes something like this. Some guy is out flying and crashes his plane. The doctors think he's a very important person; so, armed with this newfangled bionics technology, they reconstruct him. All that remains of the original pilot is the top of his head. The reconstruction is a success; the top of the pilot's head continues to function, with a totally new body. The question then is: Is this newly-constructed human being the same human being as the original pilot?
Since we have hardly ever encounter any cases that are even remotely as difficult to deal with as this, it's not surprising that we aren't quite sure what to say about such cases. These weird science fiction cases seem to many to be borderline cases of the notion of being the same human being. That is, these are cases in which our ordinary concept just isn't clear enough to let us decide whether the concept does or doesn't apply. So in the case of the reconstructed pilot, it may be that our notion of "being the same human being" just isn't clear enough to let us rule definitively that the reconstructed human being is, or isn't, the same as the original pilot.
The same can be said of the Ship of Theseus. Our concept of "being the same ship" perhaps just isn't clear enough to let us rule definitively that S2 is the same as S1; so if we find it convenient we might just arbitrary say that they are the same ship.
