Identity and change
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In the philosophical field of metaphysics, 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 is 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 is 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.
Leibniz's solution
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 if and only if 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 is 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 times. 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 really 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.
Pragmatic solution
One popular solution to the problem of the Ship of Theseus is to say that the meaning of "same" depends on what purpose the word is being used for. Let's say it turns out that the original Ship of Theseus, S1, was actually stolen property, and the rightful owner demands its return. Should the police give him S2 or S3? Instead of figuring out which ship, if either, is the "same," and then declaring that it should be returned, the pragmatic solution is to figure out which ship should be returned, and then declare that it is the "same." The current owner of S2 could argue that the original owner did not pay for any of the labor or materials of S2, but did provide at least the materials for S3. Thus the original owner should not be entitled to S2, but rather, some or all of S3. Therefore, for the purpose of legal entitlement, part or all of S3 is the same as S1.
Now, let's say that the purpose is not legal entitlement, but rather, the following situation. The admiral of the fleet believes that captains and crews who have fought alongside each other are more effective than captains and crews who are strangers to each other. So, the admiral declares that captains must serve at least one year on the same ship. One day, Captain Hercules takes command of the Theseus, and then transfers 18 months later. During this time, the ship's materials are completely replaced as in the previous example, but the crew stays the same. Is S2 = S1, S3 = S1, both, or neither? For the admiral's purpose, S2 = S1 because S2 has the same crew as S1, and Captain Hercules has thus fulfilled the admiral's objective.
So, whether S2, S3, both, or neither is the same ship as S1 is a matter of convention and what purposes we have for considering things the same or different. Two objects may be considered the same for one purpose and yet different for another. Is a watch, received as a gift, still the same after it hits the chain saw? For the purpose of returning it, no. But it will always have that same sentimental value. See pragmatism.
Identity and change in conscious beings
Now let us briefly consider the so-called problem of personal identity. Basically, the problem is the problem of change as applied to people. The molecules that make up each individual change completely over a period of years. Usually, there's no trouble saying that, for example, a little girl in 1920 is the same as an old woman in 1998, even though they share no molecules in common. 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. The question is 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 some 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 arbitrarily say that they are the same ship.
== The ship of Theseus problem: a non receivable question ==
The Ship of Theseus problem is a question that is not receivable because of the mismatch between the domain of the question and the domain of the subject matter it is applied to. Let’s review the three main knowledge domains of concern here. We have (A) the real ontological universe that exists and happens by itself. We have (B), our reality or how we experience the real universe (A). We finally have (C), or our scientific analysis of our reality (B). The distinction between (B) and (C) is demonstrated in the following example. In the evening, one can go out and see at the same moment the sun setting, the moon and a few stars; this is our reality or (B). But in the scientific domain (C), the analysis of (B) reveals that the stars are millions of years away, the sun is eight minutes away and the moon is about half a second away. Since one cannot logically consider these subjects to be both “at the same moment” and “away in time”, an exclusive choice has to be made that defines these two separate domains (B) and (C). Our reality or domain (B) is created by the complex but consistent transformation of (A) by our biological and mental makeup. Therefore, domain (B) or our reality is internally logical. The scientific knowledge or domain (C) is created by the application of a consistent methodology of analysis of our reality (B). Therefore, the scientific domain is internally logical. Domains (B) and (C) each have their own internal logic derived from a consistent approach respecting both processes and subject matter. Using the questions or processes of one domain on the subject matter of another domain will logically produce puzzles, paradoxes and inconsistencies. The Ship of Theseus problem is an example of such an inconsistency created by the use of the question of identity proper to the ontology of domain (A) applied to the subject matter of domain (B), our reality. The question about the identity of the Ship of Theseus is simply not receivable and comes from the poor practice of not respecting the proper correspondence of the question domain to the subject matter domain. The problem of identity is an ontological problem and should therefore be applied to the (metaphysical) subject matter of domain (A), the real universe.
Update:
1. The sentence "S1 now has the property that it will have mast #2" contains in itself the assumption, that S1 now and S1 later are the very same ship. It is a little like trying to prove theorem A using theorem A, is it not?
2. An example very similar to the "pilot" one, but perhaps more realistic: It is said that all the particles (atoms) that form human body change during a period of seven years. This means that seven years ago, almost all your atoms were not the same as those of your current body. Does this mean you are not the same (identical) person as seven years ago?
This having been observed, an allowance for accumulated phenomenological experience attached to identity also defines that identity is independent of change.
3. Another example are the teleporters in Star Trek, or in just about any other science fiction media for that matter, which either deconstruct and reconstruct the constituent molecules of the person being teleported, or replicate them in the exact order at the receiving end. In the first mechanism, even though the product is identical, the teleportee is still being destroyed, at least temporarily. In the second the eerie sense of separation is stronger -- not only is the teleportee completely destroyed, but nothing of him/her is actually transported, a copy is simply made.