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The relationship between identity and change in the philosophical field of metaphysics seems, at first glance, deceptively simple, and belies the complexity of the issues involved. This article explores "the problem of change and identity".
When an object changes, it always changes in some particular way. A baby grows up, and so changes in respect of size and maturity; a snake sheds its skin, and so changes in respect of its skin. "Change" may therefore be defined as follows:
- An object, O, changes with respect to property, P, if and only if O has P at one time, and at a later time, O does not have P.
That seems to be, in one way, 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, it can then be said: at one time, the banana is yellow; several days later, the banana is not yellow, but is instead brown. This appears fairly straightforward at this point, and there are no apparent problems as yet.
Another way for an object to change is to change its parts.
- An object, O, changes with respect to its part, P, if and only if O has the part P at one time, and at a later time, O does not have P.
Some philosophers believe that an object can't persist through a change of parts. They defend mereological essentialism.
 Problem of change
The question then arises as to what sort of change happens after a thing is destroyed? When a person dies, one does not say that the person's life has changed. Neither does one go around saying, "Harry just isn't the same sort of guy since he died." Instead, one says that Harry's life has ended. Similarly, when a building is demolished, one does not say that the building 'changes'; one says 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 state of its existence? This is one aspect of the problem that will be considered here. It is called "the problem of change and identity".
 The Ship of Theseus
The "problem of change and identity" is generally explained with the story of the Ship of Theseus:
- In ancient times, there was a ship, called the "Theseus" after its famous former owner. As the years wore on, the Theseus started getting weak and creaky. The old boards were removed, put into a warehouse, and replaced with new ones. Then, the masts started tottering, and soon they, too, were warehoused and replaced. And in this way, after fifty years, this ship now has all new boards, masts, and everything. The question then arises: Is the ship in the harbor, now called S2, the same ship as the ship that was in the harbor, fifty years ago (called S1, for convenience)? In other words, is S2 really the "Theseus"?
There is one answer which is a little too easy and quick. One 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 as 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 the 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, one implicitly depends on it when one says, 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.)
Going back to the definition of "change", 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 the object has a particular property. The only way that that fact can change is if the object remains in existence. One can therefore think of a continuing object as the ground of change, or the arena where change occurs, as it were. To get back to the Theseus, the question is: Has the Theseus merely changed a lot, or is the Theseus gone, being replaced by a new ship?
One may say, "Sure, it's just a refurbished Theseus, greatly changed to be sure, but still the Theseus". If one thinks in this manner, then consider what happens when the story is extended further. Suppose someone buys all the planks, masts and whatever that is stored in the warehouse, and out of all of those materials, and absolutely no others, he builds a ship according to the same plans that were used to build the ship, christened "the Theseus". And this ship, called S3, is launched and sits on the other side of the harbor where S2 is. Is S3 the same as S1? In other words, is this recently-constructed ship, the same ship as the ship originally called the "Theseus", considering that S3 was built out of the same materials, and according to the same plans as S1.
One could take this concept even further by not only the properties but also its subject matter of the "ship". What if instead the warehoused planks, masts, and other materials were used to build something completely different from a ship, like a house. (A concept explored by the artist Simon Starling, who turned a shed into a working boat and then back into a shed, winning him the 2005 Turner Prize.) The same materials and supplies are being used; yet they have taken on a new form. This relates to the concept of recreation vs. destruction.
Inevitably, the problem arises: How can one ever say that both S2 and S3 are the same ship as S1, the original Theseus? This is because if they were both the same as S1, then they would have to be the same as each other. This follows from transitivity, which states that if x = y and x = z, then y = z. With S2 and S3 being clearly different ships, sitting on opposite sides of the harbor, three choices present themselves:
- S2 is the same ship as S1;
- S3 is the same ship as S1; or
- neither is the same ship as S1, and S1 has ceased to exist.
How does one then decide which is the correct answer in this case? It is difficult to tell. Whenever one makes an identity claim (i.e. a claim which states that two things are the same), one almost always uses two different descriptions. Sometimes, one may say, "x = x", like "I am I", but such claims are not particularly interesting or informative. The interesting identity claims are claims where two different descriptions are used for one and the same thing. As an example, take these two descriptions: "the Morning Star", and "the Evening Star". Sometimes, one can look in the sky just before dawn, and see a very bright point of light — that has been called "the Morning Star". And then also, one can look in the sky just after sunset, and see a very similar point — that has been called "the Evening Star". The Morning Star is, in fact, identical to the Evening Star — both are the planet Venus. As such, they are "two" things, only in description, but in actuality, are one and the same thing under two different descriptions.
It is a similar case with S1, S2, and S3, those being three different abbreviations, standing for the following descriptions:
- "S1", referring to the ship which sat in the harbor fifty years ago, newly christened "the Theseus";
- "S2", referring to the ship which sits in the harbor now, with the new planks; and
- "S3", referring to the ship which sits in the harbor, recently constructed out of the old planks.
When one, therefore, asks a question like, "Is S2 the same as S1?", one 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 refer to the same thing, or do they not?
Philosophers are not interested in the "Ship of Theseus" problem per se, but to a more basic problem which is this: How does one decide that X is the same as Y, where X describes something at one time, and Y describes another thing at a later time? This is called the "problem of identity over time", or alternatively, the "problem of change".
 Leibniz's solution
- 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.
Applying 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. 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? One 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? To answer this question, let us consider the property, "contains mast #1". Mast #1 is one of the masts that the original Ship of Theseus had. S1 definitely had this property, but S2 is not so equipped, but has mast #2, instead. It follows that S2 must therefore be different from S1.
Many philosophers strongly oppose this view. For if this argument works, then any property that has changed from the last time we looked at a thing would mean that the thing does not exist anymore, and there is 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. If just one plank has been replaced, will we say that the ship is a different ship? Many philosophers would say surely not, as would common sense. But the ship that is floating on the ocean for a couple of years does have different properties from the original. Leibniz's Law would have us say that it is a different ship. One 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."
Leibniz's Law can be saved, by saying: Properties are to be described as occurring at particular times, i.e. they are indexed to times. A property that is described as at a particular time is said to be "temporally-indexed". For example, we can say that S1 has mast #1 in 600 BC. 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, using the word, "has", tenselessly. That means we do not say that it, at present, has the mast, but rather, we say it "has" the mast in 600 BC. We are not claiming that the ship has the mast at any other time; just at that time. But if it were a later time, say 550 BC, that very same ship could "have" mast #1 in 600 BC, considering that we are talking about a tenseless "have". 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.
Putting 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. We can then say that S1 and S2 have all the same temporally-indexed properties. According to Leibniz's Law, therefore, 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. It then follows from Leibniz's Law that they instead would be the same ship.
Can Leibniz's Law help us decide whether it is 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. How then is one to decide that they have all the same temporally-indexed properties and relations? Leibniz's Law seems to offer 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. If, supposing 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. For the purpose of legal entitlement, therefore, part or all of S3 is the same as S1.
Now, let us 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. The admiral then 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.
Thus, 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 to be 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.
 The ship of Theseus problem: a non-receivable question
One way of thinking about the Ship of Theseus problem is as follows: It 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 us review the three main knowledge domains of concern here:
- A, the real ontological universe that exists and happens by itself;
- B, our reality or how we experience the real universe, A; and
- 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. In the scientific domain C, however, the analysis of B reveals that the stars are thousands of light years away, the sun is eight light minutes away, and the moon is about a light 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.
 Persistence over time
Common-sense tells us that objects persist across time, that there is some sense in which you are the same person you were yesterday, in which the oak is the same as the acorn, in which you perhaps even can step into the same river twice. Philosophers have developed two rival theories for how this happens, called endurantism and perdurantism. Broadly speaking, endurantists hold that a whole object exists at each moment of its history, and the same object exists at each moment, while perdurantists believe that objects are 4-dimensional entities made up of a series of temporal parts like the frames of a movie.
 Identity and change in conscious beings
The problem of personal identity relates to change as applied to people. The molecules that make up each individual change almost completely over a period of years. Usually, there is no trouble in saying that a little girl in 1920, for example, is the same as an old woman in 1998, even though they share a relatively small number of molecules in common. The same person is just described in 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 names 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.
B to let us rule definitively that the reconstructed human being is, or is not, the same as the original pilot.
- 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?
- An example, very similar to the "pilot" example, but perhaps more realistic is: It is said that all the particles (atoms) that form a human body change during a period of seven years (although this is not actually so). This means that seven years ago, almost all our atoms were not the same as those of our current body. Does this mean that we are not the same (identical) person as we were seven years ago?
- Having observed this, an allowance for accumulated phenomenological experience attached to identity also defines that identity is independent of change.
- Another example are the transporters (teleporters) in "Star Trek", 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 or her is actually transported, a copy simply being made. In this second case the lack of identity between the two copies appears even clearer if the teleporter does not deconstruct the original model (as happens, for example, in The Prestige). But that doesn't necessarily mean that the new copy is an improvement on the original, as pointed out in the sitcom The Big Bang Theory.
 See also
- Stanford Encyclopedia of Philosophy on temporal parts
- Carsten Korfmacher, 'Personal Identity', in "The Internet Encyclopedia of Philosophy"