³1username³2LarrySanger³2name³2text_default³2version³21³2ts³2981080047³2ip³224.234.246.58³2data³2newauthor³31³3minor³30³3text³3Next we’re going to talk about something we’ll call <i>the</i> <i>problem</i> <i>of</i> <i>change</i>.  Let’s begin with a definition of the word "change."  First, notice that when an object changes, it always changes <i>in</i> <i>some</i> <i>particular</i> <i>way</i>.  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 ("iff" means "if, and only if") O has P at one time and at a later time O does not have P.

That’s 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.  I figure this is all fairly straightforward.  No big mysteries here.  No problems yet.

But what about the sort of change after which a thing is <i>destroyed</i>?  When a person dies, we don’t say that the person’s life has <i>changed</i>.  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 <i>ended</i>.  Or when a building is demolished, we don’t say that the building <i>changes</i>; we say that it is <i>destroyed</i>.  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 <i>that’s</i> the problem we’re going to take up; we can call it the problem of change and identity.

I am going to elaborate by telling an old story.  One day in ancient times a ship was christened "the Ship of Theseus," or "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 -- <i>the</i> <i>same</i> <i>ship</i> 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."  Now if this is how you want to answer, then let me tell you that you’re not answering the question that I wanted you to answer.  I’m talking about a sense of the word "same" in which an old woman <i>is</i> the same person at the end of her life as she is at the beginning of her life.  Definitely, 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 <i>one</i> <i>person</i> who underwent the changes.

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 <i>the</i> <i>fact</i> <i>that</i> <i>an</i> <i>object</i> <i>has</i> <i>a</i> <i>property</i>.  The only way that that fact <i>can</i> change is if the object remains in existence.  So you can think of a continuing object as the <i>ground</i> 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 <i>a</i> <i>lot</i>, 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 <i>same</i> <i>materials</i>, and according to the <i>same</i> <i>plans</i>, as S1.

But then we have a problem.  We can’t say that <i>both</i> S2 <i>and</i> 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.  Right?  That’s a rule about identity: 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 now!  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, <i>neither</i> 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 -- I mean a claim which states that two things are the same -- we almost always use <i>two</i> <i>different</i> <i>descriptions</i>.  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 "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 50 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, <i>the</i> <i>same</i> <i>ship</i> as the ship which sat in the harbor 50 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 because it’s an interesting little puzzle.  In fact, it’s just an <i>example</i> 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.

Well, the German philosopher Leibniz came up with a law, called Leibniz’s Law, and maybe it can help us answer 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, <i>does</i> the ship now in the harbor have all the same properties and relations as the ship that was in the harbor 50 years ago?  Here you might be tempted to say, "Clearly not!  They have <i>lots</i> 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 the argument.

I think this argument is fallacious.  Why?  Because if this argument worked, then, for anything at all, <i>any</i> 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!  I mean, suppose we look at ST1 just a couple of years after it was built.  Say just one mast has been replaced then.  Will we say that the ship is a different ship <i>just</i> <i>because</i> <i>one</i> <i>mast</i> <i>was</i> <i>replaced</i>?  Surely not.  But the ship that’s floating on the ocean for a couple of years <i>does</i> 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."  So should we reject Leibniz’s Law?

I don’t think so.  We <i>can</i> 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 <i>indexed</i> <i>to</i> <i>times</i>.  A property that is described as at a particular time is, we’ll say, "temporally-indexed."  So let me give you an example.  We can say that S1 has mast #1 <i>in</i> <i>600</i> <i>BC</i>.  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 <i>has</i> the mast then: but then we use the word "has" tenselessly.  That means we don’t say that it <i>at</i> <i>present</i> has the mast; rather, we say it "has" (put the word "has" in quotes) the mast at 600 BC.  We aren’t claiming that the ship has the mast at any <i>other</i> time; just at <i>that</i> time.  But if it were a later time, say 550 BC, <i>that</i> <i>very</i> <i>same</i> <i>ship</i> could "have" -- remember, we’re talking about a tenseless "have" -- it could, at that later time, "have" mast #1 <i>in</i> <i>600</i> <i>BC</i>.  In other words, that very same object has, at <i>all</i> times, all the <i>temporally</i> <i>indexed</i> <i>properties</i> it ever has throughout its entire lifetime.  That’s how, in 550 BC, the same ship could have the property "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>.  So suppose we say that all properties and relations are indexed to particular times, and all objects have, at all times, all the indexed properties, and relations, they ever have.  Well, this gives us a way to save Leibniz’s Law from the objection we gave.

We could say that S1 has the property "has mast #1 in 600 BC."  Then we <i>could</i> say, if we thought that S2 were the same as S1, that S2 also has the property "has" mast #1 in 600 BC.  Do you see?  If S2 is the same as S1, then  S2 can have these two properties at the same time: the first, "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>, and the second, <i>does</i> <i>not</i> "<i>have</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>550</i> <i>BC</i>.  And we could also say that S1, the original Theseus, has the same two properties.  The original Theseus has the property "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>, and also has the property <i>does</i> <i>not</i> "<i>have</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>550</i> <i>BC</i>.  Let me see if I can put this in plain English: S1 <i>now</i> has the property that it <i>will</i> have mast #2; and S2 <i>now</i> has the property that it <i>did</i> have mast #1.  Then we can say that S1 and S2 have all the same <i>temporally</i> <i>indexed</i> <i>properties</i>.  Then according to Leibniz’s Law, they would be the same ship.

And it goes without saying that, through the same sorts of contortions, S1 and <i>S3</i> <i>might</i> have the same temporally indexed properties.  And then according to Leibniz’s Law, <i>they</i> <i>instead</i> 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?  I hate to tell you but the answer is "No."  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 <i>temporally</i> <i>indexed</i> properties and relations.  And how are we going to decide that they have all the same temporally indexed properties and relations?  Leibniz’s Law is no help when it comes to that decision.

Well, here is my suggestion.  Which is not original to me -- it 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 <i>what</i> <i>purposes</i> 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 I think there just isn’t any fact of the matter about whether S2 or S3 is the same ship as S1; I think that’s a matter that’s up to us, to our convenience, and what purposes we have for considering things the same or different.

I should say, after this discussion of the problem of change, that in many cases, there’s little <i>practical</i> question about when something goes out of existence.  For most human beings, when the human heart has stopped beating and the brain has stopped functioning, you’re dead and you’re not going to be revived.  When you’ve eaten the apple, it’s gone.  When your old car is crushed into a cube at a junkyard, your car doesn’t exist anymore.

Now I want make a few very brief remarks about the so-called problem of <i>personal</i> <i>identity</i>.  Basically, the problem is the problem of change as applied to <i>people</i>.  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 <i>mysterious</i> just exactly why we call the old woman in 1998 the same person as that little girl in 1920.

So to see any <i>problem</i> 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 <i>the</i> <i>same</i> <i>human</i> <i>being</i> as the original pilot?  Most people, I suppose, don’t really know what to say, when they first hear such a case.

I am not going to discuss this case: I just wanted to explain it, so you can think about it, and then make one remark, the following remark.  Namely, that, since we have hardly ever encountered any cases that are even <i>remotely</i> as difficult to deal with as this, it’s not surprising that we aren’t quite sure what to say about such cases.  It seems to me that those weird science fiction cases are <i>borderline</i> <i>cases</i> of the notion of <i>being</i> <i>the</i> <i>same</i> <i>human</i> <i>being</i>.  You remember from our discussion of vagueness what a borderline case is?  It’s a case 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, my view is that our notion of "being the same human being" just isn’t clear enough to let us rule definitively that the reconstructed human being <i>is</i>, or <i>isn’t</i>, the same as the original pilot.

The same, I might add, can be said of the Ship of Theseus.  Our concept of "being the same ship" 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.  But we shouldn’t kid ourselves that we are simply applying our ordinary concept, because our ordinary concept of the sameness of ships over time doesn’t say anything about that case.

Well, that’s all I wanted to say about identity and change -- two sample relations.  There are a lot of topics in metaphysics we haven’t considered at all.  But we have at least understood some basic facts about our red apple.  We can say: when we say the red apple exists, we means that it is located in space and time, in the world that we are part of.  The apple itself, we might say, is a substance, and its redness is a property.  The redness of the apple is a trope, which resembles the redness of playground balls and flowers.  And though the apple can get soft and rotten while remaining the same apple, once it’s eaten, it is destroyed.
³3summary³3* Ch. 2, sect. 5³2tscreate³2981080047³2keepts³2981085467³2id³21001³2host³2dhcp058.246.lvcm.com³2revision³21³1username³2PhillipHankins³2name³2text_default³2version³21³2ts³2981085467³2ip³224.190.57.186³2data³2text³3<The following is a portion of LarrysText, wikification is invited> 

Next we’re going to talk about something we’ll call <i>the</i> <i>problem</i> <i>of</i> <i>change</i>.  Let’s begin with a definition of the word "change."  First, notice that when an object changes, it always changes <i>in</i> <i>some</i> <i>particular</i> <i>way</i>.  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 ("iff" means "if, and only if") O has P at one time and at a later time O does not have P.

That’s 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.  I figure this is all fairly straightforward.  No big mysteries here.  No problems yet.

But what about the sort of change after which a thing is <i>destroyed</i>?  When a person dies, we don’t say that the person’s life has <i>changed</i>.  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 <i>ended</i>.  Or when a building is demolished, we don’t say that the building <i>changes</i>; we say that it is <i>destroyed</i>.  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 <i>that’s</i> the problem we’re going to take up; we can call it the problem of change and identity.

I am going to elaborate by telling an old story.  One day in ancient times a ship was christened "the Ship of Theseus," or "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 -- <i>the</i> <i>same</i> <i>ship</i> 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."  Now if this is how you want to answer, then let me tell you that you’re not answering the question that I wanted you to answer.  I’m talking about a sense of the word "same" in which an old woman <i>is</i> the same person at the end of her life as she is at the beginning of her life.  Definitely, 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 <i>one</i> <i>person</i> who underwent the changes.

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 <i>the</i> <i>fact</i> <i>that</i> <i>an</i> <i>object</i> <i>has</i> <i>a</i> <i>property</i>.  The only way that that fact <i>can</i> change is if the object remains in existence.  So you can think of a continuing object as the <i>ground</i> 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 <i>a</i> <i>lot</i>, 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 <i>same</i> <i>materials</i>, and according to the <i>same</i> <i>plans</i>, as S1.

But then we have a problem.  We can’t say that <i>both</i> S2 <i>and</i> 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.  Right?  That’s a rule about identity: 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 now!  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, <i>neither</i> 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 -- I mean a claim which states that two things are the same -- we almost always use <i>two</i> <i>different</i> <i>descriptions</i>.  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 "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 50 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, <i>the</i> <i>same</i> <i>ship</i> as the ship which sat in the harbor 50 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 because it’s an interesting little puzzle.  In fact, it’s just an <i>example</i> 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.

Well, the German philosopher Leibniz came up with a law, called Leibniz’s Law, and maybe it can help us answer 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, <i>does</i> the ship now in the harbor have all the same properties and relations as the ship that was in the harbor 50 years ago?  Here you might be tempted to say, "Clearly not!  They have <i>lots</i> 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 the argument.

I think this argument is fallacious.  Why?  Because if this argument worked, then, for anything at all, <i>any</i> 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!  I mean, suppose we look at ST1 just a couple of years after it was built.  Say just one mast has been replaced then.  Will we say that the ship is a different ship <i>just</i> <i>because</i> <i>one</i> <i>mast</i> <i>was</i> <i>replaced</i>?  Surely not.  But the ship that’s floating on the ocean for a couple of years <i>does</i> 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."  So should we reject Leibniz’s Law?

I don’t think so.  We <i>can</i> 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 <i>indexed</i> <i>to</i> <i>times</i>.  A property that is described as at a particular time is, we’ll say, "temporally-indexed."  So let me give you an example.  We can say that S1 has mast #1 <i>in</i> <i>600</i> <i>BC</i>.  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 <i>has</i> the mast then: but then we use the word "has" tenselessly.  That means we don’t say that it <i>at</i> <i>present</i> has the mast; rather, we say it "has" (put the word "has" in quotes) the mast at 600 BC.  We aren’t claiming that the ship has the mast at any <i>other</i> time; just at <i>that</i> time.  But if it were a later time, say 550 BC, <i>that</i> <i>very</i> <i>same</i> <i>ship</i> could "have" -- remember, we’re talking about a tenseless "have" -- it could, at that later time, "have" mast #1 <i>in</i> <i>600</i> <i>BC</i>.  In other words, that very same object has, at <i>all</i> times, all the <i>temporally</i> <i>indexed</i> <i>properties</i> it ever has throughout its entire lifetime.  That’s how, in 550 BC, the same ship could have the property "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>.  So suppose we say that all properties and relations are indexed to particular times, and all objects have, at all times, all the indexed properties, and relations, they ever have.  Well, this gives us a way to save Leibniz’s Law from the objection we gave.

We could say that S1 has the property "has mast #1 in 600 BC."  Then we <i>could</i> say, if we thought that S2 were the same as S1, that S2 also has the property "has" mast #1 in 600 BC.  Do you see?  If S2 is the same as S1, then  S2 can have these two properties at the same time: the first, "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>, and the second, <i>does</i> <i>not</i> "<i>have</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>550</i> <i>BC</i>.  And we could also say that S1, the original Theseus, has the same two properties.  The original Theseus has the property "<i>has</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>600</i> <i>BC</i>, and also has the property <i>does</i> <i>not</i> "<i>have</i>" <i>mast</i> #<i>1</i> <i>in</i> <i>550</i> <i>BC</i>.  Let me see if I can put this in plain English: S1 <i>now</i> has the property that it <i>will</i> have mast #2; and S2 <i>now</i> has the property that it <i>did</i> have mast #1.  Then we can say that S1 and S2 have all the same <i>temporally</i> <i>indexed</i> <i>properties</i>.  Then according to Leibniz’s Law, they would be the same ship.

And it goes without saying that, through the same sorts of contortions, S1 and <i>S3</i> <i>might</i> have the same temporally indexed properties.  And then according to Leibniz’s Law, <i>they</i> <i>instead</i> 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?  I hate to tell you but the answer is "No."  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 <i>temporally</i> <i>indexed</i> properties and relations.  And how are we going to decide that they have all the same temporally indexed properties and relations?  Leibniz’s Law is no help when it comes to that decision.

Well, here is my suggestion.  Which is not original to me -- it 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 <i>what</i> <i>purposes</i> 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 I think there just isn’t any fact of the matter about whether S2 or S3 is the same ship as S1; I think that’s a matter that’s up to us, to our convenience, and what purposes we have for considering things the same or different.

I should say, after this discussion of the problem of change, that in many cases, there’s little <i>practical</i> question about when something goes out of existence.  For most human beings, when the human heart has stopped beating and the brain has stopped functioning, you’re dead and you’re not going to be revived.  When you’ve eaten the apple, it’s gone.  When your old car is crushed into a cube at a junkyard, your car doesn’t exist anymore.

Now I want make a few very brief remarks about the so-called problem of <i>personal</i> <i>identity</i>.  Basically, the problem is the problem of change as applied to <i>people</i>.  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 <i>mysterious</i> just exactly why we call the old woman in 1998 the same person as that little girl in 1920.

So to see any <i>problem</i> 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 <i>the</i> <i>same</i> <i>human</i> <i>being</i> as the original pilot?  Most people, I suppose, don’t really know what to say, when they first hear such a case.

I am not going to discuss this case: I just wanted to explain it, so you can think about it, and then make one remark, the following remark.  Namely, that, since we have hardly ever encountered any cases that are even <i>remotely</i> as difficult to deal with as this, it’s not surprising that we aren’t quite sure what to say about such cases.  It seems to me that those weird science fiction cases are <i>borderline</i> <i>cases</i> of the notion of <i>being</i> <i>the</i> <i>same</i> <i>human</i> <i>being</i>.  You remember from our discussion of vagueness what a borderline case is?  It’s a case 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, my view is that our notion of "being the same human being" just isn’t clear enough to let us rule definitively that the reconstructed human being <i>is</i>, or <i>isn’t</i>, the same as the original pilot.

The same, I might add, can be said of the Ship of Theseus.  Our concept of "being the same ship" 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.  But we shouldn’t kid ourselves that we are simply applying our ordinary concept, because our ordinary concept of the sameness of ships over time doesn’t say anything about that case.

Well, that’s all I wanted to say about identity and change -- two sample relations.  There are a lot of topics in metaphysics we haven’t considered at all.  But we have at least understood some basic facts about our red apple.  We can say: when we say the red apple exists, we means that it is located in space and time, in the world that we are part of.  The apple itself, we might say, is a substance, and its redness is a property.  The redness of the apple is a trope, which resembles the redness of playground balls and flowers.  And though the apple can get soft and rotten while remaining the same apple, once it’s eaten, it is destroyed.
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