Let me start with a declaration. I think the way issues about identity through time are often posed is deeply confused, and taking seriously the idea of time as a dimension, and objects as four-dimensional, can help us think more clearly about these issues. (In Lewis's terminology, I find it more useful to think of objects as perduring rather than enduring.)
|1. "Identity" (Persistence) through Space|
Let's start with the reason I put "identity" in scare quotes above. And let's further begin with the related issue of "identity" through space.
Consider the following chair:
Now, is the following statement true?
A = B
(By "=" is mean "is numerically identical with," i.e. "is the same thing as.")
Consider your answer before reading on!
OK, now I must admit that this is a bit of a trick question. The answer depends on what 'A' and 'B' are supposed to label. If 'A' and 'B' are both simply labels for the chair, then yes, A = B. On the other hand, if 'A' is a label for the right rear leg, and 'B' is a label for the left front leg, then they are very different things, and it's not true that A = B.
Either way, though, in a sense it's a trivial question. If 'A' and 'B' label the same thing, then A = B; if they don't, then Not: A = B. I would say that all questions that are really about identity are similarly trivial. (There may sometimes be an epistemological issue: if I call a piece of chalk 'Charlie' on Monday, and then on Wednesday I call a piece of chalk 'Charlene', we may not know whether Charlie = Charlene. But there's still no interesting metaphysical issue here: if 'Charlie' and 'Charlene' are labels for the same piece of chalk, then Charlie = Charlene; otherwise, it's not the case that Charlie = Charlene.
The potentially interesting, nontrivial question we might ask here is the following. Suppose A and B are chair legs. Then we can ask: is A part of the same chair as B? That is, is there a chair C such that A is part of C and B is part of C?
(We could force identity into this version of the question too, if we really wanted to. We could ask: are there chairs C1 and C2 such that A is part of C1, B is part of C2, and C1 = C2? But the formulation in the previous paragraph seems to be a simpler and more straightforward way to ask exactly the same question, which suggests that the bit about identity is not an essential part of the question.)
|2. Persistence through Time|
I think that exactly the same issues arise in the case of "identity" through time, but we're less likely to notice this, because we're not used to thinking of things as having temporal parts.
Here's part of the history of our chair, from Sunday, 9/23 to Wednesday, 9/26. Question: is A = B?
That depends! If 'A' and 'B' are both supposed to label the entire stretched-out chair, then yes, A = B. However, if 'A' labels the 9/23 stage of the chair, and 'B' labels the 9/26 stage of the chair, then no, A ≠ B! In that case, A and B are different chair-stages.
However, if A and B are different chair stages, then we can ask the potentially interesting question of whether they are stages of the same chair. And this is directly analogous to our earlier question about whether A and B were parts of the same chair.
|3. "Constituting the Same Ship" (Chisholm)|
Chisholm seems to recommend something very similar to the way of thinking of these issues just described. I say the interesting questions about persistence through time are questions like: "Is A part of the same chair as B"? Chisholm puts essentially this question by asking: "Does AB constitute the same ship as FL?"
Let's reproduce Chisholm's diagram to see what we're dealing with here:
Wednesday FB CJ
Thursday FL JH
Two odd things about Chisholm's terminology:
1. I think "partly constitute" would be clearer than "constitute". Chisholm's formulation could be taken to imply that AB constitutes a ship all by itself. But he also explicitly says that AB ceases to exist by Tuesday, and FL comes into existence on Thursday (p. 176). So if we consider the ship that includes the stem of the "Y" and the left-hand fork, AB doesn't entirely constitute it, but only partly constitutes it. (Actually, better still, in my view, is just to say that AB is part of the ship!)
2. Chisholm says: "FL constitutes the same ship as does AB" does not imply "FL is identical with AB" (p. 176). This seems surprisingly weak! In the present case, in which FL and AB are different stages, FL clearly is not identical with AB. They are different stages, different parts, even though they are stages of the same ship.
|4. The "Loose and Popular Sense" of Identity|
I don't think there is a "loose and popular sense." When I say x = y, I mean x and y are exactly the same thing. Me-as-a-baby is not identical with me-as-I-am-now (neither in the strict sense nor in any looser one); however, me-as-a-baby is part of the same person that me-as-I-am-now is part of. When I say "I am the same person now that I was then," what I mean is that my current stage is part of the same person as my baby-stage. The entire person, though, which includes both stages, is (trivially) self-identical (like everything else!).
So, for instance, when I say that the rebuilt Rome is the same city as the original, there's nothing loose and popular about this. The two Rome-stages are stages of the same city, and of the overall city, Rome, we can say that Rome = Rome in the strictest possible sense!
|5. The "Strict and Philosophical Sense" of Identity|
Chisholm is sort of odd on the strict and philosophical sense.
Chisholm, p. 182: "I wish to suggst that "x is the same person as y," where the expression in the place of "x" is taken to designate a certain person as existing at one time and where the expression in the place of "y" is taken to designate a certain person existing at a different time, does have this strict and philosophical use."
Note first of all the ambiguity in some of C's expressions. "A certain person as existing at one time" -- what does this mean, exactly? If it means the stage of the person that exists at that time, then the two stages C refers to are simply not identical.
But maybe that's not what he means. Maybe he means "a certain person, whom we identify by reference to a person-stage at one time." If so, then there is a meaningful question of identity here, namely whether the person identified by the stage at t1 is identical with the person identified by the stage at t2.
This is identity in a strict sense, all right, but it's no stricter than the identity in question when we talk about ships or cities or anything else, since we can raise an exactly parallel question about them.
[In fact, Chisholm would probably reject both interpretations, since he rejects the whole idea of stages or slices: see Appendix A, "The Doctrine of Temporal Parts," in his book Person and Object. In Lewis's terminology, Chisholm seems to be a defender of the "endurance" account of persistence through time. But I'm not quite sure what, on this view, the phrases I am interpreting would mean!]
So what difference does Chisholm think there is between the person and the ship? The answer seems to be this: (a) there is always a yes-or-no answer to questions of personal identity, but there may not be a yes-or-no answer to questions of ship identity. [I would reformulate this, personally. I'd say that there is always a yes-or-no answer to any question that is strictly a question about identity, but that there are related questions about when stages are stages of the same thing that may not have yes-or-no answers.] (b) Related to this, there is a conventional element in questions of ship identity: to some extent we can just decide what we're going to say; but there is no similar conventional element in the case of personal identity.
If this is the difference Chisholm thinks there is between personal identity and ship identity, then I don't buy it (but we should save this topic for later, when we explicitly take up personal identity). I think that Parfit has done a great job of showing that there can be indeterminate cases where people are concerned just as much as there can be indeterminate cases where ships are concerned (although the problem cases for personal identity are much more unlikely to actually occur than those for ships).
|6. Quine on Stages|
I like the way Quine puts the matter. Quine also adds an important point: using the language of identity can help explain what we are pointing to. Consider the chair with labels 'A' and 'B' again. If I say: "this [pointing to A] is identical with that [pointing to B]," it's clear that what I'm pointing to both times has to be the entire chair (or something even bigger, like the room it's in). If I say: "this [pointing to A] is not identical with that [pointing to B]," I can't be pointing to the chair both times, but to something smaller, like one of the legs.
Thus identity can help to pin down ostension!
|7. Lewis's Terminology: Persistence, Endurance, Perdurance|
Lewis offers a helpful terminology for talking about this issue. He uses "persistence" as a generic, neutral term for the way things exist through periods of time. He uses "endurance" for one view about persistence, namely that all of an object is present at every time at which it exists. And he uses "perdurance" for the opposed view that only part of something is present at any time at which the thing exists.
Lewis offers an argument for the coherence of the perdurance view in "In Defense of Stages." (But without there using the endurance/perdurance terminology.) In "The Problem of Temporary Intrinsics," he goes further, and gives an argument against endurance and for perdurance.
|8. Geach's Critique of the 4D View|
Geach criticizes "odd arguments" for the 4D view. I agree with him, the two arguments he criticizes don't show anything. (a) that I can represent time by an axis on a graph doesn't show that it's literally a dimension. (Geach doesn't mention this, but for example, we can graph height against time, height against weight, etc. Does this show that height and weight are dimensions? Of course not, except in the mathematical sense!) (b) Geach also mentions that some (he mentions Quine) have suggested that we need the 4D view in order to use symbolic logic to talk about things that exist over time. This is just as silly as Prior's opposite view that his temporal logic shows that we need to reject the 4D view for purely logical reasons! You can make up a logic to fit whatever view of time you've got; it's cheating to then use your logic to argue for your favored view of time.
But Geach then proceeds to offer arguments against the 4D view that seem to me at least as odd as the bad arguments for it that he rejects!
1. Geach accepts MacTaggart's view that if the 4D view is correct, there is no change. (Oddly, though, he does this without discussing or apparently accepting MacTaggart's weird definition of what real change would be! MacTaggart things that things can't change on any view of time, so that the only real change is the change events undergo when they go from being future, to being present, to being past.)
But Geach offers no reason whatsoever for thinking this! He simply explains the 4D account of change (different temporal parts of something having different properties), and then insists that that's not really change! (Well, I say it is! So there!) I don't get it. The 4D analysis of what change is seems entirely coherent to me. Since Geach gives no reason for thinking it incorrect beyond mere assertion, he hasn't given me any reason to change my mind.
2. Geach also argues that many of the things we predicate of people or things can't be predicated of slices. For example, he says that a slice can't be a philosopher, and a slice can't eat mice.
Well, why not? It's probably true that a momentary slice can't do these things (you have to have enough time to think philosophical thoughts, or to chew on the mouse), but I don't see any problem about longer slices doing such things.
3. Geach spends quite a while criticizing an odd hybrid view: that the physical world is a 4D object, while the mind moves through it. He's right that this is a crazy view. But since no one who accepts the 4D view holds it, it can't count against the 4D view! (Geach notes that (a) the view requires an extreme dualism of mind and body, and (b) it seems to lead to a kind of fatalism, to the view that the mind can't do anything to the physical world except observe it. I think it's often true that the cause of worries about the possibility of free will are attached to some form of dualism. Once we see the mind as part of the world, not some sort of nonphysical entity separate from it, I think a lot of worries about free will are dissolved. But that's a topic for a different day.)