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The idea of possible worlds has seemed to promise understanding and insight into several venerable problems of modality—those of essence and accident, forexample, necessary and contingent truth, modality de dicto and de re, and the nature of subjunctive conditionals. But just what is a possible world? Suppose we take it that a possible world is a

state of affairs of some kind—one which eitherobtains, is real, is actual, orelse could have obtained. But then how shall we

understand “could have” here? Obviously no definition will be of much use: Here we must give examples, lay out the connections between the concept in question and otherconcepts, reply to objections, and hope forthe best. Although I cannot do this in detail here,1_{I do wish to point out that the sense of possibility in question is widerthan that of causal}

or natural possibility—so that Agnew's swimming the Atlantic Ocean, while it is perhaps causally or naturally impossible, is not impossible in the sense under discussion. On the other hand, this sense is narrower than that captured in first- order logic, so that many states of affairs are necessary, in the sense in question, although their corresponding propositions are not provable in first-order logic. Examples of such states if affairs would include those corresponding to truths of arithmetic and mathematics generally, as well as many more homely items such as Nobody's being taller than

himself, red's being a color, (as well as a thing's being colored if red), Agnew's not being a composite number, and the like. Otherand

Problem of Transworld Identification, said to arise on the supposition that the same object exists in more than one world.

Accordingly I will concentrate on these two topics: TWI and the problem of Transworld Identity.

Why, then, should we suppose that an individual is confined to just one world—that you and I, forexample, exist in this world and this world only? According to G. E. Moore, the idealists, in arguing for their view that all relations are internal, were really arguing that all relational properties are essential to the things that have them. The argument they gave, however, if it is sound, establishes that all properties—not just relational properties—are thus essential to their owners. If this is correct, however, then for no object x is there a possible state of affairs in which x lacks a property that in fact it has; so x exists only in the actual world, the world that does in fact obtain.

Now an argument for a conclusion as sweeping as this must pack quite a punch. What did the idealists come up with? A confusion, says Moore. What the idealists asserted is

(1) If P be a relational property and A a term to which it does in fact belong, then, no matter what P and A may be, it may always be truly asserted of them, that any term which had not possessed P would necessarily have been other than numerically different from A . . . 6

Perhaps we may put this more perspicuously as

(1') If x has P, then forany object y, if there is a world in which y lacks P, then y is distinct from x which clearly entails the desired conclusion. What they suggested as a reason for accepting (1), however is

(2) If A has P and x does not, it does follow that x is otherthan A.7

If we restate (2) as the claim that

(2') Forany object x and y, if x has P and y does not, then x is distinct from y

holds in every world, we see that (2) is just the thesis that the Indiscernibility of Identicals is necessarily true. This thesis seems accurate enough, but no reason at all for (1) or (1'). As Moore, says, (1) and (2) are easily conflated, particularly when they are put in the idealists' typically opaque and turgid prose; and the idealists seized the opportunity to conflate them.

Initially, then, this argument is unpromising. It has a near relative, however, that we may conceivably find in Leibniz and that often surfaces in contemporary discussion. Leibniz writes Arnauld as follows:

Besides, if, in the life of any person and even in the whole universe anything went differently from what it has, nothing could prevent us from saying that it was another person or another possible universe which God had chosen. It would then be indeed anotherindividual.8

This is on its face a dark saying. What Leibniz says here and elsewhere, however, may suggest the following. Suppose Socrates exists in some world W distinct from the actual world (which for purposes of easy reference I shall name “Charley”). Taking the term ‘property’ in a broad sense, we shall be obliged to concede that there must be some property that Socrates has in Charley but lacks in W. (At the very least, if we let ‘π ’ name the book on Charley, then one property Socrates has in Charley but lacks in W is that of being such that every member of π is true.) So let us suppose that there is some property—snubnosedness, let us say—that Socrates has in Charley but lacks in W. That is, the Socrates of Charley, Socrates-in-Charley, has snub-nosedness, while the Socrates of W does not. But surely this is inconsistent with the Indiscernibility of Identicals, a principle than which none sounder can be conceived. For according to this principle, if Socrates-in-Charley has snubnosedness but Socrates-in-W does not, then Socrates-in- Charley is distinct from Socrates-in-W. We must conclude, therefore, that Socrates does not exist both in Charley and in W. There may be some person in W that much resembles our Socrates, Socrates-in-Charley; that person is nonetheless distinct from him. And of course this argument can be generalized to show that nothing exists in more than one world.

Such an argument, however, is less than impeccable. We are asked to infer (3) Socrates-in-Charley is snubnosed and Socrates-in-W is not

from

(4) Socrates is snubnosed in Charley but not in W

We need not quarrel with this request; but the Indiscernibility of Identicals in no way licenses the inference that Socrates-in-Charley and Socrates-in-W are distinct. For, contrary, perhaps, to appearances, there is no property that (3) predicates of Socrates-in-Charley and withholds from Socrates-in-W. According to (3) [so taken that it follows from (4)], Socrates-in-Charley (that is, Socrates) has the property of being snubnosed, all right, but in Charley. Socrates- in-W, however, lacks that property in W. But this latter, of course, means only that Socrates-in-W has the property of being such that, if W had obtained, he would not have been snubnosed. And, of course, this property—the property an object x has iff x would not have been snubnosed, had W obtained—is not the complement of snubnosedness. Indeed,

this property is not even incompatible with snubnosedness; Socrates himself is snubnosed, but would not have been had W been actual. So the Indiscernibility of Identicals does not apply here; there is no property P which (3) asserts that Socrates-in-Charley has but Socrates-in-W lacks. To suppose that Socrates has P in the actual world but lacks it in

W is to suppose only that Socrates does in fact have P but would not have had it, had W been actual. The

Indiscernibility of Identicals casts not even a hint of suspicion upon this supposition. This objection, therefore, is a snare and a delusion.

A more popular and more promising argument for TWI is the dreaded Problem of Transworld Identity said to confront anyone who rashly supposes the same object to exist in more than one world. Here the claim is that there are deep conceptual difficulties in identifying the same object from world to world—difficulties that threaten the very idea of Transworld Identity with incoherence. These difficulties, furthermore, presumbaly do not arise on TWI.9

But what, exactly, is the problem of Transworld Identity? What difficulties does it present for the notion that the same object exists in various possible worlds? Just how does this problem go? Although published statements of it are scarce,10 _{the problem may perhaps be put as follows. Let us suppose again that Socrates exists in some world W}

distinct from this one—a world in which let us say, he did not fight in the battle of Marathon. In W, of course, he may also lack other properties he has in this world—perhaps in W he eschewed philosophy, corrupted no youth, and thus escaped the wrath of the Athenians. Perhaps in W he lived in Corinth, was six feet tall, and remained a bachelor all his life. But then we must ask ourselves how we could possibly identify Socrates in that world. How could we pick him out? How could we locate him there? How could we possibly tell which of the many things contained in W is Socrates? If we try to employ the properties we use to identify him in this world, our efforts may well end in dismal failure—perhaps in that world it is Xenophon or maybe even Thrasymachus that is Plato's mentor and exhibits the splendidly single- minded passion for truth and justice that characterizes Socrates in this. But if we cannot identify him in W, so the argument continues, then we really do not understand the assertion that he exists there. If we cannot even identify him, we would not know whom we were talking about, in saying that Socrates exists in that world or has this or that property therein. In order to make sense of such talk, we must have a criterion or principle that enables us to identify Socrates from world to world. This criterion must include some property that Socrates has in each world in which he exists—and if it is sufficient to enable us to pick him out in a given world, distinguish him from other things, it must be a property he alone has in these worlds. Further, if the property (or properties) in question is to enable us to pick him

out, it must in some broad sense be “empirically manifest”—it must resemble such properties as having such-and-such a name, address, Social Security number, height, weight, and general appearance in that we can tell by broadly empirical means whethera given object has orlacks it. How, otherwise, could we use it to pick out or identify him? So, if it is intelligible to suppose that Socrates exists in more than one world, there must be some empirically manifest property that he and he alone has in each of the worlds in which he exists. Now obviously we do not know of any such property, or even that there is such a property. Indeed, it is hard to see how there could be such a property. But then the very idea of Transworld Identity is not really intelligible—in which case we must suppose that no object exists in more than one world.

The first thing to note about the objection outlined above is that it seems to arise out of a certain picture or image. We imagine ourselves somehow peering into another world; we ask ourselves whether Socrates exists in it. We observe the behavior and characteristics of its denizens and then wonder about which of these, if any, is Socrates. Of course, we realize that he might look quite different in W, if he exists there at all. He might also live at a different place, have different friends and different fingerprints, if, indeed, he has fingers. But how then can we tell which one he is? And does it so much as make sense to say that he exists in that world, if there is no way in principle of identifying him, of telling which thing there is Socrates?

Now perhaps this picture is useful in certain respects; in the present context, however, it breeds nothing but confusion. For it is this picture that slyly insinuates that the proposition Socrates exists in other possible worlds is intelligible to us only if we know of some empirically manifest property that he and he alone has in each world in which he exists. But suppose we consider an analogous temporal situation. In Herbert Spiegelberg's book The Phenomenological Movement there are pictures of Franz Brentano at ages 20 and 70 respectively. The youthful Brentano looks much like Apollo; the elderly Brentano resembles nothing so much as Jerome Hines in his portrayal of the dying Czar in Boris Godounov. Most of us will concede that the same object exists at several different times; but do we know of some empirically manifest property P such that a thing is Brentano at a given time t if and only if it has P? Surely not; and this casts no shadow whatever on the intelligibility of the claim that Brentano existed at many different times.

Still, isn't the argument made above available here? No doubt there was a time, some fifty years ago, when Spiro Agnew was a precocious baby. But if I understand that assertion, must I not be able to pick him out, locate him, at that time? If I cannot identify him, if I cannot tell which of the things that existed at that time was Agnew,

then (so goes the argument) I cannot make sense of the claim that he existed at that time. And I could identify him, at t, only if I know of some empirically manifest property that he and he alone has at t.

But here the argument is manifestly confused. To suppose that Agnew was a precocious baby at t it is not necessary that I be able to pick his picture out of a gallery of babies at t. Of course I must know who he is to understand this assertion; and perhaps to know that I must know of some property that he and he alone has. Indeed, we might go so faras to concede that this property must be ‘empirically manifest’ in some sense. But surely it is asking too much to require that I know of such a property that he and he only has at every time at which he exists. Of course I must be able to answerthe question “Which of the things existing at t is Agnew?” But the answer is trivial; it's that man sitting right overthere—the Vice President of the United States.

If this is correct, however, why suppose otherwise in the Transworld case? I understand the proposition that there is a possible world in which Socrates did not teach Plato. Now let W be any such world. Why suppose that a condition of my understanding this is my knowing something about what he would have looked like or where he would have lived, had W been actual? To understand this proposition I must know who Socrates is. Perhaps this involves my knowing of some property that is empirically manifest (whatever exactly that comes to) and unique to Socrates. But what earthly (or otherwise) reason is there for supposing that I must know of some empirically manifest property he has in that world

W? The picture suggests that I must be able to look into W and sift through its inhabitants until I run across one I

recognize as Socrates—otherwise I cannot identify him, and hence I do not know whom I am talking about. But here the picture is not doing right by us. For, taken literally, of course, this notion makes no sense. All I know about this world W is that Socrates would not have taught Plato had W obtained. I do not know anything about which other persons would have existed, or—except forhis essential properties—which other properties Socrates has in that world. How could I know more, since all I have been told about W is that it is one of the many worlds in which Socrates exists but does not teach Plato?

Accordingly, the claim that I must be able somehow to identify Socrates in W—pick him out—is eithertrivial orbased on a confusion. Of course, I must know which of the persons existing in W—the persons who would have existed, had W been actual—I am talking about. But the answer, obviously, and trivially, is Socrates. To be able thus to answer, however, I need know nothing further about what Socrates would have been like had W been actual.

But let us imagine the objector regrouping. “If Socrates exists in several worlds,” he says, “then even if there need be no empirically manifest property he and he alone has in each of them, there must at

any rate be some property or other that he and only he has in each world in which he exists. Let us say that such a property is an essence of Socrates. Such an essence meets two conditions: (1) Socrates has it in every world he graces, and (2) nothing distinct from him has it in any world. (By contrast, a property need meet only the first condition to be

essential to Socrates.) Now a property P entails a property Q if there is no world in which there exists an object that has P but lacks Q. So any essence of Socrates entails each of his essential properties—each property that Socrates has in

every world in which he exists. Furthermore, if E is an essence of Socrates, then the class C of his essential properties—the properties he has in each world in which he exists—will obviously entail E in the sense that there is no world in which something exemplifies all of these properties but does not exemplify E. (What makes this particularly obvious is that any essence of Socrates is essential to him and hence is a member of C.) An essence of Socrates, therefore, is, in this sense, equivalent to the class of his essential properties; and Socrates exists in more than one possible world only if he has at least one essence in the explained sense. But at best it is far from clear which (if any) of Socrates' properties are essential to him and even less clear that he has an essence. Nor does there seem to be any way of determining whether he has such a property or, if he does, which properties are entailed by it. So is not the suggestion that he has an essence both gratuitous and problematic? We can and should avoid this whole problem by accepting TWI.” Thus farthe objector.

What can be said by way of reply? First, that if we follow this counsel, we gain all the advantages of theft over honest toil, as Russell says in anotherconnection. The question is whetherSocrates has an essence and whetherobjects do or do not exist in more than one world—not whetherwe would be saved some work orperplexity if we said they did not.