critical study of on the plurality of worlds by david lewis

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Philosophy and Phenomenological Research Vol. XLIX, No. z, December I 9 8 8

Review Essay: On the Plurality of Worlds' ALLEN STAIRS University of Maryland

On the Plurality of Worlds is a frustrating book. On the one hand, it is written by one of the most capable and intellectually honest of contempo- rary philosophers, and it is an exemplary display of both traits. On the other hand, I am utterly and totally unconvinced of the book's central -claim: that for every possibility there is a concrete world, every bit as real as this one, and no less deserving of the epithet "world." This is the core of what Lewis calls modal realism. I want to say that even if it is true, I will never have good reason to believe it. I also want to say that even if it isn't true, this is no threat to my major metaphysical beliefs.

Of course, Lewis would disagree. He would insist that he has given me good reasons for accepting modal realism, even if those reasons aren't conclusive. And he would also argue that at least some metaphysical theses I do hold (or ought to) require something like modal realism for their truth.

Lewis's book provides a great deal to discuss and I will have to leave a great deal out. Worse luck from my point of view, I will leave out many things that I would very much have liked to have included. (Lewis's program of "Humean supervenience," which is an important part of the background of this book, his treatment of skepticism, and the larger topic of properties are among the things I most regret leaving out.) I will begin by summarizing the main outline of the book, and then will turn to a handful of particular issues - ones that seem to me to be central to the credibility of Lewis's thesis.

Modal Realism, as Lewis tells us in the preface, is the doctrine that there are other worlds and that these worlds are suited to play a variety of theoretical roles. As we noted above, these worlds are not essentially different in metaphysical character from this one. They are not actual, but

* Thanks to Jerrold Levinson, Georges Rey, and especially Penelope Mackie for helpful discussion of the issues in this paper. If they didn't keep me out of trouble, they aren't to blame.

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this doesn't really say very much. On Lewis's account, actuality is indexi- cal, and our world is in no way privileged. The inhabitants of another world would say with equal truth that their world is actual. Taken together all of this constitutes an extraordinary existence claim, and the first three of the four chapters are shaped by the task of defending it.

The main sort of reason that Lewis gives for believing in all these worlds is that doing so is theoretically useful. As Lewis puts it, "systematic philosophy goes more easily if we may presuppose modal realism in our analyses" (p. vii). In Chapter One ("A Philosopher's Paradise") Lewis considers four areas in which modal realism seems to be philosophically useful: modality, the related question of closeness or similarity among worlds, explicating various notions of content, and providing an account of properties. I don't find all of the examples uniformly convincing, but there is no doubt that Lewis has made a strong case for the usefulness of possible worlds to philosophy. The rest of the chapter spells out the nature of modal realism in more detail. Among other things, it explains distinct- ness of worlds roughly as lack of spatio-temporal relations between them and tackles the problem of plentitude - of explaining the sense in which there are no gaps in logical space. Here Lewis voices his allegiance to a principle that is crucial to his thinking on modality: what he refers to as "the Humean denial of necessary connections between distinct exis- tences" (p. 87).

The next chapter ("Paradox in Paradise?") treats a number of paradoxes and puzzles that threaten modal realism. These range from prob- lems about cardinality to the threat of skepticism. In Chapter Three ("Paradise on the Cheap?") Lewis deals with alternative conceptions of possible worlds - varieties of ersatztism. The most important of these is linguistic ersatztism, which attempts to construe possible worlds as quasi- linguistic entities. One of the virtues of this discussion is the rich develop- ment of linguistic ersatzism that Lewis provides in the process of criticiz- ing it. The other varieties of ersatzism are "pictorial" and "magical." Of these two, magical ersatzism-is the most important. It in effect treats possible worlds as abstract simples, and is "magical" because, Lewis argues, it is incapable of explaining how such ersatz worlds can represent. The view is important because as Lewis sees it, many accounts of possible worlds in the literature are really versions of magical ersatzism.

The final chapter ("Counterparts or Double Lives?") deals with a variety of questions about individuals and our modal knowledge of them. The underlying issue is transworld identity, which Lewis rejects in favour of counterpart theory. The discussion is quite rich, and the treatment of haecceitism, which Lewis rejects, is delightfully clever.

334 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH

This summary is no substitute for a reading of the book. If you haven't read it, I warmly recommend it to you. Having said that, I want to return to the fundamental question about modal realism: is it plausible? That is the question that will occupy us in various ways throughout the rest of this essay.

We noted earlier the general sort of reason that Lewis offers on behalf of modal realism. The hypothesis that there are many worlds "is serviceable, and that is reason to think it is true" (p. 3). A little more particularly, "systematic philosophy goes more easily if we may presuppose modal realism in our analyses" (p. vii). In fact, the methodological issues here seem to me to be quite murky. Why should the fact that a certain kind of theorizing goes more smoothly if we presuppose Xs be reason to believe that there are Xs? Michael Friedman offers some instructive examples (Friedman, i 9 8 I). Statistical mechanics goes more smoothly if we presuppose phase space. But physicists still regard phase space as a mere representation. Trying to do quantum mechanics without Hilbert space is extremely difficult. But physicists do not say that quantum mechanics commits us to Hilbert space in the way that general relativity (perhaps) commits us to space-time. In fact, this pattern is fairly common in physics. We talk as though certain bits of theoretical structure or processes were real, and the smoothness of the theorizing is thereby increased. But typically, we require reasons of a much more specific sort before we grant reality to a theoretical structure or entity. (For a particularly forceful develop- ment of this idea, see Cartwright's How the Laws of Physics Lie.) Furthermore, spelling out the methodological details is devlishly hard, and I think one can complain fairly that Lewis doesn't devote enough time to the problem.

Some details of Lewis's epistemological attitude come out in his reply to an argument of Skyrms's (I976, p. 3z6). Skyrms insists that if other worlds are like the many worlds of the eponymous interpretation of quantum mechanics, or for that matter, like Afghanistan or the center of the sun - if they are concrete, physical things - then they require the same sort of evidence that these other things require. This evidence is ultimately based on the existence of causal chains that connect us to the things in question. Since other worlds are causally isolated from us, we can't have this kind of evidence, and so we can have no reason for believing in them.

Lewis's first reply is that the very distinction between concrete and abstract is not nearly as clear as we tend to suppose. (Section I.7 defends this claim in detail.) He adds that none of the ways he knows of making it clear provide any obvious basis for the claim that concreta must be known causally. Standing alone, this would be a weak reply. What seems clear is

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that the intuition to which Skyrms appeals is a deeply held one - part of the data to which epistemology is responsible. Lewis may be right in pointing out that it is a brute intuition, but that is not a reason for thinking it optional.

In fact, however, Lewis offers a more systematic reply: the real distinction is between the contingent and the necessary. If contingent facts were different, our experiences and hence our beliefs would be different. Knowledge of the contingent requires causal connection because beliefs about the contingent are causally and counterfactually dependent on the details of the contingent facts. Not so for necessary truths. Since they couldn't be otherwise, there is no question of how our beliefs about them would differ if they were otherwise. But among the necessary truths are those about what possibilities there are, and as Lewis puts it,

We do not find out by observation what possibilities there are. . . . What we find out by observation is what possibilities we are. (p. i i 2)

My first worry is that even if I grant that we know a priori what possibilities there are, knowing that there are other concrete worlds is quite another matter. More important, I'm not sure I should accept the basic epistemological analysis. I will grant that contingent truths can't be known a priori, though I would want to add a caveat to Lewis's account of this. Typically, possible difference in the contingent is associated with possible difference in our perceptions. But in some cases this may not be so. What I have in mind are cases (if there are any) in which there are contingent facts to which we could not have causal access. Suppose, for instance, that some processes have dead-end epiphenomenal effects that can vary in character without being able to affect the rest of the world. Here too there would be no question of how our beliefs would differ if these facts were otherwise, though not for the same reason as in the case of necessary truths. But this lack of counterfactual difference does not make it possible to know such facts a priori.

As for necessary truths, I am certainly not willing to grant that they can always be known a priori. One reason for this is that I am much less of a Humean than Lewis is. A more important reason ties in with the caveat about contingent truths. Even if I were to grant (which in fact I don't) that the facts about Lewis-style worlds are necessary, and even if I grant that they are knowable, if at all, only a priori, I needn't therefore grant that they can be known at all. A comparison: Lewis would presumably hold that if the continuum hypothesis is true, it is necessarily true. And he would presumably say that if the truth about the continuum hypothesis is knowable at all, it is only knowable a priori. But there is no reason (I'm


sure he'd agree) to go on to maintain that we can settle the question of the continuum hypothesis.

The analogy is closer than it might seem. Some aspects of our theorizing about the world might go more smoothly if we accept the continuum hypothesis. For example, Itamar Pitowsky has explored some beautiful generalizations of probability theory that rely on the continuum hypothesis.I Furthermore, Pitowsky believes that this work may lead to a satisfy- ing interpretation of quantum mechanics. But especially if one is a realist about set theory, arguments of this sort would never be taken to settle the truth of the continuum hypothesis. Indeed, the model of a priori knowledge of the necessary is demonstrative knowledge. And "demonstrations" that theorizing would go more smoothly if a certain conjecture were true are not taken to be reasons for accepting the conjecture. Thus, there is something odd epistemologically about Lewis's style of argument. He claims to be establishing a necessary truth a priori, but the thesis he aims to establish is not intuitively obvious (far from it!) and the arguments he offers add up to something far short of a demonstration.

Now Lewis might protest that the mathematical model is not the only model we have for a priori knowledge. The venerable philosophical disci- pline(?) of ontology is another example, and here we rely on just the sorts of methods that Lewis appeals to: systematic considerations, avoidance of the arbitrary, general plausibility arguments and the like. Further, this point spills over into mathematics itself. Our knowledge (if such it be) that there are numbers or sets is not demonstrative knowledge. And even some of our opinions about sets, for example, are adopted on the basis of considerations that amount to something less than demonstration. The axiom of choice is a good example. It is not uncontroversial. It is, howv- ever, very useful. Furthermore, we know that it is independent of the other axioms of set theory. But mathematicians don't view it in the same way that they view the continuum hypothesis. Most mathematicians simply accept it.

Appeals to the tradition of ontology are of limited force. The continued prevalence of nominalist intuitions among many philosophers should at least give us pause. Doubting that we are fully sure what we are doing when we posit such things as numbers or properties seems to me far from gratuitous, though I will suggest below that the case of numbers may be more harmless than it appears.' As for the axiom of choice, if I found a

For an introduction to the program, see Pitowsky, I 9 82.. In fact, what is required is something strictly weaker, namely Martin's Axiom (see p. 1300), but this is still undecidable on the basis of the usual axioms, and so the essential point is not affected. I would hasten to add that positing such things isn't therefore gratuitous. Properties (in a non-extensional version) seem to me to be at the heart of an intellectual quandary. Deny- ing them leads to one set of mysteries, admitting them to another.

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mathematician who claimed to accept it chiefly because of its usefulness, I would suspect that this was a non-realist mathematician - perhaps one who subscribed to a version of fictionalism or if-thenism. More likely, I think, is that acceptance of the axiom of choice is part and parcel of a realism about sets: if the axiom of choice were not true, then the facts about sets would be indefinite in a way that conflicts with the idea that these facts are objective.

The matter of sets is near to Lewis's heart. The "pardise" referred to in the headings of the first three chapters is meant to remind us of Cantor's - the paradise of sets. When Lewis first stresses the serviceability of modal realism, he offers an analogy with sets. He writes

I take this [serviceability] to be good reason to think that modal realism is true, just as the utility of set theory in mathematics is a good reason to believe that there are sets. (p. vii)

Lewis does not rest his case on the analogy with sets, but the analogy is obviously important to him. I think it is also an instructive one to explore further.

Sets are serviceable in mathematics. In fact, we can say more. Sets seem intrinsically no more mysterious than mathematical entities in general. Furthermore, it is not clear how we could even formulate certain areas of mathematics without talking about sets. (Consider topology, for instance). The conclusion this suggests is that if we are going to believe in any mathematical entities at all, we should not balk at believing in sets. In fact, we can go further. It isn't just that sets are useful in mathematics; as Lewis points out, set theory affords enough primitives and principles to capture virtually the full content of mathematics. So there is no obvious need to believe in any mathematical entities other than sets. But on the face of it, this doesn't suggest an argument for expanding one's ontology; it suggests a means of reducing it.

Of course, this isn't really to get Lewis's point. Consider the following remark.

Set theory offers the mathematician great economy of primitives and premises, in return for accepting rather a lot of entities unknown to Homo javensis. It offers an improvement in what Quine calls ideology, paid for in the coin of ontology. It's an offer you can't refuse. The price is right; the benefits in theoretical unity and economy are well worth the entities. (p. 4)

Indeed, we get by with fewer kinds of entities. This is just Lewis's point about improvement in ideology. But Lewis presumably would insist that this improvement came at a price. It's not so much that we accept things that Homo javensis didn't know - that goes for the numbers, functions and so on that we already accepted. The price is that in addition to the "natural" sets that most mathematicians already believed in, we accepted


a vast infinity of infinite sets, some infinitely peculiar. This is quite like the situation for modal realism. We already believe that there are worlds - or at least we believe that there is one of them. To gain the advantages that go with belief in propositions, possibilities and the like, all we need do is believe in more of them.

On the face of it, the analogy with set theory can be pushed even further. The axioms of set theory provide principles of generation and recombination that tell us how to start with some sets and get others. So Lewis's principle of recombination (pp. 87 ff.) tells us how to start with old worlds and get new. In fact, the principle tells us how to start with a world and arrive at others. On my bookcase, a copy of Koyre's Newto- nian Studies sits beside a copy of his From the Closed World to the Infinite Universe. But the principle of recombination tells me that any thing can coexist with anything else, so long as the things occupy distinct positions (p. 88). Further, any possible individual admits of combination with itself (p. 89). So there is a world in which two copies of Newtonian Studies are side by side on (a counterpart of) my bookcase.

In spite of this apparent analogy, there is an obvious difference. The extra entities that we accept when we embrace full set theory are all constructions out of entities we already took ourselves to have on hand. They are parasitic upon those entities in the clear sense that ultimately, they decompose into them. Nothing of this sort is true of other worlds. They are emphatically not constructions out of entities that we already took to be unproblematic. That is why the principle of recombination is not really like the principles for constructing sets.

Let us explore this point a little further. What I have to say here is inspired by the papers of Haugeland and Horgan referred to in the bibliography, though, partly since they don't entirely agree with one another, I would not expect them to agree with everything I say. Begin by consider- ing mereological sums. My first instinct is to say that although my shoe, my son and the sun are all perfectly respectable entities, there is no genuine entity that is their sum. But on reflection, a different attitude suggests itself. The calculus of individuals is apparently consistent. Furthermore, the facts about mereological wholes are determined by, or "supervene upon" the facts about their apparently more respectable ultimate parts. Indeed, I am inclined to suspect that in the end, this is pretty much what the existence of such entities comes to: we have a consistent way of talking as though they exist, and the facts about the "new" entities are the resul- tant of the facts about the more familiar ones and the principles of composition embodied in the calculus of individuals.3 In the case of sets, the

Lewis has a different reason for accepting unrestricted mereological composition: if we

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principles of composition are more elaborate and the issues of consistency are darker, but I sense only a difference of degree here.4

The thought that attracts me is this. Once we admit that the facts about a putative sort of entity supervene on facts about respectable entities, and/ or that the entities are in some reasonably clear sense "constructions" from familiar entities, further questions about whether there "really" are such entities seem fruitless. This certainly applies to the sum mentioned above. It also seems a reasonable attitude to take toward committees, uni- versities, corporations and such, even though the "logic" of such things is not simply given by the calculus of individuals. The core of the attitude is that to the extent that we know what we are talking about when we ask existence questions, admitting the existence of these things is harmless.

This might seem like a sort of ehiminativism. I'm not so sure, for various reasons. The one most worth mentioning is that if the need to quantify is an indication of ontological commitment, then the same considerations that lead to favouring the notion of supervenience over reduction in many contexts will also lead to the admission of many entities that trouble the ontologically pure of heart. Serious and worthy intellectual purposes will require quantification over the entities, and there will be no parsing them away. (See Haugeland and Horgan for various ways of looking at this.)

I am not sure just how far my ontological liberality extends, and this isn't the place to make it precise. But the program I favour can't be extended to Lewis's worlds.

Now of course, I can't get off of Lewis's hook quite so easily. The facts about mereological sums, corporations and such may typically supervene on facts about innocent entities, but the pure sets of mathematics are not so innocent. And it is these very sets to which Lewis appeals in his analogy.

don't, we will have to countenance vague entities, since the restrictions on composition will be vague (pp. 2 i 2 -2 i 3). I'm not as troubled by this as Lewis is, but perhaps my intuitions have been corrupted by quantum mechanics. In any case (and independently), Lewis's argument seems to beg the question against various philosophical objections to a strong version of realism.

4 The Goodmanian nominalist would see more than a difference of degree. He would protest that he doesn't understand how two distinct entities can have the same ultimate con- stituents. I don't seem to have this worry. Consider committees (which aren't just sets, because they aren't individuated by their members.) The curriculum committee is made up of the scheduling committee, comprised of Jones and Patterson, and the teaching committee, whose members are Smith, Levine, and Abrams. The budget committee is made up of the salary committee, consisting of Levine and Jones, and the allocations committee, composed of Smith, Patterson, and Abrams. But I don't think that the curriculum committee is the same committee as the budget committee. (One committee is very efficient. The other is usually late. One has cordial meetings. The other is very fractious.)


We accept these because they are so serviceable. And they are not mere constructions out of innocent entities.'

It is true that pure sets are not so clearly innocent as sets of books or bowling balls. However, to get the sets needed for mathematics, we need accept only one dubious entity: the empty set. Given the principles of construction incorporated in set theory, all the other sets needed for mathematics are thereby given.' In the case of possible worlds, we are told that other worlds are not things different in kind from the world we already believe in. But we are also told that we must accept more of these things than we ever dreamed.

This might suggest another standoff. To get the benefits of sets, we need to accept an entity of a peculiar sort (the empty set), but having done so, we get everything else for free. With possible worlds, there is no such free ride, but we don't need to accept anything of a sort that we don't already accept.

In fact, I don't think we really have a standoff here. There is a way of rendering the empty set harmless: simply declare by fiat that some unique, unproblematic memberless object is the null set (say, for instance, the particle that caused that click of the geiger counter.) This object will do quite nicely for all the purposes of mathematics. Granted, it is arbitrary to declare this object a set, and to deny that others apparently just like it are, but as long as we make our stipulations with our eyes open, what of it? Arguably, it is not the concrete realizations of sets that matter for mathematics, but the structure. Indeed, the very fact that we could have chosen our "null set" otherwise reinforces the point. It doesn't matter what the empty set is. All that matters is that it be fit to fulfill a certain role. If this means that there really are no pure sets, since there are no unique pure sets, so be it. Mathematics is not obviously worse off. The point is that there is hope that we can deflate the ontological commitment involved in accepting sets. In their case, we may be able to find a principled way of answering "yes" to Lewis's question: "could 'abstract' just mean 'don't worry'.? " (p. i i i). And as was suggested above, I hold out similar hope for

In fact, this isn't really fair to Lewis. He notes himself (p. 83) that pure sets are "the most dispensable and suspect of sets."

6 Of course, this is not simply unproblematic. I think that worries about sets based on the Lowenheim-Skolem theorem, or the status of the continuum hypothesis, for instance, are not just silly. They undermine the sense that this notion of "construction" succeeds in picking out a definite totality. But these worries are part of what makes a non-realist attitude towards mathematics plausible. In other words, to the extent that they threaten my attempt at insouciance, they also rob modal realism of comfort from the example of set theory.

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a host of curious entities. But there is no hope that we can do anything similar for Lewis-style worlds.

Part of the point of the analogy with sets was epistemological: most of us accept sets. If the epistemological status of modal realism is like that of set theory, then modal realism inherits a measure of epistemic respectabil- ity. What I have tried to suggest is that there are metaphysical differences between the two cases that leave them in different epistemic positions. At the same time, Lewis's case is not simply built on this analogy. Further- more, there are at least some problematic entities that don't deflate so easily. Properties constitute the most troublesome example for me. In fact, I'm not sure how much epistemological comfort this admission affords Lewis. If properties or alternatively, tropes are the sorts of things consid- ered by Armstrong and Williams (and discussed at length in Lewis, i983) then at least we are causally aquainted with them. But I am quite prepared to admit that the case against modal realism would be weak if it turned on these rather delicate issues.

In any case, considerations about properties are crucial in one of the strongest arguments Lewis has on behalf of modal realism. The argument is this: the most plausible alternative to modal realism is linguistic ersatzism. Linguistic ersatzism is the attempt to make linguistic surrogates do the work of possible worlds. For a variety of reasons, Lewis thinks linguistic ersatzism is defective, but one of the most interesting objections has to do with "alien properties" - properties that aren't instantiated in this world. Before getting to that, however, the whole question of linguistic ersatzism is worth our attention.

First, a word about the nature of linguistic ersatzism. Lewis bestows a generous intellectual gift on the philosopher who would like to understand possible worlds as linguistic constructions: the idea of a Lagadonian language. The "language" out of which the ersatzist constructs his worlds need not be finitary in any respect.

All we need is a language in a generalized sense: a system of structures that can be parsed and interpreted. The words can be . . individuals that are part of the concrete world, or set- theoretic constructions out of these, or pure sets, or anything else we believe in. (p. 144)

Further, the vocabulary can be infinite, and (here is the "Lagadonian" aspect) things can serve as their own names. If needed or wanted, we can make use of infinitary connectives. Thus, the "world-making languages" available to the ersatzist are arbitrarily rich in expressive power (or perhaps almost arbitrarily rich; the difference matters to Lewis).

Lewis considers two sorts of objections to linguistic ersatzism: apparent excesses of primitive modality and inadequate expressive resources. The first problem runs thus: some would-be ersatz worlds are inconsis-


tent. Further, no merely syntactic notion of consistency will distinguish them from genuine ersatz worlds. The relevant notion of consistency will, in effect, be a modal one. Worse, the richer the expressive resources of the language, the more chances for it to fall into inconsistency by saying one thing explicitly and implying something contrary implicitly. One way to avoid the problem is to take certain sentences as axiomatic and let syntactic consistency do the rest. The axioms will avoid allowing married bache- lors and suchlike into the "worlds." They will even specify the circum- stances in which a certain arrangement of molecules, etc., will amount to there being a talking donkey. Further, the axioms need not even be part of the worldmaking language proper. If that language is to be kept simple, then the axioms can be part of a supplement.

So what's the problem? The problem, according to Lewis, is that it will be impossible to specify the axioms without resorting to primitive modality. For instance, we can't simply declare that no particle could be both positively and negatively charged. Maybe we're wrong about that. So the ersatzer will have to say that

if no particle can have both positive and negative charge, then let there be an axiom of unique charge. (p. 1 5 5)

Further, the ersatzer will have to resort to a similar ploy to deal with the relationship of the global to the local. No one could provide all the analyses of what the world must be like globally if there are to be such local entities as donkeys or concerts or beliefs. So the ersatzer will be forced to

[declare] wholesale that among all conditionals with local antecedents and global conse- quents, exactly those shall be axioms that are necessarily true. (p. 155)

Lewis notes that this is not a fatal objection, since there is plenty of work for ersatz possible worlds to do short of analysing modality. He even quotes Jackson to the effect that if our goals are ontological and not expli- catory, resort to primitive modality is not a defect. However, Lewis's responds thus:

if . . . we are trying at once to cut down on questionable ontology and to cut down on primitives, . . it is fair to object if one goal is served at too much cost to the other. (p. ' 57)

Serving both goals is what Lewis takes himself to be doing, and what he apparently thinks we ought to be doing.

All of this seems very curious. Most curious is the idea that the ersatzist might be required to spell out the details of his "worlds" to be entitled to them. The fundamental intuition that ought to lie behind any sensible version of linguistic ersatzism is this: every sentence either states a possibility

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or it doesn't. And if it does, what it states is either necessary or it isn't. But reality decides which. This is realism about modality. It is what I would like to call modal realism if the term were still available. Lewis is quite right in pointing out that we can't reduce modal notions to linguistic notions, and modal theorists should thank Lewis for the extent to which he has helped make this clear. But for many, this was never the aim anyway. On the alternative view, to avail oneself of possible worlds is to avail oneself of a very powerful representation, just as (to recall Friedman) physicists who do statistical mechanics in phase space or quantum mechanics on Hilbert space are availing themselves of a powerful representation. On this view, Lewis's challenge amounts to requiring the modal theorist to show that the appropriate representation exists. And Lewis himself has helped the modalist considerably by showing how the existence of the representation can be assumed with a clear conscience. He has explained how we can stretch the notion of a language to provide repre- sentational structures of virtually unlimited expressive power. But if we take the view I think we should, there is nothing illegitimate about simply declaring that a Lagadonian description is an ersatz world if and only if (a) it is possible for the description to be true and (b) there are no logically stronger descriptions that imply it. This gives us the existence of the representation, even if the details are not all accessible to us. Further, we know just as much, and just as little, about what is possible on this account as we do on Lewis's.

Lewis's objection is that he gives us something more. He provides an analysis of modality rather than taking it as primitive. In fact, this seems much less clear than Lewis acknowledges. Suppose I believe that there are other worlds of the sort that Lewis believes in. How does this affect my understanding of possibility and necessity? I don't think that something's being possible consists in there being a world in which it is true. Rather, I can only make sense of Lewis if I take him to be offering a hypothesis: roughly, for everything that is possible, there is a world in which it is true. Suppose that there are no worlds in which particles are both positively and negatively charged. Then this amounts to the impossibility of such particles only if there are no "missing worlds." Indeed, what we want to say is that (assuming it is so) there are no worlds with dually charged particles because such particles are impossible. (See Lycan, i988 for a similar argument.) If we don't take this point of view, then the claim that there are no missing possibilities becomes both trivial and dubious: trivial because possibility then turns out to correspond to whatever range of worlds hap- pens to exist and dubious because this is so far from the modal intuitions the theory is meant to deal with.


One more point before we turn to the second objection to linguistic ersatzism. I have doubted that Lewis really manages to reduce modality to something else. On the other hand, it would be right to object that there must be more to the analysis of modality than availing oneself of a Laga- donian language and letting the world decide what constitutes logical space. The point I want to stress is that what is left over is a task that faces both the ersatzist and Lewis. This is because there is also more to the analysis of modality than invoking concrete possible worlds and saying that the possible is what is true in some world. Lewis is well aware of this and contributes substantially to the rest of the task. One example of such a contribution is his discussion of the recombination principle. This provides a good deal of insight into what the range of possibility is. But the principle provides its insight even when stated in baldly modal terms

anything can coexist with anything else, at least provided they occupy distinct spatio- temporal positions. (p. 88)

To be sure, this needs grooming. But I don't see why the grooming requires commitment to other concrete worlds. This is especially so if the point is not to eliminate modality but to understand its structure from within.

Similarly, the problem of the relationship between the global and the local is one that we would like to understand better. The linguistic ersatzist's worlds provide no insight into the problem. Rather, it is simply assumed that some facts supervene on others - that the world could not differ in certain ways at one level without differing at another. In this way, some Lagadonian "descriptions" are kept from the class of ersatz worlds. Lewis simply assumes that there are full-blown worlds, with or without talking donkeys, and with or without certain arrangements of atomic con- stituents. But this provides us with exactly the same degree of insight into the relation between the global and the local as the ersatzist approach: virtually none. The interesting work comes in trying to say more about what sorts of things supervene on what. (Again, work to which Lewis has made important contributions.) And this is a task in which all can participate, with or without a commitment to modal realism.

Since Lewis himself admits that the objection based on primitive modality is not fatal to linguistic ersatzism, it is high time we turned to the second objection. This one holds that the expressive resources of linguistic ersatzism are inadequate; that it will leave possibilities unaccounted for. Like the previous objection, this one breaks into two parts. First, Lewis has argued earlier (especially in section i.2z on content) that in addition to possible worlds, we need possible individuals. But it is possible, Lewis

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argues, -that there should be distinct indiscernible individuals. (For Lew- is's account of indiscernibility, see section i.5 on properties.) Imagine a full description of a world of eternal recurrence, with

a certain role, say, that of a conquerer rather like Napolean - filled once in every indiscernible epoch. There are infinitely many indiscernible possibilities for filling the Napoleonic role in such a world. Or so it surely seems. But no: there is only one ersatz individual, only the one linguistic description of a filler of the role. (p. 158)

I must confess that I don't really fathom this objection. If an ersatz individual is simply a description - a bundle of predicates, as it were, then I suppose the objection holds. But the Lagadonian language has the resources to provide names for its individuals, and also will allow the means to express identity and non-identity. So why not let the names serve as the ersatz individuals? Then we get our distinct ersatz Napoleonoids. The ersatz world will even allow us to say that Napolean-a is three epochs earlier than Napolean-8. Granted, the "names" will be merely formal (except where something in this world is named); we aren't naming real individuals. Further, we haven't distinguished between any such world and any order-preserving "automorphism" of it. But we have still charac- terized the full structure and qualities of the possibility. I gravely doubt that we understand anything more than that. If there is something else missing here, I don't know what it is nor why we need it.7

We turn, then, to the more intriguing part of the objection. Lewis thinks that the most credible theories of properties are the ones

according to which there are no uninstantiated properties. But he asks us to consider the plight of an other-worldy linguistic ersatzer, whom we will call McPoor. McPoor lives in a world in which some of the properties of our world, say quark flavor and color, are not instantiated; they are alien to that world. Thus, McPoor lives in a world that fails to realize certain possibilities. Furthermore, there will be no resources in his world for getting names of these properties into the Lagadonian language. So no matter how rich the worldmaking language of McPoor's world, it will not be rich enough to capture all the possibilities. However, no commitment to full- blown modal realism is necessary to see that we might be in such a situation ourselves. It might very well be true that there could have been more properties than are instantiated in our world. But if that is so, linguistic ersatzists have no way of making room for the missing properties.

7 The clearest need for possible individuals comes from the theory of content. But I find it hard to believe that a theory of content that has "psychological reality" needs more than linguistic ersatzism has to offer. And I am inclined to stand with Freidman when he says that "any serious semantic theory must eventually be connected up with psychological -and social theory" (Friedman, i98i, p. 13).


Peter van Inwagen puts the point very nicely. The worlds of linguistic ersatzism are linguistic reflections of the recombination principle applied to this world. But, he asks,

What warrant have we to suppose that there is in actuality such a rich variety of kinds that every possibility could be realized by some numerical augmentation or diminution and clever arrangement of the things there are? Even if one believed this, one should regard it as a substantive metaphysical thesis (something to do with God's bounty, perhaps, or with some other causally effective principle that is supposed to make actuality coincide with ontological richness) and not as something that could properly be forced on us by the most general and abstract features of our modal ontology (Van Inwagen, i986, p. zoi).

Van Inwagen regards this as a decisive objection to linguistic ersatzism. My problem is twofold. First, the issues here seem to me to be much too obscure for anyone to base their opinion of linguistic ersatzism on this argument. My second objection is that I don't think Lewis has provided a credible alternative.

First, the matter of obscurity. If there are such things as uninstantiated properties, then the problem goes away. They can even serve as their own names in the Lagadonian language. Lewis thinks, rightly, that such properties are ill-understood at best. In fact, he would almost certainly go further. Nonetheless, I find in myself an inclination to believe in uninstantiated properties. I also find that when I discuss the problem of alien properties with other philosophers, they almost universally have the same instinct, typically prefacing their expression of it with a reference to the missing shade of blue or some such thing. Lewis's most important objection to uninstantiated properties is that they are like the worlds of what he calls magical ersatzism; they are incapable of doing the job they need to do. I will not attempt to rehearse that argument here. It has been carefully dissected in van Inwagen's "Two 'Concepts of Possible Worlds," and I heartily recommend that piece to anyone who wants to pursue the issue further. I will simply note that the argument is, as van Inwagen puts it, "profoundly tricky." Furthermore, if van Inwagen is right, the argument proves too much. Exactly similar reasoning would show that we don't understand the membership relation. So it would seem premature to abandon linguistic ersatzism because of the problem of alien properties.

But I also find myself with another reaction. I have admitted to a temp- tation to believe in uninstantiated properties in spite of the deflationist comments I made earlier. The uninstantiated properties I would be most sympathetic to are continuations and interpolations of properties actually instantiated. If there is a missing shade of blue, it is somehow instinct within this world. However, I am also inclined to believe that there could have been totally alien properties - properties that extend beyond the

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bounds even of whatever uninstantiated properties I may accept. So I still seem to have Lewis's problem.

Or do I? What I really want to say is that in some sense, there could have been properties that there aren't, full stop. I don't think (or at least I'm not sure) that there had to be just the properties that there are in this world, but I also don't think there are any definite facts about what properties there might have been but aren't. Indeed, if I did, I would probably be inconsistent. If there are definite facts about what properties there might have been but aren't, isn't this just to say that there are certain definite but uninstantiated properties? The problem is that Lewis has an intuition that I simply lack.

Am I not inconsistent anyway? What can it mean to say that there might have been more properties than there are, if this does not amount to a commitment to definite ways that things could have been? And indeed, if the story about McPoor is the basis for my intuition, it suggests this stronger claim.

First, McPoor. I'm not really sure that my intuition flows from his story, nor, indeed, do I want to base a great deal on that story. Unlike Lewis, I think the actual world is special. McPoor is just a character in a story about a nonactual world, and my grip on his story comes via my grip on this world. I think my intuition comes to something more like this. Lewis points out (apparently following up a suggestion in Skyrms, i98i) that the linguistic ersatzist can use Ramsey sentences to get a similacrum of alien properties. Saying that such sentences represent possibilities provides a nice way of parsing the claim that there could have been more properties than there are. But my sense is that in this area, consistency and possibility begin to collapse. That is, so long as the Lagadonian Ramsey sentences are consistent and don't require non-Ramsified claims that are impossible, there is nothing more to these "possibilities" than their structure.8 Or at least, I see no reason to believe otherwise.

Even if you aren't convinced of this, there is a remaining issue of credibility that cinches the matter for me. If I have a choice between doubting that there are any thoroughly alien properties and claiming that there are other whole worlds utterly disjoint from this one, I'll put my money on the first option every time. This is because modal realism seems to me much less credible than the denial that there are alien properties. After all, in doubting alien properties, I am unloading a commitment to something for which I have no more than purely metaphysical use. In embracing modal realism, I would be taking on a substantial and highly suspect commitment.

8 This is how I read Skyrms, i98i, and I find that I agree.


Furthermore, even if you think the problem of alien properties is genuine, our choice is not between modal realism and the denial of alien properties. We have already seen one way to get around the problem of alien properties: say, in an expansive tone of voice, that actuality really is rich enough to cover all the possibilities. Hidden away within the actual are so many properties, all instantiated, that we have no need for other worlds to instantiate alien properties. If this is so, then there would be no clear need for modal realism. The actualist would have all the resources he needs.

It is interesting to compare this hypothesis with modal realism. If we assume that it is true, great systematic advantages accrue; indeed, all (or virtually all) of those that come with modal realism. But we don't consider this to be to any degree a reason for believing the hypothesis. It might seem that this is for a straightforward reason: we actually have evidence that the hypothesis is false. There are ways things might have been that are not instantiated in our world. For example, the space-time of our world is apparently pseudo-Reimannian. This means that its structure is a general- ization of the structure posited by special relativity and hence there are space-time points that don't stand in any absolute temporal relation. But Reimannian space-times incorporating absolute temporal relations are at least possible. In what sense does actuality instance this possibility?

This case is not an especially worrisome one. We obviously have the resources in this world to describe this possibility, and that is all my hypothesis requires. But a more extreme reply is possible. We could hypothesize that the world is much bigger than we thought. Perhaps what we think of as space-time is a subregion of a space over a non- Archimedian field such as Conway's N.. This is even consistent with any evidence we might have that our space-time is infinite in spatial and temporal extent. As Philip Ehrlich pointed out to me, in a space over a non- Archimedian field, one has "relative infinities." That is, a region of the space would be infinite relative to a certain standard, but finite or even infinitesimal from the point of view of a larger portion of the space. This provides for the possibility of arbitrarily many distinct subregions, which we could think of as quite different from one another in internal structure and characteristics.9 Indeed, we could think of them as realizing the same range of possibilities as Lewis's worlds. So it appears that there is an alternative to Lewis's modal realism. Hypothesize that the actual world is much bigger than we thought; big enough to contain all the "missing possibilities" in full glory.

9 For discussion of related matters, see the papers by Ehrlich referred to in the bibliography.

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Another way to get more properties without fear of refutation: hypothesize that the missing properties are the sorts of epiphenomenal danglers we talked about earlier. In this case, we don't get a structural reflection of modal realism, but we plausibly get the resources needed for linguistic ersatzism. Now it seems to me that there is not the slightest reason to believe that either of these hypotheses is true, handy though it would be if one were. But why is there any more reason to believe Lewis's story?

I don't believe there is any more reason. Here is the main apparent advantage his story has, so far as I can tell. The facts about logical space, however construed, should be necessary. But my hypotheses are avowedly about actuality, and it is one of our most basic modal prejudices that actuality could have been different. In particular, even if actuality is as rich as I imagine, it might have been as impoverished as the poorest of Lewis's worlds. So the pretended fact that actuality provides enough resources for the theory of the possible is mere lucky contingency - the wrong sort of fact to ground the theory of modality. Lewis's hypothesis, on the other hand, is not about actuality, and so we are not forced by the very terms of the story to admit that its truth is contingent. In short, my stories are not up to the task, but Lewis's is.

In a pig's eye. The only salient difference between my wilder actualist story and Lewis's tale of many worlds is that mine is unabashedly about a single, connected (but internally diverse) space-time, whereas his is about a plethora of disconnected space-times. This allows him to define a smooth sense in which not all worlds are actual, but it doesn't touch the question of whether the facts about the Grand World are contingent. The reason we think my story is at best contingently true is not just because it is about actuality. It is largely because there are too many alternative hypotheses, all apparently possible, all equally credible, for this one to have any plausible claim to necessity.

My point, of course, is that the same goes for Lewis. Perhaps there are other worlds. Perhaps there are enough of them to represent every intra- world possibility in full detail. Then again, perhaps there are only enough worlds to provide the resources for an adequate linguistic ersatzism only enough to supply whatever properties are missing from this world. Or perhaps this world is rich enough to eliminate the problem of alien properties, either by way of one of my stories or some other. (I allow for the sake of the argument that there really is a problem to be solved here.) Lewis's hypothesis is prettier. But this seems to me to be a clear case in which beauty and truth part company.

Let us review this argument. The supposed advantage of modal realism over what we might call "extravagant actualism" (in either of the forms

3 50 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH

described above) was that extravagant actualism could be at best contingently true, whereas modal realism could be necessary. However, the core of modal realism is the doctrine that there is a gapless array of worlds the thesis of "Plurality." There are other consistent hypotheses that, if true, could allow us to do the work of modal realism. Extravagant actualism is one example, but so are various versions of the hypothesis that there is a less-than-gapless array of worlds. If Plurality is possibly true, it is hard to see why these other hypotheses aren't as well. But since these other hypotheses conflict with Plurality and are possible if Plurality is, Plurality is not necessarily true. Therefore, the supposed advantage of modal realism over, say, extravagant actualism is not real. Indeed, if modal realism requires the neccesity of Plurality, then modal realism is false.

Why might modal realism require the necessary truth of Plurality? Skyrms, 1976, in effect provides a reason. If Plurality is not necessary, then modal realism faces the threat of a runaway ontology. Lewis para- phrases thus:

Skyrms conjures up the spectre of a regress from a plurality of worlds to a plurality of grand worlds to a plurality of yet grander worlds . . . The regress works by cycling around three assumptions: (i) that 'reality' is the totality of everything, (z) that reality might have been different, and (3) that possible difference is to be understood in terms of a plurality of alter- natives. (pp. ioo-ioi)

Lewis's reply is that if "reality" refers only to what is in this world, (i) is false, and if "reality" is a blanket term, (z) is false. But what I think we have seen is that even if "reality" is a blanket term, (z) is still true. Now (3) is a key part of modal realism. So if Skyrms really has provided the means to generate a regress on the assumption of (i), (z) and (3), then a regress is what we have.

Maybe the regress can be stopped. But in the end, it seems to me not to matter. Whatever force our earlier consideration of extravagant actualism has against the necessity of plurality, its real force is surely against its very credibility. Modal realism (or more correctly, Plurality) is part of a family of metaphysical options, all of which are capable of doing pretty much the same work. All of these options are incredible. We would think it entirely inappropriate to accept any of the others on the basis of their serviceability, and there is no reason to treat modal realism any differ- ently. Modal realism remains at best a splendid speculation.

In spite of my negative view of its central thesis, there is no doubt that On the Plurality of Worlds is a valuable book. Its substantial contribution to other approaches to modality, in particular, to linguistic ersatzism, is a mark of real intellectual generosity. And it raises a host of intriguing issues, many of which have not even been broached here. Even if it pro-

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duces no converts, it will remain a central text in the literature on modality for a long time to come.

Bibliography Cartwright, Nancy. How the Laws of Physics Lie. Clarendon, 1983. Ehrlich, Philip. "The Absolute Arithmetic and Geometric Continua,"

forthcoming, Peter Machamer and Arthur Fine (eds.), PSA 1986, volume z, Philosophy of Science Association.

Ehrlich, Philip. "Universally Extending Continua," forthcoming. Friedman, Michael. "Theoretical Explanation," in Richard Healey (ed.),

Studies in the Philosophy of the Natural Sciences. Cambridge, i98i, pp. i-i6.

Haugeland, John. "Weak Supervenience," American Philosophical Quarterly i9 (198z): 91-103.

Haugeland, John. "Ontological Supervenience," Southern Journal of Philosophy zz, Supplement (1983): I-1z.

Horgan, Terence. "Psychologism, Semantics and Ontology," Nous zo (i986): 21-31.

Lewis, David. "New Work for a Theory of Universals," Australasian Journal of Philosophy 6i (1983): 343-77.

Lewis, David. On the Plurality of Worlds. Blackwell, i986. Lycan, William G. Review of On the Plurality of Worlds, Journal of

Philosophy 85 (1988): 4z-47.

Pitowsky, Itamar. "Resolution of the Einstein-Podolsky-Rosen and Bell Paradoxes," Physical Review Letters 48 (198z): lz99-130z.

Skyrms, Brian. "Tractarian Nominalism," Philosophical Studies 40 (i98i): i99-z06.

Skyrms, Brian. "Possible Worlds, Physics and Metaphysics," Philosoph- ical Studies 30 (1976): 3z3-3z.

van Inwagen, Peter. "Two Concepts of Possible Worlds," Midwest Stud- ies in Philosophy ii (i986): 185-z13.


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