Critical Notice

Mind, New Series, Vol. 97, No. 385. (Jan., 1988), pp. 117-128.

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Critical Notice

On the Plurality of Worlds. By DAVID LEWIS. Oxford, Basil Blackwell, 1986. Pp. 285. L25.00, paper L8.95.

David Lewis began the introduction to his first book, Convention, with the fol- lowing remarks about platitudes:

It is the profession of philosophers to question platitudes that others accept without thinking twice. A dangerous profession, since philosophers are more easily discredited than platitudes, but a useful one. For when a good philosopher challenges a platitude, it usually turns out that the platitude was essentially right; but the philosopher has noticed trouble that one who did not think twice could not have met. In the end the challenge is answered and the platitude survives, more often than not. But the philosopher has done the adherents of the platitude a service: he has made them think twice.1

That book was a self-described defence of a platitude-that language is ruled by convention. His most recent book might be described as a challenge to a platitude- that the actual world is the only world that really exists. There are, Lewis argues, many possible worlds, and a possible world is really a world: a thing of the same kind as the actual universe we live in, the universe that contains us and our surroundings as parts. Our modal discourse, Lewis believes, is discourse about this plurality of worlds. If it is true that there might have been talking donkeys, this is because there really are talking donkeys in one or more of these universes.

Most people will find this thesis incredible, and I think they should. I expect the platitudes that it challenges to survive, but Lewis's arguments will make us think more than twice about how to understand modal discourse, as well as the many other conceptual phenomena to which the possible worlds framework has been applied. Despite the incredibility of the thesis, this is a brilliant book: clear, fair and accurate in its exposition of alternative positions, penetrating in its criticisms, and resourceful in its defence of modal realism. The style is lively and polemical, with rhetoric to match the arguments. The book is a pleasure to read, even for one feeling the sting of its attack.

The structure of the book is simple and straightforward. The first chapter presents the positive case for modal realism. I t is argued that the hypothesis that there is a plurality of worlds is presupposed by a wide range of philosophical explanations and analyses. The second chapter responds to a number of arguments against modal realism, arguments that the hypothesis leads to paradox, or has counter-intuitive consequences. The third chapter responds to the suggestion that the possible worlds framework can be given an ontologically less extravagant interpretation, and that all of its philosophical benefits can be achieved without a commitment to the existence ofother worlds. The last chapter explores the problem of the identification of individuals across possible worlds, defending the thesis

1 David Lewis, Convention, Cambridge, Mass., Harvard University Press, 1969, p. I .

I I 8 Robert Stalnaker

that individuals exist only in one possible world, although they may have counter- parts in other worlds. Throughout, Lewis is candid about the costs as well as the benefits of the theses he defends, and about the limits of his arguments. He recognizes that others with different priorities may reach different conclusions from those he does, even if they accept all his arguments about what the costs and benefits are.

I will focus my discussion on two points: first, on Lewis's response to the epistemological argument against modal realism; second, on the interpretation and criticism of what Lewis calls ersatz modal realism, the attempt to get the benefits of modal realism without the costs.

The thesis of modal realism has two parts: first, the ontological claim that there are other universes spatially and temporally disconnected from ours; second, the semantic claim that statements about what might or must be true are to be analysed as quantifications over these universes. The epistemological objection to modal realism-the challenge that I think is the most serious-focuses on the semantic claim: if this is what modal statements mean, then how can we ever know, or have reason to believe, that they are true? Both Lewis and his critics agree that we do have modal knowledge: we know, or at least reasonably believe, for example, that it might not have rained on the day of the wedding, even though in fact it did. But according to Lewis's semantic thesis, this implies that we know that there exists a spatially and temporally disconnected universe with real flesh and blood people very similar to ourselves in which a wedding similar to the one in question took place on a day on which it did not rain. But, the critic objects, we have no reason to believe in the existence of a universe meeting these specific conditions, and so this cannot be implied by what we mean when we say that it might not have rained. A satisfactory philosophical account of modality must not only make the right modal propositions come out true, it must also help to give-or at least be compatible with-an intuitively satisfactory account of how we know the modal propositions that we take ourselves to know. Modal realism, the critic charges, forecloses such an account. Lewis objects that we do have good reason to believe in the existence of such universes-just the sorts of reasons that we all agree are good reasons for believing the modal propositions: thought experiments, appeals to intuition, consistency arguments, inferences from intuitively plausible general modal principles. But, the critic objects, how can these considerations be relevant to the existence of concrete parts of reality? Lewis and his critics agree that there can be no causal interaction with other universes. Isn't it necessary to have causal acquaintance with physical objects in order to know that they exist, or what they are like? Lewis replies that causal acquaintance cannot be a general requirement for knowledge; if it were, how could we have knowledge of mathematical entities? The critic assumes that it is knowledge of concrete, as contrasted with abstract, objects that requires some kind of causal interaction with the knower. But this distinction (which Lewis argues, effectively, is unclear and unable to bear the weight often put on it) is not the relevant one. I t is contingent facts and objects knowledge of which requires a causal transaction with the knower. Otherworldly donkeys, just because they are otherworldly, are not contingent objects, and the fact that they exist is not a contingent fact. So they can be known about in ways other than by causal interaction, perhaps the same kinds of ways that we can know

Critical Notice I 19

about numbers and pure sets. What ways are those? Here Lewis has not much to say, but he argues that this is not a problem just for the modal realist. We all must explain how we know about mathematical objects: why it is that proofs, constructions, and calculations are ways of finding out about a domain of entities bevond the reach of our causal acauaintance. ~ n v o n e who takes modal claims seriously must explain how we know them, and it does not help, Lewis argues, simply to say that the entities such claims are about are abstract entities. ('Could "abstract"', he asks, 'just mean "don't worry"?' (p. I I I).

So Lewis does not provide an answer to the question, how, on the realist account of modal truth, is modal knowledge possible? Instead the strategy is to reduce this vroblem to another vroblem. one that we all face. I think Lewis is right that it is not just modal realists who have yet to give a satisfactory account of how modal knowledge, including mathematical knowledge, is possible. But even if one does not have a finished epistemology of mathematics and other necessary truth, one may have opinions about the general shape that such an epistemology must take, and one may be able to defend conditions that it must meet, conditions that may be incompatible both with modal realism, and with a certain kind of realism about mathematical entities.

I think the analogy between knowledge of mathematical objects such as numbers and knowledge of other possible worlds is a useful one. Platonism about numbers bears a family resemblance to modal realism, and it is a familiar prima facie objection to Platonism that it seems to foreclose a naturalistically acceptable account of mathematical knowledge. But the Platonist may have options for responding to this prima facie problem that are not available to the modal realist, who makes much more specific commitments about the nature of the entities in question than does the Platonist about numbers. Let me try to make this point by comparing two kinds of Platonists who would give contrasting answers to the epistemological objection to Platonism.

The nominalist sceptic says to the Platonists, 'I just can't believe there really are such queer things as numbers existing in some Platonic heaven. If there were such things, how would we ever know about them?' The first Platonist, who I will call the liberal, replies as follows: 'Your scepticism is based on a misconception about the kind of thing that a number is. You and I agree that number theory is a legitimate enterprise that involves the acceptance and justification of what look like statements, and that there are non-trivial objective standards of correctness for the statements and for the justifications. Further, we agree that a semantics of predication, reference and quantification can be used to characterize the structure of the discourse of number theory, and that some of the statements that have, on this characterization, the form of existential quantifications-for example the claim that there are infinitely many primes-meet the standards of correctness. But this is all I mean when I say that there are numbers. Don't think of Platonic heaven as a place where there are shadowy paradigms-perhaps cloudlike numerals floating in space. The existence of numbers is just constituted by the fact that there is a legitimate practice involving discourse with a certain structure, and that certain of the products of this discourse meet the standards of correctness that it sets.'

But before the nominalist can be seduced by this casual attitude toward ontology, the second Platonist who I will call the fundamentalist, objects. 'Your alleged

120 Robert Stalnaker

misconception about what Platonism entails was no misconception. My colleague, the liberal, should really be described as an ersatz Platonist. Numbers really are numeral-like things that have shape (although just what shape we can never know) and that take up physical space (although no part of our physical space). We don't causally interact with these numbers: how could we, since they are necessary beings. But they are what our number theory is about; if that theory is true, it is because its principles correctly describe some of the relations between these things. How can we ever know about such things? I don't know, but it is clear that we can know about them. For as the liberal said, we all agree that mathematics is a legitimate enterprise. I t is up to epistemologists to come up with an account of knowledge that permits the methods of mathematicians to be ways of knowing about the inhabitants of Platonic heaven.'

Now of course my fundamentalist is a straw man. No realist about mathematics that I know of thinks that numbers have shape, or exist in a physical space. But suppose someone did defend such a theory about what kind of things numbers were. Wouldn't it be reasonable for the sceptic to press the epistemological ob- jection? 'If this is what numbers are,' he might reasonably ask, 'how could their existence or non-existence be relevant to mathematical practice? How could the proofs, constructions and calculations that mathematicians offer be ways of es- tablishing the properties of things of this kind? If this is what numbers are, aren't the axioms of number theory just completely unsupported speculations? How do we know that the natural numbers don't give out, say after a googol? If this is what numbers were, I would worry that maybe there really is a greatest prime, the fallacy in the proof to the contrary being the false premiss that every number has a successor. But I have no such worry. So I can't believe that my confident belief that there is no greatest prime is a belief about the existence of things of this kind. Furthermore,' the sceptic continues, 'if this is what numbers are I can't see how their existence is necessary for the interest and applicability of arithmetic. Suppose arithmetic really does purport to be about things of this kind. But suppose there are no such things. Most of the theorems of arithmetic are then false, but can't we still use arithmetic in all same ways that we do use it, and with just as much confidence in the conclusions that arithmetical calculations help us to reach?'

The reason that my fundamentalist is vulnerable to the epistemological objection is that he makes certain specific commitments about the nature of mathematical entities, commitments that make it impossible to understand how the methods used to establish mathematical truths are relevant to the content of those truths. While it may be that no one makes these claims about numbers, Lewis is quite clear that the modal realist makes this kind of commitment about the nature of possible worlds and possible individuals. Merely possible talking donkeys are made of flesh and blood, are born and die, and interact causally with things in their environment. So the analogue of the liberal Platonist response to the epistemological objection is not open to the modal realist. Of course the liberal view is not without its own problems. My liberal has only hinted at a rough strategy, and it is not clear that it can be developed, defended, and distinguished from instrumentalism. But I think

2 Cf. the fable of Id and Oz discussed by Bas Van Fraassen in 'Platonism's Pyrrhic Victory', in A. R. Anderson et al. (eds), The Logical Enterprise, New Haven, Yale University Press, 1975, PO. 39-50.

Critical Notice I z I

it is a reasonable necessary condition on any account of the nature of mathematical entities that it provide, or at least be compatible with, an account of how justi- fication in mathematics is relevant to mathematical truth, and how truth is relevant to the applicability of mathematical conclusions. The liberal strategy is an attempt to meet this condition, while the fundamentalist interpretation is incompatible with it. Similarly, I think it is a reasonable necessary condition on an account of the nature of possibilia that it provide, or at least be compatible with, an account of how we can know about such things, to the extent that we think we can. I don't think modal realism meets this condition.

Lewis likes to evaluate philosophical doctrines in terms of costs and benefits. He admits that it is a cost of modal realism that it makes ontological commitments that go against common sense, but he argues that it is a compensating benefit of modal realism that it provides us with a unified framework for explaining a wide range of theoretical concepts that help us to describe ourselves and our actual world: modality and probability, counterfactual conditionals, mental and semantic content. But I think the cost tends to undercut the benefit. Just as the nominalist may say to the fundamentalist Platonist, 'how can propositions about those things be relevant to the practice and applications that are why we value mathematics?' so we may say to the modal realist, 'how can the existence of other worlds be relevant to the modal, probabilistic, counterfactual, mental and 'semantic concepts we use to describe ourselves and our actual environment?' Suppose for a moment that the modal realist's semantic thesis is correct, but the metaphysical claim is false. Suppose, that is, that there are no other worlds, and so that all truths are necessary, all probabilities are one or zero, all counterfactuals are vacuously true, and true propositions all have the same informational content. Might it still not be that the one actual world has all the complexity that we normally attribute to it, and won't the concepts that the modal realist uses possible worlds to explain still be just as useful for describing that world? It is not clear how the commitments of modal realism contribute to the benefits that are claimed for it.3

The benefits claimed for modal realism are benefits of the possible worlds framework. Many philosophers try to claim these benefits while rejecting Lewis's modal realism, offering an account of possible worlds that is alleged to be more in accord with common opinion. They say that what we call 'possible worlds' are not really worlds, but are properties the one world might have, states it might be in, or ways it might be. Since Lewis grants the prima facie implausibility of modal realism, and grants that this implausibility is a cost that should be taken seriously, he needs to show that innocent interpretations of possible worlds will not work. Lewis argues that the project, which he calls 'ersatz modai realism', has its own costs. Any clear account of what an ersatz possible world is, he argues, will yield a philosophical theory that is either more repugnant to common opinion than modal realism, or it will be unable to provide an adequate explanation of the modal facts.

There are different versions of ersatz modal realism-different accounts of what a possible state of the world is and of how it represents the world-each with its

I t must be granted that what I am offering here is little more than a rhetorical appeal to intuition. One cannot take literally the question, 'if there were no other possible worlds, what difference would it make?' since according to the modal realist, it is a necessary truth that there are other possible worlds, and so one cannot coherently suppose that there are not.

I 22 Robert Stalnaker

own problems. Lewis complains that most proponents of this doctrine have little to say about what the possibilities they believe in are; he calls these philosophers 'nondescript ersatz modal realists' (one of many examples of Lewis's inspired labels for his opponents' positions). But he offers them three actualist accounts of ersatz possible worlds, and argues against them in turn. The first-the one he regards as the most serious alternative-explains possibilities as linguistic objects; the second explains possible worlds as perfect pictures of a world. The third-labelled 'ma- gical ersatzism' says that possible worlds and the means by which they represent are primitive and simple. I will say no more about pictorial ersatzism, a doctrine that no one holds and that Lewis effectively shows has all the drawbacks of modal realism without the advantages. I will have some remarks about the other two, but my main point will be to argue that we do not need a general metaphysical account of the nature of possible worlds in order to get the benefits of the possible worlds framework.

Modal realism is a metaphysical theory, a theory that makes some claims about the basic constituents of reality. The so-called ersatzist doctrines that Lewis considers are alternative metaphysical theories. Lewis's question is, what kind of metaphysical commitments do we need to make in order to have access to the philosophical clarifications provided by analyses of various modal and intentional concepts in terms of possible worlds? The argument is that modal realist meta- physics does the job better than the alternatives. But I want to argue that the real benefits of possible worlds analyses do not depend on any particular metaphysical commitments. Any application of the framework to a particular domain will have to say or presuppose something about the nature of the entities-the alternative possibilities-that it quantifies over when it makes modal and intentional claims, but different applications may say different things. All such applications will have some structure in common, and analyses of modal, probabilistic and intentional concepts are an attempt to clarify that structure. But they need not have an ontology in common, and there need not be a single set of maximally specific possible worlds to fit all contexts. I t may be that every attempt to say something substantive about what possibilities are-what structure and constituents they have-will be local in the sense that it leaves out some possibilities that may be relevant in some other context. A general account of possible worlds will be abstract, not in the sense that it says that possible worlds are a special kind of entity, an abstract entity, but in the sense that it attributes to them only a certain relational structure. Possible worlds will be primitive and unstructured in the general theory, not because they have some kind of metaphysical simplicity, but because we want to theorize at a certain level of abstractiom4

In particular contexts, structure will usually be ascribed to the possibilities used to define a model. For example, in interpretations of quantified modal logic, the worlds have domains of individuals. They might be defined as alternative ways of locating individuals in some property space. In a theory that tries to explain the interaction of tense and time-dependent necessity, possible worlds may be defined as paths through a tree structure. A theoretical computer scientist may define a set

Compare Peter Van Inwagen's remarks about the concept of possible worlds being a functional concept, 'Two Concepts of Possible Worlds', Midwest Studies in Philosophy, 1 1 , Studies in Essentialism, 1987, PP. 192-3.

Critical Notice 123

of possible worlds in terms of a distributed system of interacting state machines, each following some possibly non-deterministic protocol; the worlds will be the possible runs of the system. A game theorist might define a set of possible worlds in terms of the rules of a game; the worlds are all the ways of playing the game that conform to the rules.

Such applications of the possible worlds framework do not hypothesize the existence of some kind of mysterious magical simples, but neither do they provide us with an elimination of primitive modality. Lewis is right, I think, that if we reject modal realism, then we must give up on the project of providing a reductive analysis of modality. Lewis grants that this is not a fatal problem for ersatz modal realism. There is, he suggests, a trade off-one gives up some conceptual economy to avoid some ontological extravagance-and some philosophers may think the trade is worth it. But how great is the cost? This depends on whether the philo- sophical work done by the possible worlds framework requires that the framework provide a reductive analysis. I will argue that it does not.

Suppose one regards the analysis of modal, epistemic, causal, intentional, and semantic concepts in terms of possible worlds, not as a reduction to some more basic level, but simply as a redescription in an alternative language, a language whose interpretation is explained partly with the same concepts that are analyzed in its terms. If possible worlds analyses are circular in this way, does this com- promise the philosophical work that they are supposed to do? Let us look briefly at some of this philosophical work: consider, for example, the standard puzzles about referential opacity. The bicyclist is necessarily two-legged, while the math- ematician is not. But the bicyclist is the mathematician. How can this be? If we redescribe the situation in terms of what is true in a set of possible worlds, and use the redescription to interpret the premisses of the paradoxical argument, then we can identify some equivocations and clarify what is going on. This kind of philosophical explanation is not compromised if we use the same modal notions that create the problem to explain how the language in which the redescription is given is to be understood. Or consider the use of the possible worlds framework to clarify arguments for fatalism. Assumptions about tense, truth, and time-dependent necessity can be sorted out and their interaction clarified if we redescribe the situation in terms of a branching structure of possible histories. Modal notions- the very ones that are problematic-are needed to characterize the intended model of the semantic theory used to give such a redescription, and this prevents it from being a reductive analysis. But it does not prevent it from solving the particular problem posed by a cluster of controversial arguments. More generally, the possible worlds framework serves a unifying function, helping to relate various modal, probabilistic, epistemic, causal, semantic, and intentional notions to each other by providing a common resource for analysis. A philosopher may offer an analysis of causation in terms of counterfactuals, a theory about the relation between chance and degree of belief, a pragmatic theory that relates speech acts to changes in the intentional states of the participants in a discourse, an account of knowledge in terms of information, where information is explained in causal or probabilistic terms, an account of belief and desire in terms of dispositions to act. The possible worlds framework can help to make such philosophical explanations precise, and to bring out their consequences, and it can do this even if we understand the basic

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constituents of the framework-the possible worlds-only in terms of the concepts they are used to analyse.

The positive case for modal realism is presented in Lewis's first chapter, 'A Philosophers' Paradise', which describes 'modal realism at work'. Most of the work described is the kind of conceptual clarification and integration that I have suggested does not depend on the eliminative reduction of modality. If it is access to these philosophical explanations that constitutes the philosophers' paradise, and if the main cost of the cheap, ersatzist interpretation of possible worlds is that it requires a commitment to primitive modality, then I think we can have paradise on the cheap.

Lewis grants that ersatz possible worlds can do some limited philosophical work. What he doubts is that they can provide a general metaphysical foundation for modality. Suppose we take the set of all possible worlds to be the set of all total states of the world that are metaphysically possible and ask, just what sort of thing are these states? Can the ersatzer, or actualist, give a satisfactory answer? Lewis argues that even if he gives the ersatzer primitive modality, there are serious problems with an actualist metaphysics of possible worlds. I will look at two of the three actualist strategies he criticizes.

One familiar strategy is to explain possible worlds in linguistic terms. The paradigms are Carnapian state descriptions and Richard Jeffrey's complete con- sistent novels. Lewis points out that if one uses a liberal conception of language, the linguistic strategy is broader and more flexible than one might think. We can, for example, use things as names for themselves, and in this way define a language in which everything has a name, no matter how many things there are. Lewis suggests that any kind of combinatorial account that seeks to analyse possible states of the world in terms of individuals, properties, and relations that inhabit the actual world can be understood as an instance of the linguistic strategy. I think this is wrong, or at best misleading. Suppose an actualist metaphysician begins his account like this: possible states of the world are properties. The universe or world as a whole is the thing to which such properties are properly attributed. The universe is, of course, a very complex thing, and the properties attributed to it will normally be very complex too. The world will have such a property in virtue of having parts of a certain kind that themselves have certain properties and stand in certain relations. One explains what a possible state of the world is by saying what parts the world must have, what they must be like and how they must be related in order for the world to be in that state. The situation is the same as with complex properties of smaller complex things, such as cities. What is it, for example, for a city to have the property of being ethnically diverse? A methodological individualist might try to define such a property by saying what ethnic properties the inhabitants of a city need to have in order for the city to have the property of being ethnically diverse. Now I don't think there is any reasonable sense in which this kind of project could be described as giving a linguistic account of complex properties. I t is true that the English predicate 'is ethnically diverse', applies to New York City in part because of certain conventions of the English language, but the relation between that city and the property that this predicate expresses is not a linguistic relation, and does not depend on any actual or possible linguistic conventions. It is beside the point that in a language in which individuals name

Critical Notice I 25

themselves and properties and relations express themselves, there will be a complex predicate that both is and expresses the complex property. The individualist's analysis is an account of the relation between certain complex properties and the properties of related simpler things. The same will be true of an actualist's analysis of possible states in terms of the way the world must be arranged for the states to be actualized. If this kind of strategy of analysis is one that Lewis means to include under the category of linguistic ersatzism, then I think the category is misleadingly described. If not, then I think he has left out a plausible strategy.

Some of the problems that Lewis raises for the linguistic strategy are also problems for the conception of possible states as complex properties. This strategy, like the linguistic strategy, must define possible worlds in terms of actually existing individuals, properties, and relations. But it seems that there might have been individuals, properties, and relations other than those that actually exist. How are the possible states in virtue of which this is possible to be defined? Consider first the problem of possible individuals, a problem Lewis regards as less serious than the problem of merely possible properties. One solution is simply to say that there exist unanalysable individual essences, or what Lewis would call 'ersatz individuals' which can be used to define possible states of the world. Just as merely possible worlds are actual but unactualized states of the world, so merely possible individuals are actual but unactualized individual essences. But some may find it difficult to believe that there actually are such things. An alternative solution is to reduce individuals to properties and relations. The possibility of an individual, one might say, is just the possibility of certain properties being instantiated. One reason Lewis does not think this problem is a serious one is that he finds this kind of solution plausible. But there is a parallel problem about non-existent properties that is not subject to the same solution. A case can be made-and Lewis makes it-that there might have been properties other than those that actually exist. The point is not just that properties that are uninstantiated might have been instan- tiated. I t is rather that there might have been basic states of matter, or basic kinds of things that cannot be defined in terms of the states, kinds, or properties that things have in the actual world, and it seems reasonable to say that such prop- erties-Lewis calls them 'alien properties'-are not only uninstantiated, but non- existent.5 If it is possible that alien properties exist and are instantiated, then there must be possible worlds in which there are things that have specific alien properties. But if a possible state of the world is constituted by the properties and relations that would be instantiated if it were actualized, then the actualist must say that there are no possible worlds in which alien properties are instantiated. T o this problem, there are two possible replies: first, one may say that such properties do exist after all: in general, one might say, properties are the sort of thing that exists necessarily. We can't refer uniquely to alien proper tie^,^ but they exist none the less. I don't have very strong intuitions about the existence or non-existence of properties-if I have to choose between alien properties and real but non-actual worlds, I'll opt for the alien properties-but if I try (against my

5 Non-existent, the modal realist will say, only relative to the actual world. 6 While we can't refer to them in any language we can use, if such properties exist, we can define a

language in which they can be referred to: just use Lewis's Lagadonian language in which the properties are names for themselves.

I 26 Robert Stalnaker

inclination) to be ontologically serious, I confess that I find it hard to believe that such properties actually exist. So let's look at the second kind of reply, which is to say that possible states of the world need not have the kind of absolute com- pleteness or maximal specificity that we tend to suppose them to have. There are, this second reply must concede, certain existential possibilities (possibilities that there exist things of a certain kind) where there is no corresponding specific possibility. One has to say something like this: there is a possibility that might be realized in different ways, even though there do not exist different ways in which it might be realized. I grant that this sounds like a contradiction; and it brings out a particularly strong commitment to primitive modality. For this reply is committed to potentialities that cannot be identified with ways in which the potentialities are realized. There are possibilities that are in some sense potentially refinable, even though there are no potential refinements.

I think this second reply may be what the modal metaphysician should say if he is committed to reducing possible states of the world to actual individuals, prop- erties, and relations, and it must be granted that it is a serious concession, an admission that there is a way in which the possible worlds redescription of modal facts distorts the phenomena. But the cost of this concession should not be ex- aggerated. First, one can make coherent sense of a theory of possible worlds that makes this concession. Second, the problem arises only in the context of one particular application of the possible worlds framework. Most applications of the concept of a possible state of the world do not rely in any way on the assumption that such states meet some metaphysical condition of maximal specificity. The cost seems to me real, but small in comparison with the implausibility of modal realism.

Finally, let me consider what Lewis calls magical ersatzism. This is the doctrine that says that possible states of the world should be among the primitives of one's metaphysical theory. Lewis's magical ersatzer says that these entities 'have no relevant inner structure . . . no proper parts. They are simples.' (p. 174). But somehow, they have the power to represent the world as being a certain way.

Magical ersatzism is Lewis's invention-he does not attribute it to anyone,7 although he seems to think that possible worlds theorists who reject both modal realism and the other versions of ersatzism he considers may be committed to it. I find the doctrine quite obscure since I do not understand what it is for something to be a metaphysical simple. I also find Lewis's elaborate argument against this doctrine obscure. So far as I can see, the argument is essentially just a complaint that the theory fails to answer some unspecified questions about what possible states of the world are, and how they can do what they do.

The so-called ersatzer says that possible states of the world are properties or states that the world might have. The magical ersatzer adds that he rejects the demand for a reductive analysis of these properties or states. Unwisely, he also adds the gratuitous claim that they are metaphysical simples. I'm not sure what this last claim means. On the face of it it seems absurd to say that complete states of the world are all simple. Many such states are surely at least as complex as the

In fact, he says that there were no defenders of this doctrine at the time he developed his criticisms. Since then, as Lewis remarks in a note added in proof, Peter Van Inwagen has heroically come to its defence in an interesting and penetrating discussion of modal realism. See 'Two Concepts of Possible Worlds', op, cit.

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state that some cities have of being ethnically diverse, and it would be hard to make sense of the claim that that state was simple. But the decision to take something as primitive, and to reject a demand for reductive analysis, need not be based on a claim that the referents of one's primitive terms are metaphysical simples. That one's theory has certain primitives is a fact about the theory, and not a claim that the theory makes. I t may be useful to formulate a theory with possible states of the world as the primitives, analysing other kinds of properties and states in terms of them, even if one thinks that the states are enormously complex. A theory with possible states of the world as primitives may have the resources to say a lot about the structure of those states-about the ways in which they are complex.

Sometimes it seems that Lewis's magical theorist is just stonewalling. His strategy is this: stamp your foot, repeat 'everything is what it is and not another thing', and refuse to answer any questions. That is an unpromising way to do philosophy, whatever the issue, but one who refuses to analyse possible worlds need not refuse to talk about them. One thing he may do is to analyse lots of other things in terms of possible worlds: counterfactuals, causation, probability, informational content, various kinds of properties and relations. Such analyses contribute to an intuitive explanation of just what possible states are since the concepts analysed or inter- related are concepts with lots of intuitive content. So all of the things that Lewis cites as the benefits of modal realism are also resources the magical ersatzer may use to say more about the primitives of his theory. And he may try to make his metaphysical primitives intuitively clearer by calling them by familiar names: states of affairs, ways things might be, possibilities, properties the world might have. But Lewis is not satisfied. 'This seems to help,' he says, 'but I think it just covers up the problem. . . . Our use of the names associates them in the first instance with roles in our thought. I suppose it is a firm commitment of common sense that there are some entities or other that fill the roles. . . . But that is not to say that we have much notion what sort of entities those are.' (p. 184). By calling something a property or state of the world, we identify a role, but fail to answer the question, what is it that play the role? T o say that it is properties or states that play the role is unsatisfactory. 'You might as well interrupt a serious discussion of how to cast a play and say: who shall be Polonius?-Let it be Polonius!' (p. 184). I find this expression of dissatisfaction elusive. Suppose I were to ask what donkeys are. Then I impatiently interrupt a lengthy account of the biology, history, care, and feeding of donkeys by saying, 'I know all that-I know how to play the donkey language game-but what are they really? What are the things that play the role of donkeys? And don't avoid the question by telling me that it's donkeys that play the role!' But it is donkeys that play the role. And there is nothing more to be said, other than to describe the biology, history, care, and feeding of donkeys. Why is it different with properties and states? Perhaps it is different, but if so it is because there is some specific question about such things that the theory that takes states as ~rimitive cannot answer. We need to be told what the cluestion is.

Lewis's primary worry seems to be about the relation he calls 'selection', the relation that holds between a property or state of the world and the world if and only if the world has the property, or is in the state. The selection relation is just a special case of the relation between properties in general and things that have

I 28 Robert Stalnaker

them-the relation that holds between redness and red things, fatness and fat people, being prime and prime numbers. I am not sure what can be said, or what needs to be said, about this relation. Lewis asks whether it is an internal or an external relation. I am not completely clear about this distinction, and the cor- relative distinction between intrinsic and relational properties,E but I suppose if a property is intrinsic, as states of the world must be, then the relation that holds between the property and what has the property will be internal. Lewis finds such an internal relation mysterious. T o bring out the mystery he asks us to consider two states of affairs-there being a talking donkey, and there being a philo- sophizing cat. Then he asks, 'why is it that way around?' (p. 186). That is, why is it that the one would select the world if there were talking donkeys, while the other would select it if there were philosophizing cats, and not the other way around? I can't make sense of the question. Why does having the property red make something red rather than green? (Why is Reagan Reagan, and not Nixon? Because God said, 'let Reagan be Reagan'?) Shouldn't one say that having the property red just is being red? Of course if one had a general analysis of properties in terms of something else, then one might be able to offer an informative re- description of the relation between things and their properties. The magical ersatzer rejects such analyses, and so should reject the question. But he can still say a lot about the relation-about the role it plays in our thought. Lewis rejects such commentary as circular; it does not tell us what it is that is playing the role in our thought. But why can't the role be all there is? ('Who plays Polonius, not in some performance of the play, but in the play itself?' No one-Polonius is just one of the characters-one of the roles).

If by 'possible world' you really mean world, and if the world is something that includes everything that actually exists, then it seems to be a platitude that there is only one possible world. I think this platitude will survive Lewis's powerful attack, but an adequate response to his challenge will force those of us who accept the platitude to be clearer than we have been about a number of philosophical issues: about the epistemology of modal truth, including mathematical knowledge as well as knowledge of possibilities; about the distinction between abstract and concrete; about what kind of things states and properties are; about the status of semantic analyses in terms of possible worlds. I don't think this book will win many converts, but it will help those who reject its elegant metaphysical scheme to think twice: to be clearer about important philosophical issues, and to see them in a new way.

CorneN University ROBERT STALNAKER

8 Why is distance between spatial points a paradigm of an external relation? Why isn't it an intrinsic property of spatial points that they are where they are? Is the greater-than relation between numbers internal or external? Are numbers distinguished by their intrinsic properties, or by their relations to each other? I don't know how to answer these questions.