David Lewis: Modal Realism**

So many worlds, so much to do,
So little done, such things to be
(Alfred, Lord Tennyson -- In Memoriam)

When I profess realism about possible worlds, I mean to be taken literally. Possible worlds are what they are, and not some other thing. If asked what sort of thing they are, I cannot give the kind of reply my questioner probably expects: that is, a proposal to reduce possible worlds to something else.
I can only ask him to admit that he knows what sort of thing our actual world is, and then explain that possible worlds are more things of that sort, differing not in kind but only in what goes on at them.
(Lewis [1973], p.85)

This passage contains, or implies, the heart of David Lewis's modal realism. It explicitly states three of his six central doctrines about possible worlds, and implies at least one of the remaining three. The three doctrines explicitly formulated are:

From these three claims (and from the second in particular) we can see that, when we talk of our own world as being the only actual world, we cannot be asserting that our world has a special property not found in (or instantiated by) any other world - the property of actuality - but that we must be using the term `actual' much as we use the term `here' or `now' -- to indicate our position. This gives us Lewis's fourth doctrine: These four claims are not only central to Lewis's approach, they are essential to it. They must form the basic foundation of any theory that calls itself Lewisian realism. Lewis's fifth and sixth claims are, perhaps, more difficult to draw out, and (as I shall discuss in Chapter 10), may well turn out to be negotiable. The fifth concerns our principle of demarcation between worlds, and the sixth (although also offering some such principle) follows from the Lewisian analysis of causation. I shall take them in order.

Given that possible worlds are just the same sort of things as this world, how do we divide them up? We seem to have a vast collection of possible individuals; what principle do we use in order to fence them off into separate possible worlds?

Why don't all the possibilia comprise one big world? Or, at the other extreme, why isn't each possible neutrino a little world on its own?
(Lewis [1986], p.70)

Clearly, a possible world is not just any set of possible individuals, but what distinguishes a set which is a possible world from a set which is not? After all, "[t]he worlds are not of our own making" (Lewis [1986], p.3) -- we cannot just stipulate here. And we cannot use some principle of compossibility if we want to use possible worlds to help us explain modal concepts. Lewis's answer takes us back to our normal intuitions about our own world:

nothing is so far away from us in space, or so far in the past or the future, as not to be part of the same world as ourselves.
(Lewis [1986], p.70)

Lewis's principle of demarcation starts with a generalisation from this intuition: "whenever two possible individuals are spatiotemporally related, they are worldmates" (Lewis [1986], p.70); that is, they are parts of the same world. His principle is completed by the converse of this -- if two things are not spatiotemporally related, then they are not parts of the same world. We have thus reached Lewis's fifth doctrine about possible worlds:

As Lewis admits, this doctrine is not without problems. We are prevented, for instance, from being able to suppose that the world "consists of two or more completely disconnected spacetimes" (Lewis [1986], p.71). This, he says, is unfortunate, but a sacrifice worth making for the sake of a very useful part of his theory. Another problem concerns worlds containing spirits which exist outside space. Lewis, however, is able to allow for this by conceding that worlds may be unified by spatiotemporal interrelations in different ways:
So the interrelation of a world of spirits might be looser than that of a decent world like ours. If the spirits and their doings are located in time alone, that is good enough.
(Lewis [1986], p.73)

We might object that, on Lewis's account, there cannot be a world at which there is nothing, for a world just is the totality of its contents:

There can be nothing much [at a world]: just some homogeneous unoccupied spacetime, or maybe only a single point of it. But nothing much is still something, and there isn't a world at which there's nothing at all.
(Lewis [1986], p.73)

It is thus impossible that there might have been nothing rather than something. However, Lewis shrugs this off, pointing out that, as he does not claim to explain why there is something rather than nothing, the simple statement that there must be something should not worry us. If we find such a statement unintuitive, that is another sacrifice worth making.

The most serious objection, however, concerns the nature of space-time. It is possible that the world might have been such as to be accurately described by a theory which states that "any two spacetime points are related by a spatial distance and a temporal distance" (Lewis [1986], p.74); that is, the world might have been Newtonian. As it is, however, in our world:

any two spacetime points have only one distance between them; it may be a spatial distance, it may be a temporal distance, or it may be a zero distance which is neither spatial nor temporal.
(Lewis [1986], p.74)

Is a Newtonian world unified by the spatiotemporal inter relatedness of its constituents? That is, are what the inhabitants of that world call `spatiotemporal relations' what we call `spatiotemporal relations'? If not, then the Newtonian world is not spatiotemporally related; it has a system of external relations analogous to our spatiotemporal relations, but they are not our spatiotemporal relations.

Lewis toys with the attractively simple possibility that worlds might be unified "by external interrelatedness, of whatever sort [...] Never mind whether the relations in question are spatiotemporal" (Lewis [1986], pp 76 77), but he is eventually forced to reject it in favour of a solution that involves the devising and describing of a system of relations analogous to our spatiotemporal relations; it is by such analogically spatiotemporal relations that each world is interrelated. Although he does not detail such a system, he does set some conditions for the devising of an analogy of this sort (see Lewis [1986], p.76. I shall discuss this further in Chapter Ten).

Finally, Lewis's sixth doctrine arrives as a result of his counterfactual analysis of causation, and states:

The argument for this is roughly as follows. If, at world W, event C causes event E, then "it is the case at W that if C had not occurred, E would not have occurred either"; this counterfactual is in turn analysed in terms of possible worlds as "at the closest worlds to W at which C does not occur, E does not occur either" (Lewis [1986], p.78). Now, if worlds were causally related, event C at world Wc might be said to have caused event E at world We. Analysing as before, we get the counterfactual `if C had not occurred at Wc then E would not have occurred at We'. But how are we to analyse this in terms of possible worlds? The feeling that it ought to be analysable stems from a mistaken view of the totality of possible worlds as being a sort of meta-world; we feel that this meta-world could have been other than it is -- that, perhaps, although event C does occur at world Wc and event E at We, they might not have done. In other words, that there is a meta-world at which events occurred differently. But either Lewis has already allowed for contingency, in which case we have no need for these meta- worlds, or he has not, in which case it does not seem terribly sensible to try to allow for it by using Lewis's method over again -- we seem set for an infinite regress.

There are problems here, both with regard to Lewis's analysis of causation (the problem arising from worries about his theory of counterfactuals), and in the notion of the relative closeness of possible worlds. I shall, however, for the time being accept Lewis's six doctrines about possible worlds, and carry on to the next stage of my discussion, for a very important question demands an answer. How seriously are we meant to take Lewis's realism?

Lewis himself certainly claims to take it absolutely seriously; not only does he insist, in the quotation with which we began this section, that he wants his claims to be taken literally he also often writes of possible worlds as if he takes their real existence literally;

How many [possible worlds] are there? In what respects do they vary, and what is common to them all? Do they obey a nontrivial law of identity of indiscernibles? Here I am at a disadvantage compared to someone who pretends as a figure of speech to believe in possible worlds, but really does not. If worlds were creatures of my imagination, I could imagine them to be any way I liked, and I could tell you all you wished to hear simply by carrying on my imaginative creation. But as I believe that there really are other worlds, I am entitled to confess that there is much about them that I do not know, and that I do not know how to find out.
(Lewis [1973], pp 87 88)

In fact, of course, someone who uses `possible worlds' as a figure of speech would be equally at a loss when asked to give certain details of possible worlds; unless we are clear concerning all aspects of modality (and of the other areas in which possible world talk is used), then our models of modality will contain blank patches, waiting for our decision as to how they should be filled in. Some of these blank patches will hopefully be filled in as a result of the construction of the model (that, after all, is the point of constructing it), but not all. Stipulation is not the light- hearted act of creation Lewis makes it out to be.

Nevertheless, Lewis's admission of ignorance is perfectly appropriate, given his worlds' spatiotemporal (or analogously spatiotemporal) and causal isolation from each other, and therefore from us. It might, however, leave us wondering about some of the claims which Lewis does feel able to make. Why, for instance, is he sure that possible worlds do not differ from ours in kind? In particular, why could it not be the case that our world alone has the property of being actual in a non-indexical sense ( whatever that property might be)? Why, indeed, should we believe that possible worlds do really exist? Lewis's answer to this last question is straightforward; a plurality of worlds is philosophically useful.

As the realm of sets is for mathematicians, so logical space is a paradise for philosophers. We have only to believe in the vast realm of possibilia, and there we find what we need to advance our endeavours. We find the wherewithal to reduce the diversity of notions we must accept as primitive, and thereby to improve the unity and economy of the theory that is our professional concern -- total theory, the whole of what we take to be true. [...] The benefits are worth their ontological cost. Modal Realism is fruitful; that gives us good reason to believe that it is true.
(Lewis [1986], p.4)

Lewis then provides a tour of some of the areas in which modal realism bears fruit; these include not only modality and counterfactuals, but also verisimilitude, knowledge, belief, and desire (see Lewis [1986], Chapter 1, sections 1.2 1.5). Of course, as he is the first to point out, we have not been provided with a conclusive argument; there are a number of reasons which may cause us to reject modal realism. There is the possibility that belief in possibilia does not really offer us a `philosopher's paradise' -- that Lewis's analyses fail. After all, he does not claim to have provided incontrovertible proof that his analyses (even where he has produced fairly exhaustive ones) are correct. But even if we grant that the benefits are there, we may still want to reject the theory. We might feel that the ontological price is too high -- that our willingness to believe in the existence of a vast array of worlds, all (or all but one) beyond our experience, cannot be bought by any number of philosophical sweetmeats; or we might, upon further investigation, discover some unsuspected implication of modal realism which we cannot accept. I deal with both of these possibilities in Part Two. But there is a final possibility mentioned by Lewis; if we feel that the ontological price is too high, perhaps we can find a better deal elsewhere -- perhaps some other theory offers us the same benefits in a more acceptable way. The most likely way for this to happen would be to accept Lewis's analyses of problem notions in terms of possible worlds, but to accept another ontological theory concerning those worlds -- perhaps one of the actualist theories I discuss in Chapters Three and Four. This would not be without precedent; theories have proved useful in the past, only to be superseded by newer theories committing us to different ontologies.

Let us look more closely at this last possibility. In discussing modal realism in this way, I (like Lewis) am employing modal operators to range over statements about modality. Is Lewis's analysis applicable to these operators? Can, in other words, the statements about possibilities in the last paragraph be translated into statements about (really existing) possible worlds? It is possible that Lewis might concede that statements in the meta-language of his theory need an analysis which his theory cannot provide. This would seem to be a weakness, however; intuitively, we use modal operators in the same way when we talk about object-language statements as when we talk about meta-language statements. If, on the other hand, Lewis claims that his analysis is applicable to meta-modal statements, then the following argument surely holds.

Lewis appears to be admitting something like this: `It is possible that modal realism is wrong, and that another theory, offering the same benefits but entailing the existence of only one world (this one), is correct'. But this is translatable into possible world talk as: `There is at least one possible world at which modal realism is wrong, and at which another theory, offering the same benefits but entailing the existence of only one world (itself), is correct'. According to Lewis, "absolutely every way that a world could possibly be is a way that some world is" (Lewis [1986], p.2). So, if he is right, and possible worlds do really exist, then there is a world at which there are no such things as other possible worlds; that is, if at that world (call it Wp) its inhabitants say `Only one world exists, and it is this one', they are right. But how can they be right? After all, we know that there is at least one world other than theirs -- our own, the actual world, W . The only way that the inhabitants of Wp can be right is for Wp to be W . That is, at our world it is true that there are no other worlds. And no tricks are possible concerning restricted quantification -- it is unrestricted all the way through.

If this argument is valid, then Lewis has three alternatives. As I have already said, he can accept that a modal realist analysis cannot cope with meta-modal operators. Or he can accept that `at our world it is true that there are no other worlds' -- that modal realism is wrong. Or he can claim that modal realism is necessarily true (this would, of course, still leave him free to say that modal realism is epistemically possibly wrong). And this would presumably be his choice. For it may still be the case that, even if this is a drawback, modal realism's benefits outweigh its price, and are not to be had any cheaper. (There is, in fact, one other possibility -- a possibility chosen by David Armstrong (Armstrong [1989]). That is, we might accept that there are statements about the world which are neither necessary nor contingent, but only true or false.)

This is also the main response to what Lewis calls `the Incredulous Stare' -- the chief critical response to his modal realism. The Incredulous Stare is simply the view that modal realism is intuitively grotesque. I shall discuss this view, together with attempts to give it some theoretical underpinning, in Chapter Twelve.

References not included in the David Lewis Bibliography

David Armstrong - A Combinatorial Theory of Possibility (1989; Cambridge University Press)
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Notes:

  1. An extract from Chapter Two of my doctoral thesis
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  2. A significant part of Chapter 10 of my doctoral thesis became Other Times (Australasian Journal of Philosophy 73:4, 1995)
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  3. [See previous note]
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  4. Chapter 3 was a discussion of Non-Modal Actualism, Chapter 4 a discussion of Modal Actualism.
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  5. Chapter 12 was a discussion of Colin McGinn s paper, Modal Reality (in R.Healey [ed.] Reduction, Time, and Reality, Cambridge University Press) [Back]