Modal Realism and Ersatzism

The last article used possible worlds for a whole rung without saying what they are. That was deliberate, since the analysis runs the same way whatever the answer, but it left a bill unpaid. If "there could have been a talking donkey" means "there is a world with a talking donkey", then the second sentence says that something exists, and you are entitled to ask what.

There are two broad answers. David Lewis held that the other worlds are things of the same kind as the universe around you, so that there really are talking donkeys, in worlds other than ours. Most philosophers who use worlds hold instead that they are abstract objects which represent ways things could have been, so that the only talking donkeys are represented ones. The first buys a reduction of modality with an ontology few can believe; the second keeps the ontology respectable and pays in modal notions it cannot analyse. Each also has to say what makes the actual world actual, and they say opposite things.

Lewis's worlds

Lewis stated the view in Counterfactuals (1973), where he needed worlds for a theory of conditionals, and defended it at length in On the Plurality of Worlds (1986).

What makes our world one world is that its parts are all related to one another in space and time, and nothing outside it is related to them in that way. Lewis took this to be what a world is: a maximal sum of spatiotemporally interrelated things. Other worlds are other such sums. They are not far away, because distance holds only between things in the same world, and nothing in one of them causes anything in another.

The beginner tier found the abstract and concrete distinction hard to draw, and Lewis knew this; what he chiefly meant by calling his worlds concrete was that they are the same kind of thing as ours. A merely possible donkey is not a description of a donkey. It is a donkey, with flesh and a voice, which stands in no spatial relation to you. To make sure there are enough worlds, Lewis added a principle of recombination: roughly, a duplicate of anything can coexist with a duplicate of anything else.

Lewis's short argument for the view, in Counterfactuals, starts from something almost nobody denies.

The first three premises are hard to deny. The weight falls on the fourth, which identifies a way things could have been with a thing like the universe, and that is where the ersatzist gets off. Lewis's real case, in any event, was the work the worlds do.

The reductive payoff

The last article closed by asking whether the worlds analysis explains modality or only restates it. If a world is just a way things could have been, the analysis is circular. Kripke accepted the circle and read the framework as a model. Lewis claimed to break it. His definition of a world uses parts, wholes and spatiotemporal relations, and none of these is a modal notion. So when he says that a talking donkey is possible because some world contains one, the right-hand side says only that there exists a donkey standing in certain spatial relations to other things. Possibility has been analysed in terms of what exists.

The same stock of worlds does other work. A proposition can be identified with the set of worlds at which it is true, a property with the set of its possible instances, and a counterfactual is true when some world where antecedent and consequent both hold is closer to ours than any world where the antecedent holds and the consequent fails. Lewis compared the result to set theory, which mathematicians accept because so much can be built from it, and the first chapter of Plurality calls the worlds a philosophers' paradise.

This is a cost and benefit argument: theoretical unity and a reduction nobody else offers, against an ontology of infinitely many universes. Much of the later debate is about the exchange rate.

Actuality as an indexical

If all the worlds are equally real, what is special about ours? Lewis's answer is that nothing is, except that it is ours.

Lewis set this out in "Anselm and Actuality" (1970). Its nearest relative on the ladder is the B-theory of time, on which "now" picks out the time of utterance and no moment is objectively present. A donkey in another world who says "only my world is actual" speaks as truly as you do when you say it. Actuality, on this view, is not a status but a location.

Lewis argued that it must be so. Suppose actuality were an absolute property that only one world had. Then a merely possible person with experiences just like yours would believe she was actual, on the same evidence as you, and be wrong. Nothing in your experience separates your case from hers, so you could not know that you are actual. But you plainly do know it. On the indexical theory you know it the way you know you are here: from the meaning of the word.

Counterparts instead of identity

Modal realism has a sharp consequence for the problem the last article ended on. Nixon is part of our world, and worlds do not share parts, so Nixon is not in any other world.

Lewis's reason for refusing overlap parallels the problem of temporary intrinsics from the article on persistence. If one Nixon is wholly present in two worlds, with five fingers on his left hand in one and six in the other, he both has and lacks an intrinsic property. Lewis drew the parallel himself, and concluded that each thing is confined to one world. De re modality has to work some other way.

"Nixon could have lost" is true because, in some world, a man who closely resembles Nixon in origin, career and character loses. Strict identity across worlds is replaced by resemblance, and identity is kept for the relation each thing bears to itself.

The replacement removes the difficulties the last article found. Chisholm's chain of slightly differing worlds caused trouble because identity is transitive and similarity is not. Counterparthood is a similarity relation, so each person in the chain can be a counterpart of the next while the last is no counterpart of the first. Nor need the relation be one to one. Something can have two counterparts in one world, if two people there resemble it equally well, or none, if nothing there resembles it enough. Neither is a paradox, because counterparts are not identical with the original or with each other. In Plurality Lewis added that which resemblances count can shift with context, which matters for essentialism, the next article's subject.

The incredulous stare

The commonest response to modal realism is not an objection but disbelief. Lewis named it the incredulous stare. He did not think it could be refuted, since it is not an argument, but he agreed that it registers a cost: the view contradicts common opinion. His position was that the benefits covered the cost, and that rival theories carried costs of their own.

The sharpest version of the stare is epistemic: if the other worlds are causally isolated from us, it is hard to see how we could know anything about them. Lewis replied that modal knowledge is like mathematical knowledge. We know about numbers without causal contact with them, and given the principle of recombination, which worlds there are follows from general principles, not from looking.

Ersatz worlds

The alternative keeps the worlds analysis and changes what the worlds are.

Most ersatzists are also actualists: they hold that everything there is actually exists, and that talk of merely possible things is talk of what abstract worlds represent. Adams, in the same 1974 paper, took worlds to be world-stories: maximal consistent sets of propositions, containing either each proposition or its negation. The actual world is the world-story whose members are all true.

Alvin Plantinga, in The Nature of Necessity (1974), built worlds from states of affairs, which, as the article on facts explained, may obtain or fail to obtain. One state of affairs includes another if it could not obtain without the other obtaining, and precludes another if the two could not both obtain. A possible world is a possible state of affairs that includes or precludes every state of affairs, and the actual world is the one such state of affairs that obtains. A third family, which Lewis called linguistic ersatzism, takes worlds to be maximal consistent sets of sentences in a suitable worldmaking language.

Look at what these definitions use. "Consistent" means that the members could all be true together, and "includes" and "precludes" are defined with "could not". The ersatz definitions are modal through and through. Plantinga did not regard this as a defect, since he never aimed at a reduction and took modal notions as basic.

Ersatzists also have an answer to the argument from ways. Robert Stalnaker, in "Possible Worlds" (1976), agreed that there are many ways things could have been and rejected the fourth premise. A way things could have been is something like a property, which the world might have had. The way things actually are is then a property the universe has, not the universe itself, just as the way you are is not you.

The abstract view also changes the shape of transworld identity. An abstract world that includes Nixon's losing represents Nixon himself as losing, not a man who resembles him. This is the picture on which, as the last article's aside suggested, transworld identity was never a deep problem, and it fits Kripke's claim that worlds are stipulated rather than discovered.

Lewis against the surrogates

Lewis spent the long third chapter of Plurality on ersatzism, sorted by how the abstract worlds are supposed to represent. Linguistic ersatz worlds represent as sentences do, by meaning. Pictorial ones represent by resembling, as a scale model does; that version has had few defenders and is set aside here. Magical ones represent, and that is all you are told.

Against the linguistic version Lewis pressed two objections. The first concerns the word "consistent". If it means that the sentences could all be true together, the ersatzer has used modality to define the worlds, and the analysis of modality in terms of worlds is circular. If it means something syntactic, such as that no contradiction can be derived by the rules of logic, the account admits impossibilities, because "this is red all over" and "this is green all over" are not formally contradictory. Rules forbidding such combinations only move the problem, since they must capture every necessary connection there is, and saying which those are is modal work again. Either way modality enters as a primitive.

The second objection concerns descriptive power. A worldmaking language has words for properties instantiated in our world. But there could have been natural properties that are not instantiated here and are not built out of any that are, which Lewis called alien properties. The language has no names for them, so it can describe a world containing them only by saying that some property, distinct from all of ours, plays a certain role. Take two possibilities that differ only in that two alien properties swap roles. Both get the same description, so the ersatzer counts one world where there are two possibilities. The realist has no such problem: the alien properties are simply instantiated elsewhere.

An ersatzer who, like Plantinga, takes properties to exist whether or not anything has them can reply that alien properties are among the actual abstract objects, uninstantiated, and need no names. That gives up the linguistic version, and raises the question of how such states of affairs represent at all, which Lewis put to the third kind.

On the magical version, nothing about the abstract worlds explains what they represent. An abstract world is simply actualised just in case the concrete universe is a certain way, for instance contains a talking donkey. Lewis asked what kind of relation actualisation is. An internal relation holds in virtue of the intrinsic natures of its relata, as being taller holds in virtue of heights; but an abstract world with no relevant structure has nothing in its nature to tie it to donkeys. An external relation holds in virtue of how things are arranged together, as distance does; but an abstract object is not arranged in space with anything. So we are told that the relation holds without being told how. Lewis called this magic: the necessary connection between an abstract world's being actualised and there being a talking donkey is posited, not explained.

What actuality costs

The two sides divide the bill differently, and actuality shows it most clearly.

For the modal realist, actuality is cheap: an indexical, with no extra property or posit. The price of the cheapness is that actuality marks no difference in what there is. The talking donkeys exist as fully as you do, and the sense that our world alone is real has to be explained as a sense of location.

For the ersatzist, actuality is absolute. Of all the abstract worlds exactly one obtains, or is true, and that distinguishes it from every other wherever the speaker happens to be. Lewis's sceptical argument gets no grip, because there are no merely possible people to be deceived: the abstract worlds have only represented inhabitants, and a represented person believes nothing. The price is paid elsewhere. Possibility is explained by consistency or inclusion, so modality is primitive. And the actual world of the theory is an abstract representation, so two things have a claim to the name: the universe you live in, and the abstract world that describes it truly.

Neither side gets actuality for nothing. The realist keeps it simple by denying that it is a deep fact; the ersatzist keeps it deep by taking modality and representation as given. Which bill you prefer depends on how much you value a reduction, and on whether you can look at the realist's ontology without staring.

Next

Both sides still owe an account of which de re claims are true: the ersatzer must say which states of affairs involving Nixon are possible, and the counterpart theorist which resemblances count. Kripke argued that some answers are forced on us, among them that a thing could not have come from entirely different material, a truth necessary although known only by experience. The next article sets out that argument, the necessary a posteriori it depends on, and what becomes of it when de re modality runs through counterparts.