1

Are there possible worlds? Lewis and Everett on the plurality of worlds

Adam Tuboly

In the last few decades after having a remarkable career in science-fiction literature possible-worlds and parallel-universes talk became a respectable and useful tool in many areas of philosophical and physical investigations and explanations. In this study I attempt to show the followings.

First I will introduce in some details one of the most significant realist conception of possible-worlds, which has been proposed in the second half of the century by David Lewis. I claim that as a consequence of the presuppositions and the context of the forming of the theory we do not have crucial reasons and conclusive arguments neither to accept the existence of the Lewisian possible worlds nor to deny it. Hence if we shall continue to talk about possible worlds (in Lewis sense) we have to search for the suitable reasons and arguments somewhere outside philosophy and metaphysics it seems that the best candidate for this outside place is quantum physics.

Finally I shall make some notes about a certain phenomenon that is highly disregarded by recent literature. I want to refer to the fact that a suitable reconstruction of David Lewis (philosophical) conception of possible worlds resembles Hugh Everetts (quantum physical) many-worlds interpretation in many interesting respects. Thus the topic of possible worlds should be such a common field for philosophy and physics where both of them could contribute to each others investigations.

1. Metaphysics and Possible Worlds1 Admittedly the most famous and notorious possible-worlds realist among philosophers is David Lewis. His notoriety arises from the fact that he has proposed a rather extreme approach since the seventies. The following thesis gives the core of the theory (call it genuin possible-worlds realism, GPWR):2

(L1) There are many spatiotemporally and causally isolated concrete non-actual possible worlds, whose ontological status is the same as our worlds.

To see the extremity and the point of (L1), let us consider its components in some details. The second half of the thesis claims that possible worlds are just as real as our, the one we inhabit. Possible worlds, therefore, differ from our world in regards of their contents and events, not their type.3 (If possible worlds were some kind of mathematical entities, like sets, it would count as a type-difference). The sameness of the worlds ontological status makes it available to Lewis to claim that if we know that what sort of entity is our world we will also know that what sort of entities are the other worlds. He gives the following definition of our world:

(L2) Maximal mereological sum of spatiotemporally related objects. 1 Divers 2002 gives a very comprehensive introduction to the metaphysics of possible worlds.

2 Lewis 1973, p. 84-91 and 1986. For further issues and arguments see DeRosset 2009.

3 It comes with this conception of the status of possible worlds that our actual world is by no means special or

distinguished. We call this world actual only because we spatiotemporally connected to the other inhabitants of it, because we live in this one. That is, actual is an indexical expression just like I, here, now.

2

We could explain this as follows. Our world is the mereological sum4 of those objects that are related to us in space and time. For Lewis, this object the world is a maximal universe (that is, we should not identify our world with the Earth and a possible world with a planet which is a billion light-year far from the Earth), and in this sense

There is nothing so far away from us as not to be part of our world. Anything at any distance at all is to be included. Likewise the world is inclusive in time. No long-gone ancient Romans, no long-gone pterodactyls, no long-gone primordial clouds of plasma are too far in the past, nor are the dead dark stars too far in the future, to be part of this same world.5

The entities mentioned here are usually regarded as concrete rather than abstract objects. Where to draw the line in the concrete/abstract distinction is a delicate question, though we can refer to our intuitions and give some examples.6 It is common to treat electrons, tables, houses and planets (i.e. spatiotemporally located objects) as concrete entities, while numbers and sets are typically abstracts. Since it seems to be the case that our world is mostly built from those things that are on our first list, we could say that our world is a concrete object.

In the light of this, if our world is the maximal mereological sum of its spatiotemporally related parts and possible worlds belong to the same category, then they are also concrete objects which are the maximal mereological sum of their parts. The spatiotemporal relations, however, play an important role not only in defining the worlds but also in their demarcation.

According to (L2) Lewis is forced to say that worlds are per definitionem spatiotemporally isolated from each other. Suppose that two worlds are not isolated and so they have a common spatiotemporal part. By the definition of a world, anything that are related in space and/or time is a part of a world, so in virtue of this, the two world would be one huge world instead of two spatiotemporally related ones. As a consequence of the isolation, there could be no causation between the Lewisian worlds (thus there is no transition either) because causation7 would require spatial and/or temporally relatedness.

An issue concerning the number of Lewisian worlds could also be raised. How many are there? According to Lewis, countless worlds exist; the reason is something like this. There are countless ways our world could be, ways that differ from the one in which it actually is. For example it could have happened that the capital of Hungary is not Budapest but Pcs, and France could have won the battle of Waterloo. For Lewis these ways the world could be are just possible worlds. Since things could have been in countless different ways, there are countless possible worlds, corresponding to each way. So there are countless possible worlds where the capital of Hungary is Pcs and where France won the battle of Waterloo.

We are located, however, only in one world. Since the isolated worlds are nothing more than the mereological sum of their spatiotemporally related parts and their parts exist only in that world to which they are spatiotemporally related (call this the thesis of worldbound individuals).8 To account for the modal properties of things, Lewis introduced his 4 Mereological sum: for any n objects, if n > 1, the sum of n compose a new object. So, for example, if the Eiffel

tower and my little finger exist, then they compose a new object, namely [Eiffel-tower + my-little-finger]. In this sense will be our world a complex object that is composed out of its parts. 5 Lewis 1986, p. 1.

6 Lewis 1986, chapter 1.7.

7 Causation as it fits the ordinary usage of the term. Causation, however, based on counterfactuals is a different

matter, thought would be important to take a closer look upon it in this context. Cf. Lewis 1973. 8 This is the denying of the thesis which says that individuals exist not only in our actual world, but in other

possible worlds as well (the thesis of transworld individuals). According to this that I could be a football player means that there is a possible world where I am a football player. For the problems of this conception see Chisholm 1967.

3

counterpart theory. Counterpart theory states that x is possible-F if and only if there is a possible world where a counterpart of x is F. That is, I could be a football player if and only if there is a possible world where a counterpart of me is a football player.9

Talking about possible worlds and their inhabitants are very fruitful in the case of modal expressions. The theory of possible worlds in fact is a theory of modality. As such it should clarify our modal-talk, has to capture the meaning of our modal notions (possible, necessary etc.) and specify the truth conditions of the modal statements. Lets take an example.

(1) There could have been blue swans.

On the basis of our experience we can determine at best whether there are blue swans or not. We cannot know whether there could have been or there are necessarily none. Our abilities and the world simply do not provide modal experiences; it seems that we do not have any modality-detecting faculty. This, however, does not mean that (1) is senseless as thought earlier.10 Lewis developed his conception of modality using the following schemes:

(2) Possibly true that if and only if there is a possible world where is true (3) Necessarily true that if and only if in every possible world is true

where is any non-modal proposition. This matches the earlier mentioned approach, according to which what is possible is realized in a possible world, and what obtains in every possible world is necessary.

(2) and (3) held out a promise to give a systematic and comprehensive account for all of the modal expressions. In GPWR to say that blue swans are possible is to say that a concrete possible world, isolated from us, contains flesh and blood blue swans; to say that two plus two necessarily equals four means that in every possible world, two plus two equals four. Furthermore it shows the strength of GPWR, that among the possible worlds we will find ones whose natural laws are wholly different from ours. There are, for example, many possible worlds where spaceships fly across the galaxies, where jedi knights fight with lightsabers against the Sith Lords. And there are worlds where Frodo and Sam havent yet delivered the Ring to Mordor.

Nevertheless we have to note that Lewis formulated his view about modality and possible worlds in the context of an enormous metaphysical project. Metaphysics tries to describe the fundamental structure of Reality and list the beings and reveal their nature. For Lewis, this list contains (above our world) many merely possible worlds and their inhabitants. But metaphysics always had been disputed, and some can believe that it cannot be successful. It seems like metaphysics is not able to yield conclusive arguments and persuasive reasons for its claims.11

If metaphysics really has to face these difficulties, we should say that we do not have conclusive arguments and persuasive reasons either to claim the existence of merely possible worlds or to deny it. Denial of their existence would be also a metaphysical step and no one could exclude that even if we do not have the right approaches and arguments, the plurality of worlds considered by Lewis do exist we just wont be able to become aware of them.

2. Physics and Possible Worlds 9 For the formal and informal details of counterpart theory see Lewis 1968 and 1986, chapter 4.

10 Cf. Quine 1953/1961.

11 For a summary of these problems see the studies of Price 2011.

4

Lewis developed his theory and get to accept the existence of possible worlds by conceptual analyzes and special pragmatic arguments. Though this kind of investigation is usually very profitable, its upshots are pretty much vulnerable. Because of this for the belief in the existence of possible worlds one could require a more stable basis.12 Recent quantum physics seems to be a proper candidate for this role.

There had been made a certain amount of proposal for the interpretation of the formalism of quantum physics. In our context one of them, namely Hugh Everetts many-worlds interpretation emerges from the others.13 Before we get to the relevant points of the issue, we have to introduce some basic notions.

Some of the interpretations of quantum physics (like the Copenhagen reading) divide the world into two realms. On the one hand there is the indeterministic quantum world furnished by elementary particles which can be described only by probabilities. On the other hand there is the world of our experiences, the deterministic and macroscopic classical world. And there is the problem. In the quantum world, before a measurement is made, the elementary particles are in a so-called superposition; an electron e exists in its every possible state at the same time.14 In the macroscopic world, however, we do experience something else since our measures and experiences show us always one determined state of physical systems; i.e. we always meet with only one element of the superposition.

The measurement problem of quantum physics stems from the question that how does the two realms interact with each other, from the many possibility found in the quantum world how does exactly one single out. The answer of the Copenhagen interpretation was this. Take the mathematical entity, called wavefunction (symbol: ). describes the quantum state of e, the corresponding superposition. In this scenario consist of the possible states of e and the corresponding probabilities. If we carry out a measure on e, then according to this interpretation, collapses somehow into one of the possible states of e the others cease and so we get precise and determined solutions.

But this interpretation relies on the division of the world the measured system is a part of the quantum world, while the individual carrying out the measurement and the measuring system belong to the classical world. Besides that we do not know too much about the relation of the two realms, the Copenhagen interpretation havent provided a satisfying explanation for the collapse of the wavefunction.15 The basic equations of quantum physics do not contain the collapse, and the introduction of it into the theory requires a somehow arbitrary postulate.16

Everett, however, made an attempt to get over of the measurement problem. To do that, first of all, let us bridge the gap between the quantum and the classical world. Instead of

12

Cf. Skyrms 1976, p. 326. The defects of the method of Lewis are maybe not so particular in the sense that the argumentations of physics also require special pragmatic arguments. That would mean that philosophers and physicist stand or fall together if they use the same type of arguments during the explication of their reasons for accepting or declining a theory. This is also a point which worth a much longer and more detailed discussion. 13

Everett called his theory the universal wavefunction theory, the relative-state formulation of quantum mechanics or the metatheory of quantum theory (Everett 1957). The many-worlds tag came from Bryce DeWitt. Devitt & Graham 1973 contains Everetts original doctoral dissertation and his only publication in this area. 14

The conception of the superposition comes from a principle of quantum physics. The sum of the so-called Schrdinger equations (which describes the quantum states of a physical system during its changes in time) solutions is also a solution of it. That is, if and are solutions of the Schrdinger equation so is + . 15

At least in the sense that instead of explaining another complex phenomenon with it, the notion of collapse itself requires explanation. 16

Erwin Schrdinger noted this difficulty in his notorious cat in the box thought experience. According to it, until we carry out the measurement, the cat exists in a special superposition, in which it is alive and dead at the same time. As a consequence of the measuring process, however, the alive and dead cat superposition collapses into either the alive-cat or into the dead-cat state.

5

saying that the measuring individual and system are related to some classical world and as such measuring the quantum world from an external Gods view, let us place them in the quantum world too.

By means of considering the whole world as a quantum world, Everett could claim that the wavefunction applies to the measuring objects as well as to the measured physical system. Thus we get a universal wavefunction, which consists of all the possible states of the world (where macroscopic objects can be in superpositions too) and relates the microscopic realm with the macroscopic one.

When we are measuring, not the measured system is the only one which changes, the measuring system does too, but instead of talking about the collapse of , Everett claimed something wholly different. Take a measuring process. As earlier, represents the superpositioned possible states, but during the measuring, does not collapse into one of its element (while the others disapper), but all of the outcomes of the interaction with non-zero probability will be realized, each of them in a different world. That is, if the interaction with e has got two possible outcomes, A and B (e is in A and B at the same time in the superposition), then as a consequence of the interaction e will be in position A in one world and in position B in a different world.17

Thanks to this, Everett was not forced to claim or postulate the collapse of , furthermore the gap between the quantum and the classical world disappeared. None the less, it has its cost, namely the assumption of many worlds. If the universal wavefunction represents all of the possible states of our superpositioned world and in every physical intercourse certain probabilities realize (Everett did not deny that ordinarily we meet only with determinate outcomes and not with superpositioned probabilities), then the realization in a world of our worlds possibilities requires many worlds, each corresponding to an element of the superposition. The question is, of course, what kind of worlds we are talking about.

Likewise in the case of Lewis, we have to assume in this conception too that worlds are concrete objects, localized in space and time, since we started with irreversible interactions of spatiotemporally located physical systems. The world is one among these physical systems, though a bigger sized one. In this sense we have to exclude those world-conceptions which operate with special abstract worlds (like the ersatz and fictionalist theories of possible worlds).18

One of the most extreme claims of Lewis was that the merely possible worlds are just as real as the one we inhabit. But this claim appears here too when Everett says that From the viewpoint of the theory all elements of a superposition (all branches) are actual, none any more real than the rest.19 Suppose again that the electron e has got two possible positions, A and B. When we interact with e (measuring it, for example), it will be the case that in world w1 it is in position A, while in the other branching world w2 it is in position B. But since w1 and w2 are the elements of the superposition determined by the same universal wavefunction, both of them are equal real, since both of the possibilities became (e-in-A and e-in-B) realized, actualized and not disappear (as earlier).20 17

Because of this, Schrdingers cat will be alive in one world, while die in another, likewise the individual, who carries out the measuring process, due to the opening of the box will meet in one world with a living cat and in the other a dead one. 18

For ersatz possible worlds see Adams 1974 and Plantinga 1976. For the approach of fictionalism our classic reference is Rosen 1990. 19

Everett 1957, p. 459, footnote. 20

The use of the notion of actuality does not seems to be too elaborated, and in virtue of this it would be useful to confront it with some more precise definitions. (Cf. Adams 1974). For Lewis, actuality is an indexical expression and we could use this approach in the Everettian story too. The inhabitants of the branching worlds are right in calling their own worlds actual, since every one of them are equal real and no one is special or distinguished in its ontological status with respect to the others.

6

These equal real worlds, however, do not interact with each other, which is a consequence of the branching/splitting. In helping to understand the branching of the worlds, Everett used the amoeba metaphor. Like the amoebas constantly split, does the worlds split or branch into new ones. During the branching of each element of the superposition the branching stuff consist of not only the elementary particles, but also we, the measuring individuals. That is, during every physical interaction, like the writing of these lines, countless real worlds split from this one, where instead of m and e I typed something different.

At this point it seems that Lewis and Everett are in conflict, since Lewis in virtue of his thesis of worldbound individuals claims that any individual (in the present context, physical system) exist only in one world. That is, for Lewis, in a different possible world who instead of m and e types y o u is not me, but one of my counterparts. The notions of branching and splitting are highly unclear and even the fact the we split into other new ourselves (who are identical to us) needs more clarifying and are puzzling philosophical issues. The Lewisian counterpart theory could serve here as a living alternative to the branching-but-identical-individuals conception.

As mentioned earlier, in the many-worlds theory of Everett we have to deal with countless worlds too if we assign to each of the superpositioned possible states of the physical systems a world, where the given possible states realizes. Nevertheless of the countless worlds, the Lewisian reality consists of much more world, since he can account for physically impossible worlds too worlds, which do not obey the laws of nature of our world. After the interaction between physical systems, presumably the branching physical systems do not permit physically impossible worlds, thus Everett can allow only physically possible worlds.

3. Which way to go? In these few pages I wanted to note the followings. While the metaphysical investigations cannot give us conclusive arguments for the existence (or non-existence) of possible worlds, we are not forced to leave this field of studies. The fact, that we can detect certain similar conceptions among the recent physical theories, has to serve as a much stronger reason to accept some sort of possible-worlds theory for those who expect the list of beings from physics instead of metaphysics.

Though the Everettian many-worlds theory shows many interesting analogy with the conception of possible worlds given by Lewis, the literature still lacks the detailed and comprehensive comparison of them. While the philosophical reception of the many-worlds theory is increasing,21 the ontological upshots of it with respect to GPWR are still unrevealed. This is also required because of whether we accept Lewis arguments or not, it is undeniable that he developed his own theory with great clarity and conceptual exactitude.

So both the philosophers should revise the Everettian and the other many-worlds theories if they want to work within the area of possible worlds, and both for the physicists would be fruitful to take a look at the Lewisian theory if they require a conceptually deliberate and coherent many-worlds interpretation for the formalism of quantum physics, since the informal interpretations, in effect, are mostly coherently developed conceptual systems, something which is very similar to the project of certain philosophies.

References Adams, R. M. 1974, Theories of Actuality, Nos 8, pp. 21131. Chisholm, R. M. 1967, Identity through Possible Worlds: Some Questions, Nos 1, pp. 1-8. 21

See Skyrms 1976, Wilson 2011, Saunders et al. 2010, and also Lewis devoted one of his last studies to the interpretation of quantum physics (Lewis 2004).

7

Derosset , L. 2009, Possible Worlds I: Modal Realism, Philosophy Compass 4 (6), pp. 998-1008.

DeWitt, B. S. Graham, N. (ed.) 1973, The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton.

Divers, J. 2002, Possible Worlds. Routledge. Everett, Hugh 1957, Relative State Formulation of Quantum Mechanics. Review of Modern

Physics 29 (3), pp. 454462. Lewis, D. 1968, Counterpart Theory and Quantified Modal Logic, The Journal of

Philosophy 65, pp. 113-126. Lewis, D. 1973, Counterfactuals. Basil Blackwell, Oxford. Lewis, D. 1986, On the Plurality of Worlds. Basil Blackwell, Oxford. Lewis, D. 2004, How many lives has Schrdingers cat?, Australasian Journal of

Philosophy 82 (1), pp. 3-22. Plantinga, A. 1976, Actualism and Possible Worlds. Theoria 42, p. 139-160. Price, H. 2011, Naturalism without Mirrors. Oxford University Press, New York. Quine, W. V. O. 1953/1961, Reference and Modality, in. From a Logical Point of View, 2nd

edition. Harvard University Press. Rosen, G. 1990, Modal Fictionalism. Mind 99, p. 327-54. Saunders, S. Barrett, J. Kent, A. Wallace, D. (ed.) 2010, Many Worlds? Everett,

Quantum Theory and Reality. Oxford University Press, New York. Skyrms, B. 1976, Possible Worlds, Physics and Metaphysics, Philosophical Studies 30, pp.

323332. Wilson, A. 2011, Macroscopic Ontology in Everettian Quantum Mechanics, The

Philosophical Quarterly 61 (243), pp. 363382.