the method of possible worlds

METAPHILOSOPHY Vol. 23, Nos. 1 & 2, January/April 1992 0026-1068 $2.00

THE METHOD OF POSSIBLE WORLDS

SIMON BECK

In a footnote to Sameness and Substance, David Wiggins argues that “those who use the method of possible worlds to determine answers to questions of necessity and identity or necessity and origin are using a mistaken method”.’ According to Wiggins, it is because of the nature of possible worlds that the method cannot be used to reach conclusions in these areas. These claims suggest two avenues of enquiry, which can be summed up in the following questions:

(1) just what are possible worlds? (2) how does their nature affect the method of possible worlds?

This paper does not start by suggesting a final answer to question (1). Rather, the issue investigated is whether different views of possible worlds have different consequences as to the conclusions we can reach via the method of possible worlds; and if so, whether any conclusions can be drawn regarding the method itself or the nature of possible worlds.

Something needs to be said first about what is to be taken as the method of possible worlds. I will be concerned only with the use of possible worlds in arguments relating to the debate around the notions of person and personal identity. Most of the problems to be discussed are probably peculiar to this field; however, implications for other debates would not be difficult to find.

As far as the personal identity debate is concerned, arguments depending crucially on various kinds of appeal to possible worlds have been central in the literature, and are used at one time or another by most of the major contributors. One point to be noted immediately is that (as one might expect) there is no single set way in which possible worlds or their surrogates are used to establish conclusions. Sometimes we are asked to consider certain worlds and concur with some judgement about what goes on in them, or to compare certain worlds and judge whether they agree or differ; sometimes to judge that a described world is not a possible one; sometimes to accept that the possibility of a given world falsifies or confirms a judgement about our own or some other world; and so on. All appeals to possible worlds which play a role in an argument I will take as lumped together, albeit uncomfortably, under the title of “the” method of possible worlds. The

’ Wiggins, longer note 4.02 p. 213.

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instances of the method which will be discussed will be drawn from the existing literature.

A second point is that the arguments which are used in the literature are not always couched in possible worlds terms. Some are presented as thought experiments involving science fiction or imaginary counterfactual cases. The question then arises as to why they should be classed as possible worlds arguments. All of these sorts of cases are, I believe, metaphysically on a par. In the interests of tightening up very loose usage and making clear what is really going on and what assumptions are being made in the relevant arguments, it makes sense to talk of all of them as possible worlds arguments. Possible worlds have received closer philosophical scrutiny than science fiction and imaginary experiments, and there are obvious drawbacks in taking these other settings as fundamental. For while science fiction is concerned with worlds other than our own, it is entitled to deal with the impossible, whereas the use of impossible cases can only distort our understanding of personal identity.

Likewise, the use of imaginary examples is hampered by the fact that what is imaginable and what is possible don’t coincide: for instance, it is just as easy for us to imagine someone constructing a regular polygon of 19 sides with a ruler and pair of compasses as it is for us to imagine her so constructing one of 17 sides; however, while the latter construction is possible, the former is not.2 In reaching conclusions about identity from counterfactual cases, we need to deal only with what is possible. Thus classing imaginary examples as possible worlds examples rules out those which would only confuse the issues; the connection between the semantics of counterfactuals and possible worlds is sufficiently well known and widely accepted to justify omission of further discussion here.

Section 2 In this section, the standard views as to what possible worlds are will be set out, and in the succeeding sections the consequences of adopting the various views will be investigated. There are three fundamentally different views: what I will call (i) realism, (ii) abstractionism or reductive realism and (iii) anti-realism.

(i) Realism: (also called “concretism” and ‘‘possibilism’’3) This is the view made famous by David Lewis. The world we inhabit is just one of an infinite number of possible worlds. All of these are equally real, concrete worlds,

* As was proved by C. F. Gauss back in 1796. The example is due to Lewis. ’ Although this view is sometimes called “possibilism”, for example by McMichael, the label is misleading since some take possible worlds to be reducible to abstract possibilities or possible histories - see Humberstone, for instance.

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made up of concrete individuals. All of the worlds are ontologically on a par; “actual” (as in “the actual world”) is simply an indexical, indicating the world at which the utterer exists. (ii) Reductive realism4: (also called “abstractionism”, ‘‘actualism”s and “ersatzism”) Possible worlds are abstract objects of some kind; they are usually held to be constructions out of states of affairs or certain linguistic entities, or something else claimed to be less problematic than worlds. The most common version of the view is that a possible world is a maximal consistent state of affairs, and this is what I will take reductive realism to state. Other worlds are thus real, but different in kind from the actual world - being abstract (and false) representations of it. (iii) Anti-realism6: There are no such things as other possible worlds; they and their inhabitants do not exist in any sense. Possible worlds talk is at best a convenient manner of speaking - it is in no sense explanatory of ordinary modal discourse.

There have been various arguments put forward for and against each of these views, the most vigorous debate being between (i) and (ii). Lewis has argued that only realism can give an adequate reductive account of modality, and that it provides an account of propositions, properties and counterfactuals as well. The most common argument against realism is the obvious one that it is metaphysically excessive, while reductive realism can do all that it can do. I do not propose to argue this out here, but the investigation of the consequences of these views for possible worlds arguments in the literature on persons may well contribute to this debate.

Section 3 To start the investigation into the consequences of the various views above, we can return to the argument of Wiggins cited at the beginning of the paper. Wiggins argues that the method of possible worlds can’t yield conclusions about the necessity of identity or origin because of the nature of possible worlds. Because possible worlds (following Kripke’) are suppositions, scenarios which we construct, we must stipulate the identities of any individuals appearing in them when we construct them. We will only be able to identify the relevant possible world if we know the identities of its component individuals. Thus it would be out of line to ask questions about whether a given individual is identical or not to another in a given world, and as a result we can’t use other possible worlds to reach answers about the necessity of identity or origin.

This is the view put forward by Plantinga, van Tnwagen, Chisholm and others. Reasons for opting for a states-of-affairs view rather than a linguistic entities view can be found in Pollock, Ch 3 sec 2 and in Bricker.

This label is also misleading, for anti-realists also believe that only what is actual exists.

This view is held by Forbes. ’ Kripke circa p. 44.

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Questions of identity must thus be decided in the postulation of possible worlds. What one cannot do is to “read off” from a world the identities of individuals appearing in it. To attempt to do so is to confuse other possible worlds with distant planets which can be investigated with powerful telescopes. Because they are not like other planets, such investigation is out, and the method of possible worlds is irrelevant to the mentioned questions.

This may all sound extremely reasonable and neutral between the conflicting views of possible worlds. But that neutrality is merely apparent; for Wiggin’s argument is strongly dependent on a view of possible worlds other than the realist view. For to say that possible worlds are suppositions, that the identity of the individuals in them depends on how to describe the worlds (our description including stipulations of identity), is to view them as abstract representations (if anything at all), rather than as concrete worlds. If one has to stipulate identities in order to have a world, then extreme realism like Lewis’s is not true - the correct view must be an abstractionist or an anti-realist one. The stipulation theory of transworld identity is widely held among abstractionists - Plantinga and van Inwagen are leading examples. Although there may be other ways for the reductive realist or abstractionist to solve the problem of transworld identity, I will take the stipulation theory to be part of the reductive realist account, and it is with this version of reductive realism that the paper is concerned.’

The moral to be drawn from Wiggins’s argument, as far as our investigation is concerned, is that if you’re a reductive realist or an anti- realist, then beware of the telescope fallacy - you can’t read off identities from possible worlds. In this way, non-extreme-realist views may have important consequences for the method of possible worlds. (One question which immediately arises is whether realism does not hamper the method of possible worlds in much the same way. I will not look into this here, but will return to the question later.)

Section 4 One must be careful of not drawing too strong a conclusion from the above considerations. Wiggins himself is guilty of this: for although it is true that if transworld identities are a matter of stipulation, one cannot read off identities from a world, it does not follow that one cannot use the method of possible worlds to argue for the necessity of origin or identity. On the contrary, the most convincing argument for the necessity of origin depends crucially on the use of possible worlds, and yet is innocent of the telescope fallacy.

To be noted is the abstractionist aversion to counterpart theory; dependence on counterpart theory often being held by abstractionists to be a weakness of full-blown realism.


The argument to which I refer is that of Graeme Forbes.’ Forbes sets up a number of possible worlds, and argues that if one rejects the necessity of origin (i.e. the thesis that a particular individual could not have had an origin other than its actual origin) then one is committed to ungrounded claims of identity (or non-identity) regarding the individuals in these worlds. Because such claims are unacceptable, he argues that scepticism about the necessity of origin must be rejected.

He asks us to accept that in the actual world w* XI and X2 have a child. If the necessity of origin thesis were false, then in another world, w, the same child could have been born to Y1 and Y2. But then consider a third world, u, which is just like w (the Y’s child in u is indistinguishable from the child in w) except in that XI and X2 also have a child in u. Now we are asked, which child in u is the actual child?

It can’t be the X’s child, because then the Y’s child in u would not be identical with the Y’s child in w, since the latter is the actual child. The trouble is that there is no relevant difference between the Y’s child in u and the Y’s child in w in virtue of which this non-identity could obtain. Since the two are indistinguishable in all relevant respects (the existence of another child in the one world is, according to Forbes, not a relevant respect), the sceptic would be left with an ungrounded claim of non- identity. The sceptic must then (given the formal properties of identity) say that either the Y’s child in u is the actual child, or that neither child is the actual child.

Whichever he chooses, it follows that the X’s child in u is not the actual child. But then consider a fourth world, v, in which a child just like the X’s child in u exists. Since it is quite plausible that the actual child could have been just like the X’s child in u, we can claim that this is the actual child. It follows, then, that the X’s child in v is not identical to the X’s child in u, since according to the sceptic the latter is not the actual child, whereas the former is. The two are indistinguishable in all relevant respects, however, and so the sceptic is once again faced with an ungrounded claim. Since all the sceptic’s options have been used up, Forbes comes to the conclusion that scepticism about the necessity of origin is mistaken.

That rather complex argument is Forbes’s case for the necessity of origin. It is clearly a possible worlds argument, and is thus in defiance of Wiggins’s ban. What it shows is that Wiggins is wrong in claiming that, given the abstractionist’s view about the stipulation of transworld identities, possible worlds arguments to the necessity of origin must commit the telescope fallacy. For nowhere does Forbes need to, or attempt to, read off the identities of individuals from a given possible

’ Forbes Ch 6 sec 3; I have replaced his oak trees and acorns by people to bring it into line with the present subject matter. He intends the argument to apply in both instances, or to be more accurate, in the case of people, he intends it to apply to people and their “propagules”.

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world. Forbes does not go about trying to discover identities or non- identities. There may be one or two points in Forbes’s argument to which some will take exception, but there is nothing in his handling of possible worlds which conflicts with abstractionist principles.

Forbes’s strategy is to argue that if one denies the necessity of origin, then one is inevitably left with certain claims of transworld non-identity which are arbitrary or ungrounded. He avoids the charges of committing the telescope fallacy or dealing with inadequately specified worlds by arguing in effect that no matter what identities one assigns the individuals in his set of worlds, if one rejects the necessity of origin, certain of the identities assigned will be ungrounded. As a result, Wiggins’s claim can be seen to be too strong. The abstractionist, even if he is bound to the stipulation view of transworld identity, does not have to be an agnostic about the necessity of identity or origin: that is not a consequence of his view of possible worlds.

Section 5 Before drawing any further conclusions about reductive realism and possible worlds arguments, let us take a look at the effects on such arguments of overtly adopting an anti-realist view of possible worlds. One effect can be brought out by examining an example used by Derek Parfit in Reasons and Persons. He calls the example the “Branch-line case”, and describes it as follows. First, the standard case”:

I enter thc Teletransporter . . . When I press the button, 1 shall lose consciousness, and then wake up at what seems a moment later. In fact I shall have been unconscious for about an hour. The Scanner here on Earth will destroy my brain and body, while recording the exact state of all my cclls. It will then transmit this information by radio. Travelling at the speed of light, the message will take three minutes to reach the Rcplicator on Mars. This will then create, out of new matter, a brain and body exactly like mine.

Then the Branch-line’’ :

Suppose that the New Scanner has not destroyed my brain and body, but has damaged my heart. I am here on Earth, and expect to die within a few days. Using the Intercom, I see and talk to my Replica on Mars. He assures me that he will continue my life where I leave off.

Parfit asks what his attitude should be to his Replica; does his relation to this Replica contain what matters in survival?

These examples describe two possible worlds, neither of which is the actual world. For the anti-realist to make perspicuous what is being claimed and asked, he must rephrase the description and questions in

l o Parfit p. 199. ” Parfit p. 287.


standard modal language, since for him it is such language (and not possible worlds talk) which is fundamental. But the result is puzzling, for the anti-realist will need to talk about counterfactual individuals. He will take Parfit as asking what his attitude should be to “the person who would have been created on Mars”, and whether the relation between this person and the person who would have been left on Earth is as good as survival. This is puzzling because there are (and will be) no such people - these definite descriptions don’t refer to anyone, concrete or abstract. Given that we have a reference failure here, there seems to be no sense to the question of what the relation between the two is, or what Parfit’s attitude should be. At best his attitude should be scepticism, since there is no object for him to consider.

The same phenomenon is to be observed with regard to other possible worlds arguments. Take for instance Forbes’s argument for the necessity of origin examined in the previous section.” Once again, the anti-realist is required to rephrase the argument in modal terms rather than possible worlds terms. This time he ends up with the question as to whether the child which would have been born to the X’s or the child which would have been born to the Y’s is identical to the actual child. Here the problem is even clearer than before, since “the actual child” has a referent, but both the other descriptions fail in this regard. The result is that we are faced with something like a pseudo-question, a question which has no sensible answer: for the question suggests that there is a fact-of-the-matter where there is none.

As a result of his metaphysical views, the anti-realist is unable to make sense of Parfit’s Branch-line case, or Forbes’s possible worlds argument against the necessity of origin. This need not imply that we must reject anti-realism immediately. It may be the case that the two arguments just don’t make sense, and the anti-realist’s making this clear is in his favour. But this option is implausible, for there is nothing unintelligible about these possible worlds examples; with a bit of thought it is not at all difficult to understand the cases that Parfit and Forbes put forward, even if one does not agree with the conclusions that they draw. It should also be clear that on a realist or abstractionist construal of possible worlds the examples involve no reference-failure, and so it is not the case that every construal hits trouble in these cases in the way that anti-realism does. The inference to be drawn, then, is that we must be careful about any easy adoption of anti-realism with regard to possible worlds.

Section 6 The contention of the previous section was that the anti-realist has difficulty in making sense of the possible worlds arguments considered.

That reference failure problems appear here is pointed out by E. J. Lowe in his review of Forbes in Mind, Vol 95 (1986).

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As was mentioned above, however, it is the debate between realist and reductive realist which has captured the attention of the majority of philosophers working in the area. The question now is whether an abstractionist foundation has any effect on the examples.

The reductive realist view of possible worlds does not preclude the method of possible worlds from informing the necessity of origin debate, nor does the view lead to failures of reference as does the anti- realist view. But does the abstractionist principle that transworld identity is a matter of specification not have some important effects on the method of possible worlds?

I believe that reductive realism does have consequences for our examples, and that they have the same source as Wiggins’s objection. That this is true can be seen from consideration of the Branch-line case. In suitably abstractionist terms, we are asked to consider the state-of- affairs of Parfit’s Replica being created on Mars, but his body on Earth being merely terminally damaged, not destroyed. We are then asked what Parfit’s attitude should be to his Replica on Mars; as Parfit points out, the answer depends on the answer to his other question, “does my relation to this Replica contain what matters?”. What Parfit wants to know is whether his attitude to the Replica should be like an attitude to somebody else or an attitude to him~e1f . l~

The answer to this question, as Parfit sets it up, hinges on whether (in the proposed world) the relation between himself and his Replica “contains what matters”. Now, given the illegitimacy of the telescope, we must be wary of any attempt to discover whether the relation is what we’re after by examining the state-of-affairs under consideration. But Parfit is not asking us to do that. He argues14 that on considering an analogous case, we will concur with him in his judgement that “I do not need to assume that my Replica is someone else”, that is, that the relation does contain what matters. By seeing that an analogous relation contains what matters, we can infer that this relation does so as well. For the reductive realist’s comfort, this appears to avoid the telescope problem.

The analogy used is the example Parfit calls his “Physics Exam”,” in which he is an individual with two exactly similar brain hemispheres equipped with some device enabling him to shut off and reconnect communication between the hemispheres at will. During the exam, he makes use of this mechanism to try two distinct ways of working out a problem simultaneously. On using the device, his stream of consciousness splits into two, each stream working on one of the solutions, and each stream unaware of what is going on in the other. Problem solved, the

l3 He makes this plain on p. 288. l 4 Parfit p. 288. l5 Parfit pp. 24&7.


streams are reunited into one stream and reunited Parfit can remember doing two calculations. The crux of his appeal to this argument is that in this case Parfit thinks it is clear that there are not two (or more) persons involved, but only one. And the situation in the exam is precisely analogous to the Branch-line case - there one stream of consciousness is divided into two which have no means of communication (other than by Intercom). Thus, he argues, he has no need to assume that his Replica is someone else.

But this argument should not alleviate suspicions about the Branch- line case. This argument is itself a possible worlds argument, and must be treated along reductive realist lines, taking into account the warnings of Kripke and Wiggins. It involves a speculation, a scenario given by the descriptive conditions we associate with it, and in which we must stipulate the identities of all the individuals involved in advance. In setting up the world, then, Parfit must stipulate the identities of the individuals in it, and as a consequence, how many individuals there are in the world, or it will be (unacceptably) incompletely specified. As a result, there may be a fact of the matter as to whether we are dealing with one person or two, but this is only because of the way things have been set up - because of the original stipulation. Thus, if Parfit were a reductive realist, his conclusion that there is only one person in the Physics Exam should come as no surprise; and he could just as well, and just as unsurprisingly, have concluded that there were two people.

These points serve to illuminate the Branch-line case as well. By Parfit’s analogy, we should not be surprised that there is no need to assume that his replica is someone else, although of course he is free to assume this - all that is required is a different stipulation. And so, for the reductive realist, Parfit’s example is not at all informative, and the questions that he asks about it are senseless and out of order. The questions asked are ones which must already have been answered - to ask them afterwards is to commit the telescope fallacy.

We are left with the problem of whether Parfit is asking stupid questions or whether reductive realism is lacking. One way of sorting this out is to see whether the realist avoids the problems outlined. If he does not, then we can fairly safely conlude that Parfit’s examples are not worth the consideration of personal identity theorists. If he does, then we will have to treat the second option more seriously.

Section 7 The aim of this section is to establish whether or not the realist falls foul of the problems which emerged in section 6. The question to be faced is specifically, do the identities of the individuals in the realist’s worlds not also depend upon his stipulation’?

In order to see why the realist view has different consequences from the abstractionist view, and thus escapes some of the problems, it is

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necessary to take a brief look at why the abstractionist adopts the view that the identity of the individuals in a world is a matter of stipulation. The abstractionist takes up this position as a solution to the problem of trans-world identity: the problem posed by the apparent fact that there is no (non question-begging) way of identifying individuals across worlds in terms of the properties they have at worlds. Such trans-world identification seems to be required for an account of de re modality, among other things. The abstractionist gets around the problem rather neatly by his insistence that trans-world identity is a matter of stipulation.

This is not the method adopted by the realist, however. The realist acknowledges the problem of trans-world identity and instead of attempting to solve it, gives up the relation of trans-world identity and opts instead for a relation of “counterparthood”.’6 Individuals, to the realist, are worldbound: if an individual exists at a world she exists at that world only. What exists in another world is the individual’s counterpart (if she has one) at that world. Something like this view is an inevitable consequence of realism, given that doctrine’s views on the concreteness and isolation of worlds. The counterpart at some other world of a person is, roughly speaking, the person she would have been if she had existed in that world. The realist can use the counterparthood relation instead of transworld identity in an account of de re necessity, and it serves additional1 to avoid certain paradoxes, such as Chisholm’s,

realist will understand Parfit as making reference to his counterpart/s - and it is of these that the relevant questions are asked.

For the realist, then, the question of stipulating the identities of individuals in a world does not even arise. Moreover, the number of individuals in a given world, and whether there is one counterpart of a given person or more than one, depends on the nature of that concrete world. These are facts of the matter in that world, and not functions of any stipulation on the part of the realist, as trans-world identity is a function of stipulation on the part of the abstractionist. It appears, then, that the realist avoids the problems of section 5 .

One immediate response to this defence of the realist may be to say, “yes, there is a fact of the matter independent of any stipulation in the case of the realist, but how do we know what the fact is? How do we know whether the relation contains what matters in the relevant worlds?” This brings us back to the question whose answer I deferred at the end of section 3, the question as to whether realism is not also dogged by Kripke’s telescope. It may seem, at first glance, that the realist does not commit a fallacy by treating possible worlds like other

which plague this area.’ ?- In examples like those used by Parfit, then, the

I‘ For more detail on counterpart theory see Lewis, Ch 1 sec 1 l7 See Forbes, Ch 7.


planets. For the realist’s possible worlds are like other planets in a number of ways: they are concrete and robust, just like this world and its planets; and as we have seen, they are independent of our description in a way in which the abstractionist’s worlds are not. Indeed, one argument against the existence of realist possible worlds contends that “they require the same sort of evidence for their existence as other constituents of physical reality.””

But despite these similarities between other worlds and other planets, the realist must still be denied use of the telescope. This is because the realist’s worlds are isolated: there are no causal links between distinct realist possible worlds.*’ So there is no way in which the realist can discover what goes on in his worlds by observation; in this regard he is in precisely the same position as the abstractionist. This does not, however, alter the fact that the realist can make sense of Parfit-type arguments even though the abstractionist cannot. For the realist and the abstractionist are in the same epistemological boat for different reasons: the abstractionist because certain facts depend on his stipulation, the realist because of the causal isolation of his worlds.

Opponents of realism might still want to apply pressure on that view by following up the argument mentioned a paragraph ago, and demanding from the realist an account of how he can know anything about his worlds. The realist response is to argue that knowledge of possibility is (at least sometimes), like knowledge of necessity, a priori knowledge. The problem of how the realist knows anything about his worlds is then the problem of a priori knowledge - and this latter is a problem which confronts realist and abstractionist alike. As an account of a priori knowledge of possibility, David Lewis gestures at a principle of recombination, whereby one finds out what is possible, or counterfactually true, by (imaginatively) trying out recombinations of things we already know to be possible. He acknowledges that there are difficulties here, but denies that they are difficulties specific to the realist.20

A final stab against the realist at this point would be to insist that it is unacceptable to separate metaphysics and epistemology in the way the realist appears to. The claim would be that there must be some sort of link between what makes our modal opinions true and how we come to modal knowledge, and that there can be no such link when one is dealing with the realist’s isolated worlds. But as it stands, this sort of argument simply begs the question against the realist: it may just be true that, in the case of our knowledge of what is possibly, necessarily or counterfactually true, metaphysics and epistemology come apart.

In the light of these points in defence of realism, it appears that Parfit- type examples are not of necessity uninformative and the accompanying

l8 Skyrms p. 326. j9 See Lewis Ch 1 sec 6. ’* Lewis Ch 2 sec 4.

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questions pointless, given realist underpinnings, as they are in the case of reductive realism.

Section 8 The paper set out to investigate the consequences on the method of possible worlds of adopting different views of possible worlds. This has been done with regard to a number of influential possible worlds arguments in the field of personal identity. The results were that the arguments discussed made sense given the realist view of possible worlds, but ceased to do so given the anti-realist or reductive realist views. But this does not lead to any clear conclusion. Perhaps the best thing is to take a leaf from David Lewis’s book. He argues for the existence of concrete possible worlds by claiming that their systematic usefulness outweighs the cost of metaphysical “excess”. We are left in a position where we must weigh the costs - are the possible worlds arguments examined sensible and important enough to justify our retaining them (and arguments like them) at considerable metaphysical cost? If not, we can adopt one of the metaphysically more appealing theories and cease using such arguments in the personal identity debate.”

University of Natal P . 0. Box 375 Pietermaritzburg 3200, South Africa

Identity Without Thought Experiments. This is the sort of option I envisage here. ’’ Kathleen Wilkes has recently published a book entitled, Real People: Personal

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