Worldmates and internal relatedness

Worldmates and internal relatedness

Richard Woodward

� Springer Science+Business Media B.V. 2012

Abstract In recent work, Jonathan Schaffer (Mind 119: 341–376, 2010) has

attempted to argue that counterpart theorists are committed to holding that any two

actual objects are bound together in a modally substantial sense. By clarifying the

core elements of counterpart theory, I explain why Schaffer’s argument fails.

1 Introduction

Priority monism is the view that there is a single concrete object upon which all

other concrete objects are metaphysically dependent. It is not the view that only one

concrete object exists, for the many clearly need to exist if they are to be dependent

upon the one. Nor it is the view that all objects are dependent upon the one, for it is

a view about the metaphysical structure of concrete reality and says nothing about

whether concrete reality is itself fundamental. Nor should monism be confused with

its necessitation, for it is only a view about the metaphysical structure of our world.

Monism is what it is, and should not be confused with these stronger views.

In recent work, Jonathan Schaffer (2010) has been busy trying to revive priority

monism, both by defending it against its attackers and by offering arguments in its

favour. And perhaps the key argument that Schaffer has offered in favour of monism

is the argument from internal relations. This argument proceeds in two stages. In

the first, Schaffer argues that monism follows from the premise that all objects are

internally related to each other. In the second, he defends the key premise of internal

relatedness.

My focus is on the second stage of this process. (I’ll spot that monism follows

from the internal relatedness of all things.) As we’ll see, Schaffer’s strategy is to

R. Woodward (&)

LOGOS: Grup de Recerca en Logica, Llenguatge i Cognicio, Facultat de Filosofia,

Universitat de Barcelona, Montalegre, 6-8, Barcelona 08001, Spain

e-mail: [email protected]

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Philos Stud

DOI 10.1007/s11098-012-0027-0

find a relation R, argue that R is a internal relation, and then argue that all things are

R-related. If successful, this suffices to show that all things are internally related—

because everything is R-related to everything else—which is the minor premise in

the argument from internal relatedness.

Now, Schaffer suggests a number of candidate relations which might be plugged

into this style of argument, and it is beyond the scope of this short paper to deal with

each. Instead, I’ll focus on one particular candidate: the relation of beingworldmates. It’s easy to see that this relation is pervasive, since all actual concrete

objects are worldmates. So the question is whether it is not only pervasive but

internal too. Schaffer claims that counterpart theorists are committed to answering

this question positively. It is this claim that I shall dispute.

2 Modal freedom

Call an object basic if there is no other object upon which it is metaphysically

dependent. Where u denotes the whole concrete cosmos, priority monism can then

be formulated as the claim that u is the only basic concrete object. This claim,

Schaffer argues, follows from the premise that all objects are internally related. But

to what does this latter claim amount?

In one sense, things are straightforward: to claim that all objects are internally

related is to claim that there is some internal relation R such that every object is

R-related to every other object.1 But in another sense, things are less straightforward:

we also need to know exactly what it means to say that a relation is an internal one.

Consider the different intrinsic natures that Billy could have: being this way, that

way, etc. Think of these as being the how-possibilities for Billy. Now consider the

different locations that he can occupy: being here, being there, etc. Think of these as

being his where-possibilities. Now consider the different existential statuses Billy

could have: existing, or not. Think of these as being the different whether-possibilities

for Billy. Finally, consider the metaphysically possible combinations of Billy’s how

and where possibilities. The set of all of these combinations, plus the whether

possibility of Billy’s not existing, can be thought of as Billy’s personal modal profile.2

Given the notion of an individual’s modal profile, we can characterize what it is

for two individuals x and y to be modally free of each other. For consider the

Cartesian product of Wx and Wy and say that each member of this set is a

combination-pair for x and y. Then we have:

x and y are modally free of each other iff each combination pair for x and y is

realized at some metaphysically possible world3

1 Strictly speaking, the claim is weaker than this. All that is required is that for each pair of objects hx,yithere is some internal relation which holds between x and y. And that doesn’t require that there is a single

internal relation R by which everything is related.2 I assume here that Billy can’t have properties at worlds where he doesn’t exist, so that Billy’s how-

possibilities can’t be combined with the whether-possibility of not existing.3 That’s not quite right, of course, since we need to rule out combination pairs where x and y are

co-located. See Schaffer (2010, pp. 13, 14) for discussion.

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The intuitive idea that two things are modally free of each other iff how-where-and-

whether one of these things is doesn’t put any constraints upon how-where-and-

whether the other thing is. To borrow Schaffer’s metaphor, the idea is that modally-

free objects ‘‘are like two knobs on a stereo, in the sense that all combinations are

possible.’’

With the notion of modal freedom in place, we can specify the notion of

internality—that of an internally constraining relation—that is relevant to

Schaffer’s argument:

R is an internally-constraining relation iff VxVy (if Rxy, then x and y are not

modally free)4

When Schaffer argues that all things are internally related, what he is after is the

claim that there is a relation R that is both internally-constraining in the sense

introduced above and pervasive in the sense that every object is R-related to every

object. Since it’s clear that some relations (e.g. identity) are internally-constraining,

the question emerges: are there any relations that are both internally-constraining

and pervasive?

3 Being worldmates

Schaffer argues that the relation of being worldmates, given a counterpart theoretic

conception of de re modality, is both internally-constraining and pervasive. That it

is pervasive is obvious: every (actual) concrete object is a worldmate of every other

(actual) concrete object. The issue, then, is whether this is an internally-constraining

relation to boot.

David Lewis, the architect of counterpart theory, famously held that all

individuals were worldbound, in the sense that ‘‘nothing is in two worlds’’ (1986,

p. 114).5 Taking this thesis as his point of departure, Schaffer writes:

Consider any two given actual concrete objects a and b. Given the

worldboundness thesis of counterpart theory, there is only one world at which

a is found (namely, actuality), and likewise only one world at which b is found.

So for the ways associated with a one only finds Wa = {a is as it actually is,

a does not exist}, and likewise for the ways associated with b one only finds

Wb = {b is as it actually is, b does not exist}. So now consider the following

two combination pairs in Wa 9 Wb ha is as it actually is, b does not existi and

ha does not exist, b is as it actually isi. These combination pairs have no

realizing worlds, for they describe modally incoherent scenarios. (2010, p. 28)

Let’s unpack this a bit. The starting point is Lewis’s thesis that no individual is in

more than one world. So pick two (actual) worldmates. When we look across the

4 This definition only covers the binary case, but it generalizes in an obvious way.5 It’s worth noting that Lewis means that nothing is wholly located in more than one world. Lewis does

believe in the existence of fusions of things from different worlds, and these things are partially in many

worlds.


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space of worlds, we notice that the only world where we find Billy is the actual

world: he is here and nowhere else. (Ditto for Alice.) And at the actual world, Billy

is as he actually is. (Ditto for Alice.) So far so good.

The next thought is that because Billy is here and nowhere else, his modal profile,

WB, is just {Billy doesn’t exist, Billy is as he actually is}. (Alice’s, WA, is just

{Alice doesn’t exist, Alice is as she actually is}.) But then one of the combination

pairs for Billy and Alice is a scenario where Alice doesn’t exist and Billy is as he

actually is. And when we look across the space of worlds, we see that there is no

world which realizes this combination pair because Billy is only to be found at the

actual world and there will also find Alice. But our definition of modal freedom tells

us that Billy and Alice are are modally free of each other iff every combination pair

is realized at some metaphysically possible world. So given that Billy and Alice are

worldmates, it follows that they are not modally free of each other. And that means

that being worldmates is an internally-constraining relation. Since we know that

being worldmates is a pervasive relation, we can thus conclude that there is an

internally constraining relation—being worldmates—that every actual individual

bears to every other actual individual.

4 Counterparts

The crucial element in Schaffer’s argument for the conclusion that beingworldmates is an internally constraining relation is the claim that nothing is in

more than one world. It’s somewhat odd, then, that Schaffer writes as if this

argument will only be persuasive to adherents of counterpart theory. After all, the

argument sketched above didn’t once mention counterparts!

At this point, Schaffer may suggest that I go and read my Lewis. After all, Lewis

told us that ‘‘your counterparts resemble you closely in content and context in

important respect’’ but also that ‘‘they are not really you’’ (1968, p. 114). So it looks

as though counterpart theory goes hand-in-hand with the claim that individuals are

world-bound. What’s distinctive about Lewis’s counterpart theory, it seems, is the

idea that the Billy that we know and love isn’t the same thing as mere possibilia that

represent him at other worlds. But this is misleading.

What’s true is that you interpret the possibilist language a la Lewis, it’ll turn out

that Billy is only part of just one world and that his other worldly representatives,

however similar, are not really him. But if you interpret the possibilist language in a

different way, you get the same result. For just note that if you interpret talk of

possibilia in terms of individual essences, a la Plantinga (1974), you certainly won’t

also think that your individual essence is really you. Saying that Billy and his

representatives are distinct isn’t, contra Lewis, to say anything distinctively

counterpart-theoretic.

But isn’t the point that Plantinga holds that what represents Billy at the actualized

world—his essence, Billyness—is the same thing as the thing which represents Billy

at other worlds? Isn’t that what it means to be a transworld identity theorist? Is thatwhat counterpart theorists reject?

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No: even a transworld identity theorist can hold that Billy’s representative at one

world is numerically distinct from his representative at another world. For instead of

taking Billy to be represented at a world w by his essence, Plantinga could have said

that what represents Billy at a world w is the pair hBillyness, wi. And he can say that

without jettisoning transworld identity: even if Billy’s representatives are different

at each world, the facts in virtue of which they count of representatives of the same

thing can analyzed in terms of identity: what the transworld identity theorist will say

is that hq, wi represents the same thing as hl, vi just in case q = l. In this way,

multiple representatives can be reconciled with genuine transworld identity.

The next thought is that whether you are a counterpart theorist turns upon how

you understand the relationship between the possibilist language and the modal

language, with its talk of what’s possible, necessary, and the like. But even this isn’t

right. Everyone can hold that the modal language sentence ‘Billy might have been

happy’ should be translated by the possibilist language sentence ‘Billy has a

counterpart who is happy at some world’. Plantinga, e.g., can just say that what it

is to be a counterpart of Billy is to be identical to Billy’s essence and what it is

for Billy’s counterpart to be happy at some world is for Billy’s essence be

coinstantiated with happiness.

Even though the friend of genuine transworld identity can say lots of counterpart-

theoretic things, there is one thing she cannot do and that is accept Lewis’s own

account of what it is to be one of Billy’s counterparts. Firstly, whether one thing is a

counterpart of another thing is a context-sensitive matter: what counts as a

counterpart in one context needn’t count as a counterpart in another. Secondly, the

counterpart relation is not an equivalence relation: though reflexive, it is neither

symmetric nor transitive. And as is well-known, these two features are beneficial,

allowing us to account for the inconstancy of our de re modal judgements and solve

puzzles generated by the conflicting modal properties of statues and lumps of clay.

So there are three important elements to counterpart theory: the claim that

possible individuals are worldbound objects, the story about when two possible

individuals are counterparts, and a story about how our ordinary de re modal

judgements relate to claims about counterparts. And since even an adherent of

genuine transworld identity can accept both the first and third elements of this

package, it’s the second element, the story about when two things count as

counterparts, that’s distinctive to counterpart theory as its normally understood.

5 Two perspectives on logical space

Counterpart theory allows us to see logical space, the space of possibilities, from two

very different perspectives: one from which we talk about what could and couldn’t

happen to Billy, and one from which we talk about what does and doesn’t happen to

his counterparts. When Lewis claims that Billy and his ilk are worldbound

individuals, it’s crucial to bear in mind that he’s viewing logical space from the latter

perspective. For only when we take this perspective on logical space can we see that

Billy and his worldmates are bound together, found in just a single world. But it’s

equally crucially to remember that this shouldn’t lead us to conclude that there is


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some strange necessary connection between Billy and his worldmates. For that

would involve one of two things.

On the one hand, we might be trying to modalize about Billy’s connection to his

worldmates from within our original perspective, from within the language of

counterpart theory. But to try to do that would be a mistake. The perspective from

which we talk about counterparts and the rest is, according to the counterpart

theorist, a perspective which is free from de re modal notions, for the counterpart

theorist’s goal is to show that de re modality can be reduced to something else. The

perspective from which we view logical space and talk about counterparts is

metaphysically privileged: from it, we see logical space as it fundamentally is. And

when we view logical space from this perspective, we’ll see a vast array of

individuals, related in various ways, and nothing more. True, we’ll find that some

(sums of) individuals are related in a special way, and we’ll call these sums

‘worlds’. But what we won’t find—until we shift perspective—is de re modality

itself.

On the other hand, we might have shifted perspective from the one where we talk

about Billy’s counterparts to the one where we talk about what could and couldn’t

happen to Billy. Now we can ask whether Billy could exist without his worldmates.

But the question is what entitles us to assume that there is a necessary connection

between Billy and his worldmates? All we said was that Billy and his worldmates

were part of only one world, and we didn’t say anything about whether Billy has

counterparts in worlds where his worldmates do not. And without that, we have no

right to conclude that Billy and his worldmates couldn’t exist without each other.

That’s not, of course, to say that we might have previously been interested in a

certain strange notion of resemblance which meant that Billy only has counterparts

in worlds where each of his worldmates have counterparts too. And then we will be

able to say, from within the modal perspective, that Billy and his worldmates are

necessarily connected. But so what? It was built into counterpart theory that,

relative to certain strange kinds of similarity and resemblance, strange modal claims

would turn out to be true. (If the only respect of resemblance you care about is self-

identity, you can say that I might have been a pure set.) In other words, counterpart

theory cannot give us an argument for the conclusion that you and I are necessarily

connected to not only each other but to all our worldmates too. At best, counterpart

theory allows for alien contexts in which that modal claim expresses a truth. So it’s

no surprise that if you build the requisite contextual features into the example—

perhaps without realizing that you’ve done so—you’ll end up with an example

which suggests that worldmates are bound to each other.

It’s very surprising, then, that Schaffer’s counterpart-theoretic argument for the

internal relatedness of all things basically tries to argue from the idea that Billy and

Alice are worldmates to the conclusion that Billy and Alice are not modally free of

each other. And that transition, you’ll remember, is negotiated simply by appeal to

the fact that Billy and Alice are worldbound individuals. But the moral of the

preceding discussion was exactly that the worldboundness of individuals doesn’t

entail that any two worldmates are necessarily connected. Again, Schaffer is free to

care about unfamiliar notions of similarity which allow him to say that Billy

couldn’t have existed without Alice. But that’s not to say that his argument for his

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conclusion works, but merely that he’s set the context up to ensure that his

conclusion expresses a truth.6

Schaffer seems to think that this line of response is irrelevant. He tells us that

whilst the counterpart theorist can recognize a world which represents the

possibility that Billy exists without Alice, she cannot recognize a world which

realizes this possibility (2010, p. 29). And that’s because even though she can

recognize a world which contains a counterpart of Billy but lacks a counterpart of

Alice, this world doesn’t realize the possibility that Billy exists without Alice

precisely because it is not a world that contains Billy himself. And since his original

argument was formulated in terms of whether there were worlds which realized

certain combinations of possibilities, the details I’ve been pressing are simply

irrelevant.

I disagree. And that’s because the proposed distinction between the represen-

tation of a possibility and a realization of a possibility doesn’t even make sense from

the counterpart theorist’s point of view. For the only kind of de re modality that the

counterpart theorist recognizes is one that gets analyzed in terms of counterparts. So

when faced with the question of whether Billy could exist without Alice, the only

interpretation of this sentence that the counterpart theorist allows is one on which

the sentence is true iff Billy has a counterpart in a world lacking a counterpart of

Alice. There is no question of whether there is a world which ‘realizes’ the

possibility by containing Billy but not Alice. And to see that, just note that if the

distinction made sense then the counterpart theorist would have to admit that Billy

has two thoroughly different modal profiles—one specified in terms of counterparts

(representations of possibilities) and one specified in terms of Billy himself

(realizations of possibilities). But that runs against the whole spirit of counterpart

theory, and its quest to reduce talk of de re possibility and necessity to talk of

counterparts.

This sheds light on where Schaffer’s analogy between counterpart theory and

hyperessentialism—the view that every feature of an object is essential to it—breaks

down. Schaffer (2010 p. 28) writes:

The hyper-essentialist looks over her worlds and (assuming that all worlds are

discernible) sees no individual at more than one world. For if she sees some

individual x at a world w, then she will see x as essentially having the property

of being in a world with the distinctive features of w. In this respect the

counterpart theorist has exactly the same picture of the worlds as the hyper-

essentialist. The counterpart theorists and the hyper-essentialist merely have a

semantic dispute, as to how to interpret claims in the modal language against

their shared metaphysical picture.

6 To be clear: I’m not suggesting that these strange and unfamiliar notions of similarity play a role in

Schaffer’s argument. The point is rather that the counterpart theorist insists that de re modal claims—such

as claims about modal freedom—must be negotiated by appeal to counterparts and thereby similarity

relations. So Schaffer cannot conclude that the counterpart theorist is committed to a given de re modal

claim without making some assumptions about which similarity relations are contextually salient. And as

far as I can tell, Schaffer’s conclusion only follows in some quite bizarre contexts. Thanks to an

anonymous referee for forcing me to be clear on this.


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But this is incredibly misleading. The hyperessentialist holds that objects have real

and genuine essences that are fixed independently of how we refer to those objects,

where the counterpart theorist thinks otherwise. So when the counterpart theorist

sees an object x in a world w she will not see x as essentially having the property of

being in a world with the distinctive features of w. And that is just to say that the

only notion of essence that the counterpart theorist allows is one specified in terms

of what’s true of all of x’s counterparts. So the dispute isn’t merely semantic: it’s

metaphysical too.

Moreover, it’s not like the counterpart theorist recognizes the notion of essence

that the hyperessentialist embraces and then finds a clever way to interpret modal

language ‘‘to make the metaphysical picture more palatable,’’ as Schaffer (2010,

p. 28) suggests. The counterpart theory rejects the notion of essence that is integral

to hyperessentialism and replaces it with one specified in terms of counterparts. And

that, in essence—pun intended—is because the counterpart theorist has no truck

with the notion of a possibility’s being realized that is distinct from that of a

possibility’s being represented. At best, a hyper-essentialist picture of essence could

be coupled with a counterpart-theoretic account of de re modality. But then we

would have to allow that while Billy (e.g.) is essentially human, he is not necessarily

human. Feel free to make sense of that if you want. Just dont think that such a

bizarre view follows from counterpart theory, or is even a natural option for the

counterpart theorist to take.

In sum: I submit that, far from being irrelevant, the details of counterpart theory

do matter, and they are telling against the conception of counterpart theory which

Schaffer offers.

6 Conclusion

There is no path from counterpart theory to the internal relatedness of all things. For

the mere fact that individuals are worldbound does not entail anything substantial

about the necessary connections between one object and its worldmates. Of course, I

allow that Schaffer can set up a context where he speaks truly when he says that

Billy couldn’t exist without his worldmates. But that’s not what Schaffer was after:

he wanted a robust sense in which worldmates failed to be modally free from each

other. Moreover, and contra Schaffer, this point is not irrelevant to the assessment of

his argument. For what it reveals is that Schaffer’s argument requires a notion of dere modality that is thoroughly different to the only notion of de re modality that the

counterpart theorist countenances. And that’s because Schaffer needs to hold that

worlds which represent a possibility do not thereby realize that possibility. But not

only is this a distinction that the counterpart theorist rejects, it’s also unclear

whether the distinction is so much as coherent given counterpart theory. Given his

aims, Schaffer has found a false friend.

Acknowledgments With thanks to Ross Cameron and Tatjana von Solodkoff. My research on this

paper was partially supported by my involvement in the Nature of Assertion: Consequences forRelativism and Fictionalism project (FFI2010-169049), the Vagueness and Physics, Metaphysics, and

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MetaMetaphysics project (FFI2008-06153), and the PERSP-Philosophy of Perspectival Thoughts and Factsproject (CSD2009-00056). Many thanks to the DGI, MICINN, and the Spanish Government for

supporting these projects.

References

Lewis, D. (1968). Counterpart theory and quantified modal logic. Journal of Philosophy, 65, 26–113.

Lewis, D. (1986). On the plurality of worlds. Oxford: Basil Blackwell.

Plantinga, A. (1974). The nature of necessity. Oxford: Oxford University Press.

Schaffer, J. (2010). The internal relatedness of all things. Mind, 119, 341–376.


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Worldmates and internal relatedness