Dear Haecceitism

Abstract

If a counterpart theorist’s understanding of the counterpart relation precludes haecceitist differences between possible worlds, as David Lewis’s does, how can he admit haecceitist possibilities, as Lewis wants to? Lewis (Philosophical Review 3–32, 1983; On the Plurality of Worlds, 1986) devised what he called a ‘cheap substitute for haecceitism,’ which would allow for haecceitist possibilities while preserving the counterpart relation as a purely qualitative one. The solution involved lifting an earlier (Journal of Philosophy 65(5):113–126, 1968; 68(7):203–211, 1971) ban on there being multiple intra-world counterparts. I argue here that serious problems for ‘cheap haecceitism’ lurk very close to its surface, and they emerge when we consider the effect of using an actuality operator in our language. Among the most serious of the problems is the result that being the case in some possible world does not always suffice for possibly being the case. The result applies to any counterpart theory that employs a purely qualitative counterpart relation. The upshot is that if we are to admit haecceitist possibilities, as we should, then we must reject any purely qualitative relation as the one involved in the analysis of what might have been for an individual.

My goal here is to argue against counterpart theories that employ a purely qualitative counterpart relation. A counterpart theory is a theory of de-re modality according to which an individual possibly has a given property just in case there is a counterpart of that individual that has that property in some possible world. I use the term ‘counterpart theory’ liberally: to include all theories on which the counterpart relation is a relation other than identity, whether that relation be purely qualitative or not. (On the most liberal usage, even identity would count as a kind of counterpart relation—a very strict one—so that even an identity theory of de-re modality would count as a counterpart theory.)

I argue that the qualitative-counterpart theorist who admits haecceitist possibilities precludes himself from accepting very plausible and traditional, if not incontrovertible, claims about actuality. In particular, the qualitative-counterpart theorist cannot in general accept both (i) that if something’s the case in the actual world, then it’s actually the case; and (ii) that the actual world is a possibility. If he does, then for him being the case in the actual world does not always suffice for possibly being the case.

1 What is Haecceitism?

To me, the intuitive idea of haecceitism is this: our identity is so separable from the way we happen to be that which things would have been which had things been different is independent of which things would have had which properties. I might have been just the way you in fact are. And I might have been just the way you in fact are even if you hadn’t existed. Moreover, this isn’t just a false description of the genuine—but distinct—possibility that you might have existed (just the way you are) without my existing; in the imagined scenario, it would be me being just the way you in fact are, but without you around at all. We might haggle over the question whether a plausible haecceitism, so conceived, is compatible with a plausible essentialism, understood as the doctrine that for some things, and some of the ways those things are, those things couldn’t but have been those ways. But that issue is not my concern here. Rather, I want to show that a similarity-based counterpart theory, such as David Lewis’s, cannot, even in Lewis’s ‘cheap’ way, coherently admit enough plausible haecceitist possibilities. More importantly, the difficulty extends to any counterpart theory that employs a purely qualitative counterpart relation.

Let’s begin by developing a clear statement of what haecceitism is. ¹ Throughout, we will use the notion of a qualitative description, along with other related notions suitably defined mutatis mutandis. A qualitative description is one that involves no reference to individuals (including places and, perhaps, times). On one interpretation, haecceitism is the doctrine that there are distinct possible worlds that are qualitatively just alike. ² We will call this ‘haecceitism*’. On a second interpretation, haecceitism is the doctrine that there are distinct possible worlds that are qualitatively just alike and that differ with respect to the de-re possibilities they represent for some individual—with respect, that is, to how they represent that individual as being in that world. We will call this ‘Haecceitism’ (with a capital-‘H’).

Instead of talking about how individuals are ‘represented’ as being in a possible world it would be nice to talk about how individuals are in a possible world. It would be nice to say that (capital-‘H’) Haecceitism is the doctrine that there are possible worlds that are qualitatively just alike but that differ with respect to what particular individuals are like in them. The talk of ‘representation’ is here, however, so as not to require, by fiat, that you be a haecceitist just because you hold that no particular individual exists in more than one possible world. For if an individual exists in one world only, then that individual will not be one way in some possible world but some different way in some other world; it would not be in any other possible world at all. So no two worlds, on this view, could differ with respect to what some individual was like in them, whether or not those worlds were qualitatively indistinguishable.

We may then use ‘representation’ as a neutral word to denote the relation that’s relevant for a possible-worlds analysis of de-re possibility: being-Φ is a possibility for a thing just in case there’s a possible world in which that thing is represented as being Φ. An identity theorist is one who thinks that representation is identity: that being-Φ is a possibility for a thing just in case there’s a possible world in which something identical to that thing is Φ. Those who think that identity is not the relevant relation then owe us an account of what relation an individual must bear to a possible world in order to count as being represented as Φ in it.

A counterpart theorist is someone who thinks that an individual is represented as being Φ in a world just in case that individual has a counterpart that is Φ in that world. The counterpart theorist is one who agrees with the identity theorist that the analysis of de-re possibility involves a relation holding between individuals in different possible worlds, but who disagrees in thinking that the relation involved is not the identity relation.

Note that I’ve set up the classifications so that a counterpart theorist is just one kind of non-identity theorist. For one might reject the idea that the analysis of de-re possibility involves a relation that an individual bears to an individual that’s in a world as opposed to bearing some other sort of relation to the world itself. I’ve also set up the classifications so that one could be a counterpart theorist without thinking that the counterpart relation is a relation based on similarity. Finally, I’ve allowed that in particular cases an individual might be identical to her counterpart in another possible world. A counterpart theorist needn’t require that individuals are ‘world-bound’. This may deviate somewhat from the standard classifications. I find this way the most useful.

It would be nice if we could eliminate reference to possible worlds when defining haecceitism. We might like to say that haecceitism is the doctrine, for example, that I might have been born before 1970 while things were completely described in some purely qualitative way, and that I might also have been born after 1970 while things were completely described in that very same purely qualitative way. Given the schema ‘a might have been Φ while things were completely described by a purely qualitative description D, while a might also not have been Φ while things were completely described by D’, haecceitism would be the doctrine that the schema is true for at least one of its instances. We could call this doctrine ‘haecceitism⁺’. We now have three statements of what haecceitism is:

• (1) There are distinct possible worlds that are qualitatively just alike; (haecceitism*)

• (2) There are distinct possible worlds that are qualitatively just alike that also differ with respect to how they represent some individual as being in that world; (Haecceitism with a capital-‘H’)

• (3) The following schema is true for at least one of its instances: ‘a might have been Φ while things were completely described by a purely qualitative description D, and a might also not have been Φ while things were completely described by D’. (haecceitism⁺)

The third interpretation of haecceitism is not equivalent to either of the other two. Within some theories of modality, it can be upheld while the other two are rejected. Lewis’s is an example. Here’s why: his theory allows for an individual to be represented in more than one way in a single possible world—when that individual has more than one counterpart in that world. This alone suffices to make the theory haecceitist⁺. To see this, suppose that there’s an individual who might have been tall and also might not have been tall. Call her Alberta. Let us suppose that Alberta has these two modal properties in virtue of there being a world w in which she has a pair of counterparts, one of whom is tall, the other of whom is not. Suppose that S is a complete, purely qualitative description of this world w. Obviously, if a description S describes the world w, then it will describe it twice over. ‘Alberta’, ‘tall’, and S therefore provide the requisite substitution instance of the schema ‘a might have been Φ while things were completely described by a purely qualitative description D, while a might also not have been Φ while things were completely described by D’. But the theory need not thereby be capital-‘H’ Haecceitist, however. For it may nevertheless be that any world that’s indistinguishable from w also represents Alberta both as being tall and also as being not tall—which would mean that it’s not (capital-‘H’) Haecceitist. ³

Despite its independent interest, however, we will ignore haecceitism⁺ for the remainder of this paper.

The distinction between the first two interpretations of haecceitism comes from Lewis. ⁴ If it is difficult to see how they can come apart, that is because they do not come apart on the most plausible theories of what possible worlds are like.

On any theory according to which possible worlds are individuated no more finely than the sets of propositions they verify are, the first two haecceitisms must stand or fall together. ⁵ This would include theories according to which a possible world is the set of all the propositions that are true at that world, or the big conjunction of all the true ones of those that are propositional ‘literals’ (either propositionally atomic or a negation of such). For on any such theory, distinct possible worlds always hand down a different verdict on at least one proposition, in which case distinct worlds would hand down the same verdict on all qualitative propositions only if they differed with respect to some non-qualitative proposition—one which could be expressed only by mentioning some particular individual or individuals. That is to say that such theories would be haecceitist* only if they were Haecceitist (with a capital-‘H’). Conversely, every Haecceitist theory is trivially haecceitist*, since if there are distinct worlds that are qualitatively just alike and that differ with how they represent some individual as being, then a fortiori there are distinct worlds that are qualitatively just alike, full stop. So on a theory of possible worlds according to which worlds are individuated no more finely than the sets of propositions they verify, haecceitism* and Haecceitism stand or fall together.

The first two haecceitisms are not equivalent, however. On a theory that allows for distinct possible worlds to verify exactly the same propositions, haecceitism⁺ could stand while (capital-‘H’) Haecceitism falls. Lewis’s concrete modal-realism is an example. Lewis deems all possible worlds to be concrete objects that are just as real as the actual world. If that’s right, why shouldn’t there be any number of possible worlds (many or just one) verifying any given complete qualitative description? To borrow Kripke’s suggestive imagery (Kripke 1972), if possible worlds are concrete objects not differing in kind from the actual world, why should we be able to tell whether there are distinct but qualitatively indiscernible ones using just our modal telescope? If there were such distinct ones, then haecceitism* would be true. But even with the admission of such distinct worlds, a concrete modal-realist theory could still preclude (capital-‘H’) Haecceitism. Depending on the theory of de-re modality combined with it, a concrete modal-realism might require any distinct but qualitatively indistinguishable pair of worlds to represent exactly the same possibilities for any given individual. This is precisely why Lewis introduced the distinction between what I’m calling haecceitism* and Haecceitism.

Here I am more interested in what the correct theory of de-re modality is than I am in what the correct theory of the nature of possible worlds is. In fact, I find any theory of possible worlds that allows distinct ones to verify just the same propositions to be incredible. Since this aspect of the theory under discussion does not affect my arguments against it, I prefer to ignore it and will therefore confine my attention to (capital-‘H’) Haecceitism.

2 Haecceitist Possibilities

A Haecceitistic possibility for a thing is a possibility that it be different without there being any difference in any of the qualitative facts. I admit that some Haecceitistic possibilities can be hard to accept. It is hard to accept, for example, that my daughter’s toy yellow bunny could have been just the way her twin toy blue bunny actually is—and vice versa—while everything else was just the same. This would require not only that Chi-Chi, the yellow bunny, have been blue and that Ki-Ki, the blue bunny, have been yellow; and that Chi-Chi have been called ‘Ki-Ki’ and Ki-Ki ‘Chi-Chi’; but also that Chi-Chi have been held by my daughter first, whereas Ki-Ki in fact was; and that Chi-Chi have come off the production line first, whereas Ki-Ki in fact did. Et cetera. The identity of a toy bunny seems too insubstantial, for lack of a better way to put it, to allow for this sort of bare switching. ⁶

But some Haecceitistic possibilities, Lewis admits (1986, pp. 227–233), can be hard to reject. For example, the world might contain temporal intervals or spatial regions that viewed alone through a telescope would look just like others of its temporal intervals or spatial regions. History might well keep repeating itself—exactly. And it might in addition consist of three regions, each just like the other, spatially arranged in single file. ⁷ (The stuff called ‘water’ on the triplet Earths would, in this case, be made of H₂O molecules.) It’s compatible with what we know (with what I know, anyway) that the actual world is such a world. For ease of exposition, I will suppose that it is.

So suppose that I live in the 17th epoch, in region two (the middle one). I certainly don’t live in more than one epoch, since that would require me to have portions of my life separated by long stretches of time; it would require me to have multiple childhoods interspersed with multiple adulthoods, which, I’ll suppose, I don’t (no time-travel for me). And I certainly don’t live in more than one region of the universe, since that would require me to have three bodies—six legs, three spleens, et cetera—occupying distant regions of space, which I don’t. In the actual world I live only in the 17th epoch, in region two. Still, I might have lived in the 18th epoch, and I might have lived in one of the outer regions of the universe.

These are Haecceitist possibilities since what we envision for me is that I be different by living in a different epoch and region from the ones I in fact live in while the totality of the epochs and regions were qualitatively just as they in fact are. Can Lewis’s similarity-based counterpart theory allow for this?

On Lewis’s understanding of de-re possibility, an individual o is possibly-Φ just in case there’s a possible world in which o is represented as being Φ—i.e., one in which o has a counterpart that’s Φ. So to allow for the Haecceitist possibility in question, while adhering to this understanding of de-re possibility, would be (i) to admit the existence of a world qualitatively just like the actual world, but which represented me as living in the 18th epoch in region three. But Lewis had originally stipulated (ii) that the actual world could represent me in only one way. ⁸ Combining (i) and (ii), while adhering to the understanding of de-re possibility, means that to allow for the Haecceitist possibility in question, Lewis would have to admit a non-actual world that was qualitatively just like the actual world, but which represented me differently from the way I’m represented in the actual world. This indistinguishable-from-actuality world would contain a counterpart of me (viz., the person in the 18th epoch there) that was qualitatively just like someone who is not a counterpart of me (viz., someone living in the 18th epoch in the actual world).

3 Cheap Haecceitism

Rather than admit a less-than-purely qualitative counterpart relation, Lewis decided to accommodate the desired Haecceitist possibilities ‘on the cheap,’ as he puts it, by rejecting stipulation (ii)—in this case, by allowing my twins in the other epochs and regions of our world to be my counterparts (1986, p. 230). ⁹ In this case, the actual world represents me as living in the first epoch, and as living in the second epoch, and as living in the third, ..., and as living in the 18th, .... And it represents me as living in each of the three regions of the universe. This suffices for my possibly living in the first epoch, ..., and for my possibly living in the 18th, and for my possibly living in the first region, and for my possibly living in the third. We no longer need a qualitative duplicate of the actual world to represent me as living in the other epoch-region pairs. The actual world does the needed representing all by itself. Going in for this ‘cheap substitute for Haecceitism’ requires giving up one specific postulate of Lewis’s original (1968) version of counterpart theory. The postulate is P5, according to which nothing can be a counterpart of anything else in its own world. ¹⁰

This is Haecceitism because it allows for Haecceitist possibilities; it is cheap because it does this without admitting Haecceitist differences between worlds—differences, that is, in the de-re possibilities represented by distinct worlds when there are no qualitative differences between them. (A Haecceitistic possibility, recall, is a possibility for a thing that it be different without there being a difference in any of the qualitative facts.)

On the revised proposal, my twin in the 18th epoch in the actual world is a counterpart of me. Her living in the 18th epoch is what constitutes my possibly living in the 18th epoch. So the following is analyzed as true, as desired:

• (1) Fara lives in the 17th epoch $\wedge\;\diamond$ Fara lives in the 18th epoch.

Similarly, my duplicates in the outer regions of the universe are counterparts of me, rendering the following true, also as desired:

• (2) Fara lives in the middle region of the universe $\wedge\;\diamond$ Fara lives in an outer region of the universe.

The main problem I want to raise here is a simple technical one. When our expressive resources include an actuality operator (as they should do)¹¹ acceptance of Lewis’s cheap substitute for Haecceitism—his way, that is, of achieving Haecceitist possibilities without employing Haecceitistic differences between worlds—commits us either to rejecting obviously true claims about the validity of certain arguments involving the actuality operator or to accepting obvious falsehoods.

4 Not So Cheap

If every interval and region of the actual world that’s just like the interval and region that I’m in contains a person who’s a counterpart of me—in the sense that’s relevant for determining what’s possible for me—then since this counterpart actually lives in the 18th epoch, actually living in the 18th epoch is a possibility for me. So the following is true:

• (3) ACT Fara lives in the 17th epoch $\wedge\;\diamond$ ACT Fara lives in the 18th epoch.

Assuming that what’s possibly actual is actual (which one could conceivably refuse to do) we have the truth of what I take to be an obvious falsehood:

• (4) ACT Fara lives in the 17th epoch $\wedge$ ACT Fara lives in the 18th epoch.

If the actuality of a conjunction were equivalent, on this view, to the conjoined actuality of its conjuncts, as it is normally considered to be, we would have the actual truth of two conjoined claims that are incompatible with one another (incompatible because their joint truth would require, for example, that I be 33 years old long after I’m 35 years old, and that I be born again after I die):¹²

• (5) ACT (Fara lives in the 17th epoch $\wedge$ Fara lives in the 18th epoch).

The proponent of the view at hand will presumably deny, however, that the actuality operator does commute with conjunction in this way, on the grounds that one counterpart relation is operative in the first conjunct (one entailed by the relation of actual identity), and a different counterpart relation is operative in the second conjunct (one not so entailed).¹³ The proponent will say that in order for possibly-Φ to be true of an individual it must be that there is a single counterpart relation such that the individual is related, by that relation, to someone of whom Φ is true. And in particular, in order for possibly-actually-Φ (and so actually-Φ) to be true of an individual it must be that there is a single counterpart relation such that the individual is related, by that relation, to someone actual of whom Φ is true. So if I’m related to each of my twins in each of the n epochs by a different counterpart relation, C _i —where C ₁₇, we’re supposing, coincides with the identity relation for individuals in the 17th epoch—then there is no single counterpart relation that makes the conjunction in (5) true.

I don’t see that the denial of (5)’s truth helps much, however, since (4) already strikes me as a very bad consequence of the theory. It doesn’t seem right to say that I’m actually one way and also actually not that way. It doesn’t help matters much to deny that this requires me to be actually that way as well as not.

The main objection at this stage is that in order to save Lewis’s cheap Haecceitism from an unacceptable consequence, its proponent must reject either of two obviously valid argument-forms involving the actuality operator: either (i), that from possibly-actually-P to actually-P,¹⁴ or (ii), that from the conjunction of two actualities to the actuality of their conjunction, as exemplified in the argument from (4) to (5).

$$ \hbox{(i)} \frac{\diamond ACT\P}{\therefore\ ACT\ P} \quad\quad \hbox{(ii)}\frac{(ACT\ P\ \wedge\ ACT\ Q)}{\therefore\ ACT(P\ \wedge\ Q)}$$

I would, on the one hand, consider the rejection of argument-form (i) to be a move of serious desperation since (i) is partially constitutive of the meaning of the actuality operator as most would understand it.¹⁵ I don’t see, on the other hand, that rejection of the validity of argument-form (ii) would be very helpful since when P and Q are incompatible—as they are when P is the claim that I live in the 17th epoch and Q is the claim that I live in the 18th—the conjunction of their actuality already strikes me as sufficiently implausible to reject any theory that has it as a consequence.

Nevertheless, it might be said that this last complaint begs the question: that my objection to the conjunction of the actuality of P with that of an incompatible Q is based on my straightaway thinking of this conjunction as entailing $ACT(P \wedge Q)$. Moreover, the retort continues, unlike rejection of argument-form (i), the rejection of argument-form (ii) already seemed to have independent motivation within a context-dependent version of counterpart theory that, like Lewis’s (1971), allows for there to be multiple counterpart relations. Different ones can be associated with different names, and also, in principle, with different occurrences of a single name or variable when no occurrence of a modal operator has both of them in its scope.¹⁶

For in general, when different counterpart relations may be associated with different names or variables in the scope of a single modal operator, or with different occurrences of the same name or variable in the scope of different modal operators, we do not expect that modal operator to commute with the other operators (e.g., possibility with disjunction, actuality with negation, and necessity with conjunction) that it would otherwise commute with.

For example, take a putative case of contingent identity, of the kind that helps motivate multiple (and contextually variable) counterpart relations. We have a statue that’s contingently identical with the lump of clay it’s made up of. It’s possible for the statue to be made up of (and hence, on the view in question, identical to) something other than a lump of clay since it’s possible for its nose to get broken off and replaced by a bit of bronze. And it’s possible for the lump of clay to make up no statue at all since it’s possible for the lump of clay to be squashed completely flat.

So we could have the conjunction of two necessities:

• (6) $(\square\;a\ \hbox{is a statue if it exists}\; \wedge \square\;a\ \hbox{is a lump of clay if it exists})$,

without the necessity of the their conjunction:

• (7) $\square (a\hbox{ is both a statue and a lump of clay if it exists})$.

Although the statue and the clay are identical—a (short for ‘Alfred’) the name of ‘both’—we could have it that (6) is true since the first conjunct would be true when the occurrence of the name ‘a’ in it is associated with the ‘statue-counterpart’ relation since all of a’s statue counterparts are statues; while the second conjunct would be true when the occurrence of the name ‘a’ in it is associated with the ‘lump-of-clay-counterpart’ relation, since all of a’s lump-of-clay counterparts are lumps of clay. But it needn’t therefore be that (7) is true since it needn’t therefore be that there is any single counterpart relation C such that everything that a is C-related to is both a statue and a lump of clay. The statue might survive a total replacement of clay parts with non-clay ones; the lump of clay might survive a squashing. Normally, we’d take the necessity and conjunction operators to commute with each other; but in those cases where the context dependence of the necessity operator is well motivated, we have good reason for expecting them not to.

That’s as may be. It’s nevertheless implausible that occurrence-variant counterpart relations would come to the rescue every time they were needed to save cheap Haecceitism. The similarity-based counterpart theorist is still in the woods. I offer two reasons that should convince you of this.

First, only very few contexts allow for the needed sort of counterpart-relation switching. The cases in question, (4) and (5), are not among them since they are not like (6) and (7) in a crucial respect: the two occurrences of the single name ‘Fara’ in (4) and (5) are not in the argument positions of predicates involving different sorts of things.

Second, the actuality operator and the necessity operator are different in another crucial respect: the necessity operator quantifies over a multitude of possibilities while the actuality operator quantifies over just one. The range of predicates that an object could satisfy is something that varies with different ways of conceiving of it (on the view in question). Qua statue, a possibly satisfies ‘is made entirely of bronze’; qua lump of clay, he does not. But the range of of predicates that the object does satisfy does not so vary. The object actually satisfies the predicates it satisfies in the one actual world—no matter how we conceive of it. There can be variance across a multitude of worlds but not across a singleton. This is why (ii) can be valid even though (6) does not entail (7).

Recall the particular arguments of forms (i) and (ii) that we made in reaching the absurd conclusion (5)—the conclusion that I actually live in both the 17th and 18th epochs of our universe.

• (i′)
  $$ \frac{\diamond\textsc{ACT}\hbox{ Fara lives in the 18th epoch.}} {\therefore\ \textsc{ACT}\hbox{ Fara lives in the 18th epoch.}} $$
• (ii′)
  $$ \frac{(\textsc{ACT}\hbox{ Fara lives in the 17th epoch and} \textsc{ACT}\hbox{ Fara lives in the 18th epoch})} {\therefore\ ACT (\hbox{Fara lives in the 17th epoch and Fara lives in the 18th epoch}).} $$

Combined with the conclusion of (i′), our assumption that I actually live in the 17th epoch forces us to accept the premise of (ii′). We have seen two reasons why the similarity-based counterpart theorist cannot justifiably resist the conclusion of (ii′) by appealing to the idea that argument (ii′) is not truth-preserving, even if it is an instance of an argument-form that he does not generally regard as valid.

First, the general reasons for rejecting the validity of argument-form (ii) do not apply to this instance of it. In particular, the name in it does not occur in the argument place of different sortal predicates, rendering it unlikely that different counterpart relations would be involved.

Second, and what’s worse, this counterpart theorist’s general reason for blocking commutation of conjunction with modal operators (e.g. necessity) does not extend to the actuality operator since, unlike the necessity operator, the actuality operator does not quantify over a multitude of possibilities.

In any case, even if the conclusion of (ii′) is resisted, the premise of (ii′) is already so repugnant that merely blocking the argument to its conclusion, (ii′), does little to shore up the theory.

So it’s the soundness of (i′) that has got to go. But rather than desperately chop down the validity of argument-form (i), the stingy Haecceitist should deny (i′)’s premise. He should deny that I might have actually lived in the 18th epoch. I might have lived in the 18th epoch, he should say, but I could not have actually lived in the 18th epoch. He should say that since we are not considering the 18th epoch as an actual possibility, but rather as an alternative possibility, we should deny that the actions and states of my counterpart there are actual actions or states. Since these are actions and states of my counterparts, they are possible actions and states of mine. But since they are not actual, they are not possibly actual actions or states of mine.

This brings to the fore the feature of cheap Haecceitism that both gives it its power and ultimately betrays it. In allowing me to have counterparts in each of the various epochs, each of whom represents possibilities for me, Lewis admits possibilities that are not themselves possible worlds—says (Lewis 1986, p. 230). In the case at hand, none of the epochs is itself a possible world, merely a part of one. Nevertheless, each of the epochs is among the possibilities quantified over by the possibility operator. These epochs are qualitatively just like the epoch you and I live in, but they represent different possibilities for us than our own epoch does. That’s the powerful part.

The betrayal comes when we realize that these possibilities must not be treated as actual, even though they are parts of the actual world. They are genuinely alternative possibilities. Given this, the cheap Haecceitist has not only admitted possibilities that aren’t possible worlds, he has also ceased to treat every possible world as a possibility: in particular, he does not treat the actual world as itself a possibility. How so? Once we admit possibilities that are not themselves possible worlds we must revise the statement of counterpart theory to allow for this.

Revised Counterpart Theory: An individual might have been Φ just in case there is a possibility (formerly possible world) in which some counterpart of that individual is Φ.

But now consider the following chain of reasoning which shows that the cheap Haecceitist must accept the premise of the dreaded argument (i′):

• (1) In the actual world, I have a counterpart that lives in the 18th epoch;

• (2) In the actual world, I have a counterpart that actually lives in the 18th epoch;

• (3) There is a possibility in which I have a counterpart that actually lives in the 18th epoch;

• (4) I might have actually lived in the 18th epoch;

Accepting (1) allows the qualitative-counterpart theorist to admit the Haecceitist possibilities without admitting the corresponding Haecceitist differences between possible worlds. From (1), (2) follows since what goes on here in the actual world actually goes on here. From this, (3) follows unless we deny that the actual world is a possibility. But then (4) follows by the revised statement of counterpart theory. But this conclusion is the unwanted premise of the troublesome argument (i′) above (page 18). That argument, recall, led to the conclusion that something could both be actually one way and also be actually not that way—an incoherence if not a downright contradiction.

What’s worse—though I have not explicitly argued it here—is that the qualitative-counterpart theorist is committed to (1) as long as he thinks that there are worlds in which history repeats itself and in which we have qualitative duplicates that are distinct from us in the various epochs. It’s only a non-qualitative property that distinguishes my duplicates from me: the property of being distinct from me. So if the counterpart relation is to be purely qualitative, then they are counterparts of me if I’m a counterpart of myself. This is all to say that the unwanted conclusion that I actually live in the 17th epoch and also actually live in the 18th epoch, cannot be resisted just by rejecting Haecceitist possibilities and selling back cheap haecceitism. The qualitative-counterpart theorist is stuck with cheap haecceitism whether he wants it or not.

Since we should accept counterpart theory in order to preserve the principle of one object to a place—to preserve, for example, the identity of the statue and the lump of clay it’s made up of—we should accept a counterpart theory that shuns a purely qualitative counterpart relation. Doing so affords us the possibility of my living in the 18th epoch without the possibility that I actually live in the 18th epoch. This is because we admit a non-actual world, qualitatively just like our own, in which I have a ‘counterpart’ that lives in the 18th epoch (but none in any other). With no commitment to (1), above, there is no commitment on this view to the absurd possibility that I actually live in the 17th epoch and also actually live in the 18th epoch. We keep our Haecceitism, but we pay less for it. ¹⁷