Notice, though, that on all Abstractionist views, Lyle is represented by two worlds w1 and w2 if and only if w1 and w2 literally have something in common. In the case of Magical Abstractionism, there is sharing of a property; in the case of Linguistic and Pictorial Abstractionism, there is sharing of a part, whether a name or an abstract simulacrum. Because of this, it is right to say that, had a world representing Lyle been actual, Lyle himself would have existed. That is, he would have been part of our spatiotemporal surroundings. In this sense, these views are committed to, or at least are compatible with, Transworld Identity, the claim that it is possible that actual objects would have existed even if a different world had been actual. One way to express the idea of Transworld Identity is as the thought that a single object can exist in many worlds. Given that the word ‘in’ can be understood either representationally or mereologically, we must be careful to say to what exactly Abstractionists are committed. Concretists no less than Abstractionists agree that many worlds represent a single individual. The distinctive commitment of Transworld Identity is the claim that it is possible for some actually existing thing to be a mereological part of the concrete universe even were a different world actual. The view may crystallize by considering its chief rival, Counterpart Theory.
16.1.2 From Concretism to Counterpart Theory
Concretists take possible worlds to be like parallel universes. If that it right, though, it would be very odd to say that a single thing could exist in multiple worlds, where ‘in’ is understood to mean ‘be a part of’. The only way for this to work, given Concretism, would be for possible worlds to overlap one another, that is, for possible worlds to share a part. Here's an example. Suppose Joe Biden could have been a plumber. This is a possibility involving Biden himself, not someone else. So this very individual (namely, Biden) exists in a possible state of affairs in which he is a plumber. But he is not a plumber in the actual world. Therefore, Biden must exist in another possible world, too, one where he is a plumber. Call that world w. The actual world and w must share a part, they must overlap, and the part they share is Biden. If this is the story the Concretist tells about de re modality, then we get Overlapping Concrete Worlds:
16.1T.1 Overlapping Concrete Worlds. It is possible for something to fail to exist if and only if there is a concrete universe in which it (and not just a counterpart of it) does not exist.
The idea is that we keep Lewis's thought that something exists in some world just in case that thing is a part of that world, and we add the thought that something can literally exist as a part of more than one world. Thus it would follow that you are a part of many worlds, and thus that worlds share parts in common. Worlds overlap, which is just to say that worlds share parts.
David Lewis pointed out a critical problem for the Overlapping Concrete Worlds. Suppose that there is an iron meteor that in the actual world is spherical and always has been spherical, but which might have been cubical instead. Such a meteor would then be part of two different possible worlds. If the two worlds are concrete, overlapping universes, then the meteor would have to be both spherical and cubical at once. It is cubical in one world and spherical in the other, but there is only the one thing that is part of the two worlds!
Such overlap would be possible only if the things in the overlapping region had exactly the same intrinsic properties in both worlds.2 Certain abstract objects, such as universals, numbers, and pure sets (like the empty set) would pose no problem, since they have all of their intrinsic properties of necessity. However, concrete, changeable things are another matter. If a rod is in fact bent but could have been straight, then it would seem that it could not exist in two worlds, in one of which it was straight and in the other of which it was bent, since being straight and being bent are incompatible properties.
Concretists might imagine that possible worlds can overlap at certain times and not at others. So, there could be two possible worlds that share the same history up to some point in time and that diverge thereafter. Perhaps there is a world in which Harold Godwinson defeated King William the Conqueror at the Battle of Hastings. Such a world might overlap our world up until that fateful day in 1066, diverging radically afterward. There might also be, in certain cases, converging worlds, worlds that share the same future but differ in the past, as well as worlds that repeatedly converge with and diverge from each other.
There is however, a decisive objection to such a branching-world version of Concretism: it is incompatible with Modal Indexicalism (14.2T). If worlds can converge or diverge, then there could be individual thoughts and speech acts that exist in multiple worlds. Consider again the thought expressed in Chapter 15's sentence (14):
(14) Dragons actually exist.
Suppose that, in fact, there never have been and never will be dragons, although there is a possible world diverging from actuality in the future in which geneticists construct dragons, or other possible worlds converging with the actual world some time in the past, in which dragons once existed. A use of (14) here and now could be neither determinately true nor determinately false, since it belongs simultaneously to worlds containing dragons and to other worlds not containing them. The word ‘actually’ would fail to act as a true indexical, since the thought has no definite location in logical space.
Hence, it seems that Concretists must embrace Worldbound Individuals. However, Worldbound Individuals pose an obvious problem for the Concretists: if each individual exists in only one world, then every individual in the actual world has all of its properties (both intrinsic and extrinsic) essentially. Nothing could have been different from the way it is, which seems wildly false.
Lewis offered Counterpart Theory as a solution to this problem. According to Counterpart Theory, individuals in one world can have one or more counterparts in other worlds. In most cases, a thing's counterpart in a world will be that thing in that world that most resembles it. So, although Socrates exists only in the actual world, other worlds contain philosophers whose biographies closely resemble the actual story of Socrates. Maybe they are named ‘Socrates’, live in a city called ‘Athens’, devote themselves to philosophical conversation, are forced to take hemlock for corrupting the youth, and so on. To say that Socrates might have been acquitted is to say that there exists a possible world containing a counterpart of Socrates who is acquitted. More generally, to say that some particular individual could have been otherwise is to say that it has a counterpart in some possible world that is (in that world) otherwise. This is Ludovician3 Counterpart Theory:
16.1A.1 Ludovician Counterpart Theory. It is possible for something to fail to exist if and only if there is an isolated universe in which it has no counterpart, it is possible for something to have a property if and only if there is an isolated universe it which a counterpart of it has that property, and it is possible for some things to stand in some natural relation if and only if they have some counterparts that do stand in that relation in some isolated universe.
The counterpart relation needn't be one-to-one. Socrates has no counterparts in some worlds; these are worlds according to which Socrates doesn't exist. But he also might have several counterparts in others; these are worlds that make it true, say, that Socrates might have been twins. A thing might even have a counterpart in its own world. For example, imagine a world in which history endlessly repeats itself. Such a world would have, for example, an infinite series of “Nietzsches”. Each of the infinitely many “Nietzsche”-like persons in such a world might well count as a counterpart of the others.
The Humphrey Objection
Abstractionists have objected to Counterpart Theory on the ground that it makes de re modal facts have to do with things other than, for example, Socrates. But it's Socrates that might have been acquitted of corrupting the youth. What is true of the counterparts of a thing is irrelevant to what could be true of the thing itself. The fact that there exist beings similar to THP in certain ways who are in fact plumbers has nothing whatsoever to do with the question
of whether or not THP himself might have been a plumber. Kripke (1980) famously pressed this objection against Ludovician Counterpart Theory, using an example about the possibility that Hubert Humphrey might have won the 1968 Presedential election. Here is Kripke:
According to Counterpart Theory] if we say ‘Humphrey might have won the election’…, we are not talking about something that might have happened to Humphrey but to someone else, a ‘counterpart’. Probably, however, Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. (Kripke 1980: 45)
The worry has therefore become known as the ‘Humphrey Objection’ to Counterpart Theory.
Counterpart Theorists ought to say that, as stated by Kripke anyway, the objection is just misguided. Socrates himself really does have the property of possibly being acquitted, though he has this because a world represents him as having the property of being acquitted by having a counterpart of him who is acquitted. In other words, what is true of your counterparts has everything to do with what you yourself might have been like. What it is for you to have the property of possibly being a plumber is for you to have a counterpart that is a plumber. And what it is for you to have the property of necessarily being a human is for all of your counterparts to be human. But to emphasize, you yourself have the modal properties needed.
Importantly, there are at least two ways to read the Humphrey Objection in light of these observations. The first is that, if Counterpart Theory is true, too many objects are involved in accounting for a thing's modal properties. The second is that the wrong objects are involved in accounting for a thing's modal properties. On both readings, the Humphrey Objection accuses Counterpart Theory of problematically involving things that exist in other worlds in the truth-conditions for de re modal truths about actual objects. The first reading of the objection says that the problem is that Humphrey alone ought to matter. The second reading of the objection says that the problem is that otherworldly objects should not matter.
It isn't clear that Abstractionists can elude the objection when formulated in the first way, however. Abstractionists would agree that Socrates doesn't represent himself, since all of them (except for Lagadonian Linguistic Abstractionists) have worlds built up out of abstract representations or out of nothing at all. In this way, all parties agree that facts about the instantiation of modal properties involve or implicate representations that are not the objects themselves. Take Magical Abstractionism, for example. On this view, Humphrey might have won if and only if there is some world that represents Humphrey as winning. This account involves an abstract object which represents that Humphrey wins, and so in that sense there are objects other than Humphrey involved in the de re modal fact that Humphrey might have won, namely, possible worlds.
On some Abstractionist views, the similarities are even more acute. For example, suppose one thought that a world represents Humphrey by having Humphrey's haecceity, H, as a part. On this view, it is plausible that one ought to count H as a counterpart of Humphrey. H represents Humphrey in other worlds without being identical to Humphrey. Humphrey might have won if and only if there is some possible world which contains H as an element and the property of winning as an element in whatever way is required to represent that were the world actual, H would be co-instantiated with the property of winning. This sort of Counterpart Theory is not Ludovician, since it does not commit to the claim that counterparts are concrete objects that are very similar to the objects they represent. However, it could plausibly be construed as an Abstractionist-friendly sort of Counterpart Theory, since the structure of the view is very similar to Ludovician Counterpart Theory. There are objects in the universe with certain modal properties, and an object has its modal properties if and only if there is something non-identical to it that represents its existence and its having certain properties. The difference concerns the nature of the counterparts rather than whether there are such counterparts.4
The second reading of the objection, on the other hand, according to which the problem is the involvement of the wrong things, is the de re version of the problem of irrelevance for Concretism discussed in Section 14.3. To the degree that one finds that objection compelling, one ought to find the Humphrey Objection compelling as well. However, to the degree that one finds the problem of irrelevance unproblematic, one ought not be worried by the Humphrey Objection either.
Part of the problem arises from the fact that we can mean two very different things by ‘existing in a world’. The first way is simply be being a part of that world. For Concretists, the most basic way for a thing to exist in a world (a way that has nothing to do with counterparts) is for it to have a property like the property of existing in Philadelphia: it is simply a mattter of where something concrete is located. For Linguistic Abstractionists, to exist in a world in this literal way is to be something like a symbol within the propositional language used to build up the propositions that constitute possible worlds. For Magical Abstractionists, nothing literally exists in a world: worlds are simply entities with no parts. Let's call this being in a world mereologically.
The second way of existing in a world is to exist according to a world. To use Plantinga's formulation (Plantinga 1974: 46–48): x exists in world w if and only if, x would exist if w were actual. This kind of existing in has nothing to do with location or parthood. We could call this being in a world representationally.
One important takeaway from this discussion is that Ludovician Counterpart Theory seems compatible with Transworld Identity where ‘in’ is understood representationally, while also being a version of Worldbound Individuals where ‘in’ is understood mereologically. Humphrey is not a part of other worlds, nor is he spatially located there, so in that sense he is not in them. However, Humphrey is represented by other worlds, by having counterparts that are parts of those worlds, and in that sense he is “in” them.
Perhaps we can capture the difference between the two accounts by using Kit Fine's notion of ontological dependence, which we discussed in Section 3.3 (Fine 1994b):
16.1T.2 Strong Transworld Identity. There is an object x and distinct worlds w1 and w2 such that both w1 and w2 represent x in part because each is ontologically dependent on x.
Counterpart Theorists will deny Strong Transworld Identity, since they will hold that if x is an inhabitant of world w1, then any distinct world w2 will not include x or any facts about x intrinsically but will merely represent x by virtue of similarities between x and its counterpart in w2: something's being similar to something external to is a paradigm of an extrinsic fact about it. In contrast, those who believe in Strong Transworld Identity suppose that x itself must enter into the very constitution of the essence of any world that represents x as being a certain way. Even if x is not literally a part of the possible world, the essential properties of that world, the properties that make it a possibility according to which x has certain properties, do involve x, in the sense that a full definition of their essence would include x. If a possible world is something like a book of sentence-like or map-like propositions, it will include its representational properties in its very essence, and so its essence will include any object, like x, whose possible properties are represented de re in that world. Counterpart Theorists, in contrast, will suppose that any representational properties of a world (with respect to inhabitants of other worlds) are entirely extrinsic to that world. For Concretists, what makes a possible world a world has nothing to do with its representational properties. And that might be the issue that the Humphrey Objection is pointing to.
The proponent of the Humphrey Objection might argue in this way: suppose that Biden is not a plumber but might have been one, and we're looking for the truthmaker for this de re possibility about Biden. Finding a world w in which something is a plumber can be relevant to this task only if that world is ontologically dependent on Biden himself. Otherwise the fact that something is a plumber is w could not even be a partial ground fo
r the fact about Biden that he could have been a plumber (contrary to Counterpart Theory). What are the grounds for this claim? Some sort of reflection on our concept of de re possibility, perhaps.
The strength of this argument against Counterpart Theory obviously turns on the likelihood that Strong Transworld Identity is true. Before we turn to a worry about Strong Transworld Identity, however, we must explore how Abstractionists respond to the Leibniz's Law argument sketched above. One might think that it doesn't matter whether one is committed to Counterpart Theory. So long as Biden exists in more than one world, it can seem that one is committed to the claim that Biden both exemplifies and fails to exemplify the property of being a plumber. That's bad whether or not Counterpart Theory is true!
Importantly, Abstractionists do not think that Biden actually exemplifies the property of being a plumber, and Abstractionists all agree that the only Biden that exists in any sense is the actual Biden. Biden fails to exemplify the property of being a plumber but does exemplify the properties of being represented by w as a plumber and of possibly being a plumber. Further, had w been actual, Biden himself would have existed and would have exemplified the property of being a plumber and the property of being represented by α as not being a plumber. Nothing identical to Biden actually exemplifies the property of being a plumber. That claim is not, according to Abstractionists, the denial of the claim that w-Biden is identical to α-Biden. Abstractionists commit to the claim that w-Biden is identical to α-Biden. The trick is that say that w-Biden actually exists and deny that w-Biden exemplifies the property of being a plumber! w-Biden just is Biden, and Biden doesn't exemplify the property of being a plumber. w-Biden (= Biden) would have been a plumber, had w been actual. It is Biden himself who is represented by both w and α. The problem, then, lies in the move from the fact that w represents Biden as a plumber to the claim that w-Biden exemplifies the property of being a plumber. That move only works if one is thinking as Concretists do, that possible worlds have as parts objects exemplifying all their properties like Biden himself. Since Abstractionists deny that this is so, they can elude the Leibniz's Law argument.
The Atlas of Reality Page 58
