Truthmakers or truthmaking supervenience?

I argue that counterpart theory is incompatible with truthmaking supervenience, the thesis that truth supervenes on what there is and how things are. I further argue that David Lewis’s “qua” strategy for providing ontologically innocent and Humean-friendly truthmakers for predications faces a number of difficulties. I propose and assess various solutions to those difficulties, each of which comes at the cost of sacrificing one of the two main virtues of the qua strategy.


Introduction
According to truthmaker theory, every truth is made true by some entity, and a truth is made true by an entity only if that entity necessitates the truth. But exactly which entities do the truthmaking? Consider the truth that Fido is brown. Some maintain that it is the state of affairs somehow involving Fido and brownness that makes it true that Fido is brown, for the state of affairs cannot exist without the proposition being true. 1 Others maintain that it is the trope that is the exact shade of brown of exactly Fido, for the trope cannot exist without the proposition being true. 2 Even more problematic cases, such as universal generalizations (e.g. that all water is composed of hydrogen) and negative truths (e.g. that there are no unicorns), have been assigned truthmakers, e.g., in terms of negative and totality facts. These cases, but even the less problematic ones as well, have led many to believe that truthmaker theory comes with an ontological cost, for it commits one to the existence of dubious entities such as negative facts. Nevertheless, many have been allured by the intuitive and theoretical charm of truthmaker theory. David Armstrong, for instance, uses it as one of his main arguments for states of affairs and claims that "to raise the truthmaker question […] makes for ontological honesty" (Armstrong 2004, p. 43). Theodore Sider similarly suggests that the demand for truthmakers is a way to catch "cheats"-any theory that fails to provide legitimate truthmakers for what is by its own lights true hasn't paid its ontological due. 3 David Lewis objects to truthmaker theory, not on purely ontological grounds, but because he thinks it requires a rejection of Hume's famous dictum that there be no necessary connections or exclusions between distinct existences-any distinct (i.e. mereologically non-overlapping) things can coexist or fail to coexist with each other. Yet the state of affairs of Fido's being brown, for instance, seems to require the existence of Fido and seems to exclude the possible state of affairs of Fido's being black. Lewis therefore asks why we should defy our intuition that a negative existential is true "not because things of some kind do exist, but rather because counterexamples don't exist" and that predications seem to be true "not because whether things are, but because how things are". 4 In other words, truthmaking doesn't require truthmakers, it requires only that truth somehow supervene on what there is and how things are. It is here where Lewis endorses a retreat from truthmaker theory to truthmaking supervenience. 5 Following Lewis (Lewis 2001), let us formulate truthmaker theory in terms of explicit quantification over worlds and propositions: (TM) For any proposition P and any world w, if P is true in w, there exists something T in world w such that for any world v, if T exists in v, then P is true in v. 6 As we just noted, Lewis rejects (TM) in favor of the following ontologically safer and allegedly more Humean-friendly truthmaking supervenience principle: (TM=) For any proposition P and any worlds w and v, if P is true in w but not in v, then either something exists in one of the worlds but not in the other, or 3 See Sider (2001, pp. 40-41). 4 See Lewis (1992, p. 216). 5 The following kinds of truths have cast doubt on the plausibility of truthmaker theory: predications, such as 'Fido is brown' (where single quotes name propositions rather than sentences); negative predications, such as 'Fido isn't red'; negative existentials, such as 'There are no talking donkeys'; universals, such as 'Everything is material'; past and future tensed propositions, such as 'Socrates was wise'; and necessities, such as '2 + 2 = 4' or 'Possibly, Fido is black'. On (1), see e.g. (Mulligan et al. 1984), on (2) and (3) (Dodd 2007), on (4) and (6) (Armstrong 2004), and on (5) (Caplan and Sanson 2011). I am not here suggesting that there are no accounts of truthmaking that successfully deal with the above problematic cases. I am only indicating some sources of worry philosophers have expressed toward the tenability of truthmaker theory and why one might retreat to a weaker position or abandon truthmaking altogether. 6 This view might be restricted in various ways, e.g. to the contingent truths, or the positive truths, etc., and it can be stated without quantification over possible worlds and their inhabitants: necessarily, for any true proposition P, there is something T such that, necessarily, if T exists then P is true. While this formulation of truthmaker theory is simple, it has its drawbacks when taken unrestrictedly; e.g., it yields that every necessary truth is made true by everything. else some n-tuple of things stands in some fundamental relation in one of the worlds but not in the other. 7 Many of the problems that arise for (TM) are avoided by the retreat to (TM=). Indeed, one can be an anti-realist about all sorts of things-such as states of affairs or tropes, general, negative or totality facts, and past or future entities-all while maintaining truthmaking supervenience. If (TM=) captures our truthmaking intuitions just as much as (TM) (though this is debatable), then it is certainly the ontologically safer principle to accept. 8 Lewis originally had doubts about there being truthmakers for predications because he was wanted to remain neutral on the metaphysics of modality. But when he later abandons neutrality in favor of his preferred counterpart theory, he thinks he can "do better" by providing truthmakers for predications that are both Humean-friendly and ontologically innocent. If Lewis is right, he has succeeded in two respects where others have failed. First, he claims that his account is Humean-friendly while its competitors are not. Second, since he claims that the subject of the predication is its truthmaker, Lewis's account is nominalist-friendly and hence it is not committed to ontologically dubious entities.
In what follows, I argue that counterpart theory is incompatible with truthmaking supervenience, and that Lewis's counterpart-theoretic "qua" strategy for providing ontologically innocent and Humean-friendly truthmakers for predications faces significant difficulties. I propose and assess two separate variations of the qua strategy, but conclude that each comes with significant costs. Lewis (2001) endorses the retreat to (TM=) partly because he thinks there are no plausible Humean-friendly truthmakers for predications such as 'Fido is brown', let alone for negative predications and negative existentials. Suppose there is a truthmaker for 'Fido is brown'. Then there would be a necessary connection between it and Fido, for the truthmaker couldn't exist without Fido existing. If the truthmaker and Fido are non-overlapping, as they are according to many accounts, then we have a violation of Humeanism. 9 Even if one could find a plausible Fido-overlapping truthmaker for 'Fido is brown', this will not help with the problem of necessary exclusions that arise. For if there is something that is a possible truthmaker for 'Fido is black', then it could not possibly coexist with a truthmaker for 'Fido is brown', whence a violation of 7 See Lewis (2001). It is important to restrict (TM=) to the fundamental relations, for otherwise the principle comes out trivial on certain sparse conceptions of properties. For if P is true in w but not at v (and necessarily, something exists), then trivially there is something at w but not v that instantiates the property of being such that P. The motto that truth supervenes on being is sometimes reserved for the stronger principle that if P is true then either an entity exists that wouldn't were P false, or else an entity fails to exist that would were P false; see Bigelow (1988). While this principle is less contentious than (TM) as regards negative existentials, it otherwise faces the same objections. 8 Some who have endorsed the retreat to (TM=) include Lewis (2001), Dodd (2002), Crisp (2007), Hornsby (2005), and Melia (2005). 9 For Armstrong, e.g., the state of affairs of Fido's being brown does not contain Fido as a mereological part, whence the two are distinct.

Truthmaking supervenience and counterpart theory
Humeanism. As Lewis remarks concerning Armstrongian totality facts as truthmakers for negative predications and negative existentials, "the idea [behind Humeanism] was that anything can exist with anything, yet these totality facts have as their raison d'etre to refuse to coexist with other facts" (Lewis 1992, p. 217). 10 Does this rule out truthmaking for the Humean? Lewis thinks not, for he thinks that our truthmaking intuitions are satisfied by truthmaking supervenience according to which the truth of 'Fido is brown' depends merely on Fido's being brown and not on some further entity. 11 To show that this retreat will not work for the counterpart theorist, we need to look at two separate versions of the theory, the first being Lewis's original presentation of Lewis (1968) and the second being the purely qualitative counterpart theory endorsed in Lewis (1986, Sect. 4.4) as a way of obtaining haecceitistic possibilities without a genuine commitment to haecceitism. 12 According to the 1968 theory, Lewis endorsed the following axiom: (P5) Nothing is a counterpart of anything else in its world.
Even though Lewis later rejects (P5) as a postulate, he still thinks that some determinations of counterparthood will satisfy (P5), which is why it is important to discuss both versions of the theory. Note that (P5) does not rule out the having of multiple counterparts within a world, which will become important later. Now suppose ours is a world of one-way eternal recurrence, and that Lewis inhabits the first epoch. Even though Lewis has intrinsic duplicates in every other epoch, P5 prohibits any of them from being his counterpart. This entails that the actual world represents concerning Lewis that he inhabits the first epoch and that he does not inhabit the second. 13 Now consider a world qualitatively indiscernible from ours. Each of its epochs contains a duplicate of Lewis that qualifies as his counterpart, so this world represents concerning Lewis that he does inhabit the second epoch. Therefore, it is false according to our world and true according to the indiscernible other that Lewis inhabits the second epoch-in other words, we have a difference in truth without a difference in whether or how things are, and hence a counterexample to (TM=).
There are two ways to avoid this violation of (TM=) in the context of 1968 counterpart theory. First, deny that there exist distinct, indiscernible worlds. Second, reject (P5) and allow things to have distinct, worldmate counterparts. The first is not an option for Lewis since he wishes to remain agnostic on the existence of indiscernible worlds, but the fact that he is agnostic also makes the failure of (TM=) in the context of counterpart theory [cum (P5)] hostage to the existence of such worlds. If they exist, 10 For a detailed discussion concerning Humeanism and truthmaking, see Cameron (2008). 11 As a referee of this journal points out, this sounds just like Armstrong's position, according to which 'Fido is brown' is made true by Fido's being brown, which is a state of affairs. Lewis agrees that his position and Armstrong's are not so different. However, in constrast with Armstrong, Lewis does not believe that Fido's being brown is some further entity distinct from Fido and brownness or their sum. 12 For Lewis, haecceitism is the view that two worlds may differ in what they represent de re concerning an individual without differing qualitatively. It is thus the denial of a supervenience thesis less general than (TM=). 13 A referee suggests that it is a confusion to speak of worlds, rather than e.g. sentences, as representing anything. I don't think this is the only legitimate understanding of representation, but in any case I am simply following Lewis here in speaking of worlds as representing that a certain proposition be true or, concerning an individual, that it have a certain property.
(TM=) fails. But the mere consistency and coherence of their existence should give the counterpart theorist a reason to doubt the truth of (TM=). The first option will not help in any case for two reasons. First, the intuition underlying truthmaking supervenience is undermined as long as two worlds could differ in what they make true concerning the intrinsic nature of their duplicate parts. For instance, imagine a world of eternal recurrence that is a duplicate of ours save for an extra atom out in causal isolation. Since Lewis has a duplicate in each epoch, as he did in the exact duplicate world, that world represents concerning Lewis that he inhabits an epoch other than the first, and so the truth of a proposition concerning only a certain spatiotemporal region fails to supervene on that region. Surely that goes against truthmaking supervenience intuitively conceived. 14 Second, given that counterparthood is non-functional, possibilities cannot be worlds and, as I will now argue, any adequate account of possibilities for a counterpart theorist must render (TM=) false.
While the first option will not help in saving (TM=), there might be hope for the second option. Indeed, Lewis explicitly rejects (P5) in favor of what he calls the "cheap substitute" for haecceitism because he thinks there are compelling cases of haecceitistic possibilities, such as Lewis possibly having been someone else, call him 'Fred' or, as with the example above, Lewis possibly having been one of his distinct counterparts in another epoch. 15 But he does not think these possibilities are accounted for in terms of indiscernible worlds that represent differently concerning some individual, for he thinks that representation de re supervenes on the qualitative. Once (P5) is banished, we can say e.g. that the possibility that Lewis be Fred is got from our own world all by itself; for on a liberal counterpart relation according to which all it takes for something to qualify as a counterpart of Lewis is that it be human, our very own Fred counts as a counterpart of Lewis. Such a haecceitistic possibility does not require an indiscernible world where the individual thisnesses of Fred and Lewis are swapped, and so it does not require what Lewis calls "mysterious" determinants of counterparthood.
However, once we drop (P5) in favor of qualitative counterpart theory, it becomes even clearer that we can no longer identify worlds with possibilities. For the actual world represents concerning Lewis that he is not Fred, and it also represents concerning Lewis that he is Fred, and these two possibilities are incompatible. Since the actual world does not represent inconsistently concerning Lewis, it becomes clear that it is not a world by itself that does all the representational work, i.e., it is not a world by itself that corresponds to a possibility in the relevant sense. 16 This much Lewis admits 14 A first pass at a better formulation of truthmaking supervenience for the counterpart theorist is the following: (TM= ) For any proposition P and any worlds w and v, if P is true in w but not in v and concerns only spatiotemporal region R, then either (i) R has no v-counterpart, (ii) something exists in exactly one of R or its v-counterpart, or (iii) some things in R stand in some fundamental relation whose v-counterparts fail to stand in the same relation in R's v-counterpart, or conversely.
The main disadvantage of (TM= ) over (TM=) is that it depends on spelling out what it means for a proposition to concern only some spatiotemporal region, but this poses no problem provided we have an account of intrinsicality at hand, such as Lewis's duplication account; see e.g. Lewis (1986, pp. 61-62). 15 See Lewis (1986, pp. 226-233) for more examples.
since a context is also required to determine a counterpart relation, but even a world and a counterpart relation will not suffice to give us a possibility. Lewis takes this to be a cost of the cheap substitute, but one worth its price, for it gives us haecceitistic possibilities without having to posit mysterious determinants of counterparthood. The cost comes by "making a break with established theory, on which all differences between possibiltiies are supposed to be differences between possible worlds" (Lewis 1986, p. 235). However, he thinks that in most cases one world provides at most one possibility for a given individual: The exceptions come only if we get multiple counterparts within a world, either because we have an uncommonly repetitious world or because we use an uncommonly lax counterpart relation. Therefore, for the sake of familiarity, I shall mostly revert to speaking of representation de re by worlds, or of what is the case about an individual according to a world. (Lewis 1986, p. 235) This is not exactly correct, however, since even in a world with twins, which need not be uncommonly repetitious like a world of recurrence is, we cannot speak of representation de re by worlds. 17 If a possibility cannot be a world, nor a world plus a counterpart relation, exactly what is a possibility according to counterpart theory? One way of understanding a possibility in the context of counterpart theory is as a counterpart function c telling us for each world what exists according to it. Let c(w, x) = y mean that y is the unique w-counterpart of x. 18 Since possibilities are not worlds, and since (TM=) is ultimately a thesis about the supervenience of truth according to a possibility, it needs a slight reformulation: (TM=*) For any proposition P and any two possibilities, if P is true according to one but not the other, then either something exists according to one but not the other, or else some n-tuple of things stands in some fundamental relation according to one but not the other.
However, once we reformulate the truthmaking principle this way so that it is neutral on what possibilities are, it is again made false, not just by counterpart theory cum (P5) plus the assumption that there are indiscernible worlds of eternal recurrence, but by qualitative counterpart theory without any assumption about the existence of indiscernible worlds. For suppose ours is a world of one-way eternal recurrence. Let c and c be exactly alike except that c(@, Lewis) = Lewis and c (@, Lewis) = Ludwig, where Ludwig is a counterpart of Lewis from another epoch. Then these possibilities are qualitatively indiscernible even though they differ in what they represent concerning Lewis: one represents of him that he inhabits one epoch, and the other represents of him that he inhabits another. In other words, we have a counterexample to (TM=*) 17 There are many other cases that yield multiple counterparts within a world which do not require an uncommonly repetitious world or an uncommonly lax counterpart relation. For example, just consider two nearby hydrogen atoms. 18 Counterpart functions will be defined from a given counterpart relation. They will also be partial, since everything needn't be represented at a given world. The value of c(w, x), when it has one, is an inhabitant of w, and it is not required that when x is an inhabitant of w, that c(w, x) = x. This gives us the possibility, e.g., that c(@, Lewis) = Fred, for @ the actual world.
that does not depend on assuming the existence of indiscernible worlds of eternal recurrence. I conclude that truthmaking supervenience is incompatible with counterpart theory, qualitative or not, and independently of whether or not there are indiscernible worlds. The counterpart theorist could avoid this problem by requiring that counterparthood be functional, but such a requirement comes at the cost of giving up virtually all of the flexibility and advantages of counterpart theory.

Truthmakers and counterpart theory
Lewis originally had doubts about there being truthmakers for predications because he was trying to remain neutral on the metaphysics of modality, but when he later abandons neutrality in favor of his preferred counterpart theory, he thinks he can "do better". 19 Consider the truth that Fido is brown and the entity Fido qua brown, as Lewis puts it. Fido qua brown just is Fido, claims Lewis, but because of the way he's picked out, he has only brown counterparts-that is, Fido qua brown is essentially brown. Fido qua brown therefore necessitates the truth that Fido is brown, and that is good enough for Lewis to dub him a truthmaker for 'Fido is brown'. Fido just as he is is also a truthmaker for the proposition (assuming color is intrinsic), and indeed for any true intrinsic predication concerning Fido. Finding truthmakers for extrinsic predications turns out to be a special case of finding truthmakers for intrinsic predications. The truthmaker for 'John is taller than Jane' is, for instance, the sum of John and Jane just as they are. Negative existentials, argue Lewis and Rosen, are covered by considering the intrinsic nature of the world: 'There are no talking donkeys' is made true by the world qua lacking talking donkeys. (TM) is thus vindicated. 20 By giving us truthmakers that are Humean-friendly and ontologically innocent, Lewis thinks he has done better, and indeed, he will have since, as I have argued, counterpart theory is incompatible with truthmaking supervenience. Without truthmakers, the counterpart theorist would be forced to give up truthmaking altogether. 21 But does the qua strategy work? Lewis portrays truthmaking as a relation between a thing and a proposition. He says: One way for the truth of a proposition to supervene on being is for that proposition to be made true, in any world where it is true, by a truthmaker. If a is a possible individual and P is a proposition, call a a truthmaker for P just in case every world where a exists is a world where P is true. By 'world where a exists' I mean, of course, 'world where a has a counterpart'. (Lewis 2003, p. 28) However, given Lewis's strategy for providing truthmakers for predications, it seems he cannot treat truthmaking as such. For Lewis wants to maintain the following apparently mutually inconsistent claims: 1. Fido is not a truthmaker for 'Fido is brown'; 2. Fido qua brown is a truthmaker for 'Fido is brown'; 3. Fido just is Fido qua brown.
If truthmaking predications are referentially transparent, then Fido is a truthmaker for 'Fido is brown' iff Fido qua brown is, assuming the two are identical. Thus, the only way to consistently maintain all three claims is to deny either (i) that truthmaking contexts 'o makes true P' are referentially transparent (in their first argument), (ii) that Fido qua brown is the truthmaker for 'Fido is brown', or (iii) that Fido is identical to Fido qua brown. The last option is, I believe, a non-starter, for it takes away any reason we have for thinking that qua expressions even refer, and it also strips the account of its alleged friendliness to Humeanism and nominalism. I will therefore address only the first two options. 22 (i) Intuitively, whether an object makes true a proposition is a de re modal property of the object, and on a standard account of de re modality, de re modal predications are referentially transparent. Whether it is true of an object that it has a certain modal property does not, on a standard account, depend on how the object is named. That is what justifies the claim that one cannot substitute coreferring terms within a de dicto context such as 'Necessarily, t is greater than seven', but that one can substitute coreferring terms-rigid or not-into a de re context, such as 'It is necessary of t that it is greater than seven'. 23 Counterpart theory deviates from a standard account of modality by allowing that de re modal contexts, like de dicto ones, be referentially opaque. It can be true to say of an object that it can survive squashing when picked out by 'the statue' but false to say the same thing of the same object when picked out by 'the lump'. Similarly, it may be false to say of Fido that he is essentially brown when he is picked out by 'Fido' but true to say of him that he is essentially brown when picking him out by 'Fido qua brown'. And if it is true of him that he is essentially brown under some expression, then it is true on a simple (TM) conception of truthmaking that Fido is-under some expression-a truthmaker for the fact that Fido is brown. Or so says the qua strategy.
According to Lewis's original 1968 presentation of counterpart theory, de re modal predications are always referentially transparent because whether an object has a counterpart in a world does not depend on how the object is named. However, Lewis later abandons transparency in defense of materialism. For he claims that, necessarily, a person and their body are identical, but also that a person could have had a different 22 Thanks for a referee for prompting me to elaborate on the first. 23 See e.g. Smullyan (1948). body (at a time) than they actually have (at that time). How? A person can have both a personal counterpart and a bodily counterpart that exist in the same world and yet are distinct. The same trick gives us a solution to the monist's more general problem of maintaining that a thing is identical to its constituent matter. While Lewis does not make much of this embracement of de re modal opacity, it is a significant cost of his defense of monism (and materialism). For it brings de re and de dicto modality and on a par by stripping the former of its distinguishing characteristic. It allows one to question whether de re predication is, according to counterpart theory, genuinely de re-i.e. genuinely of the object and hence independent of the way it is named.
In response to this objection, Lewis says: [I]n the present revision of counterpart theory, de re modal predications are not in general transparent […] Nevertheless, these modal predications are still de re, not de dicto. We still find the denoted thing in our actual world and then find counterparts of that thing elsewhere. We do not at all consider the things denoted by the subject term in other worlds, as we would in the case of a de dicto modal predication. (Lewis 1971, p. 211) However, while Lewis is right that there is a distinction here, it does not alleviate the worry that allegedly de re modal contexts on a counterpart-theoretic analysis resemble de dicto ones in that both are sensitive to the way things are named, a feature that, on the standard account, is what separates de re from de dicto modal contexts. While this is not a definitive reason to reject modal analyses that posit de re opacity, it does provide a reason to prefer analyses that do not, all else being equal. Similarly, if truthmaking predications are intuitively transparent, then there is some-though not a definitive-reason to prefer an account that does not posit opacity. Lewis motivates opacity by way of various examples, the most persuasive of which concerns material coincidence. Suppose we have a statue, Goliath, and we ask whether Goliath could have survived squashing. Intuitively, the answer is "no". However, if we ask whether Goliath's material constituents could have survived squashing, the answer is "yes". One who believes in the identity of a thing with its material constituents and who wants to account for the difference in judgment here will have to posit the opacity of de re modality. However, I don't think the opacity of truthmaking contexts can be similarly motivated. Part of the problem concerns the expression 'Fido qua brown'. Intuitively nothing is essentially brown, and intuitively we are not free to name things in a way that secures their having certain features essentially. Moreover, if anything were intuitive, it would be that Fido qua brown makes true 'Fido qua brown is brown', a concern I will return to shortly. Another part of the problem concerns the fact that 'makes true' is technical jargon we may lack intuitive judgments about.
Lewis sometimes suggests that de re modal predications can be opaque (what he calls 'inconstant') by denying that such predications play the sort of explanatory role many associate with certain modal predications. For instance, according to counterpart theory, the fact that an object could survive squashing does not depend on intrinsic features of the object the having of which sheds light on why the object has the property rather than not. The modal fact simply depends on a subjective way of looking at the object that makes salient certain features rather than others. However, among those who take truthmaking seriously it is common to assign truthmaking predications a privileged explanatory role, which is why almost no truthmaker theorists will take seriously a conception of truthmaking according to which the fact that something is a truthmaker for a proposition depends on how that thing is named. It certainly does not strike us as informative to say that the reason 'Fido is brown' is true is not because of Fido, but because of an identical dog, Fido qua brown. 24 In his discussion of truthmaking supervenience, Lewis has claimed that truthmaking predications need not be explanatorily informative, but his reasons for denying their informativeness are unconvincing. He says: Martin has noted that when I say that a negative existential truth is true for lack of falsemakers, my statement that there are no falsemakers is itself a negative existential (Martin 1996, p. 61). Sometimes, in fact, as in the case of the proposition that there are no unicorns, it is the very same negative existential. So the proposition that there are no unicorns is true just because there are are no unicorns! What sort of explanation is that?-No explanation at all, I agree. But who says a Truthmaker Principle, whether weakened or not, must yield informative explanations? I say to Martin: Tu quoque! His original, full-strength Truthmaker Principle says that a positive existential, for instance the proposition that there is a cat, is true because it has a truthmaker. The statement that it has a truthmaker is itself a positive existential. In fact, it is the very same positive existential. The proposition that there is a cat is true just because there is a cat. What sort of explanation is that?-No explanation at all, and none the worse for that. (Lewis 2001, pp. 611-612) First, however, a positive existential such as 'There is a cat' isn't true just because there is a cat, it is made true by the existence of particular cats such as Garfield, Fifi, and so on. Each truthmaking predication 'Garfield makes true 'There is a cat", 'Fifi makes true 'There is a cat", and so on, yields a genuinely informative explanation as to why the positive existential is true, and so Lewis's tu quoque fails. Second, when Lewis said 'There are no unicorns' is true for lack of falsemakers, he was not offering an informative truthmaking explanation-indeed, he was denying that there is one. Third, and this is an ad hominem, if truthmaking predications need not yield informative explanations, why care about truthmaking? In particular, why devote effort to defending truthmaking supervenience and and to providing truthmakers for simple predications? Why not just say that 'Fido is brown' makes true that 'Fido is brown' and leave it at that? Lewis has no reason to deny, in the way he suggests, the informativeness of truthmaking, and I don't think that he should. 25 Taking de re modal predication to be opaque does not require taking truthmaking predications to be, even if one analyses the latter in terms of the former. For this reason it would be beneficial to the counterpart theorist to assess some proposals that 24 One could say that because (i) Fido qua brown makes true 'Fido is brown' and (ii) Fido qua brown is Fido, we are entitled to say that Fido does indeed make true 'Fido is brown'. However, by analogous reasoning we would be entitled to say that Fido qua brown does not make true 'Fido is brown' because (i) Fido does not make true 'Fido is brown' (which Lewis accepts) and (ii) Fido is Fido qua brown. Given opacity, it only makes sense to speak of an object under a mode of presentation as making true a proposition or not. 25 However, for further considerations, see MacBride (2005, pp. 133-139). maintain the spirit of the qua strategy but which do not render truthmaking contexts referentially opaque. This is what I will therefore pursue in the remainder of the paper. The assessment of these proposals should therefore be seen as a friendly service to the counterpart theorist.
(ii) The simplest way to avoid inconsistency, on the now active assumption that truthmaking contexts are transparent, is to treat truthmaking as a relation between propositions, given the natural correspondence between an individual and the proposition claiming the individual to exist. 26 The truthmaker for 'Fido is brown', then, isn't Fido qua brown, but rather the proposition that Fido qua brown exists. Clearly on this view the propositions 'Fido qua brown exists' and 'Fido exists' need to be distinct to allow that only one of them serve as a truthmaker for 'Fido is brown', and indeed they are distinct for the counterpart theorist since they are true in different worlds.
This raises a complication. If propositions are truthmakers that necessitate contingent propositions, then they cannot necessarily exist. For if 'Fido qua brown exists' necessarily exists and if it were to make true-and hence necessitate-'Fido is brown', then 'Fido is brown' would be necessarily true. Indeed, propositions that are truthmakers can only exist at worlds at which they are true. This would make truthmakers as propositions on the qua theory look very much like Armstrongian states of affairs, and it is not a view of propositions that Lewis himself held. I will at any rate set this complication aside since it can be avoided in various ways and since there are more substantial worries for this proposal.
Having to give up that the truthmakers for predications are their subjects is a significant cost for Lewis. First, because truthmaking is intuitively a relation between possibly non-propositional objects, such as dogs, and propositions, and Lewis wants to preserve this pretheoretic intuition. Second, because Lewis touts as an advantage of the qua strategy over Armstrong's theory that it is the subject of a predication that is its truthmaker rather than some potentially dubious entity such as a state of affairs. On the first point, Lewis says: Imagine something, call it Long qua black, that is very like Long in most ways, but differs from him in essence. Long is accidentally black, and might have been striped, orange all over, or even green. Long qua black, however, is essentially black. Long has counterparts of many colours, whereas all counterparts of Long qua black are black. Indeed, the counterparts of Long qua black are all and only the black counterparts of Long. Long qua black, if there were such a thing, would be a truthmaker for the truth that Long is black […] If wishes were horses, we would believe in these qua-versions of things, and they would serve nicely as truthmakers for intrinsic predications. Since wishes are not horses, what reason have we to believe in these novel and peculiar entities we have just imagined?
[…] I deny that Long qua black is a novel and peculiar sort of thing. Long qua black is none other than Long himself. (Lewis 2003, pp. 30-31) It is clear that if there were such a thing as Long qua black, it would be a truthmaker for the essential predication 'Long qua black is black'. What is not clear is that it would also be a truthmaker for the inessential predication 'Long is black'. It does not help to say that Long qua black just is Long, for the missing premise is obviously that every world according to which Long qua black exists is a world according to which Long exists, that is, that every counterpart of Long qua black is a counterpart of Long. If the identity gave us that, since identity is symmetric, it would also give us that every counterpart of Long is a counterpart of Long qua black, which it does not. So on what grounds can Lewis claim that every counterpart of Long qua black is a counterpart of Long? He could appeal to the way the name is formed which intuitively makes salient a certain feature of Long and not potentially some other individual, and so it evokes a counterpart relation according to which Long has only black counterparts. But this bit of reasoning could be questioned for a number of reasons. Even if one holds e.g. that statues are identical to their constituents-say that Goliath, a statue, and Goliath qua lump of matter, its constituents, are identical-the fact that the qua name makes salient certain features of Goliath (viz. that it is a mere lump of matter) does not imply that a counterpart relation is evoked according to which every counterpart of Goliath qua lump of matter is a counterpart of Goliath. Indeed, many counterparts of Goliath qua lump of matter will not be counterparts of Goliath because they survive squashing while Goliath cannot. The mere syntax of the qua expression is insufficient to give Lewis what he needs. Indeed, Lewis in effect stipulates that the qua expression has the referent it does, but one might even question the content of this stipulation. For if one does not believe in things that are essentially brown-intuitively, what could be essentially brown?-or at least if one does not believe in essentially brown dogs, then one could simply deny that the expression 'Fido qua brown' picks out anything. Moreover, one might argue that if the expression picks out Fido, then it does not pick out something that is essentially brown, since Fido is not. Lewis clearly has a very liberal view about the kinds of essences that are instantiated; for any object o and property φ that it possibly has, there is the object o qua φ which possibly exists and has φ essentially. I will, however, bracket this issue.
Let us return to the cost of taking truthmakers for predications to be something other than the subjects of those predications. One might think that this cost is insignificant because, first, most other theories have the same commitment. For example, it is popular to take truthmakers to be tropes or states of affairs, neither of which are the subjects of typical predications. Second, there is a natural correspondence between a thing and the proposition stating that that thing exists. The problem for Lewis, however, is that he touts it as an advantage of the qua strategy that truthmakers for predications just are their subjects. 27 When comparing his view to Armstrong's, Lewis says: So in the end, the only difference I can find between Armstrong's proposal and mine is that I claim in full generality, and Armstrong claims only in a special case, that the truthmaker for a true predication is identical with the subject of that predication. (Lewis 2003, p. 35) But as we have seen this is not an advantage Lewis can tout, since the proposition that Long qua black exists is not the subject of the predication. So as far as that point is concerned, the victory goes to no one. This is a significant cost for Lewis since it undermines two main advantages of the strategy: (i) that the truthmaker of a predication is ontologically innocent, and (ii) that it is Humean-friendly. For propositions are ontologically more suspect than typical subjects of predications such as Fido, and the proposition that Fido qua brown exists cannot possibly coexist with the (possible) proposition that Fido qua black exists. 28 Recall that the problem with most other truthmaker theories, according to Lewis, is that they are not Humean-friendly. For instance, the trope that makes true that Fido is brown could not exist without Fido and it could not coexist with a possible trope making 'Fido is black' true, even though the two may be wholly mereologically distinct. 29 But we should now ask ourselves how the qua strategy is any better off even if we forget for the moment that truthmakers for predications are propositions and grant with Lewis that they are the subjects of predications. For Fido qua brown and the merely possible Fido qua black cannot coexist either. In defense of the qua strategy, Lewis will of course appeal to the fact that we can freely recombine duplicates of Fido qua brown and any merely possible Fido qua black, and that this is the relevant sense in which there is no necessary exclusion between the two. 30 But the same holds regarding certain competitor theories; for instance, duplicate tropes of this particular brown of Fido and that particular black of merely possible Fido can equally coexist. We should be skeptical, then, whether the alleged Humean-friendliness of the qua strategy is really an advantage it has over its competitors. 31 A more significant worry concerns taking propositions to be truthmakers on the qua strategy. For this move is simply unfeasible given most accounts of what propositions are. Lewis in particular takes propositions to be sets of worlds, so the proposition that Fido is brown is the set of worlds at which Fido is brown. This proposition is supposed to be made true by the proposition that Fido qua brown exists, but that proposition is identical to the set of worlds at which Fido is brown. So according to the most natural rendering of the qua strategy, the truthmaker for a predication is the very predication itself, and since predications like 'Fido is brown' don't make themselves true, the most natural rendering of the qua strategy does not succeed. 32 It does not matter that Lewis takes propositions to be sets of worlds. On any account of propositions according to which the proposition 'Fido qua brown exists' is the same proposition as 'Fido is brown', the strategy fails. And even according to an account 28 Even if we grant Lewis that the truthmaker for a non-relational predication like 'Long is black' is its subject, the strategy does not to work for relational predications like 'John is taller than Jane'. For the subject of that predication is John, but its truthmaker according to Lewis is the sum of John and Jane. 29 According to some trope theories, the trope can exist without Fido existing. But then the trope cannot serve as a truthmaker for the predication, since it would not necessitate its truth. That is why we can safely ignore such theories. 30 See Lewis (1986, pp. 87-89) concerning Lewis on Humeanism which he spells out in terms of duplication: two distinct things can coexist if there is a world in which intrinsic duplicates of them exist, and they can fail to coexist if there is a world in which duplicates of them fail to coexist. 31 See Cameron (2008) for additional challenges to Lewis's claim that the qua strategy holds an advantage over its competitors as regards Humeanism. Lewis later notes, in Lewis (2015), that the "mysterious connections" objection to tropes and states of affairs fails if the essences of these entities are analyzed counterpart-theoretically. 32 There may be special cases in which a predication makes itself true, such as the truthteller or 'This proposition exists'. But ordinary predications such as 'Fido is brown' are not like these.
whereby the two are distinct, it does not follow that it will be plausible to take one to be the truthmaker for the other. For example, on a Russellian view of propositions according to which Fido qua brown, existence is distinct from Fido, brownness , it is not plausible that the former serve as a truthmaker for the latter because the former is identical to Fido, existence which does not necessitate the truth of the latter.
Another potential way of saving the qua strategy runs as follows. Instead of taking 'Fido qua brown exists' to be the truthmaker for 'Fido is brown', take the sum of all Fido qua brown's counterparts (i.e. the sum of all brown counterparts of Fido) to be a truthmaker. In effect, we take the truthmaker for 'Fido is brown' to be the intensional, rather than extensional, referent of 'Fido qua brown'. Since the intensional referents of 'Fido' and 'Fido qua brown' differ, there is no issue in having just one of them serve as the truthmaker for 'Fido is brown'. This transworld individual (as Lewis calls them) is not-according to Lewis anyway-what is referred to by 'Fido' or 'Fido qua brown', but it overlaps entirely at our world with Fido. 33 Since the sum does not wholly exist in any one world, (TM) needs to be adapted for this to work. First, call the sum of counterparts of a thing (relative to a name) a *-individual, which we may refer to by starring the thing's name. Thus the sum of counterparts of Fido qua brown we refer to by 'Fido qua brown*'. 34 Then truthmaker theory for counterpart theory we may formulate as follows: (TMCT) For any proposition P and any possibility w, if P is true in w, there exists a *-individual T with a modal stage in w such that for any possibility v, if T has a modal stage in v, then P is true in v. (We should also demand that T correspond to the subject of the predication by requiring that every modal stage of T is a modal stage of the subject.) In other words, a transworld individual necessitates the truth of a proposition if wherever it has a modal stage, the proposition is true.
There is a sense in which this account does justice to the intuition that truthmakers for predications are their subjects because Fido and Fido qua brown* entirely overlap at our world. If ordinary objects like Fido were transworld sums, a view Lewis considers and rejects, then the truthmaker for the predication would not be its subject since Fido* is distinct from Fido qua brown*. 35 But again, since these two transworld individuals entirely overlap at our world, there is still a good sense in which the two are identical, for they are identical when we restrict our attention to the inhabitants of our world.
Would Lewis accept the resulting account of truthmakers for predications? Likely not, for even though he believes in the existence of transworld sums since he believes in unrestricted mereological composition, he denies that ordinary objects are transworld sums and suggests that such sums have no interesting theoretical role to play. 36 However, let me briefly list some reasons for thinking otherwise. First, transworld sums can 33 See Lewis (1986, Sect. 4.3) for Lewis's attack on the idea that ordinary objects are transworld sums. 34 There are two assumptions made concerning the counterpart relation that unites *-individuals: it is symmetric and satisfies (P5); see Lewis (1986, Sect. 4.3). 35 Contra Lewis, see e.g. Wallace (2014) and Graham (2015) for arguments in support of the claim that ordinary objects are transworld sums. A sustained defense of the thesis can be found in Yagisawa (2010). As far as I know, the idea that ordinary objects be transworld sums was first discussed and rejected by Quine (1976). 36 See Lewis (1986, Sect. 4.3). serve as truthmakers for predications as we have just seen. The transworld sum corresponding to Fido qua brown is distinct from the transworld sum that is Fido, which explains how exactly one of them can serve as the truthmaker for 'Fido is brown'. Second, one solution to the problem of coincidence is to say that the statue and the lump of clay from which it is formed are distinct transworld sums, and this is why they can have different modal properties. This solution to the problem of coincidence exactly mirrors the perdurantist solution to the problem of temporary intrinsics that Lewis defends. 37 Third, one solution to the Humphrey objection that does not beg the question against the modal realist is to say that Humphrey is a transworld sum, and so he himself literally does exist at more than one world in much the same way the perdurantist says he exists at more than one time. 38 Fourth, one might think that the argument from vagueness that motivates the thesis of temporal parts (i.e. perdurantism) can be paralleled to provide an argument that motivates the thesis of modal parts (i.e. the modal analog of perdurantism), at least if one is already willing to accept modal realism. 39 Let us pause to take stock. Unsatisfied with truthmaker theory, Lewis retreats to truthmaking supervenience as a safer alternative. However, Lewis's retreat, he claims, rested on his remaining neutral on the metaphysics of modality. He then argues that once he abandons neutrality in favor of counterpart theory, he has the resources to provide truthmakers for predications (and, perhaps, negative existentials). However, Lewis's qua strategy yields that Fido is not a truthmaker for 'Fido is brown', that Fido qua brown is, and yet that Fido and Fido qua brown are identical. In order for these three claims to be consistent, the qua strategy must render truthmaking contexts referentially opaque. Since this is a major drawback of the strategy, I proposed maintaining transparency by considering two variations of the qua strategy. The first was to take truthmakers to be propositions, e.g. the proposition that Fido qua brown exists, but that this requires giving up Lewis's alleged advantage that truthmakers for predications are their subjects. I then argued that this move fails in any case because the proposition 'Fido qua brown exists' is the same proposition as 'Fido is brown', and propositions such as these do not make themselves true. The second was to take transworld individuals to be truthmakers and adopt (TMCT). Thus the truthmaker for 'Fido is brown' is the sum of brown counterparts of Fido, i.e. the intensional referent of 'Fido qua brown'. Since this object entirely overlaps Fido at our world, there is a good sense in which the truthmaker for the predication just is its subject.
in modal truth without a change in anything because there can be no change in modal truth. Because of this, Lewis restricts his attention to contingent truths. 40 However, since counterparthood need be neither symmetric nor transitive, it allows for contingent modal truth. Thus, when Lewis abandons neutrality for counterpart theory, he can no longer ignore truthmaking for modal truths.
Consider the following entities called 'ab', 'bc', and 'cd' composed entirely of a and b, b and c, and c and d respectively. Suppose that ab inhabits w, bc inhabits u, and cd inhabits v, and that one is a counterpart of the other just in case they share a part. Finally, suppose that all of ab's counterparts, i.e. ab and bc, have the property φ but that not all of bc's counterparts have it. The situation is consistent with counterpart theory and can be depicted as follows (omitting arrows for reflexivity): Then it is true in w that ab is essentially φ, but false at u that ab is essentially φ. For instance, φ might be the property of having either a or b as part. Thus even if ab is intuitively a truthmaker for the proposition that ab is essentially φ, ab cannot, according to (TM), be its truthmaker since not all of its counterparts make it true, i.e. ab does not necessitate its truth. In other words, in the context of counterpart theory, the subject of a predication 'x is essentially φ' may fail to be its truthmaker even when x is the truthmaker for the essential predication 'x is φ', and this is certainly counterintuitive.
Qua expression to the rescue? While ab just as it is can't be a truthmaker for the fact that ab is essentially φ, what prevents us from saying that ab qua essentially φ is the truthmaker? This makes the modal and amodal cases analogous, for the relevant predicate in the modal case is 'is essentially φ', so it should be used in the qua expression. There may, however, be an important difference between the modal and amodal cases that concerns whether the counterpart relation evoked by a 'qua essentially φ' expression counts as a genuine counterpart relation. In discussing whether the qua strategy is a cheat, Lewis considers whether we can say that, for any individual x and property φ, x qua unaccompanied by φs is a truthmaker for the truth that there are no φs. If it were, the qua strategy would extend in a trivial way to negative existentials. However, he says: It should be obvious that this is just a cheap trick, and does not give the friends of the Truthmaker Principle what they wanted. But why is it any worse than my own proposal for truthmakers for predications? Answer: because the 'peculiar counterpart relation' is so very peculiar as not to be a genuine counterpart relation at all. The 'similarity', if we may call it that, between things that are unaccompanied by unicorns is, in the first place, one that would strike us in almost any context as an utterly unimportant similarity. It is, in the second place, an entirely extrinsic similarity. (Lewis 2003, p. 32) One may find this unconvincing for a number of reasons. First, because as far as peculiarity goes, a counterpart relation relative to which a dog (i.e. Fido qua brown) is essentially brown is just as peculiar as one relative to which something is essentially unaccompanied by unicorns-intuitively, nothing is essentially brown and nothing is essentially unaccompanied by unicorns. Moreover, the similarity between things that are irregularly shaped would strike us in almost any context as utterly unimportant even if it is intrinsic, and yet Lewis will want to say that the truthmaker for 'Fido is irregularly shaped' is Fido qua irregularly shaped. Second, how could an entirely subjective and loose notion like non-peculiarity be a requirement on counterparthood? Third, if it is intrinsic properties that matter when forming qua expressions-though I cannot see why, since extrinsic similarity is often important to determining counterparthood-one could argue that the property of being essentially φ is intrinsic, e.g. when φ is intrinsic. For the counterpart theorist, this will be difficult, however, since the property of being essentially φ is the property of having only counterparts that are φ, and that property, being a relation that holds between wholly distinct things, is intuitively extrinsic. 41 So if there are grounds for dismissing the qua strategy as applied to contingent modal predications as a cheap trick, it seems to lie in the fact that the similarity involved is extrinsic. If these grounds are good, there is a large and important class of contingent predications that are left unaccounted for by the qua strategy. 42 There may be a way out. Let us consider a more ordinary modal truth, e.g., that Hubert Humphrey could have won the election. What is its truthmaker? 43 Certainly not Humphrey, for he lost the election and a losing Humphrey all by himself does not, according to counterpart theory, make true (let alone necessitate) the truth that he could have won. Perhaps it is Humphrey qua winner since every world in which Humphrey qua winner exists is a world in which it is true that Humphrey could have won the election. The problem is that Humphrey qua winner doesn't exist at our world to secure the truth here. But why is this a problem? The existence of Humphrey qua winner at any world is enough to secure the truth here. Unfortunately (TM) and (TMCT) demand that the truthmaker for the actual truth exist in the actual world (in the case of (TMCT), by having a modal stage at our world).
Clearly these formulations of truthmaking aren't cut out for the task when it comes to modal truths since they require that if P is true in w, then the truthmakers for P be drawn from w. But whatever the truthmaker for the fact that Humphrey could have won is, it is not to be found in our world. This suggests doing away with one requirement of (TMCT) to obtain the following: 41 We might also ask whether the property is intrinsic or not according to Lewis's preferred account of intrinsicality according to which a property is intrinsic iff it never differs among duplicates. Many modal properties relative to certain contexts won't count as intrinsic on the duplication account either; see De (2016) for details. 42 See Cameron (2008, pp. 30-31) for related discussion.
(TMCT*) For any modal proposition P and possibility w, if P is true in w, there exists a *-individual (which needn't have a stage in w), such that for any possibility v, if T has a modal stage in v, then P is true in v.
(TMCT*) yields, e.g., that the intensional version of Humphrey qua winner is a truthmaker for the fact that Humphrey could have won, as we had previously hoped. Note that (TMCT*) is restricted to modal truths, for we would not want a non-modal proposition that is actually true, say that Fido is four-legged, to be made true by something that does not actually exist, such as the sum of counterparts of Fido qua black and fourlegged, which, like the sum of counterparts of Fido qua four-legged, also necessitates the truth of 'Fido is four-legged'.

Final remarks
Lewis once said that he did not think that taking naturalness of properties as primitive held any advantage over taking similarity of tropes as primitive. 44 The desire to satisfy truthmaking intuitions may give him, and the counterpart theorist more generally, an argument for adopting tropes and primitive similarity over primitive naturalness.
Recall that it was suggested that tropes fail to provide Humean-friendly truthmakers for predications because, e.g., Fido's brownness here and now cannot coexist with his possible blackness here and now. We noted, however, that this sense of necessary exclusion is irrelevant to Humeanism, for otherwise the same necessary exclusion holds between Fido qua brown and Fido qua black. What makes the qua strategy Humean-friendly is that duplicates of Fido qua brown and Fido qua black can coexist, and the same is true concerning the allegedly incompatible tropes. And since taking tropes to be truthmakers is free of the specific problems that plaque the qua strategy, one could recommend that the counterpart theorist with a desire to meet truthmaking demands strongly reconsider their primitives, especially given the other work that trope theory can do.
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