| P a g e FICTIONAL REALISM AND INDETERMINATE IDENTITY Brendan Murday Ithaca College To appear in Journal of Philosophical Research Department of Philosophy and Religion Ithaca College 953 Danby Road Ithaca, NY 14850 bmurday@ithaca.edu Abstract: Fictional realists hold that fictional characters are real entities. However, Anthony Everett ["Against Fictional Realism", Journal of Philosophy (2005)] notes that some fictions leave it indeterminate whether character A is identical to character B, while other fictions depict A as simultaneously identical and distinct from B. Everett argues that these fictions commit the realist to indeterminate and impossible identity relations among actual entities, and that as such realism is untenable. This paper defends fictional realism: for fictions depicting non-classical identity between A and B, the realist should hold that there are two salient fragments, one with a single character (named both „A‟ and „B‟) and the other with two (named „A‟ and „B‟, respectively). Truth according to the fiction depicting indeterminate identity is determined by supervaluating over truth according to those salient fragments. For fictions depicting impossible identity, truth is determined by subvaluating over truth according to those two salient fragments. 2 | P a g e I. INTRODUCTION The following statement intuitively expresses a truth: (1) Sherlock Holmes is a fictional character. This claim entails the existentially quantified claim there exists a fictional character. If we embrace the Quinean approach to ontological commitment, we can thereby motivate the "fictional realist" position according to which fictional characters are real, where one of them is the referent of „Sherlock‟ as used in (1). A popular version of this fictional realism specifies that fictional characters are actual abstract objects, which are depicted by the story as exemplifying various properties. 1 Significantly, fictional realism is not motivated by sentences like (2) Sherlock is clever. That sentence also entails that there is something that is clever. But it is easy enough to say that while (2) is true according to the Conan Doyle stories, it is not true simpliciter; in denying that (2) is true simpliciter, there is no longer any reason to believe that (2) motivates realism about fictional characters. That dodge is not available in the case of (1); (1) is not merely true according to a certain story, since the Conan Doyle stories represent Sherlock as a real person, not as a fictional character. (1) is true simpliciter, and (1) entails there exists a fictional character. We have found that what motivates realism about the fictional character is not how the fiction depicts Sherlock, but that there is a fictional character that is depicted in some way or other. 2 Anthony Everett (2005) observes that in some fictions it is metaphysically indeterminate whether a character exists; in others it is indeterminate whether character A is identical to character B; in still others, it is both true and false that A is identical to B. As we will see, 3 | P a g e Everett argues that these cases threaten fictional realism; in each case, the realist is pressured to say that the indeterminacies and impossibilities apply to actual entities. Realism thus stands in danger of having implausible metaphysical consequences. 3 Schnieder and von Solodkoff (2009: 140) draw a further distinction; where Everett speaks of fictions in which it is indeterminate whether A is identical to B, Schnieder and von Solodkoff distinguish two situations. A fiction might directly specify that the character Alwin is indeterminately identical to the character Miki. In such a case, one would say that according to the fiction bivalence is violated –the fiction explicitly represents the proposition Alwin=Miki as being neither true nor false. Alternatively, a fiction might leave open the relationship between Alwin and Miki in the fiction; here the fiction fails to specify a truth-value for the proposition Alwin=Miki. These cases merit separate discussion. In §3 and §4 we will develop a realist account of fictions that explicitly depict an indeterminate identity in a fiction, while taking care to address Everett‟s objection. §5 we will extend this account to fictions that leave open the truth value of an identity statement in the fiction, and §6 will address more complex examples. Each of these sections will indicate as well how a parallel treatment can be offered for cases where a character is depicted as existing indeterminately or where the character‟s existence is left open. Finally, §7 develops an account of fictions that represent an identity between characters as being simultaneously true and false. II. A REALIST PROPOSAL Consider a story (due to Schnieder and von Solodkoff (2009: 141)) featuring an indeterminate identity: Bah-Tale 2 There once was a man called Bahrooh 4 | P a g e There once was a man called Bahraah But nothing determined if Bahraah was Bahrooh Or if they were actually two. According to Bah-Tale 2, Bahraah is indeterminately identical to Bahrooh. (This indeterminacy is not epistemic; the narrator is not merely ignorant of the identity relation between Bahraah and Bahrooh.) Everett‟s objection to fictional realism presupposes that the realist will accept the following principle: (P2) If a story concerns a and b, and if a and b are not real things, then a and b are identical in the world of the story iff the fictional character of a is identical to the fictional character of b. (Everett (2005: 627)) (P2) applied to Bah-Tale 2 poses a problem for the fictional realist in the following way: Bahraah is a character in the story; the same can be said about Bahrooh. The realist posits an actual abstract object corresponding to Bahraah, and an actual abstract object corresponding to Bahrooh. But is there just one abstract object thereby posited, or are there two? Since Bahraah is indeterminately identical in the story to Bahrooh, the realist appears to be committed to indeterminate identity among actual abstract objects. For those unwilling to countenance indeterminate identity in the actual world, this result is unacceptable. A realist could bite the bullet and accept real indeterminate identity, but most will be reluctant to abandon the classical notion of identity. And as Everett (2005: 633) observes, even if she were willing to countenance indeterminate identity, she might blanch at the suggestion that metaphysical indeterminacy can be created simply by composing a story. The question at hand, then, is whether a fictional realist can respond to Everett while forswearing any commitment to actual ontological indeterminacy. Schnieder and von Solodkoff (2009: 143) propose the following revision to (P2): where two names are used in the fiction, those names designate distinct fictional characters unless the fiction explicitly represents them as co-referring. Bah-Tale 2 fails to explicitly represent 5 | P a g e „Bahraah‟ and „Bahrooh‟ as co-referring, so the names designate distinct characters, albeit ones who are represented by the fiction as indeterminately identical. This approach ensures that there is always a determinate fact of the matter how many abstract objects actually exist, even if it is indeterminate in the story how many characters there are. Schnieder and von Solodkoff propose an analogous solution for Everett‟s other cases as well: if a fiction fails to specify whether Alwin is identical to Miki, or if it depicts Alwin and Miki as simultaneously identical and distinct, the names designate distinct abstracta simply in virtue of the fact that they are distinct names. Caplan and Muller (forthcoming) object that Schnieder and von Solodkoff‟s approach is arbitrary in the following sense: there is an alternative principle 4 that would do the same explanatory work, and there is no basis to endorse one over the other. But it would be arbitrary to suppose in such a scenario that one principle correctly answers ontological questions while the other principle is incorrect. One could forestall this problem by embracing the original (P2), avoiding any appeal to a default principle regarding whether indeterminate identities in the fiction constitute representations of a single character or representations of distinct characters. Such an account will be presented in §4, after clarifying some preliminaries in §3. III. BACKGROUND FOR A RIVAL REALIST PROPOSAL Let us stipulate some background claims for the account to be developed. In writing The Da Vinci Code, Dan Brown created a fictional character. This fictional character is a simple abstract object; it is depicted by the work of fiction as having many properties: being named „Robert Langdon‟, being a Harvard professor, foiling a sinister plot, and so forth. The simple abstract object counts as a fictional character in virtue of being depicted by a fiction as exemplifying various properties. In addition to creating the simple abstract objects that count as 6 | P a g e fictional characters, Brown created a complex abstract object that counts as the fiction itself. For present purposes, we can construe this abstract object as a set of propositions. 5 The abstract object named by „The Da Vinci Code‟ is the set of propositions whose constituents include the following: A [the abstract object that is the fictional character Brown created] is named 'Robert Langdon'. A is a Harvard professor. A travels to Paris. There exists a secret society dedicated to keeping secrets about the Catholic Church. ... Prefixed sentences, those of the form ┌ According to the story, Langdon is F ┐ , are true in virtue of the way the story depicts the fictional character. For instance, „According to The Da Vinci Code, Langdon is a Harvard professor‟ is true in virtue of the fact that the fiction depicts A as being a Harvard professor. Un-prefixed sentences, those of the form ┌ Langdon is F ┐ , are true in virtue of the character (the abstractum) itself. So „Langdon is a fictional character created by Brown‟ is true in virtue of the properties of the character, whereas „According to The Da Vinci Code, Langdon is a fictional character created by Brown‟ is false. Since Brown has authored multiple books featuring the Langdon character, the realist should say that Brown has created multiple abstracta depicting the character as exemplifying certain properties. Because these multiple books form a series, it may be useful to think of fictions as (at least potentially) complex abstracta. „The Robert Langdon series‟ names a fiction comprising various fictions; The Da Vinci Code is one of the latter fictions. 6 7 | P a g e The Robert Langdon series constitutes a series of books. Since each book is identified as a set of structured propositions, it would be natural to suppose that the series is the set of all propositions that compose each individual book. But while this might be the right way to think of a series, there are situations where a corpus is not simply the sum of its constituents; in the case of fan fiction, a story inherits truths from other works in the corpus (and hence belongs to the corpus in some sense), but not everything true-in-the-fan-fiction is thereby true-in-thecorpus. Accordingly, we should not legislate that truth-according-to-a-corpus is necessarily the sum of all truths-according-to-its-parts. Instead, the corpus is constituted by both the constituents and the specific relationship the constituents have to the whole, where the nature of that relationship is explicable in terms of the relationship between the truths-according-to-thecorpus and truths-according-to-the-constituents. In what follows we will find it useful to suggest that truth-according-to-a-fiction need not be equated with the truth of the propositions that constitute the fiction. IV. INDETERMINATE FICTIONAL IDENTITY The fictional realist can account for Bah-Tale 2 as follows: in writing the story, the author has created a set whose members are the following structured propositions, where „A‟, „B‟, and „C‟ name three distinct simple abstract objects: (BT1) A is called 'Bahraah' (BT2) A is called 'Bahrooh' (BT3) B is called 'Bahraah' (BT4) C is called 'Bahrooh' (BT5) Bahrooh = Bahraah (BT6) Bahrooh ≠ Bahraah In this case, however, what is truth according to the story is not simply these six propositions. Instead, we must identify two subsets of the created set: the subset "X", which has as members 8 | P a g e propositions (BT1), (BT2), and (BT5), and subset "Y", which has as members propositions (BT3), (BT4), and (BT6). We might think of X and Y as "salient fragments" of the complex abstract object that the author created. X is a fragment according to which there is exactly one character, and no indeterminacy is depicted; Y is a fragment according to which there are exactly two characters, and no indeterminacy is depicted. Although the set containing propositions (BT1)- (BT6) is the complex abstract object created by the author, truth-in-Bah-Tale-2 is not simply the fictional truth of (BT1)-(BT6). Just as a series is composed in some way of constituent books, Bah-Tale 2 is a fiction composed of X and Y. Unlike a series, however, where truth-in-the-series is [typically, at least] the sum of all truths-in-each-book, truth-in-Bah-Tale-2 is defined by supervaluating 7 over the truths according to X and Y respectively. Consider a statement made outside of the content of the fiction, such as the following as uttered by a literary critic: (3) The fictional character Bahraah is identical to the fictional character Bahrooh. There is a precisification of the names such that (3) is true and a precisification such that (3) is false, and hence through supervaluation the truth of (3) is indeterminate. This indeterminacy is purely a semantic matter of the referents of „Bahraah‟ and „Bahrooh‟; A, B, and C determinately constitute three characters. Thus the realist can explain how the identity statement (3) is indeterminate without any commitment to metaphysical indeterminacy. 8 A complication arises when considering a statement (again external to the content of the fiction) explicitly concerning indeterminate identity: (4) The fictional character Bahraah is indeterminately identical to the fictional character Bahrooh. The referents of the two names are semantically underdetermined, but neither precisification of the names suggests that (4) expresses a truth, since A is determinately self-identical while B and 9 | P a g e C are determinately distinct. Intuitively, (4) is true, but the supervaluationist technique does not offer a path to sustaining that intuition. The realist can motivate her account of (4) by reminding us of the context of Evans‟s (1978) argument; consider: (5) Bahrooh is determinately self-identical. [i.e., Bahrooh is determinately identical to Bahrooh.] (6) Leibniz‟s Law is true. [i.e., if A and B do not exemplify all and only the same properties, then A and B are determinately non-identical.] There is a tension between (4)-(6); we cannot embrace all three statements, though each of the three statements is intuitively plausible. It is thus common ground to all theories that some intuition must be denied. To be plausible, any reconciliation of this tension should explain why the false statement seemed to be true. The supervaluationist can accomplish this by denying (4), but embracing the claim that (3) is indeterminate. (3) is literally indeterminate on the supervaluationist framework, since on one precisification of the names the identity claim is true, while on the other precisification the identity claim is false. The realist who adopts the supervaluationist approach can thus offer an error theory for our intuition that (4) expresses a truth – we may equate the literal truth of (4) with the indeterminate truth of (3), but Evans‟s argument constitutes a surprising philosophical discovery that these are not equivalent. 9 Evans shows us that the indeterminate identity relation cannot possibly be exemplified, even though identity statements can be indeterminate. The semantic indeterminacy serves to explain why we thought an indeterminacy obtains. This develops the supervaluationist strategy for un-prefixed statements about the characters; what of claims about the characters as depicted by the story? The title „Bah-Tale 2‟ 10 | P a g e determinately refers to the set containing (BT1)-(BT6) with the specification that truth-in-BahTale-2 is determined by supervaluating over particular salient fragments of that set. Supervaluation is thus invoked in two ways: the truth-value of ┌ According to Bah-Tale 2, p ┐ is determined by supervaluating over truth-according-to-X and -Y, and the truth-value for statements of the form ┌ Bahraah is F ┐ is determined by supervaluating over the precisifications of „Bahraah‟, i.e., A and B. Consider, then: (7) According to Bah-Tale 2, Bahraah is identical to Bahrooh. X depicts Bahraah and Bahrooh as identical, since the two names as used in X co-refer to A. Y depicts Bahraah and Bahrooh as distinct, since the two names in Y refer respectively to distinct abstracta B and C. Thus X and Y assign different truth-values to the embedded statement „Bahraah is identical to Bahrooh‟, and so (7) is evaluated as indeterminate. This captures our intuitive judgments about (7), since any acceptable account of Bah-Tale 2 should tell us that (7) is neither determinately true nor determinately false; in addition, the supervaluationist obtains this result while maintaining (P2) and avoiding commitment to any metaphysical indeterminacy. Matters are again more complicated with sentences explicitly invoking indeterminacy: (8) According to Bah-Tale 2, Bahraah is indeterminately identical to Bahrooh. 10 There is a temptation to say that (8) is true, and as with (4), the supervaluationist will struggle to accommodate that intuition. X does not depict A as indeterminately self-identical, and Y does not depict B as indeterminately identical to C, so the identity claims A=A and B=C each have a determinate truth-value in the respective fragments X and Y. The supervaluationist is thus unable to say that (8) literally expresses a truth. We noted in the previous paragraph that any acceptable account should grant that (7) is indeterminate; should we not also require that (8) come out true? 11 | P a g e As with (4), the realist should begin by noting that every theory must abandon one of a few claims that intuitively seem true. We motivated the denial of (4) by arguing that we can make our peace with abandoning (4) once we note that we can maintain that (3) is indeterminate, and that this verdict captures the fact that our intuitions were tracking. In making that argument, it was clear that abandoning (5) or (6) would have done even more violence to our intuitions than denying the truth of (4). In the case of (8), the parallel argument will be slightly more complicated, but it will take the same form. The statements that are jointly inconsistent with (8) are: (9) According to Bah-Tale 2, Bahrooh is determinately self-identical, i.e., Bahrooh is determinately identical to Bahrooh. (10) According to Bah-Tale 2, Leibniz‟s Law is true, i.e., if A and B do not exemplify all and only the same properties, then A and B are determinately non-identical. (11) If p and q are each true according to Bah-Tale 2, then the conjunction of p and q is true according to Bah-Tale 2. (12) According to Bah-Tale 2, Bahraah and Bahrooh are not both indeterminately identical and determinately distinct. Each of (8)-(12) has intuitive merit, but no view can allow that all five statements are true. Let us first consider why each statement is intuitively true. (8) seems true because the fiction explicitly says "nothing determined if Bahraah was Bahrooh / Or if they were actually two"; as we noted above (see note 5), we may not always hold that a proposition explicitly expressed in the story counts as true in the fiction, but we will surely do so in the vast majority of cases. (9) is not explicitly expressed in the story, but surely there is no temptation to think that distinct uses of the name „Bahrooh‟ in the story fail to co-refer. The fiction depicts something odd in the relation 12 | P a g e between Bahraah and Bahrooh, but the narrator takes great care to use distinct names in expressing the oddness; that suggests that the state of affairs depicted in Bah-Tale 2 is different from the state of affairs depicted in Bahrooh 2: Bahrooh 2 There once was a man called Bahrooh, But nothing determined whether Bahrooh was one individual or two. According to Bahrooh 2, Bahrooh is perhaps not determinately self-identical; in considering Bah-Tale 2, however, (9) seems true. Bah-Tale 2 does not literally express (10) either, but since nothing is said in the story about the principles of identity that hold in the fiction, a plausible account of truth-in-fiction will suggest that the actual principles of identity are imported into the story. Since Leibniz‟s Law is a fundamental principle of identity, we expect that it is true in the fiction unless the story gives us strong reason to believe otherwise, and nothing in Bah-Tale 2 provides such a reason. As for (11), if truth in the fiction is not closed under conjunctive entailment, it will be hard to understand how to make sense of truth-in-fiction at all. It is certainly implausible to suppose that truth-in-fiction is closed under deductive entailment in general, but when p and q are each true in the fiction, we will surely want to hold that p and q is true in the fiction. Finally, the last line in Bah-Tale 2 seems to entail that (12) is true in the fiction. If in the story nothing determines whether Bahrooh and Bahraah are one or two individuals, then in the story they are not determinately two individuals. No one can maintain all of (8)-(12), despite the fact that intuitions support each of them. One might think that (8) and (12) are the strongest intuitions, since those are the two propositions that seem supported by explicit statements in the text. If that were the only consideration in debating which intuition to abandon, we might conclude that (9) or (10) is the best proposition to 13 | P a g e identify as false. But at issue is not just which intuition is strongest; we must also consider the strength of the explanation we can give for why that intuition should be abandoned, and what approximations of the intuition we can maintain. As with (4), we can identify an approximation of (8) that can be maintained even if we rule that (8) is false: (13) It is indeterminate whether According to Bah-Tale 2, Bahraah is determinately identical to Bahrooh. The realist who adopts the supervaluationist maneuver and hence rules (8) false can suggest that the truth of (13) captures the fact that we were latching onto in thinking that (8) is true. We can take Evans‟s argument as showing that our intuitions about indeterminate identity are easily misled – intuitively we would have thought it conceptually possible for the indeterminate identity relation to be exemplified, but that argument revealed that the relation is more strange than we would have thought. (8) and (13) turn out to be inequivalent, contrary to initial impressions. So there is an error-theoretic explanation that can be offered for our intuition that (8) is true. It is much harder to give such an explanation for (9) and (10), which express relations so commonplace that all actual entities satisfy them. Ruling (8) as false is a cost of the realist theory, but it is the least costly concession that can be made given the inconsistence of (8)-(12). 11 Let us turn to other worries; consider: (14) Bah-Tale 2 has three characters. One might worry that the supervaluationist has to say that (14) is true, since (BT1)-(BT6) feature three characters. The supervaluationist is not committed to the truth of (14) however, because (as suggested in §3), for a fiction to have a character is for it to depict a character as exemplifying properties. The facts about how Bah-Tale 2 depicts matters are determined by 14 | P a g e supervaluating over how X and Y depict matters, and neither X nor Y represents three characters as exemplifying properties. One might worry instead that the supervaluationist must say that no characters exist according to the story; after all, since Y does not represent A as exemplifying properties, the supervaluationist will surely deny: (15) A is a character in Bah-Tale 2. Any value replacing „A‟ in (15) generates the same result, since X and Y have no characters in common. But to conclude that Bah-Tale 2 thereby has no characters would run afoul of a de dicto / de re ambiguity. No character is such that it is depicted by both X and Y as exemplifying properties, but X and Y both depict some character or other as exemplifying properties. Thus while the supervaluationist denies (15), she does not say that according to the story no characters exist. Now consider the following, all of which intuitively express truths: (16) It is indeterminate whether Bahraah is Bahrooh. (17) In writing Bah-Tale 2, the author has created no more than two characters. Schnieder and von Solodkoff‟s proposal suggests that (16) is false, though they explain away that result by saying that while Bahraah is determinately distinct from Bahrooh, the story represents the identity of those characters as being indeterminate. Their proposal does imply that (17) is true. The supervaluationist, on the other hand, easily explains the truth of (16), but she says that (17) is false -she counts A, B, and C as characters. Is it unacceptably counterintuitive to say that (17) is false? 15 | P a g e The supervaluationist can motivated her denial of (17) by calling our attention to the way in which an author creates a story with indeterminate identity. If all indeterminacy is semantic, then for any indeterminacy there must be multiple candidate referents to generate the indeterminacy. There must be a candidate referent who is distinct from another candidate referent, and a candidate referent who is not distinct from any salient candidate. Thus the author must create three characters to ground the way Bah-Tale 2 depicts matters. The supervaluationist thus has points to offer in defense of denying (17). Schnieder and von Solodkoff‟s denial of (16), however, is harder to accept. Because Bahraah and Bahrooh are characters in Bah-Tale 2, and because Bah-Tale 2 explicitly represents the identity of Bahraah and Bahrooh as indeterminate, the realist should want (16) to come out true. Schnieder and von Solodkoff cannot accommodate this result; the supervaluationist can. Supervaluationism thus offers a more attractive account of Bah-Tale 2. We have been addressing a fiction where an identity statement is indeterminately true in the fiction. There are also fictions where the existence of a character is explicitly indeterminate. The supervaluationist machinery will handle such a case in parallel fashion: if it is indeterminate whether Steve exists according to a fiction, we can suppose that the author has created a set of structured propositions with two salient fragments X and Y, where X features a character A that is represented as the extension of „Steve‟, and Y depicts „Steve‟ as extensionless. When we supervaluate over X and Y, the sentence „According to the fiction, Steve exists‟ comes out indeterminate. V. UNDERSPECIFIED FICTIONAL IDENTITY Let us now consider a fiction that leaves open whether certain identity relations obtain: 16 | P a g e Frackworld No one was absolutely sure whether Frick and Frack were really the same person or not. Some said that they were definitely two different people. True, they looked very much alike, but they had been seen in different places at the same time. Others claimed that such cases were merely an elaborate hoax and that Frick had been seen changing his clothes and wig to, as it were, become Frack. All that I can say for certain is that there were some very odd similarities between Frick and Frack but also some striking differences. (Everett 2005: 629) Nothing suggests that according to the story it is metaphysically indeterminate whether Frick and Frack are identical. However, it is plausible to say that the story leaves open whether Frick and Frack are identical. One could take the narrator to be merely under-informed, and hence think that there is a fact of the matter in the story about which the narrator is ignorant, but this interpretation is not compulsory. The story itself fails to represent any identity relation obtaining between Frick and Frack, leaving open whether they are determinately identical, determinately distinct, or perhaps even indeterminately identical. While this is a different case than that of Bah-Tale 2, Schnieder and von Solodkoff ultimately offer the same solution for both types of fiction – there is a default presumption that an author has created two abstracta when she uses different character names, and this presumption bears out unless the fiction explicitly indicates that the two names designate the same individual in the story. Cameron (2013) finds Schnieder and von Solodkoff‟s explanation satisfying in this case, though he favors the supervaluationist approach for fictions like Bah-Tale 2. Having argued that supervaluationism is superior to Schnieder and von Solodkoff‟s account of Bah-Tale 2, a supervaluationist approach to both types of fictions is preferable over Cameron‟s two-pronged strategy for two reasons. Before we can examine those two reasons, however, we must first present the supervaluationist approach to this type of fiction. 17 | P a g e The supervaluationist account of this case begins as before: the author has created a set of propositions, including: (F1) A is depicted as being called 'Frick'. (F2) A is depicted as being called 'Frack'. (F3) Frick = Frack. (F4) B is depicted as being called 'Frick'. (F5) C is depicted as being called 'Frack'. (F6) Frick ≠ Frack. (F7): No one is absolutely sure whether Frick = Frack. (F8): Some think Frick ≠ Frack; Frick and Frack look alike. (F9): Frick and Frack have been seen in different places at different times. (F10): Some claim that when Frick and Frack have been seen in different places at different times, it was a hoax. (F11): Frick has been seen changing his clothes and wig to take on Frack's appearance. (F12): Frick and Frack share some odd similarities. (F13) Frick and Frack share some striking differences. There are two salient fragments, subsets of this set. X is the subset that is composed of propositions (F7)-(F13) and (F1)-(F3), and thus depicts a determinate state of affairs in which Frick is identical to Frack, where A is the character thus depicted. Y is the subset consisting of propositions (F7)-(F13) and (F4)-(F6), and thus depicts a determinate state of affairs in which Frick and Frack are numerically distinct, where B and C are respectively the depicted characters. But the account of Frackworld must differ in some respect from the account of Bah-Tale 2 to capture the difference between fictions depicting explicitly indeterminate identities and those depicting underdetermined identities. That difference need not be located in a difference in the ontology of created objects; it can be accounted for instead as a difference in what constitutes a sanctioned interpretation of the fiction in question. A reader who interpreted Bah-Tale 2 as representing exactly the state of affairs represented by X would be misinterpreting Bah-Tale 2. The author has presented Bah-Tale 2 in such a way that the only sanctioned interpretation of the author‟s creative endeavors is to take truth-in-Bah-Tale-2 to be determined by supervaluating over the states of affairs represented by 18 | P a g e X and Y. In a case like Frackworld, however, competing interpretations of the story have not been ruled out. Here, one might say that it is semantically indeterminate whether „Frackworld‟ refers to X or Y; the author has created both X and Y, each of which might be deemed a sanctioned interpretation of the story, and it is indeterminate which of these two objects is designated by the title „Frackworld‟. The contrast between Bah-Tale 2 and Frackworld can be summarized as follows: the author of Bah-Tale 2 has created a set of propositions where there is only one sanctioned interpretation of her efforts; ontologically, that fiction consists in the set of propositions (BT1)- (BT6) such that truth-in-Bah-Tale-2 is determined by supervaluating over the salient fragments X and Y. There are three simple abstracta A, B, and C, though the names „Bahraah‟ and „Bahrooh‟ fail to determinately latch onto any of those abstracta. The author of Frackworld, on the other hand, has created two (or perhaps three) sanctioned interpretations. The first two are the salient fragments (F7)-(F13) + (F1)-(F3) and (F7)-(F13) + (F4)-(F6) where truth in each of those fragments is determined in the normal way. The potential third sanctioned interpretation is the complete set of (F1)-(F13) where truth-in-the-interpretation is determined by supervaluating over the salient fragments. Truth-in-Frackworld is determined by supervaluating over truth-inthe-sanctioned-interpretations. Where all interpretations represent proposition p as true, then p is true-in-Frackworld; where the interpretations do not all represent p as having the same truthvalue, then p is left-open-in-Frackworld. The difference between Bah-Tale 2 and Frackworld is thus explained by whether or not X and Y are each sanctioned interpretations of the author‟s efforts. Once that difference is established, the supervaluationist machinery is employed in precisely the same way. 12 19 | P a g e This shows that the supervaluationist strategy can be applied to this sort of case. But why prefer the supervaluationist account? Compare Cameron (2013) on this question: In the case where the fiction simply leaves open the identity or distinctness of a and b it seems reasonable to think that reality settles the distinctness of the fictional characters: using different names creates a presumption that they do not co-refer – one that is easily defeated, of course, but presumably (since it leaves the issue open, ex hypothesi) the fiction does not defeat it, and hence it is plausible that in that case there really are two fictional characters. But to claim that distinctness is the default even when the fiction positively establishes the indeterminacy of the issue seems wrong: here the indeterminacy is a part of the fiction itself, and to hold to a presumption of distinctness in reality for these cases is no longer to simply have reality settle what was left open in a principled manner, it is for reality to overrule the fiction. (Cameron (2013: 188); underlining added for emphasis) Cameron thus advocates a mixed strategy in response to Everett‟s problem: adopt Schnieder and von Solodkoff‟s proposal for cases like Frackworld, but endorse the supervaluationist proposal for cases like Bah-Tale 2. If, as suggested in this section, the supervaluationist proposal can handle both cases, that approach would be preferable to Cameron‟s on grounds of theoretical economy. There is in addition a second reason to prefer the supervaluationist approach to Frackworld over Cameron‟s and Schnieder and von Solodkoff‟s proposal. The underspecification can be accounted for as a semantic indeterminacy -it is semantically indeterminate whether „Frackworld‟ names X or Y (or, again, perhaps the set-theoretic union of X and Y where truth in this interpretation is determined by supervaluating over X and Y). The fact that X and Y are each sanctioned interpretations of Frackworld mirrors the fact that X and Y are each candidate referents of „Frackworld‟. This allows us to explain the difference between fictions that explicitly depict an indeterminate identity and fictions that leave open the status of an identity – in the latter case, but not in the former, the title of the fiction is semantically underdetermined, such that X and Y are each candidate referents. In the former case, the title of the fiction determinately refers to the set-theoretic union of X and Y such that truth in the story is determined by supervaluation. 20 | P a g e The advantage here, as noted in §2, is that the supervaluationist can thus endorse (P2) without qualification. (P2) states: If a story concerns a and b, and if a and b are not real things, then a and b are identical in the world of the story iff the fictional character of a is identical to the fictional character of b. (Everett (2005: 627) Frackworld leaves open the identity of Frick and Frack; the supervaluationist approach to such fictions allows us to say the identity of Frick and Frack is left open, due to semantic indeterminacy. Thus the supervaluationist offers a way to stay closer to Everett‟s motivating principle. Schnieder and von Solodkoff (2009: 143) abandon this principle in favor of a weaker version in order to answer Everett‟s objections. The supervaluationist technique allows the realist to answer Everett‟s objections while endorsing his principle in its strongest version; this is an important advantage of the supervaluationist solution. There is one last point worth emphasizing. Every fiction leaves some questions open – the year of Sherlock‟s birth, Raskolnikov‟s favorite color, Iago‟s preferred breakfast foods, and so forth. In order to say that these facts are left open by the fiction, one might wonder whether we must suppose that the complete set of propositions created by Conan Doyle includes the propositions: A was born in 1880. A was born in 1879. A was born in 1878. Etc. One might think that the inclusion of these propositions in the set will be required in order for the supervaluationist to allow that the Sherlock stories leave open in which year Sherlock was born. But the supervaluationist need not require that these propositions are part of the set, because she 21 | P a g e does not need to appeal to supervaluationism to account for the fact that the story leaves open the year of Sherlock‟s birth. As noted above (see note 3), the problems raised by Everett for the realist are unique to indeterminate, underspecified, or impossible existence and identity in the fiction, not just any indeterminate, underspecified, or impossible predications in the fiction. (P2) tells us that indeterminate/underspecified identity in the story entails indeterminate/underspecified identity of fictional characters; it does not suggest that indeterminate/underspecified property-exemplification in the story entails indeterminate/underspecified property-exemplification by the actual entities the realist identifies as fictional characters. So the problems motivating the supervaluationist treatment are not as ubiquitous as one might have feared. VI. MORE COMPLICATED FICTIONS 13 Let us pause a moment to review. Bah-Tale 2 and Frackworld are respectively a fiction depicting metaphysically indeterminate identity conditions and a fiction with underspecified (i.e., epistemically indeterminate) identity conditions. While we have not considered in detail fictions with indeterminate or underspecified existence conditions for some character, we have observed 14 in passing how to apply the supervaluationist view to those cases: postulate two complex abstract objects corresponding to fragments of the complete set of propositions the author created. One of these fragments contains propositions that represent the character as existing (but no propositions that would make it true in the fragment that the character fails to exist), and the other fragment contains propositions that represent the character as failing to exist (but no propositions that would make it true in the fragment that the character exists). Supervaluating over these fragments allows us to say that the existence of the character is 22 | P a g e indeterminate or left open in the fiction as appropriate. In all four of these cases (indeterminate and underspecified identities, indeterminate and underspecified existence), the supervaluationist postulates one set of propositions with two salient fragments: a fragment representing the identity/existence as determinately obtaining, and a fragment representing the identity/existence as determinately not obtaining. One might wonder how to apply this framework to fictions that leave open (or represent an indeterminacy) when an identity/existence obtains, as opposed to whether an identity/existence obtains. Consider, for instance, the following story: Swampman Emerges There was once an uninhabited swamp. But then something strange began to happen – the water began to churn, and twenty years later, Swampman emerged. Not even God could say which moment during those twenty years was the first moment of Swampman‟s existence; because it happened so gradually, there was no fact of the matter. The only determinate facts concerning Swampman‟s emergence were that twenty years earlier, Swampman did not exist, and at the end of those twenty years Swampman did exist. Let us designate the time at which Swampman is specified as determinately not existing t0, and the time at which Swampman is specified as determinately existing tn. For all times between t0 and tn, Swampman Emerges represents the existence of Swampman as indeterminate. One might expect that we would treat Swampman Emerges by supposing that the author created a simple abstractum A depicted as Swampman, and a complex abstract object that is a set containing propositions like the following: (SE0) At t0, Swampman does not yet exist. (SE1) At t1, Swampman comes into existence. (SE2) At t2, Swampman comes into existence. .... (SEn-1) At tn-1, Swampman comes into existence. 23 | P a g e (SEn) Swampman exists at tn. (SEn+1) There are many uninhabited swamps. (SEn+2) The water in the swamp begins to churn at t0. (SEn+3) A is depicted as the referent of 'Swampman'. We might then say that truth-in-Swampman-Emerges is determined by supervaluating over a great many fragments: fragment X1 consisting of propositions (SE0) + (SE1) + (SEn)-(SEn+3), fragment X2 consisting of propositions (SE0) + (SE2) + (SEn)-(SEn+3), ... and fragment Xn-1 consisting of propositions (SE0) + (SEn-1) + (SEn)-(SEn+3). But as it turns out, the realist can offer a simpler account of Swampman Emerges. Consider the principle that motivates the problem for the realist: for identities that are left open or depicted as indeterminate, (P2) generates Everett‟s problem, but for fictions that leave open or depict as indeterminate whether a character exists, Everett begins by formulating the following principle: (P1) If the world of a story concerns a creature a, and if a is not a real thing, then a is a fictional character. Everett (2005: 627) Now distinguish between the following: (18) According to the fiction, character A indeterminately exists. (19) According to the fiction, character A indeterminately exemplifies feature F. (P1) and (18) combine to pose the challenge for the realist. (P1) and (19) do not; the realist is free to say that a fiction depicts a character as indeterminately exemplifying a property without having to say that there is in fact an actual abstract object that indeterminately exemplifies a property. Swampman Emerges suggests that it is indeterminate which time Swampman comes into existence. But it is perfectly determinate whether Swampman exists. Swampman Exists and 24 | P a g e (P1) thus do not pose even an initial problem for the realist; (P1) does not entail that there is a fictional character that indeterminately exists at any time. On the contrary, the character determinately comes into existence when the author creates the object, and determinately exists forever after. Swampman Emerges would pose an initial threat to the realist if she endorsed the following principle: (P3) If a story concerns a, and if a is not a real thing, then a exists at time t in the world of the story iff the fictional character of a exists at time t. But the fictional realist will have no inclination to endorse (P3). There is some time in the fiction at which Swampman indeterminately exists, but there is no actual time at which the simple abstract object A indeterminately exists. The facts about when the actual abstract object A exists are determined by the facts about the author‟s creative process, not by the content of the story. There is a related case that we might also consider: Swampman 3: One Million Swampmen There are one million uninhabited swamps in the world. Each swamp has a unique name. At one moment in time, something strange began to happen – the water in every single swamp began to churn. In that moment, it was indeterminate whether a swampman came into existence at each swamp. Any swampman who exists is named after the swamp from which it emerged. While it was indeterminate whether each of these one million swampmen came into existence, it was at least determinate that the existence of any one swampman was independent of the existence of any other swampman. After all, the swamps are spatially disconnected, and the events at one swamp had no causal or counterfactual dependence on the events at other swamps. Thus it was indeterminate not just whether any particular swampman came into existence; it was in addition indeterminate how many swampmen came into existence. The end. Here, the realist posits one million fictional characters, since each of the depicted swampmen are determinately distinct, insofar as they exist at all. We must also posit more than two salient fragments, since what is indeterminate is not just whether none or all of these million swampmen 25 | P a g e exist, but in addition whether exactly two swampmen exist, whether exactly three swampmen exist, etc. The realist thus needs one fragment [determinately] featuring exactly one character, a second fragment [determinately] featuring exactly two characters, and so forth all the way up to the one millionth precisification [determinately] featuring exactly one million characters. She gets that result by supposing that the created set of propositions includes a sequence of propositions such that each is a member of a distinct salient fragment: Exactly one swampman exists. Exactly two swampmen exist. ... Exactly one million swampmen exist. In addition, the set of created propositions includes propositions that are common to all salient fragments: There are one million swamps. The water begins to churn at each swamp simultaneously. Etc. From this set of propositions, there are one million salient fragments. Each salient fragment contains all of the common propositions and exactly one of the determinate existential claims. Truth in the story is determined by supervaluating over these salient fragments. VI. IMPOSSIBLE FICTIONAL IDENTITY Can the realist adapt the supervaluationist account for fictions depicting the facts about identity as inconsistent? Consider this story: Dialethialand 26 | P a g e When she arrived in Dialethialand, Jane met Jules and Jim. This confused Jane since Jules and Jim both were, and were not, distinct people. And this made it hard to know how to interact with them. For example, since Jules both was and was not Jim, if Jim came to tea Jules both would and wouldn‟t come too. This made it hard for Jane to determine how many biscuits to serve. Then Jane realized what to do. She needed both to buy and not to buy extra biscuits whenever Jim came. After that everything was better. (Everett 2005: 633-4) It is true in Dialethialand both that Jules and Jim are identical and that Jules and Jim are distinct. Schnieder and von Solodkoff hold that the abstract objects Jules and Jim are distinct, though represented by the story as being both identical and distinct. But as noted above, it is disturbingly arbitrary to say that the abstracta are unambiguously distinct; we might equally say that there is one object that is represented as being both self-identical and not self-identical. 15 The supervaluationist strategy offered in the previous sections can be applied here as well to questions about the reference of the fictional names „Jules‟ and „Jim‟. As before, the author has created an abstract object that is a set of propositions. From this set we can identify two salient fragments X and Y; X depicts just one abstract object A as exemplifying properties, whereas Y depicts two abstracta B and C as each exemplifying properties. X represents „Jules‟ and „Jim‟ as co-referring to A; Y represents „Jules‟ and „Jim as referring to B and C, respectively. The names „Jules‟ and „Jim‟ are thus semantically underdetermined, just like the names in Bah-Tale 2 and Frackworld. The name „Dialethialand‟ is not semantically underdetermined; it does not name either of the salient fragments X or Y. It names instead the complete set of propositions constituted by the set-theoretic union of the propositions in X and Y, with a specification about how truth-in-the-story is determined. However, the supervaluationist explanation of truth in the fiction cannot be applied here. 16 That strategy offers a way of accounting for truth-value gaps, but in Dialethialand some identity both does and does not obtain. And those facts cannot be 27 | P a g e exported to the actual world, since few would want to say that actual objects are simultaneously identical and distinct. Fictional realists should explain truth in this sort of fiction by appeal to subvaluation over truth-according-to-X and -Y. 17 Where X represents p as being true, that is sufficient for p to be true according to the story. Similarly, where Y represents p as being true, that too is sufficient for p to be true in the story. For the most part, X and Y represent the same propositions as being true. They differ, however, with respect to how they represent facts about Jules and Jim. It is true in the story that Jules and Jim are identical, in virtue of the way that X represents the identity facts. It is also true in the story that Jules and Jim are distinct, in virtue of the way Y represents the identity facts. Thus it is true in the story both that Jules and Jim are identical and that they are distinct. But there are no impossible identity facts in the actual world – there are three abstracta depicted as exemplifying properties. Fictional realists should thus treat stories with indeterminate identity and stories with impossible identity differently; although in both of the examples discussed above the author creates two abstracta depicting exemplifications and three abstract thus depicted, truth-in-Bah-Tale-2 is determined by supervaluation while truth-inDialethialand is determined by subvaluation. Of course, some stories may depict both indeterminate identities and impossible identities. One might worry in that case that the realist would be unable to explain both features simultaneously, since she would have to choose between supervaluationism and subvaluationism. Closer inspection, however, reveals that the problem can be easily solved. Suppose an author writes a story combining the details of Bah-Tale 2 and Dialethialand. We need supervaluation to capture the indeterminate identity depicted in the former, and subvaluation to capture the impossible identity depicted in the latter. We get what we need by 28 | P a g e supposing that the author has created four salient fragments W, X, Y, and Z. W depicts the character A as the extension of both „Bahraah‟ and „Bahrooh‟, and depicts the character C as the extension of both „Jules‟ and „Jim‟. X features A depicted as Bahraah, B depicted as Bahrooh, and C depicted as Jules and Jim. Truth according to the W-X amalgamation is determined by supervaluating over W and X, generating a complex in which it is indeterminate whether Bahraah is Bahrooh but Jules and Jim are determinately identical. Similarly, Y and Z will generate a complex whose truth is determined by supervaluating over Y and Z, where the resulting depictions are such that it is again indeterminate whether Bahraah is Bahrooh, but Jules and Jim are determinately distinct. We then subvaluate over the W-X and Y-Z amalgamations to generate a W-X-Y-Z complex according to which Jules are Jim are both identical and distinct, while Bahraah and Bahrooh are indeterminately identical. Given a story in which identity is not well-behaved, what will make it the case that truth in that story is determined by supervaluation as opposed to subvaluation, or vice versa? One should not be misled into thinking that there is a genuine problem here. In reading Dialethialand, how does one tell that Jules and Jim are represented as standing in an impossible identity relation, as opposed to an indeterminate identity relation? Simply by reading the story – the content of the story tells us how to interpret matters. There is no epistemic problem here; one merely has to read and understand the fiction to see whether the content is determined by supervaluation or by subvaluation. Neither is there a metaphysical problem lurking here. An author creates a fiction whose content is determined by supervaluation by creating a story that represents an indeterminacy; this is what it is to create a story in which the identity facts are indeterminate. There is nothing arbitrary about the fact that truth in Bah-Tale 2 is determined by 29 | P a g e supervaluation while truth in Dialethialand is determined by subvaluation; the difference is simply a function of the difference in content between the stories. VIII. CONCLUSION Fictional realism faced a challenge – how to account for non-classical identity relations between characters without being committed to non-classical identity relations between actual abstract objects. By supervaluating or subvaluating over fully determinate actual abstracta, the fictional realist can answer that challenge. 18 30 | P a g e BIBLIOGRAPHY Cameron, Ross. 2013. "How to be a Nominalist and a Fictional Realist". In Art and Abstract Objects, ed. Christy Mag Uidhir. Oxford University Press, 179-196. Caplan, Ben, and Muller, Catherine. (forthcoming). "Brutal Identity". Evans, Gareth. 1978. "Can There Be Vague Objects?". Analysis 38 (4): 208. Everett, Anthony. 2005. "Against Fictional Realism". Journal of Philosophy 102 (12): 624-649. Hanley, Richard. (2004). "As Good as it Gets: Lewis on Truth in Fiction". Australasian Journal of Philosophy 82 (1): 112-128. Lewis, David. 1978. "Truth in Fiction". American Philosophical Quarterly 15: 37-46. Reprinted with postscripts in Lewis. 1983. Philosophical Papers volume 1. Oxford University Press: 261-280. ---. 1988. "Vague Identity: Evans Misunderstood". Analysis 48:3 128-130. Reicher, Maria. 2010. "Nonexistent Objects". The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), Edward N. Zalta (ed.), http://plato.stanford.edu/archives/fall2010/entries/nonexistent-objects/. Schnieder, Benjamin, and von Solodkoff, Tatjana, 2009. "In Defence of Fictional Realism". Philosophical Quarterly 59: 138-149. Thomasson, Amie. 1998. Fiction and Metaphysics. Cambridge University Press. Van Inwagen, Peter. 1977. "Creatures of Fiction". American Philosophical Quarterly 14 (4): 299-308. Walton, Kendall. 1990. Mimesis as Make-Believe. Harvard University Press. 1 There are alternative versions of fictional realism. Possibilists hold that characters are real but non-actual; some Meinongians hold that fictional characters are real but do not exist (this characterization of Meinongianism 31 | P a g e comes from van Inwagen 1977: 299, who notes that it may not accurately label Meinong‟s own view; see also Reicher 2010: section 4 on that question). For present purposes, however, focus on the version of fictional realism according to which Sherlock is an existing abstract object (van Inwagen 1977 and Thomasson 1998 advocate this view). We will assume further that these abstracta are created, not discovered, though nothing turns on this assumption. 2 See van Inwagen 1977: 301, 308 on this point. 3 The objections depend essentially on statements about existence or identity conditions. As noted above, van Inwagen 1977: 308 emphasizes that the fictional realist is not threatened by cases in which a fiction fails to specify whether character A has feature F; in that case, the realist can simply say that the character is neither depicted as having F nor as lacking F. Similarly, if a fiction depicts A as indeterminately exemplifying F, the realist can say that the fiction depicts a metaphysical impossibility (namely, indeterminate property-exemplification), but that in reality it is determinate that A exists, and determinate that A is depicted in this metaphysically impossible way. But statements about fictional characters do license existential quantifications, so the realist is committed to existence and identity conditions for characters; Everett‟s examples challenge the realist to account for cases where those conditions are ill-behaved in the fiction. 4 Namely: the principle that distinct fictional names used in a story co-refer to a single abstract object, unless the content of the fiction explicitly specifies that they are distinct characters. 5 Which propositions will count as members of the set? There are two obvious candidate answers. One option is that the propositions constituting the fiction are all and only the propositions that we want to count as true according to the fiction. Alternatively, we might say that the propositions constituting the fiction are all and only the propositions expressed by the sentences that literally appear in the text of the story [or that were spoken, in the case of oral storytelling]. Those two answers can come apart in multiple ways. First, where a fiction is silent about some commonplace feature of reality (such as the fact that Uruguay is in South America), we may be tempted to say that it is true according to the fiction even though that proposition is not explicitly expressed in the story. Second, we can imagine a typographical error in the story such that the sentence appearing in the text expresses proposition p, but it is obvious that the author meant to write a different sentence that expresses proposition q, such that we would want to say that q and not p is true according to the story. 32 | P a g e A definitive answer to the question which propositions constitute the set lies beyond the scope of this paper. The presentation of the positive account in subsequent sections of the paper will be clearer, however, if we at least outline a rough approach to the matter. Let us stipulate, then, that not every proposition true in the fiction need be a member of the set of propositions constituting the fiction, but that any proposition literally expressed in the text of the story is a member of the set unless an interpretation shows that it is not true according to the story. We thereby leave space to allow that a proposition like Uruguay is in South America may count as true according to the fiction without being a member of the set, and similarly for some propositions that are deductively entailed by propositions that are members of the set. We can make space for the latter claim without supposing further that truth according to the fiction is closed under deductive entailment; that supposition is generally implausible. 6 If one prefers, we could use the label „fiction‟ more narrowly: one could hold that The Da Vinci Code is a fragment of a fiction but not itself a fiction, or that a series comprises several fictions but is not itself a fiction. The terminological question how to use „fiction‟ is not our focus here. 7 Cameron 2013 has independently formulated a similar account of Bah-Tale 2 relying on supervaluation, though the two proposals diverge with respect to the case of fictions that leave open the identity of characters, and he is silent about numerous claims made here (understandably, as his paper focuses on a broader question entirely). 8 Lewis 1988 presents this as the point Evans 1978 was after all along; Cameron 2013 also explains how this appeal to semantic indeterminacy answers Everett‟s objection without invoking metaphysically indeterminate identity. 9 It is worth noting that Schnieder and von Solodkoff ‟s proposal also suggests that (4) is false; the counterintuitive result that supervaluationism delivers here does not constitute an advantage for the Schnieder and von Solodkoff‟s rival proposal. 10 Thanks to an anonymous referee for pressing me on this example. 11 Thanks to Fred Kroon for prompting me to consider (4) and (8) more carefully. 12 A similar treatment can be offered for fictional existence that is indeterminate or left open. Tatyana Tolstaya‟s novel The Slynx leaves open whether a Slynx exists; in this case, the supervaluationist may say that Tolstaya has created two salient fragments X and Y, such that X represents A as the extension of „the Slynx‟ and Y represents „the Slynx‟ as extensionless. It is then semantically underdetermined whether „the Slynx‟ designates 33 | P a g e something, and the truth of „According to The Slynx, a Slynx exists‟ is determined in parallel fashion to truth-inFrackworld. 13 Thanks to Fred Kroon for raising the concerns addressed in this section. 14 In the final paragraph of §4 and in note 12 above. 15 Again, Caplan and Muller (forthcoming) press this objection. 16 Thanks to an anonymous referee for pressing this point. 17 The invocation of subvaluation takes a page from the postscripts to Lewis 1978, where he considers a "method of union" as well as a "method of intersection". He considers the two techniques as alternative treatments of the well-behaved fragments of an impossible fiction; in using subvaluation for impossible fictions, we are using the method of union for those fragments, while employing the method of intersection for the fictions depicting indeterminate or underspecified identities. Hanley 2004 offers a good discussion of objections to the Lewisian approach and replies that can be offered on its behalf. While the view defended here resembles the Lewisian approach in its appeal to supervaluation and subvaluation, the similarities between them do not extend much further, since Lewis uses possible worlds while the realist appeals to abstract objects, which need not depict possible or complete states of affairs. [Thanks to an anonymous referee for pointing out the connection to Lewis and Hanley.] 18 Thanks to Ben Caplan, whose presentation on the subject at the 2010 Central States Philosophical Association first piqued my interest in the issue, and to the audience at that meeting for helpful discussion. Thanks also to audiences at the 2011 New Mexico – West Texas Philosophical Society (particularly my commentator Pablo Zavala) and the 2011 Midsouth Philosophy Conference (particularly my commentator Cody Cash), and to anonymous referees for many thought-provoking comments.