Fictional names and individual concepts

This paper defends a version of the realist view that fictional characters exist. It argues for an instance of abstract realist views, according to which fictional characters are roles, constituted by sets of properties. It is argued that fictional names denote individual concepts, functions from worlds to individuals. It is shown that a dynamic framework for understanding the evolution of discourse information can be used to understand how roles are created and develop along with story content. Taking fictional names to denote individual concepts provides accounts of a number of uses of fictional names. These include non-fictional uses, fictional uses, metafictional uses, interfictional uses, counterfictional uses, and negative existentials. It is argued that this account is not open to objections that have been raised in the literature.


Introduction
This paper argues that fictional names denote individual concepts. In particular, I propose a version of this view that belongs to a group of realist views, according to which fictional characters are abstract entities that exist in the actual world and are created by authors. 1 Specifically, the view I will argue for agrees with instances of this form of realism that hold that fictional characters are roles constituted by sets of properties. 2 For the role-realist, the fictional character Anna Karenina is an abstract entity that exists in the actual world, and which was created by Tolstoy. But Anna Karenina is not an individual, abstract or concrete. The fictional character Anna Karenina is a role that an individual could occupy. A role, in this sense, is a set of properties, such as being Russian, being a countess, being called "Anna Karenina," and so on.
On the approach I want to develop in this paper, roles of this kind are represented semantically as individual concept. Individual concepts are functions from possible worlds to individuals. The fictional name "Anna Karenina" will be seen as denoting the function that maps a possible world w onto the unique individual x in w, if there is one, such that x in w has all the properties constituting the role of Anna Karenina.
I develop a version of this kind of role-realism that implements it in a particular framework for understanding the semantics and pragmatics of fictional discourse. The roots of this framework are the forms of dynamic theories of communication originating in the work of Stalnaker (1999Stalnaker ( [1970), Karttunen (1974Karttunen ( , 1976, Kamp (2002Kamp ( [1981), Heim (1982), (2002 [1983]), and others. A fictional discourse-the telling or hearing of a fictional story-is a paradigm case of the kind of incremental accumulation of information that these frameworks were designed to model. The account I develop here follows Heim (1982) in representing this kind of dynamic discourse as an increasingly more specific set of pairs of possible worlds and variable assignments, also called a "file." At any point after the inception of the story, a fictional name denotes an individual concept specifying the properties that have so far been associated with the relevant character.
This approach to fictional discourse has several advantages. First, it accommodates the intuitive idea that fictional characters develop along with story content. Second, we will see that taking fictional names to denote individual concepts provides satisfactory ways of understanding a number of different uses of sentences involving fictional names.
Used non-fictionally, (1) makes an assertion about the actual world. The view I argue for counts this use as neither true nor false. A fictional use of (1) is one on which it is used to tell the story of Anna Karenina. The dynamic view I favor takes such uses to have the effect of adding information to the developing story content. On its metafictional use (1) is used to say something about what is true in the story. I argue that such uses are best understood along the lines of the operator approach introduced by Lewis (1983Lewis ( [1978).
Further, we will see that understanding fictional names as denoting individual concepts provides accounts of some challenging cases. Among these are interfictional statements like (2), counterfictional statements like (3), and negative existentials like (4).
(2) Anna Karenina is smarter than Katerina Ivanovna. The version of role-realism I develop sees all of these as being statements about the role of Anna Karenina.
(2) will be seen as, roughly, making the claim that any possible occupant of the Anna Karenina role is smarter than any possible occupant of the Katerina Ivanovna role. Similarly, (3) is analyzed as claiming that any possible occupant of the Anna Karenina role could have remained faithful. Finally, (4) will be seen as true if and only if the role of Anna Karenina is unoccupied.
In Sect. 2 I recapitulate the central tenets of the form of role-realism I want to pursue here, and I introduce the notions of roles and occupants. Section 3 outlines the fundamental elements of the framework I favor, in which fictional characters are seen as roles that are created and develop along with story content. Sections 4 and 5 develop this view in more detail by showing how it captures a number of uses of fictional names, and how it can respond to some potential objections.

Abstract realism
The realist about fictional characters holds that there are fictional characters. One brand of realism, typically called "Meinongian" realism, agrees that there are fictional characters but insists that, nevertheless, fictional characters do not exist. 3 A wellknown instance of this view is that of Parsons (1980Parsons ( , 1982 who held that Sherlock Holmes, for example, is an object that is a detective, solves crimes,…, and doesn't exist. His nonexistence doesn't prevent him from having (in the actual world) quite ordinary properties, such as being a detective. (Parsons 1982, p. 81) Most realists, however, reject the Meinongian conclusion that there are things that do not exist. Most agree with van Inwagen's (1977, p. 300) complaint that it is hard to find "any important difference between "there is" and "there exists" [...]." Instead, the most common kind of realism accepts that fictional characters exist. For this realist there is at least a sense in which it is true to say that Anna Karenina, Sherlock Holmes, Clarissa Dalloway, or Sancho Panza exists. Within this anti-Meinongian camp a widespread view is that fictional characters are abstract entities. This kind of abstract realism also typically endorses the claim that fictional characters actually exist. The abstract realist, then, holds that fictional characters are abstract entities that exist in the actual world.
The view I will be defending here is a form of abstract, actualist realism. In particular, it endorses the view that fictional characters are roles. On this view fictional characters are not individuals. The fictional character Anna Karenina is not a Meinongian non-existent individual, nor is it an abstract, actually existing individual. 4 Rather, the fictional character is a role that can be occupied by different individuals in different possible worlds. This role is an abstract entity that exists in the actual world.
I now go on to further flesh out the notions of roles and occupants.

Roles and occupants
The difference between roles and occupants has been discussed by a number of writers in different connections. Here is an example from Tichý (2004Tichý ( [1987): One person cannot become another person. For instance, George McGovern cannot become Richard Nixon. But he can conceivably, though rather unlikely, become the President of the United States.
[...] But then the president of the United States cannot be a person, since no one can become a person distinct from the one he is in the first place. But there is hardly any puzzle here. Of course, the President of the United States is not a person: it is an office. One person may hold the office now and another person next year, but no person can ever be identical with that office. We do say that Mr. Nixon is the President of the United States, but by this we do not mean that the office and the man are one and the same thing but rather that he happens to occupy the office. (Tichý 2004(Tichý [1987 Many ways of using definite descriptions are plausibly seen as picking out roles, in this sense. Here are some examples: (5) a. The pope is the bishop of Rome. b. After WWII the president of the United States became the most powerful figure on the world stage. c. In most universities the deans are responsible for approving faculty hiring.
A natural way of understanding (5a) is as a claim about what is involved in being the pope, rather than as a claim about any particular pope. As we might say, (5a) is about the papacy, rather than any particular pope. Correspondingly, (5b) is most naturally read as saying something about the role of post-war US presidents. And similarly, (5c) is most naturally read not as making a claim about any particular deans, but about the office of being a dean.
It should be noted that, as demonstrated by Rothschild (2007), there is considerable variation in when descriptions permit role readings. In particular, Rothschild (2007, p. 75) points out that role readings are typically available only when it is assumed that "there is exactly one person (or one salient person) satisfying the descriptive content across a range of relevant metaphysically possible situations and that the satisfier sometimes varies from situation to situation." For the most part, this kind of contextual variation in the availability of role readings of definite descriptions will not matter for my purposes here. We can note that Rothschild's criterion applies straightforwardly to the examples in (5).
The version of abstract realism about fictional characters I want to pursue in this paper claims that fictional characters are roles like the pope or the dean. 5 What more precisely is a role? Intuitively, someone occupies the role of pope when she has certain properties, such as having been elected, being the head of state of the Vatican, being the bishop of Rome, and so on. Similarly, among role-realist views of fictional characters it is common to say that a role is constituted by a set of properties. For instance, the role of Anna Karenina is constituted by properties such as being a woman, being Russian, being a countess, being called "Anna Karenina," being married to Alexei Karenin, and so on. The properties that constitute Anna Karenina are determined by the fiction Anna Karenina.

Individual concepts
The account I will develop here represents roles semantically as individual concepts. This means that, on my account, fictional names denote individual concepts. An individual concept is a function from worlds to individuals. On my view fictional names denote individual concepts that pick out individuals satisfying a set of properties, that is, occupants of the role that is the relevant fictional character. By contrast, non-fictional names, such as "Barack Obama," denote constant individual concepts that pick out the same individual, such as Barack Obama, in all worlds. I spell this out in more detail in the next section. First, I want to flesh out the idea of an individual concept a bit more.
Consider the expression "The president of the US in 2008." In the actual world this description picks out Barack Obama. In other worlds it picks out someone else, such as Joe Biden, Hillary Clinton, or John McCain. Here is a simple way of specifying this individual concept: (6) λw. the president of the US in 2008 in w.
For any world w, (6) returns the individual who is the president of the US in 2008 in w. Individual concepts of this kind are partial functions. There are worlds in which there is no president of the US in 2008. For such worlds (6) is undefined, it has no value. 6 This way of representing the role of being the president of the US in 2008 allows us to distinguish between the role and its possible occupants in our theorizing. We can distinguish between the role of being the president of the US in 2008, as represented by (6), and its possible occupants. Compare (7a) and (7b).
(7) a. The president of the US in 2008 was born in Hawaii.
b. The president of the US in 2008 was more powerful than Congress.
On its most natural reading (7a) says something about Obama, the actual occupant of the role of the president of the US in 2008. Roughly, we can capture this reading as (8), where α is the actual world.
(8) [λw. the president of the US in 2008 in w](α) was born in Hawaii in α.
The value of the individual concept in (6) for the actual world is Obama. In other words, (8) says that Obama was born in Hawaii in α. By contrast, on a natural reading (7b) is a claim about the role of the president of the US in 2008. Of course, (7b) can also be used to say something about Obama. But there is a clear sense in which (7b) can be read as a statement about what is involved in being the president of the US in 2008 (as opposed to earlier US president). (7b) might occur 100 years from now in a book about the history of the presidency. The role reading, in this sense, says something about the properties of any president of the US in 2008. To a first approximation, this reading of (7b) is specified by (9). 7 (9) For all w such that [λw. the president of the US in 2008 in w](w) = #, [λw. the president of the US in 2008 in w](w) was more powerful than Congress in w.
(9) states that in all worlds where there is a president of the US in 2008, she is more powerful than Congress. This corresponds to the reading of (7b) on which it states that any president of the US in 2008 is more powerful than Congress. To be sure, there are worlds in which the 2008 president is not more powerful than Congress. (Perhaps the actual world is like this. We are using this only as an example.) Similarly, there are worlds in which the president of the US did not become the most powerful figure on the world stage after WWII, or where the pope is not the bishop of Rome. Most of the time we discount such possibilities when we have role readings in mind. Role readings typically apply to a restricted range of possibilities. Ultimately, our account should reflect this fact. Yet, for simplicity, we leave it aside here.
(10) The president of the US in 2008 could have been the last president of the US.
Again, at least one reading of (10) is the role reading on which it says that any president of the US in 2008 could have been the last president of the US. How do we capture this way of understanding (10)? Obviously, it will not do to analyze it as claiming that in each world in which there is a president of the US in 2008, she is the last president of the US in that world. For one thing, Obama was not the last president in the actual world. Instead, taking a simple view of the modal could have been, the role reading of (10) can be understood as in (11).
(11) For all w such that [λw. the president of the US in 2008 in w](w) = #, there is a w such that R(w, w ) and [λw. the president of the US in 2008 in w](w) is the last president of the US in w .
(11) states that in each world where there is a president of the US in 2008, she is such that she could have been the last one. This contrasts with the occupant reading of (10) on which it says that Obama could have been the last president: (12) There is a w such that R(α, w) and [λw. the president of the US in 2008 in w](α) is the last president of the US in w.
(11) entails (12), which is what we want. What makes role readings true or false? Take the role reading of (7b). Intuitively, the role reading of (7b) is true (if it is) because being more powerful than Congress is part of being the president of the US in 2008, rather than being a property of a particular occupant of the role. Role-theorists standardly spell this out by taking roles to be constituted by sets of properties. To be an occupant of the role of the president of the US in 2008 is to have a particular range of properties, such as being the commander in chief, being a natural-born US citizen, being over 35 years of age, and so on. Someone who does not have all the relevant properties is not an occupant of the role, and anyone who has all the relevant properties is an occupant of the role.
This conception of roles as constituted by sets of properties has an important consequence for how to understand modal claims like (10). As represented by (11), the role reading of (10) is true or false depending on whether any possible occupant of the role of the president of the US in 2008 is such that she could have been the last president. Whether this is so depends on how things are with individuals who satisfy all the properties associated with the role of the president of the US in 2008. We are not claiming that a modal property is part of the properties that constitute the role. Rather, we are claiming that the properties that constitute the role are such that anyone who has them could have been the last president.

Telling stories and creating characters
Having introduced the general view of abstract realism and the notions of roles and occupants in the previous section, in this section I go on to set out the central components of the way I propose to use these ideas in an account of fictional names and characters.

The story of Jack's morning
Let us begin with an artificially simple example. Consider Currie's (1990, p. 151) example of the story in (13).
(13) Jack got up in the morning and ate breakfast.
As Currie suggests, a plausible first stab at spelling out what we intuitively understand from hearing this story is something like the following existentially quantified content: 8 (14) There is someone called "Jack" who got up in the morning and ate breakfast.
Currie argues that, ultimately, this will be too simplified. But for now we can focus on this basic way of understanding story content.
How more precisely should we understand the suggestion that the story in (13) conveys the information in (14)? I propose to develop this general idea within a particular framework for understanding discourse structure, namely the kind of dynamic approach to discourse stemming from the work of Stalnaker (1999Stalnaker ( [1970), Karttunen (1974Karttunen ( , 1976, Kamp (2002Kamp ( [1981), and Heim (1982Heim ( ), (2002Heim ( [1983). 9 The guiding idea of these frameworks is that the central purpose of sentences, or utterances of sentences, is to increment a body of contextual information. A standard type of example concerns anaphora, as in (15).
(15) A man came in. He sat down.
The dynamic approach assumes that the interpretation of a chunk of discourse like (15) keeps track of cross-sentential relations like anaphora. This is represented by associating indices in the form of natural numbers with expressions like indefinites, definites, pronouns, and names. So the interpretation of (15) might be as in (16).
In Heim's (1982) system an index functions as what Karttunen (1976) called a discourse referent. 10 Briefly, a discourse referent is something that "justifies the occurrence of a coreferential pronoun or definite noun phrase later in the text." (Karttunen 1976, p. 367) What is the informational import of (15), that is, the entire discourse? In the present framework the information conveyed by (15) is seen as ruling out possibilities in which there is no man x such that x came in and x sat down. Following Heim (1982), we specify this kind of information as a set of pairs of worlds and assignments of values to indices. The informational content of (15), then, can be represented as the following set: (17) {< w, g >: g(1) is a man in w, g(1) came in in w, g(1) sat down in w} (17) is a simple example of what Heim called a "file" comprising information about discourse referents. Now consider the story in (13). Again, we assume that the interpretation of (13) associates an index with the name "Jack:" (18) Jack 1 got up in the morning and ate breakfast.
We can then characterize the information in (13) as a set of pairs of possible worlds and variable assignments: is called "Jack" in w, g(1) got up in the morning in w, g(1) ate breakfast in w} This represents the sense that the content of (13) rules out possibilities in which it is not the case that someone called "Jack" got up in the morning and ate breakfast.
(19) is a way of understanding the information conveyed by the story to its audience. It does not tell us anything about the semantics of the fictional name "Jack." Yet it tells us something important about the name. It tells us that, as the name is used in the story, it names someone who got up and ate breakfast. Indeed, the story rules out possibilities in which there is no one called "Jack" who did those things.
The properties of being called "Jack" and getting up and having breakfast are properties that many possible individuals could have. Taken together, they constitute a role that different possible individuals could occupy. This role is the fictional character Jack. Like other roles-such as the president of the US or the pope-it can be represented as an individual concept. Yet, unlike the president of the US or the pope, the Jack role is a fictional character because it is constituted by a set of properties determined by a fictional story. (I will say more about this in 3.3.) With respect to our story the fictional name "Jack" denotes the function that maps any world w onto the unique individual x (if there is one) such that x in w has the properties of being called "Jack," getting up, and eating breakfast: 11 (20) Jack = λw. the unique x such that x is called "Jack" in w and x got up in the morning in w and x ate breakfast in w.
As before, this individual concept is a partial function. It is defined for a world w only if there is exactly one x such that, in w, x has the properties in question, that is, only if there is exactly one individual who plays the Jack role. As before, we call such an individual a (possible) "occupant" of the Jack role. Now suppose the author of (13) decides the story is not done yet. She adds one more sentence to it: (21) He went to work.
We assume that the interpretation recognizes the co-reference and hence associates the index 1 with the occurrence of he in (21). So the information conveyed by (21) is the following set: Given this, what it means to add (21) to the story of (13) is represented by intersecting the two sets: 12 Adding (21) to the story rules out all the pairs from (19) in which g(1) did not go to work in the world in question. So we are left with the set of pairs in which, in the relevant world, g(1) is called "Jack," got up and ate breakfast, and went to work.
As the story is expanded, the Jack role is expanded. The Jack role now includes going to work. Hence the individual concept denoted by "Jack" is updated. After the story is expanded, "Jack" denotes the updated individual concept: (24) Jack = λw. the unique x such that x is called "Jack" in w and x got up in the morning in w and x ate breakfast in w and x went to work in w.
Fictional characters develop as stories develop. Roles become richer. So the denotations of fictional names change as stories develop. Usually, we use fictional names to talk about characters as they are portrayed by the entire work. Usually, we use "Anna Karenina" to talk about the character of Tolstoy's book as a whole. Yet it is an advantage of this framework that it is able to acknowledge that characters develop.

Predication and non-fictional uses
Just as the story of Jack determines the properties of being called "Jack," getting up, eating breakfast, and going to work, any story determines similar sets of properties. For convenience, let c("ν") be the property of being called "ν." Then consider the following set of properties: Suppose this set of properties is determined by some story S. Along the lines of Jack's story, with respect to S, the fictional name "ν" denotes the corresponding individual concept: 13 ν is a partial function from worlds to individuals. Its domain only includes worlds in which there is exactly one individual who has the relevant properties. For each world w in its domain, ν maps w onto the unique individual y such that y has all the properties c("ν"), f 1 , . . . , f n in w.
For ease, we use the notation [c("ν"), f 1 , . . . , f n ] w as an abbreviation of the right hand side of (25). 14 That is: We can therefore give the more manageable definition: is just a more convenient notational variant of (25). More generally, we assume that all proper names denote individual concepts. Yet non-fictional names, like "Barack Obama," refer rigidly. We therefore let "Barack Obama" be a constant function that maps worlds onto Barack Obama: 15 (28) Barack Obama = λw. Barack Obama.
As we said earlier, in this kind of intensional system, non-fictional names denote constant individual concepts.
We will see that to give an account of role readings of fictional names it is advantageous to adopt a version of the kind of standard system that allows for object-language quantification over worlds. 16 In particular, we take both names and predicates to select bound world arguments at Logical Form (LF). 17 For example, "Russian" is treated as follows: Here is how this works for a simple case like (30).
The LF of (30) is roughly as follows: The world variables represent the world arguments for the name and the predicate. Hence, just as we would expect, (30) denotes a function that maps a world w onto true if and only if Barack Obama (w) is Russian in w. Accordingly, (30) is false at the actual world. "Barack Obama" picks out Barack Obama at α, and since he is not actually Russian, (30) is false at α.
Yet a consequence of our proposal is that (1) is undefined for the actual world. Given (27) and (29), since "Anna Karenina" is undefined at α (assuming that there is no unique individual who actually has all the Anna Karenina properties), (1) itself is undefined. That is, it does not have a truth value at α. This reflects the judgement that if used non-fictionally, that is, to make an assertion, (1) is neither true nor false. Someone who asserts (1) as a claim about the actual world is not making a false claim, but is exhibiting confusion. Unless one is confused about the existence of Anna Karenina, one would not utter (1) as an assertion about how things actually are. (This contrasts with asserting (1) as a statement about the fiction Anna Karenina. I give an account of such uses in 4.2.) We therefore preserve the intuitive difference between assertions of sentences involving fictional names and sentences involving non-fictional names. To be sure, this rests on the assumption that we can distinguish fictional names from non-fictional names. Yet it might be asked by what criterion we can do so. I address this question in the next section. Before that I want to end this section by commenting on the way this account sees fictional characters as created by story content.

Creating fictional characters
When a fictional name occurs in a fictional text, its main function is to either introduce or reactivate a discourse referent. Consider the first sentence of Achebe's Things Fall Apart: (32) Okonkwo was well known throughout the nine villages and even beyond. (Achebe 1988(Achebe [1958, p. 17) Uncontroversially, Achebe did not use of (32) to make an assertion about the actual world. Views differ on which speech act authors of fictions are performing, given that they are not making assertions. Some hold a view according to which fictional utterances are pretend-assertions (Searle 1975;Recanati 2000;Schiffer 2003;Kripke 2011). Others think that fictional utterances belong to some other class of non-assertoric speech acts, a well-known version of this position being the view that fictional utterances are prescriptions to imagine (Currie 1990;Walton 1990;Friend 2011;Maier 2017). My account of fictional characters focuses on the informational aspect of fictional discourse, that is, the building up of content as the telling of the story unfolds. In this respect fictional discourse is not fundamentally different from non-fictional discourse. Someone who wants to inform you of what your friend Jack did yesterday might assert that he got up, had breakfast, and went to work. This discourse likewise introduces a discourse referent and increments a set of pairs of worlds and assignments, or a file. Since this is besides my aim here, I will not give an account of the difference between telling the Jack story as a fiction and telling the Jack story as a report, or assertion, about an actual event.
Since (32) is the first sentence of the story, the name "Okonkwo" occurs here for the first time, too. Assuming the name is indexed with 1, we represent the information conveyed by (32) as (33).
(33) {< w, g >: g(1) is called "Okonkwo" in w, g(1) was well known throughout the nine villages and beyond in w} We are here abstracting away from a number of complications, in particular, the contributions of the definite, "the nine villages", and the focus-sensitive particle, "even". Still, (33) is a reasonably clear representation of the information conveyed by (32). If one thinks fictional utterances are pretend-assertions, one can take (33) as representing what the author of (32) is pretending to assert. If one thinks fictional utterances are prescriptions to imagine, one can take (33) as representing what the audience is being prescribed to imagine. Our account captures the more general fact that when Achebe put forward (32), his aim was to convey the information in (33), while refraining from making an assertion about the actual world.
For the creationist realist, the character of Okonkwo was created by Achebe. When precisely did Achebe create this character? This is a difficult question, since theorists can disagree about whether the character was created at the moment Achebe first thought about Okonkwo, or at the moment when Achebe first decided to tell the story, and so on. 18 Here I will assume that fictional characters are created when they first appear in a fictional discourse, such as the text of a novel or an orally told story.
As the first sentence of the novel, (32) is also the first time the character Okonkwo is introduced. I take it that the character of Okonkwo was created by Achebe's utterance of this sentence (presumably, by writing it down). This means that, on my view, a fictional character is created by the author introducing a discourse referent. As laid out earlier, my view takes "Okonkwo" to denote an individual concept, as in (34). Lamarque (2010, ch. 9) for discussion. This individual concept represents the Okonkwo role, which is the fictional character Okonkwo. The character is the set of Okonkwo properties. How do we know which properties these are? We know what they are because a discourse referent has been introduced and various bits of information have been given about it. Achebe created the Okonkwo role, that is, the fictional character Okonkwo, by introducing of a discourse referent and accumulating information about it.
(32) introduces a discourse referent, an index, and conveys certain information about it, as represented by (33). This is sufficient for determining the role consisting of the properties (again simplifying) of being called "Okonkwo" and being well known throughout the nine villages and beyond. Once we have a role, a set of properties, we have an individual concept. Indeed, if (32) were also the last sentence of the novel, "Okonkwo" would denote the individual concept that takes a world w to the individual in w, if there is one, who is called "Okonkwo" and is well known throughout the nine villages and beyond in w.
In fact, introducing a discourse referent (by means of a fictional utterance) is usually sufficient for determining a role, and hence an individual concept. Imagine a novel that consists of just one word: This abnormal novel succeeds in introducing a discourse referent, say 1. Moreover, the novel conveys some information about it, at the very least that g(1) is called "William" in the relevant worlds. (Perhaps at least some names also convey gender-information. I leave this aside here.) So even this one-word novel succeeds in creating a fictional character, the William role.
Assuming that being called "William" is all we know about this role, the fictional name will have the following denotation: This individual concept is undefined for many worlds, including the actual world, since in many worlds more than one individual is called "William." It is to be expected that a fictional character that is created by means of just (35) will be unusual. But the case illustrates the point that introducing a discourse referent (by means of a fictional utterance) is usually sufficient for determining an individual concept, and hence for creating a fictional character.
A similar view is endorsed by Schiffer (2003) who argues that it is a conceptual truth that using the name 'n' in writing a fiction creates the fictional character n. (Schiffer 2003, p. 53) To be sure, as Sainsbury (2005, pp. 109-110) and Recanati (2018, p. 27) have pointed out, this idea can be embraced even if one wants to reject anything more than a thin sense of the realist's claim that there are fictional characters. 19 I take it to be an advantage of my view that it is compatible with this kind of more neutral interpretation, even if my preferred interpretation of the framework is along the lines of the kind of abstract role-realism described in Sect. 2. Currie reminds us that fictional characters do not necessarily have names: There is nothing special about a fictional character because it gets a name in the fiction, and a general account of fictional characters should be an account of the named and the unnamed. (Currie 1990, p. 128) Consider, for example, the following story: (37) Something moved. It was green.
Our view represents the content of this story as follows, where 1 is the index of the discourse referent introduced by "something": (38) {< w, g >: g(1) moved in w, g(1) was green in w} In other words, (37) is sufficient to determine a role consisting of the properties of moving and being green. As such, (38) determines a corresponding individual concept. Let m be the property of moving and let r be the property of being green. Then our story determines the following individual concept: This individual concept picks out occupants of the role introduced by (37). Yet there is no fictional name that denotes it. Nevertheless, as a role, this character is no different from fictional characters like Okonkwo or Anna Karenina. It is a role that an individual could play, which in our framework is seen as a partial function that maps worlds onto the unique individual that occupies the role in that world, if there is one. To be sure, like the artificial William character, this function will be undefined at many worlds, since many worlds are such that more than one individual moved and was green. This, however, is merely an artefact of this simplistic example.

Relations between characters
Most fictional stories involve characters that have names. Moreover, most fictional stories involve more than one character. Consider the next three sentences of Things Fall Apart, immediately following (32): (40) His fame rested on solid personal achievements. As a young man of eighteen he had brought honour to his village by throwing Amalinze the Cat. Amalinze was the great wrestler who for seven years was unbeaten, from Umuofia to Mbaino. (loc. cit.) Again, 1 is assigned to the expressions that are co-referential with "Okonkwo" in (32). Further, we assume that 2 is assigned to Amalinze: (41) His 1 fame rested on solid personal achievements. As a young man of eighteen he 1 had brought honour to his 1 village by throwing [Amalinze the Cat] 2 . Amalinze 2 was the great wrestler who 2 for seven years was unbeaten, from Umuofia to Mbaino.
(40) provides a substantial amount of new information. Let us focus on the following: (42) {< w, g >: g(2) is called "Amalinze" in w, g(2) was a great wrestler in w, g(1) threw g(2) in w} Along the lines suggested earlier, adding (40) to (32) means intersecting the two sets: (43) (33) ∩ (42) = {< w, g >∈ (33): g(2) is called "Amalinze" in w, g(2) was a great wrestler in w, g(1) threw g (2) in w} This means that, after updating the story with (40), the Okonkwo role now includes a relation to another character, Amalinze. Like Okonkwo the latter is a role constituted by a set of properties. As illustrated by (43), in the story so far, the Amalinze role includes, at least, being called "Amalinze" and being a great wrestler. Let the set of properties constituting the Amalinze role be as follows: {c("Amalinze"), h 1 , . . . , h n } Given this, we can think of the property included in the Okonkwo role as a result of the update as: This is the property that x has at a world w just in case, in w, x threw the unique woccupant of the Amalinze role, if there is one. As a result of the story being incremented with (40), this property is included in the Okonkwo role. Hence, subsequent to this development of the story content, the Okonkwo character has developed to include being such that Okonkwo threw Amalinze. Conversely, of course, the Amalinze role includes having been thrown by Okonkwo.
There is nothing surprising in the fact that roles relate to each other in this way. The corresponding phenomenon is evident from role readings of cases like (45).
(45) The president appoints the chief justice.
The role of the president includes the property of appointing the chief justice.

Non-fictional names, fictional names, and metafiction
In the previous section I introduced the account of fictional names and characters I favor. In this section and the next I will flesh it out by showing how it handles a range of uses of sentence involving fictional and non-fictional names. In this section I consider the difference between fictional and non-fictional names and the way both may appear in metafictional uses.

Fictional versus non-fictional names
I have suggested that while fictional names, like "Anna Karenina," denote individual concepts constituted by properties determined by the relevant fictions, non-fictional names, like "Barack Obama," denote constant individual concepts. But what is our reason for taking "Anna Karenina" to be a fictional name and "Barack Obama" to be a non-fictional name?
An attractive approach was suggested by Kaplan (1973): The 'Aristotle' we most commonly use originated in a dubbing of someone, our 'Pegasus' did not. Some rascal just made up the name 'Pegasus', and he then pretended, in what he told us, that the name really referred to something. But it did not. Maybe he even told us a story about how this so-called Pegasus was dubbed 'Pegasus'. But it was not true. (Kaplan 1973, p. 505) This suggestion relies on the familiar idea that, for instance, "Barack Obama" as used by you and me refers to Obama in virtue of a chain of communication leading back from our use of the name to Obama himself, perhaps to an initial dubbing or some other relevant event. Equally familiarly, there are challenges to this answer, but let us assume for the moment that something along these lines is correct. 20 What is important is that there is an individual who exists in the actual world, Obama, such that the name refers to him in virtue of some mechanism involving him. By contrast, there is no chain of communication leading back from Tolstoy's use of "Anna Karenina" to any individual. 21 A view along these lines also applies to cases of non-fictional names being used in fiction. Consider the stock example of Napoleon's appearance in War and Peace. We should accept that the name "Napoleon," as it is used in War and Peace, refers to the actual Napoleon. 22 As Friend (2007) notes, it was certainly Tolstoy's intention to write about the real Napoleon, and [...] there is no bar to imagining real individuals being different from how they actually are. (Friend 2007, p. 142) In other words, we want "Napoleon," even when the name appears in War and Peace, to denote a constant individual concept, like the one denoted by "Barack Obama," in order to ensure that "Napoleon" refers rigidly to Napoleon.
Given the sort of criterion suggested by Kaplan, "Napoleon" is not a fictional name as used in War and Peace. There is an actual chain of communication leading back from Tolstoy's use of "Napoleon" in War and Peace to Napoleon. We therefore have an independent reason for classifying "Napoleon" as a non-fictional name, and hence for taking it to denote a constant individual concept, as opposed to the kind of individual concept denoted by fictional names.
A potential problem here concerns descriptive names like the familiar examples of "Jack the Ripper" (Kripke 1980) or "Julius" (Evans 1985(Evans [1979). Such names are non-fictional and refer rigidly. Scores of novels have been written about Jack the Ripper. The name "Jack the Ripper," as it occurs in (at least some) such novels, is not a fictional name. That is, just as our use of "Jack the Ripper," it refers rigidly to the actual killer, whoever he or she was. Yet the reference of descriptive names is not secured by the same kind of chain of communication as the one leading back from our use of "Barack Obama" to Obama himself. Roughly, that is, while the reference of "Barack Obama" is underpinned by a chain of communication originating in an initial act of ostension (or dubbing), the reference of "Jack the Ripper" is underpinned by a chain of communication originating in some act of reference fixing by means of a description.
So, it might be objected that taking non-fictional names like "Barack Obama" to be distinguished from fictional names in terms of chains of communication leading back to actual individuals will incorrectly classify descriptive names like "Jack the Ripper" as fictional names. 23 However, there is a central difference between descriptive nonfictional names like "Jack the Ripper" and fictional names like "Anna Karenina." Briefly, it is common to point out that descriptive names have their reference fixed by descriptions that are used attributively, and correspondingly, their reference is secured satisfactionally. 24 This may be said to apply even to empty descriptive names, that is, names introduced by a description (used attributively) which fails to pick anyone out. As we have seen, on my view fictional names are not introduced via reference-fixing descriptions. But regardless, even if one thinks that they are, they are not introduced by attributive uses of descriptions, and their reference is not secured satisfactionally.
To be sure, we do not have to imagine that "Jack the Ripper" was introduced by someone ceremonially declaring that its reference be fixed in such and such way by an utterance involving a definite description. We can imagine that the name was introduced by a practice by which people started using the name for the killer, whoever he or she might be. They might do so by saying things like (46).
(46) a. Jack the Ripper was at Victoria Station last night.
b. This is another of Jack the Ripper's victims. c. Jack the Ripper is left-handed.
This situation looks similar to the way I have suggested that authors of fictions introduce fictional names, that is, by introducing a discourse referent. However, as before, there is a clear difference. (46a-c) are used attributively, and as such the reference of "Jack the Ripper" in such utterances is determined satisfactionally, that is, it refers rigidly to the actual killer, whoever he or she is. By contrast, authors of fictions are not speaking attributively in using fictional names. Further, while there is a distinction between fictional and non-fictional names, even when they appear in fictional discourse, it is nevertheless true to say that, for example, Napoleon is a character in War and Peace. 25 The novel makes up a story about Napoleon. In our terms, War and Peace determines a set of properties-the Napoleon role-which includes the property of being called "Napoleon," as follows: {c("Napoleon"), f 1 , . . . , f n } Yet, given what we just argued, we do not want "Napoleon" to denote the corresponding individual concept. Even though Napoleon is a character in War and Peace, and hence there is a set of properties that we can point to as constituting the Napoleon role in that fiction, the name "Napoleon" refers rigidly to Napoleon himself.
We therefore restrict the application of (27) to fictional names: 23 Thanks to an anonymous reviewer for pressing this point. 24 See Jeshion (2004) for relevant discussion. 25 Cf. Currie (1990, p. 128).
To illustrate, consider this passage from War and Peace: (48) Napoleon was positioned just ahead of his marshals, mounted on a little grey Arab horse, wearing the same blue overcoat he had worn throughout the Italian campaign. [...] He had slept a few hours before dawn and woken up feeling fresh, in good health and high spirits. (Tolstoy 2007(Tolstoy [1869, p. 290) In other words, the Napoleon role in War and Peace includes, roughly, wearing a blue overcoat, sleeping a few hours before dawn, and so on. Suppose that even though, according to (48), Napoleon wore a blue overcoat, this did not happen in the actual world. Hence, if used to make an assertion about α, (49) should be false.
So we correctly predict that (49) is false at α.
Next, we turn to metafictional uses of both fictional and non-fictional names.

Metafictional uses
We do not only use fictional names to tell stories. We also use fictional names to talk about stories. On this use, for instance, (1) is used to convey something about Anna Karenina.
There are many different labels for this use of fictional names. 26 I will call them "metafictional" uses. It is commonly agreed that metafictional uses are assertionsthat is, when not used ironically, or in some other non-standard way. When one uses (1) to make a claim about Anna Karenina, one typically asserts something about Anna Karenina. Correspondingly, qua assertions, metafictional uses have truth-values at the actual world. As Recanati (2018, p. 29) says, metafictional uses are "true or false; by uttering them one makes serious assertions about the fiction." 27 For instance, if used to make an assertion about Anna Karenina, (1) is true at α. The standard approach to metafictional uses follows Lewis (1983Lewis ( [1978) in seeing them as having the same content as the corresponding sentence prefixed with an operator like "In Anna Karenina," as in (51).

(51) In Anna Karenina Anna Karenina is Russian.
The claim that, when used metafictionally, (1) has the same content as (51) can be understood in different ways. One can understand it to mean that, when used in this way, the LF of (1) includes the operator, that is, the operator is present at LF but is unpronounced. 28 Alternatively, one can hold that a metafictional use of (1) succeeds in expressing the content of (51), even though the operator is not present in the LF of (1). 29 I will not take a stand on this difference here. Instead, I want to show how, regardless of this choice, the role-realist framework I am advocating can incorporate the Lewisian approach to metafictional uses. Lewis (1983Lewis ( [1978) proposed more than one way of understanding the truthconditions of explicit cases like (51). Below I spell out a version of Lewis's "Analysis 1," according to which what is true in a fiction, roughly, is what would be true if the fiction were true.
On our view, when a story is finished we have narrowed down a specific file. Consider a set of pairs S representing the content of a particular story. We can then mirror Lewis's Analysis 1 as follows: 30 (52) F S (φ) (w) = 1 iff for some < w , g >∈ S, φ (w ) = 1 and w is closer to w than any world w such that < w , g >∈ S and φ (w ) = 0.
Here is how this works for the metafictional use of (1). Let A be the set we are left with at the end of Anna Karenina. So the relevant instance of (52) with respect to the actual world α is: Anna Karenina is Russian (w) = 1 and w is closer to α than any world w such that < w , g >∈ A and Anna Karenina is Russian (w ) = 0.
This means that (51) is true just in case there is a world w, which is a member of some pair in A, such that the unique individual that plays the Anna Karenina role in w is Russian in w. And further, we follow Lewis in spelling out the idea that w is close to α as the condition that there is no closer world w that is a member of a pair in A in which the unique individual that plays the Anna Karenina role is not Russian. Clearly there are many pairs <w, g> in A such that the unique occupant of the Anna Karenina role in w is Russian in w. Indeed, given the rich information provided by the novel, one might think that most pairs in A are like that. Suppose, for instance, that the interpretation associates the index 23 with Anna Karenina. So A might include information like g(23) is the daughter of Arkady Oblonsky, speaks Russian, is a Russian countess, and so on. These things will in turn be included in the properties constituting the Anna Karenina role. Hence, in any world, "Anna Karenina" picks out the unique individual that has all of those properties, if there is one. Many of these worlds are worlds in which that individual is Russian. And equally plausibly, there will be at least one pair like that such that the world in question is close to α in the relevant sense.
This way of understanding metafictional uses of fictional names also accounts for metafictional uses of non-fictional names. Take (49) again. (49) Napoleon wore a blue overcoat. We are assuming that (49) is false-rather than neither true nor false-at the actual world. Yet if used metafictionally about War and Peace, (49) should be true. As before, we analyze the metafictional use of (49) as (54). (54) In War and Peace Napoleon wore a blue overcoat. Let W be the set of world-assignment-pairs determined by War and Peace. Then, since "Napoleon" qua non-fictional name refers rigidly to Napoleon, we predict that (54) is true at α if and only if there is a pair <w, g>∈ W such that w is close to α and Napoleon wore a blue overcoat in w. Since the story explicitly states that Napoleon wore a blue overcoat, all pairs in W are like that. So (49) is true at α when used metafictionally.
It is worth commenting briefly here on another type of example. 31 Consider (55ab). 32 (55) a. Anna Karenina is an individual concept.
b. Anna Karenina is a role. How should we understand statements like (55a-b)? One way to read (55a-b) is as metafictional claims. If used in this way, we predict that (55a-b) are false. Take (55a). Since being an individual concept is not among the properties constituting the Anna Karenina role, no occupant of the Anna Karenina role is an individual concept. This reflects the sense that, intuitively, it is not the case that Anna Karenina is an individual concept in Anna Karenina, as opposed to, for example, it being the case in Anna Karenina that Anna Karenina is Russian.
Yet (55a-b) arguably also have readings on which they are true. I want to point out one of these. (55a-b) can be read as analogous to (56). (56) The president is an office. (56) does not say of the actual president, or any other occupant of the president role, that he is an office. But nor is a role reading plausible for (56). That is, (56) does not say that anyone who has all the president properties is an office. Rather, it is plausible to read (56), roughly, as (57). (57) There is an office o such that anyone who occupies o is the president. As motivation for this analysis, note that it makes sense of ordinary statements like (58). (58) The president is an office established by the Constitution. It is natural to understand (58) as saying that there is an office o such that anyone who occupies o is the president and o was established by the Constitution.
Similarly, we can read (55a), roughly, as stating that there is an individual concept k such that anyone who is the value of k at some world w is Anna Karenina in w. (We return to this in 5.4 below.) This helps make sense of theoretical claims like (59).

(59) Anna Karenina is an individual concept defined in terms of a set of properties.
(59) is plausibly read as saying that there is an individual concept k such that anyone who is the value of k at some world w is Anna Karenina in w and k is defined in terms of a set of properties. The same applies, mutatis mutandis, to (55b).

Some more challenging uses
We have seen that taking fictional names to denote individual concepts and understanding story content as developing incrementally provides a way of analyzing core uses of fictional names. In this section I show how the account extends to some more challenging cases. In particular, we consider interfictional uses, counterfictional uses, and negative existentials. Finally, we will look at some potential problems for the view.
Most agree that interfictional statements like (2) can be true or false. Large swaths of our everyday talk about fiction, along with literary criticism, would be rendered defective if such statements as (2) were analyzed as neither true nor false along with non-fictional, assertoric uses of cases like (1).
Interfictional statements are often regarded as motivating realism of one form or another. One reason is that, prima facie, they look like poor candidates for being prefixed with Lewisian operators. Lewis himself acknowledged this difficulty. Consider one of his examples: (60) Holmes could have solved the A.B.C. murders sooner than Poirot. (Lewis 1983(Lewis [1978, p. 263) Lewis speaks of this and other examples he groups with it as "truths about Holmes," and moreover he notes that it is insufficient to say that they are "true just because "Holmes" is denotationsless." (loc. cit.) The problem is that it is not clear that statements like (2) and (60) (60) is not true in either the Holmes or Poirot stories. On the other hand, Brock (2002) suggests that at least some interfictional statements can be analyzed along metafictional lines. For example, following Brock (2002, p. 7), (2) might be understood as (61).

(61) In Anna Karenina Anna Karenina is smart to degree x and in The Brothers
Karamazov Katerina Ivanovna is smart to degree y and x > y.
There are two main problems with this kind of suggestion. First, it is unclear that paraphrases of this kind will be available for all interfictional cases (cf. Brock 2002, p. 7). Second, the strategy looks ad hoc. As Thomasson (1999) says, The issue is not whether one can devise some analysis of language that avoids reference to fictional objects, but what the best theory of language is, and whether it is one that accepts or denies that there are fictional objects referred to by fictional terms. It might be hoped that a smoother, more adequate, and less ad hoc analysis of language could be offered by admitting that there are fictional objects to which we can refer. (Thomasson 1999, pp. 99-100) The version of role-realism that sees fictional names as denoting individual concepts has an elegant way of analyzing interfictional uses. (2)  This suggestion gains initial support from the observation that we often use role readings of definite descriptions to make comparisons: (62) a. The president of the US is more powerful than the king of Sweden.
b. The provost has more responsibilities than the dean.
Given that fictional names denote roles, interfictional uses are naturally seen as parallel. What more precisely does (2) say about the Anna Karenina and Katerina Ivanovna roles? Clearly, it will not do to suggest that (2) claims that the properties that constitute the Anna Karenina role include the property of being smarter than Katerina Ivanovna. The set of Anna Karenina properties as determined by the novel do not include relations to characters in other fictions. Yet our account has another resource at its disposal, namely the possible occupants of the role. Specifically, we analyze (2) as claiming that any possible occupant of Anna Karenina is smarter than any possible occupant of Katerina Ivanovna.
As for one-place predicates, we assume that two-place predicates take world arguments, as in (64).
According to (63), the interfictional reading of (2) is true just in case at any world where both the Anna Karenina role and the Katerina Ivanovna role are occupied, the unique occupant of the former is smarter than the unique occupant of the latter. What does it mean to say that (2) has this content on the interfictional reading? Parallel to the account of metafictional readings in terms of Lewisian operators, we can define an operator R that generates the role reading of an embedded sentence as follows (where n 1 ...n n are names): (65) R(φn 1 ...n n ) (w) = 1 iff ∀w n 1 (w ) = #... n n (w ) = #, φ (w ) ( n 1 (w ))...( n n (w )) = 1.
We now have the same choice as for the treatment of metafictional uses in terms of Lewisian operators. We can maintain that R is present in the LF of sentences like (2), when they are used metafictionally, or we can say that such uses express the contents corresponding to the prefixed sentences. As before, we will not take a stand on this. All we are assuming here is that, just like metafictional uses, interfictional uses express contents like that in (63), and more generally these contents are generated along the lines of (65). There are two things to note about (63) as an analysis of the interfictional reading of (2). First, it assumes that there are worlds in which both the Anna Karenina and the Katerina Ivanovna roles are occupied. This I take to be a plausible assumption. Second, (63) is true at any world if and only if any world where both roles are occupied is a world where the occupant of Anna Karenina is smarter than the occupant of Katerina Ivanovna. This means that this analysis predicts that if (2) is true, it is necessarily true. If (2) is true at α, then for all worlds w where both roles are occupied, Anna Karenina is smarter than Katerina Ivanovna in w. But if so, then (2) is true at any world.
At first sight, this may look like an implausible consequence. Yet it is important to be clear about what is being claimed. First, we are not denying that Tolstoy could have written another novel in which a character was called "Anna Karenina" and in which that character was not smarter than the actual character of Katerina Ivanovna. Nor are we denying that there are worlds in which both the novels are different, and so on.
On the realist account I am proposing (2) concerns the fictional characters that Tolstoy actually created, and which are the denotations of the fictional names. So it follows Thomasson's advice. It takes interfictional statements to be about the characters involved, that is, the roles. In particular, it sees them as claims about the range of possible occupants of the roles.
But moreover, as we will see next, my account predicts that (2) is consistent with (66).
(66) Katerina Ivanovna could have been smarter than Anna Karenina.
The reason is that, on the role reading, (66) is the claim that for any pair of worldmate occupants x and y of Anna Karenina and Katerina Ivanovna, y could have been smarter than x. In particular, (66) does not claim that for any such pair, there could have been a different pair x and y such that y is smarter than x . Rather, our account takes (66) to be a claim about x and y themselves.
Consider first how standard (or "specific") de re readings are analyzed in the kind of semantic framework we have adopted. Take von Fintel and Heim's (2007, p. 83) example of (67).
(67) Mary wants a friend of mine to leave.
The standard de re reading is one on which, for example, Mary wants John to leave, but she does not know that John is a friend of mine. von Fintel and Heim represent this reading by the following LF: The de re interpretation is generated because a friend of mine is evaluated at the base (actual) world w, and not in Mary's desire worlds.
Consider the parallel analysis of (66), not yet prefixed by R: This represents a reading of the modal claim analogous to de re readings of sentences like (67). Again we assume a simple semantics for the modal, as in (70).
Given this, (69) is true at a world w if and only if there is a related world w such that, in w , Katerina Ivanovna (w) is smarter than Anna Karenina (w). Of course (69) is undefined at α, since both Katerina Ivanovna (α) and Anna Karenina (α) are undefined. That is how it should be, since (69) represents a use of (66) as an assertion about the actual world. However, on the role reading (66) is analyzed as R( (66)). In particular, the role reading is the result of applying R to the (let us call it) de re interpretation of (66). Hence, we predict truth-conditions along the following lines: In other words, the role reading of (66) is true just in case for any world where both roles are occupied, the occupant of the Katerina Ivanovna role could be smarter than the occupant of the Anna Karenina role. As with (2), the role reading of (66) has the profile that if it is true, it is necessarily true. But note that, even so, the truth of R( (2)) is compatible with the truth of R( (66)). Suppose the former is true at w. Then for all worlds w in which both roles are occupied, the w -occupant of Anna Karenina is smarter than the w -occupant of Katerina Ivanovna in w . Yet that does not rule out that for all such worlds w there is a related world w such that the w -occupant of Katerina Ivanovna is smarter than the w -occupant of Anna Karenina in w . This analysis of (66) preserves the intuitive idea that if Katerina Ivanovna could have been smarter than Anna Karenina, it is because the properties of Katerina Ivanovna according to The Brothers Karamazov are such that if someone had all of them they would be such that they could have been smarter than someone who has all the properties of Anna Karenina according to Anna Karenina.

Counterfictional uses
Interfictional uses like (2) and (66) have important similarities with so-called counterfictional statements. Friend (2011) observes that we often engage in imagining what things might or would have been like for a fictional character had things gone differently than they do in the stories in which they appear. Take her example of this kind of counterfictional imagining concerning Kafka's The Metamorphosis: I might imagine what the Samsa family's life would have been like had Gregor never changed into a vermin. Even though I imagine contrary to what Kafka's story prescribes -I continue to imagine about the same character. (Friend 2011, p. 188) Friend takes this to be a problem for views that "interpret imagining that Gregor Samsa has been changed into a beetle as, roughly, imagining that there is a bearer of certain properties that has been changed into a beetle." (loc. cit.) Friend is interested in imagining things about fictional characters. Yet there is a clear parallel to uses of sentences involving fictional names. Consider, for example, (72).
(72) Samsa might not have turned into a vermin.
(72) is a perfectly intelligible statement, which could occur as part of a meaningful discussion about Kafka's story. Yet, as we will see next, even though the version of role-realism I favor fits Friend's target in being a view according to which (72), on the relevant reading, claims that bearers of the Samsa properties might not have turned into vermin, this is not a problem for our view.
For the role-realist, to be sure, there are no worlds in which the occupant of the Samsa role in that world did not turn into a vermin in that world. However, just as for interfictional uses, we have a natural way of understanding counterfictional statements.
In particular, we will analyze the counterfictional use of (72) as R( (72)), corresponding to the result of applying the operator to the de re reading of (72). In other words, on the counterfictional use, (72) says that for each world w in which the Samsa role is occupied, Gregor Samsa (w) might not have turned into a vermin. Depending on how one understands might, the truth or falsity of (72) will depend on the modal profile of these possible occupants.
As for the interfictional cases, this means that we understand (72) to be a statement about the possible occupants of the Gregor Samsa role, that is, the fictional character Gregor Samsa. However, since the truth or falsity of (72), on this reading, depends on how things are with anyone who has all the Samsa properties, there is a clear sense in which this is directly in line with Friend's suggestion that we "continue to imagine about the same character." (loc. cit.)

Negative existentials
The perennial problem for theories of fictional names are negative existentials, such as (4).
Standard role-realism interprets this as the claim that the role of Anna Karenina is not occupied, that is, there is no (unique) individual who has all the Anna Karenina properties, at the relevant w. To see how this will be implemented consider first (73): (73) Anna Karenina exists.
We analyze (73) as (74): Correspondingly, (4) has the following truth-conditions: (73) is true at α if and only if for some x, x is the value of Anna Karenina (α). Yet we are assuming that there is no individual that has all the Anna Karenina properties in α. That is, the function has no value when applied to α. In other words, there is no x which is the value of the function at α. So (73) is false at α. And hence, (4) is true at α.
Here is an analogy to help motivate this analysis of (4). 34 Consider the question, is there a number n such that n = 2 0 ? The answer is "no." There is no such number. Now consider the function that results from abstracting over n, namely λn.n = 2 0 . Call this function "Z ." Applying Z to any n yields no value. Z is undefined for any n. In turn, therefore, ∃m m = Z (n) is false for any n. There is no number m such that m is the value of Z (n), for any n. Analogously, for any w such that Anna Karenina (w) is undefined, ∃x Anna Karenina (w) = x is false.
This account of negative existentials is consistent with the arguments that have been made by , von Solodkoff (2014), and others, to the effect that the realist needs to accommodate a wider range of negative existentials than simple forms like (4). In particular, these writers-building on Thomasson (1999)-suggest that the realist should allow that statements of the form "a doesn't exist" are context-sensitive in the sense that they may express that a does not belong to a particular class of object, where the relevant class is determined by the context. On the present proposal, this can be accommodated by allowing that, depending on the context, statements like "Anna Karenina is not real," "Anna Karenina is fake," or "Anna Karenina is fictive" may have the denotation in (75).
Of course, for the role-realist, there is also a sense in which (73) is true. Namely, it is true that the role, that is, the fictional character of Anna Karenina, exists. Indeed, for the creationist, the character Anna Karenina exists because Tolstoy created it.

Three Kripkean objections
The role-realist view resembles what Kripke (2013Kripke ( [1973, p. 10) calls the "orthodox doctrine," which he describes as the view that "to affirm the existence of, say, Sherlock Holmes, is to say that there is a unique person satisfying the properties attributed to Holmes in the story." (loc. cit.) Kripke objects to this view on grounds parallel to the familiar arguments from Kripke (1980). We can distinguish three different but related points of criticism that Kripke makes. Consider first this passage: Suppose the Sherlock Holmes stories were all true of one unique detective: does that amount to concluding that Sherlock Holmes really existed? The dust-jackets of many books of this type contradict such a thesis. The opening page may say The characters in this work are fictional and any resemblance to anyone living or dead is purely coincidental. What is meant by this is that even if by some bizarre accident the stories told in this work are substantially true of some particular people, and even true of them uniquely, the resemblance is purely fortuitous and was unknown to the author. They are not the referents of the names that occur in the story, and it is just a coincidence that the story is substantially true of them. (Kripke 2011, p. 56) I take it that there are two objections here, which we can summarize as follows: K1 Even if some actually existing individual, call him "H α ," has all the Sherlock Holmes properties, H α is not the referent of the occurrences of "Sherlock Holmes" in the story. I go through each of K1-3 in turn. We will see that, in fact, our version of the role-realist approach agrees with all of Kripke's observations. First, my account agrees with K1, since on my view the name "Sherlock Holmes" denotes the individual concept corresponding to the Sherlock Holmes role, and does not denote any individual occupant of the role. Hence, even if some individual in the actual world, H α , turns out to have all the Holmes properties, H α is not the referent of "Sherlock Holmes," although, in that scenario, H α is the actual occupant of the Holmes role.
Correspondingly, even in the scenario in which H α exists, "Sherlock Holmes" is still a fictional name on our account. The name "Sherlock Holmes," as used by Doyle is unlike, for instance, "Napoleon" as used by Tolstoy in War and Peace, since there is no actual chain of communication from H α to Doyle's use of "Sherlock Holmes," in Kripke's scenario. Hence, even if H α exists, our account does not imply that "Sherlock Holmes" denotes H α .
Second, my account agrees with K2. There are two ways in which, on this view, even if H α exists, Doyle's stories are merely accidentally true of H α . On the one hand, as Kripke himself implies, given that the name "Sherlock Holmes" as it occurs in the stories does not refer to H α , if the stories turn out to say thing that are true of H α , they are merely accidentally true.
On the other hand, as we noted in 3.3, it is uncontroversial that when Doyle wrote the Holmes stories, he was not making assertions. So, even if the Holmes stories say things that are true about H α , Doyle was not asserting those things about H α . So there is a clear sense in which, in this case, the truths about H α that Doyle wrote are accidental truths. Compare another kind of utterance that is uncontroversially nonassertoric, namely irony. Suppose we are discussing whether your friend, Michael, likes me. Feeling convinced he does not, you say in an ironic tone of voice: (76) Oh yeah, sure, Michael really likes you! You did not assert that Michael likes me. Accordingly, if it turns out that he in fact does like me, even though there is admittedly a sense in which you said something true about Michael, it is clear that what you said was merely accidentally true.
Finally, consider K3. This objection assumes that the individual we call "Charles Darwin" could have had all the Sherlock Holmes properties. Even though there are questions to be addressed about this, let us grant this assumption for the sake of argument. Kripke then comments that "This is not to say of him, or of anyone else, that he would have been Sherlock Holmes or might have been Sherlock Holmes. He could have played the role of Sherlock Holmes, he could have fulfilled the stories that are told about Sherlock Holmes." (Kripke 2011, p. 59) Yet this is of course precisely what our account will say of this case. A world in which the individual we call "Charles Darwin" has all the Sherlock Holmes properties is a world in which that individual is the occupant of the Sherlock Holmes role.
As suggested in 5.3 above, on our account, in a scenario in which the individual we call "Charles Darwin" does in fact have all the Sherlock Holmes properties, there is a true reading of (77).
(77) Charles Darwin is Sherlock Holmes. This is the reading on which (77) is analogous to (78).
(78) Donald Trump is the president.
(78) states that Donald Trump occupies the office of president. Similarly, (77) can be used to say that Charles Darwin plays the role of Sherlock Holmes. Indeed, we are familiar with similar usages from ordinary speech. If we are playing Jeopardy after dinner, you might say, (79) I'm Alex Trebek.
Even though there are complications, and we cannot give a full account of this kind of example here, it is at least plausible to say that (79) states that the speaker plays the role of Trebek. Similarly, our view agrees with Kripke that, in his example, Charles Darwin plays the role of Sherlock Holmes, and hence we should not be surprised that we can use (77) to describe this scenario.
It might be said that Kripke's objections should be understood as directed against the kind of analysis of existential statements like (73) that I proposed earlier.
On our account (73) is true at a world w just in case there is an individual x who occupies the Anna Karenina role at w. Correspondingly, as we noted, in some places Kripke describes the position he wants to reject as the view that "to affirm the existence of, say, Sherlock Holmes, is to say that there is a unique person satisfying the properties attributed to Holmes in the story." (Kripke 2013(Kripke [1973, p. 10).
Yet if this is indeed to be understood as Kripke's target, then his objection to the view seems to be the alleged consequences that we have summarized as K1-3. We have seen that these are not consequences of the account I have laid out here. It is not a consequence of my view that, if some actual individual turns out to occupy the Anna Karenina role in the actual world, then this individual is the referent of the name as it occurs in Tolstoy's novel. Nor is it a consequence of the view that the contents of the novel are anything more than accidentally true, in such a situation. And finally, it is not a consequence of our view that the fact that some individual who actually does not have the Anna Karenina properties could have had those properties means anything more than that this individual could have played the Anna Karenina role.
More generally, in the spirit of Kripke's arguments, one might object to the suggestion that, for example, the pope or the president of the US is a role. Indeed, it seems natural to say things like, (80) a. The pope isn't a role. The pope is an individual who lives in the Vatican.
b. The president of the US isn't a role. The president of the US is a flesh-andblood human being.
Yet these statements are compelling because they strongly suggest occupant readings. Take (80a). The first sentence conveys that Francis, the individual who was born in 1936 in Argentina, and so on, is not a role. That is of course true. Similarly, the second sentence has a true occupant reading. Francis is indeed an individual who lives in the Vatican. However, the observation we have relied on here is that, at the same time, much of our talk about the pope, the president of the US, and similar things, has a different aim. For instance, it is a datum that (5a), repeated here, can be used to say something about the papacy, not about any particular pope.
(5) a. The pope is the bishop of Rome.
Indeed, the second sentences of (80a-b) clearly have role readings, as well. Many definite descriptions have both occupant readings and role readings.

Conclusion
Fictional names denote individual concepts. This is an instance of the role-realist view on which fictional characters are roles constituted by sets of properties and relations. The dynamic framework for understanding the evolution of discourse information can be used to understand how such roles develop along with story content. Introducing a discourse referent and adding information about it to the file representing the content of the story amounts to creating an individual concept, and hence a fictional character. Taking fictional names to denote individual concepts provides accounts of a number of uses of fictional names, in particular, non-fictional uses, fictional uses, metafictional uses, interfictional uses, counterfictional uses, and negative existentials.
Acknowledgements Open access funding provided by Uppsala University. I owe a special debt of gratitude to David Davies and Graham Oddie for extensive discussion and help with this paper. I am also grateful to Emar Maier, Matti Eklund, Nils Franzén, Olle Risberg, Pål Antonsen, and two anonymous reviewers for helpful comments and suggestions. For financial support, I thank Riksbankens Jubileumsfond and the Swedish Collegium for Advanced Study.
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