TURNING ABOUTNESS ABOUT

There are two families of influential and stubborn puzzles that many theories of aboutness (intentionality) face: underdetermination puzzles and puzzles concerning representations that appear to be about things that do not exist. I propose an approach that elegantly avoids both kinds of puzzle. The central idea is to explain aboutness (the relation supposed to stand between thoughts and terms and their objects) in terms of relations of co-aboutness (the relation of being about the same thing that stands between the thoughts and terms themselves).


ABOUTNESS AND CO-ABOUTNESS
Representations are often about things. My belief that Porto is beautiful is about Porto, and the name 'Greta Thunberg' is about Greta Thunberg. This aboutness, also known as intentionality, 1 is the focus of this paper. Although many sorts of representations (thoughts, attitudes, linguistic items, maps, pictures, etc.) have aboutness, I will mostly discuss beliefs. Not much hangs on this choice; much of what I say here can be generalized to other kinds of representations.
To use a common illustration, consider a pair of archers drawing their bows at a range of targets. The archers stand in for representations, and (according to the orthodox conception of aboutness at least) the various targets that the archer might hit stand in for the objects that are candidates to be what the representation is about (candidate intentional objects).
There is a related feature of representations that will be of special interest here. Some representations have a common intentional focus, they are about the same thing. Two beliefs of mine may be about Stockholm. Different agents often have beliefs about the same thing. In terms of the archer illustration, the archers may direct their shots at the same target. This relation of having a common focus is sometimes called 'intentional identity', a label due to Geach (1967, p. 627). I will use 'intentional identity', 'co-aboutness', and 'co-intentionality' interchangeably. 2 We can ask whether any pair of representations are co-intentional, but the question is particularly interesting when it concerns apparently empty representations, that is, representations that appear to be about things that do not exist.

TARGET FIRST APPROACHES
According to a common approach to explaining aboutness and co-aboutness, we ought to focus on the objects representations are about (their 'intentional objects'). These are what I will call 'target first' conceptions of aboutness. In terms of the archer simile, target first approaches suggest that which objects the arrow actually hits captures the intentionality of the archer's shot. If this is right, to understand the intentionality of a given representation, we need only identify its intentional object, and to explain why a given representation has the intentionality it has, we need only explain why it is about that object. Roughly speaking, those who adopt the target first approach suggest that aboutness is just reference and that co-aboutness is just co-reference.
According to the target fist approach, what explains co-aboutness is the presence of some object that the representations are about. Priest (2005, p. 65 n. 12), Salmon (2005, pp. 105-108), Parsons (1980, p. 65 n. 2), and others defend theories of co-aboutness that are target first in this way.
Target first approaches to aboutness and co-aboutness are attractive and plausible. However, there are puzzles that are almost universally taken seriously by those working on aboutness that arise only if we adopt the target first approach. This suggests that those figures in the literature are committed, implicitly or explicitly, to the target first approach.

GOALS AND THE PLAN
My primary goal in this paper is to propose an alternative approach to aboutness. I propose that when explaining aboutness and co-aboutness, we ought to focus on the representations themselves and the relationships that stand between them (how the bows are directed). What is distinctive about non-target first approaches is that they do not give a central explanatory role to intentional objects. My proposal gives the objects the representations are about no role in explaining the aboutness of representations. The proposal is also distinctively co-aboutness first; it is not just archer first, so to speak, it is archers first. In a nutshell, the idea is that the aboutness of particular PACIFIC PHILOSOPHICAL QUARTERLY representations is explained in terms of which representations they are co-intentional with. I propose to explain aboutness in terms of relations of co-aboutness. 3 For those familiar with abstractionism in the philosophy of mathematics, my proposal can be understood as a kind of abstractionism about intentionality. I will argue that understanding aboutness in this co-aboutness first way helps us dissolve stubborn and influential puzzles that many leading theories of aboutness face and leads to an otherwise attractive and interesting approach to aboutness.
Here is the plan. I first distinguish the narrow content of representations and their aboutness. In the process, I clarify the explanatory roles that aboutness plays. This will yield some important tools that will allow us to evaluate theories of aboutness later in the paper. I then discuss two sorts of puzzles that most theories of aboutness face, underdetermination puzzles and puzzles concerning representations that appear to be about things that do not exist. These puzzles are seldom tackled together. This is significant because some well-received solutions to one of these kinds of puzzles do not help (and sometimes hinder) efforts to solve the puzzles of the other kind. I will then give a diagnosis of these puzzles; they arise only if we adopt a target first approach to aboutness and co-aboutness. I then sketch my own approach, discuss some constraints on how it should be implemented, and explain how it dissolves the puzzles in question. Finally, I will consider and respond to two lines of objection.

ABOUTNESS AND NARROW CONTENT
Let us distinguish the aboutness of an attitude from its narrow content. I will follow Lewis (1981Lewis ( , 1986 and Jackson (2010Jackson ( , 2015 in claiming that an attitude's intentionality does not supervene on its narrow content. Suppose there are two situations in which Jill is sitting at a bar when she sees a man walk in and sit down. In both cases, she sees the man is wearing a hood (she cannot see his face), and in both cases, she does not recognize the man but forms the belief that the man sitting at the bar is tall. The only difference between the cases is that the man at the bar is Jill's brother in one case, but a stranger in the other. What Jill's belief that the man at the bar is tall is about is different in these two cases; in one, it is about her brother; in the other, it is not. But there is also something that her beliefs have in common across the cases. They are the same from her point of view, at least in some sense. Let us call the feature of beliefs that captures this commonality the 'narrow content' of those beliefs. Suppose the beliefs in question are also true; the man at the bar really is tall in both cases. An attitude's narrow content captures its role in the psychology of the agent, guiding behavior and cognition, and any phenomenology associated with that attitude. The contrast between the two cases is a good reason to believe that an attitude's intentionality does not supervene on its narrow content.
Between the two scenarios, there is a difference in what the beliefs are about but no difference in their narrow content, so an attitude's aboutness does not supervene on its narrow content. By taking the claim that an attitude's intentionality does not supervene on its narrow content as a starting point, I am setting aside views according to which the narrow content of an attitude fully determines its aboutness. 4 Narrow content and aboutness play different theoretical roles. An attitude's narrow content is tied to its psychological, cognitive, behavioral, and phenomenal role. Exactly how to understand narrow content is not the focus of this paper.
A representation's aboutness helps explain co-ordination, communication, agreement, and disagreement concerning the intentional target of that representation. We often communicate, agree, coordinate, or disagree about things. Aboutness allows agents to track things across representations. For example, when I go from knowing little about some object to knowing more about that same object, one of the reasons that this is an instance of learning more about one thing rather than coming to represent a different object is that the earlier and later representations are about the same thing. Or to take an interpersonal example, when someone thinks that Daniel is in his office and someone else thinks Daniel is at home, they may be disagreeing partly in virtue of their beliefs being about the same thing. The aboutness of the representations unifies distinct representations by their tracking of the same subject matter, what they are about. Yablo (2014), Fine (2014Fine ( , 2016, and others suggest that what a representation is about crucially depends on what makes it true or would make it true. In this way, the aboutness (or subject matter) of a representation is supposed to supervene on its truth conditions. For present purposes, I will stay neutral on whether this is correct. It is not obviously correct. For example, on a plausible view of the truth conditions of beliefs, Pierre's belief that London is pretty might be true just in case there is a Londonish thing (a Londonizer) that is pretty, but this belief could be about London all the same (Lewis 1981(Lewis , 1986. For a recent discussion concerning how aboutness and truth conditions might come apart, refer to Sandgren (2019b, sect. 4).

UNDERDETERMINATION
Underdetermination puzzles are much discussed and influential. They take many forms and differ in detail (Wittgenstein 1953;Quine 1960;Benacerraf 1965;Devitt 1981;Kripke 1982;Lewis 1983b;Putnam 1988). 5 Underdetermination puzzles have a common structure; there are too many things that are candidates to be the intentional object of a representation PACIFIC PHILOSOPHICAL QUARTERLY and not enough resources to distinguish between them. That is, it is often underdetermined what the intentional object of a representation is.
Here are two examples to illustrate the structure of underdetermination puzzles, the first adapted from Wiggins (1968) and the second from Kripke (1982). Suppose Harriet, on coming into a room, forms the belief that Tibbles is on the mat. What is this belief about? One thing it seems to be about is Tibbles. But what is Tibbles? There are many objects on the mat, cat legs, whiskers, ears, fusions of whiskers and ears, catsminus-17-hairs, cats-minus-18-hairs, and so on. 6 Which one of these is what the belief is about? Perhaps Harriet intends to pick out a cat, rather than a cat leg and this goes some way to rule out some objects as candidates to be what the belief is about. The problem is that however rich the relevant intentions are, there will always be several objects that are candidates to be what the belief is about that fit these intentions equally well. That is, which object this relatively banal belief is about is underdetermined. There appear to be too many candidates to be what the belief is about and not enough resources in the intension of the believer or anywhere else, to uniquely determine which object the belief is about. 7 Suppose Jack is learning how to add for the first time. His mathematics teacher demonstrates how to add two numbers together and gives him some practice sums. On completing the first sum, 3 and 4, and arriving at 7 as the answer, Jack forms the belief that he has just performed addition. What operation is this belief about? The natural answer is 'addition'. But there are, to put it mildly, a whole lot of different operations that deliver the same output as the plus function when 3 and 4 are the inputs, but deliver quite different results when the inputs are different. Given the sheer number of functions, this will be true for any function and set of inputs. There will always be more than one function that delivers the same outputs as a given function over some set of inputs but deliver different outputs if given other inputs. If there are any functions at all, there an awful lot of them. For this reason, if all we have to go on when assigning functions to representations is the outputs the function delivers in a relatively small set of cases, there will always be more than one function fit to be what the attitude is about. One particular function will never be uniquely selected from the throng. Again, what the representation is about is underdetermined; there are too many candidate targets and not enough resources for distinguishing between them.
When confronted underdetermination puzzles of this kind, some, like McGee and McLaughlin (2000), deny that we can have genuinely singular thoughts about particular objects. Weatherson (2003, pp. 488-489) proposes instead that these problems force us to revise our conception of what it takes to think about particular objects, suggesting, with Jeshion (2002), that it is possible to have a de re belief about an object without being acquainted with it, either directly (e.g., via perception) or indirectly (e.g., via testimony).
Recently, Merlo (2017) and Openshaw (2020) have suggested that representations are in fact about all the candidate intentional objects.
Another common response to these kinds of underdetermination puzzles, defended by Lewis (1983bLewis ( , 1984, Sider (2011), and others, is to claim that some of the candidate objects are especially eligible to be what representations are about. Eligibility is standardly conceived of as coming in degrees; some object might be more eligible than a second but less eligible than a third. This relative eligibility is taken to be independent of the psychology and conventions of representers. If some objects are more eligible than others, we have a way to break the troubling ties between candidate intentional objects. The relevant attitudes might be about the plus function partly because the plus function is intrinsically more eligible to be an intentional object than other similar functions. Harriet's belief might be about the cat on the mat partly in virtue of the relations of relative eligibility that stand between the different candidate intentional objects. To return to the archer illustration, if the eligibility suggestion is correct, some of the targets attract arrows to them more strongly than others. I will not address or evaluate this kind of eligibility move directly, although it will help to keep it in mind as we proceed.

'EMPTY' REPRESENTATIONS
The second kind of puzzle concerns representations that are apparently about things that do not exist. Puzzles concerning empty representations are also influential and stubborn. They significantly guided early analytic philosophy of mind and language (Brentano 1874;Meinong 1960;Russell 1905;Quine 1948). 8 Again, these puzzles come in many forms but have a common structure; certain representations seem to have aboutness, but there appears to be no object such that they are about it. There are apparently not enough candidate intentional objects. Suppose that an agent believes that Vulcan is rocky. This belief appears to be about Vulcan. But how could this be if there is no such planet? The apparent intentional object of this belief appears to be missing. So it seems hard to make sense of the intentionality of this belief (it seems hard to find an intentional object for that belief).
A common response to this kind of puzzle is to bring exotic objects into the picture. The central idea is that apparently empty representations have intentional objects, appearances notwithstanding. They are just not the sort of familiar everyday objects we are familiar with. Different versions of this view involve different claims about the objects that apparently empty representations are about. Some, like Meinong (1960), appeal to non-existent objects. Others appeal to abstract objects (Salmon 2005;Thomasson 1999). Still others appeal to merely possible objects (Lewis 1978(Lewis , 1983a. In each case, the idea is to add in some more objects as possible candidates to be what representations are about so that apparently empty representations end up with intentional objects after all.

INTERPLAY
Appealing to exotic objects to handle cases involving empty representations makes underdetermination puzzles harder. Underdetermination puzzles arise because there are too many candidate objects. By adding the exotic objects as candidate objects, we add even more objects that must be distinguished when assigning intentional objects to representations. Not only will there be all the everyday objects to choose from, there will be all the exotic objects as well.
Maybe there are eligibility constraints on aboutness that will help us distinguish between everyday objects as candidate intentional objects. But it seems like these eligibility constraints will not allow us to make the appropriate distinctions between exotic objects. Exotic objects are one thing; relatively eligible exotic objects are quite another.
Note that eligibility constraints can make some distinctions between exotic objects but not the distinctions we need to handle underdetermination. For example, maybe all the non-existent witches are more eligible than all the non-existent schwitches (where schwitches are the same as witches, except on Tuesdays when they are unicorns). But this sort of relative eligibility will not suffice. To do the required work, the eligibility constraints would have to distinguish between different particular exotic objects and not merely between different kinds of exotic objects. After all, we are interested in representations about particular objects. It seems quite implausible that particular exotic objects stand in these sorts of relative eligibility relationships; that one non-existent, merely possible, or abstract witch is inherently more eligible than another to be what an attitude is about.
These puzzles tend to be discussed separately, and this interplay is seldom noticed. Here is a lesson to take away: when considering and evaluating solutions to these two puzzles, we ought to keep an eye on how the resources to which we are appealing in our solution to one puzzle interact with the other kind of puzzle.

A DIAGNOSIS
These two kinds of puzzles have been hugely influential in shaping the course of (at least) analytic philosophy of mind and language. Each kind of puzzle has given rise to its own enormous literature.
It seems to me that both kinds of puzzles (as they are traditionally posed) only arise if we adopt the target first approach. Underdetermination poses a problem because if it is radically underdetermined which object the representation is about, then the aboutness of those representations is also radically TURNING ABOUTNESS ABOUT underdetermined. In cases involving apparently empty representations, the relevant target appears to be missing and yet the representation has aboutness. This is puzzling if the aboutness of a representation is supposed to be captured in terms of the object it is about.
The observation that the puzzles are so influential, combined with this explanation of how the puzzles arise, is evidence that the target first approach is common, even if it is seldom stated explicitly. Of course, I do not claim that it is impossible to find a solution (rather than a dissolution) to both kinds of puzzles consistent with the target first approach. But if the target first approach gives rise to these stubborn and influential puzzles, it is worth considering alternative approaches. This diagnosis also reveals some interesting theoretical possibilities; if we can explain aboutness and co-aboutness in a non-target first way, we can sidestep these puzzles altogether.

CO-ABOUTNESS AGAIN
The target first conception of aboutness and co-aboutness leads naturally to the following conception of aboutness, co-aboutness, and the relationship between the two: what explains the aboutness of particular representations is the object they are about and what explains co-intentionality is that the representations are about the same object. In terms of the archer illustration, the target hit captures the directedness of the shots and the shots are directed in the same way if, and only if, the archers both hit the same target.
Geach famously poses a challenge to this way of understanding co-aboutness in line with the archer illustration.
[A] number of archers may all point their arrows at one actual target…but we may also be able to verify that they are all pointing their arrows the same way, regardless of finding out whether there is any shootable object at the point where the lines of fire meet (intentional identity). We have intentional identity when a number of people, or one person on different occasions, have attitudes with a common focus, whether or not there actually is something at that focus. (Geach 1967, p. 627) The idea is that representations can be co-intentional even when there is no thing such that they are about it. That is to say, apparently empty representations (such as beliefs about Vulcan, a witch, or the fountain of youth) can be co-intentional. Priest (2005, p. 65 n. 12), Salmon (2005, pp. 105-108), and Parsons (1980, p. 65 n. 2) uphold the target first approach to co-aboutness in the face of Geach's challenge. They argue that when the relevant representations are apparently empty, their co-aboutness is explained by the presence of the object they are about. These accounts differ in detail but involve the same basic explanation of co-aboutness. Co-aboutness is explained by the presence of the object the representations are about (the target both archers hit).
These theories of co-aboutness face significant underdetermination problems of roughly the kind discussed earlier (Thomasson 1996(Thomasson , 1999Sandgren 2018). This should not be surprising if my diagnosis of underdetermination puzzles is correct and given the interplay between the two puzzles discussed earlier. What follows is a summary of a recent formulation of this underdetermination challenge from my 'Which Witch is Which? Exotic Objects and Intentional Identity' (Sandgren 2018, pp. 729-731). The collections of exotic objects are typically uncomfortably large. There is not just one (non-existent, merely possible or abstract) witch, or merely a hundred, or merely a thousand. If we are committed to such things at all, there are ever so many witches, inter-Mercurial planets, and magic fountains. If the presence of an exotic object is going to explain why two apparently empty representations are co-intentional, we need a story about how each representation gets assigned this exotic object rather than some other and how two representations come to be about the very same exotic object. But the abundance of exotic objects, combined with the observation that these objects do not stand in causal relations with agents in the way that everyday objects do, means that it is extremely difficult to give a principled story about how two representations get to be about the same exotic object. There are just too many objects to select from and not enough resources to appeal to when assigning them to representations. This is a kind of underdetermination argument that threatens target first theories of co-aboutness in full force.
Others claim that we can make sense of co-aboutness without appealing to intentional objects in our explanation; they propose archer first theories of co-intentionality. Dennett (1968), Donnellan (1974), andGeach (1976) make early attempts at archer first explanations of co-aboutness. More recently, Perry (2001), Sainsbury (2010), Crane (2013, p. 165), Friend (2014, Pagin (2014), Sandgren (2019a), and Garcia-Carpintero (2020) have all defended archer first theories of co-aboutness. These views differ in detail, but they all attempt to explain co-aboutness without appealing to intentional objects (exotic or not). Instead, these accounts center on the features of the representations themselves and the relations that stand between them. 9 3.2. AN ALTERNATIVE EXPLANATION I propose that we first adopt an archer first conception of co-aboutness and then appeal to relations of co-aboutness to explain the aboutness of particular representations. This proposal reverses the direction of explanation characteristic of target first approaches in two ways. First, instead of the TURNING ABOUTNESS ABOUT aboutness of the respective representations in combination explaining their co-aboutness, their co-aboutness explains their individual aboutness. In this sense, the proposal is archers (in the plural) first. This is the most novel part of the proposal and the part which distinguishes it from other archer first accounts.
Second, according to the proposal, the relations of aboutness and co-aboutness are explanatorily prior to the object the representations are about. Accordingly, the object representations are about does no work in explaining their aboutness.
Here is an illustrative case: suppose I indicate some belief and ask 'what is that belief about?' Suppose you correctly answer 'Stockholm'. When you give this answer, are you providing Stockholm, the city itself, as the answer? In a sense you are, your answer involves representing Stockholm. But there is a sense in which you do not supply the object itself as an answer. To see this, consider a case in which the correct answer to a 'what is that belief about?' question appears to involve representing something that does not exist. For example, the correct answer might well be 'Vulcan', even if the questioner and the answerer agree that there is no such planet. In cases like these, the correct answer seems to involve representing Vulcan without requiring the answerer to produce the planet, as it were. So it seems as if when correctly answering questions like 'what is that belief about?', we indicate an object or set of objects but we do not, in general, provide the object itself as the answer. So perhaps when one correctly answers 'Stockholm' in response to the question, one does not provide Stockholm itself as an answer, rather one provides a representation which, if the answer is correct, is about the same thing as the belief in question. This is an alternative explanation of what is going on in our talk of what representations are about; we are really negotiating relations of co-aboutness, rather than dealing in the objects themselves. The aboutness of a given representation is, on this picture, a product of a broader representational economy. We can, it seems, make sense of much of our discourse about what representations are about while appealing only to relations of co-aboutness roughly along the lines just mentioned. What is more, as long as we adopt an archer first approach to co-intentionality, we can do all this without having to appeal to a fact about which of the many candidate objects the relevant representations are about in our explanation.
Recall that aboutness allows us to track things across representations, thereby facilitating disagreement, agreement, communication, and so forth. According to the orthodox view, the presence of an intentional object is required to unify the relevant representations as being about the same thing. I propose that on the contrary, we deal in co-aboutness directly when explaining this kind of tracking. What is more, many of the phenomena often associated with co-aboutness such as communication, disagreement, and agreement can arise in cases in which the relevant representations appear to be about things that do not exist. We can track what beliefs are about even when the intentional objects are apparently missing. However identification of subject matter is achieved in cases in which the relevant representations are empty; it is not obviously achieved in virtue of there being some object such that the representations are about it. In other words, aboutness is not just reference, and co-aboutness is not just co-reference.
Although the proposal is archers first, it is not archers only. The proposal leaves room for the objects representations are about; it is just that these objects do not do any work in explaining the aboutness of representations. Once we have the relations of being about the same thing that stand between the relevant representation and other representations, we get the object it is about for free. The presence of the object the representations are about is not taken to explain their co-intentionality, rather it is a descriptive (rather than explanatory) fact that when you have relations of co-intentionality, you also have the target the representations are about. This move fits with and is motivated by a kind of easy ontology approach defended by Carnap (1950) and, more recently, Thomasson (2015). We can still talk about 'the object the representation is about', but this target is, so to speak, a mere shadow of the relations of co-aboutness the representation stands in.
Note that the co-aboutness first approach leaves room for representations to have reference. We can sensibly ask about whether a representation has reference, where reference is taken to be something distinct from aboutness. For example, one might suggest that a belief about Stockholm refers to Stockholm in a way that a belief about Vulcan does not refer to Vulcan. This is perfectly compatible with my proposal. The crucial point is that unlike those who adopt a target first approach, my proposal involves rejecting the claim that aboutness just is reference and the claim that aboutness can be explained in referential terms. If my proposal is right, reference and co-reference are not what explains aboutness and co-aboutness. But that does not entail that there is no such thing as reference.
The central idea is that no matter how much a representer tries to think or talk about an object itself, they will, at best, only be able to produce yet another representation about the object. But this need not worry us. We can, I suggest, get everything we need with respect to aboutness and co-aboutness without appealing to the object itself as doing any explanatory work.

CHOOSING A THEORY OF CO-ABOUTNESS
The co-aboutness first proposal crucially involves appealing to an archer first theory of co-aboutness, and we had better choose an archer first view that allows us to recapture as many of the attractive features of the target first approach as possible. There are a number of options here. For the purposes of illustration, it will be helpful to have an example of an archer first view of co-aboutness in mind. To this end, I will outline the causal theory of co-aboutness defended by Donnellan (1974), leaving some details to the side. In broad terms, the idea is that co-aboutness is a matter of the representations themselves standing in the right sort of causal relations with each other. These causal relationships are characterized as usually involving individual psychological connections or deferential uses of words or concepts. 10 Crucially, the causal chain in question need not involve the object or objects the respective representations are about (although sometimes it will). For instance, consider a case in which two people who live in the same village read the same newspaper report claiming that there is a witch terrorizing the village. It seems as if these people can form beliefs about the same witch. According to the simple causal account of co-intentionality, any beliefs they might form concerning the witch are co-intentional because they have a common causal history involving the newspaper article.
I do not endorse the simple causal theory of co-aboutness. In fact, I think the simple causal theory is crucially limited. For example, as Edelberg (1992, pp. 574-575) and Everett (2013, p. 96) argue, there are cases of co-aboutness that do not involve the kind of common causal history present in the newspaper case. Edelberg and Everett discuss cases analogous to Frege's well-known Alpha-Ateb case except that the putative target of the representations is missing. For a recent discussion of this point, refer to Garcia-Carpintero (2020, p. 14). These cases suggest that although causal links between the representations in question are often crucial for explaining co-aboutness, co-aboutness does not always require such a link. There are also complications concerning how causally isolated agents might represent the same abstract object (e.g., a universal or a mathematical function). Again, whatever the explanation of co-aboutness in cases like this is, it cannot involve a causal link between the beliefs themselves because, ex hypothesi, the agents are causally isolated. Finally, there are issues arising from some ingenious cases due to Edelberg (1986Edelberg ( , 1992, which seem to show that co-aboutness is sensitive to how the believers take the facts about the identity to be. It is not clear how one can accommodate these data within a simple causal account. The co-aboutness first approach does not stand or fall with the simple causal account of co-aboutness. There are a number of not-purely-causal archer-first accounts of co-aboutness to choose from, for example, Crane (2013, p. 165), Pagin (2014), Friend (2014, Sandgren (2019a), and Garcia-Carpintero (2020).
Which one do I favor? The short answer is, predictably, my own. My proposal handles both the newspaper case and the cases just discussed that cause trouble for the simple causal account (Sandgren 2019a, p. 3690). Moreover, some of the other not-purely-causal archer-first rivals to my proposal are not as general. For instance, Garcia-Carpintero's view only applies to fictional cases (in which the believers do not take the target of their beliefs to be actual, concrete objects) and not to mythical cases (in which the believers believe that the target of their beliefs is actual and concrete.) 11 My theory also accounts, in a natural way, for the Edelberg-style cases I alluded to earlier that suggest that facts about co-aboutness are often sensitive to how the believers take the identity facts to be (Sandgren 2019a, p. 3692). These cases seem hard to capture within models based on similarity of representation (like Crane's), at least without augmenting the story considerably, refer to Sandgren (2019a, pp. 3683-3685). However, because my proposal is fairly complex and my primary goal here is to discuss the co-aboutness first approach, it is beyond the scope of this paper to spell out and further motivate my theory of co-aboutness. For the purposes of illustrating the co-aboutness first approach to aboutness, I will work with the simple causal view. This choice is harmless for present purposes because my view and many of the other not-purely-causal archer-first theories of co-aboutness behave similarly to the simple causal theory (delivering the same verdicts for similar reasons) in the cases of co-aboutness discussed here.

IGNORANCE, ERROR, AND DISAGREEMENT
Target first approaches to aboutness and co-aboutness have a natural account of how agents can be ignorant or mistaken about what representations are about. Jill in the hooded man case is one such example. When the hooded man is her brother, her belief is about her brother, although she is ignorant of that fact. The explanation in line with the target first account is simple, what makes the difference is that the man she sees in the bar really is her brother in one case but not in the other.
The target first approach also yields a simple and attractive account of how it is possible for agents to disagree about a target. Often part of what is required for disagreement is that the relevant elements of thought and talk are about the same thing. According to the target first approach, inasmuch as thinking and talking about the same thing is required for disagreement, they are disagreeing only if and because there is an object such that the relevent thought and talk is about it.
These and other features of the target first approach can be recaptured on my proposed picture, provided we are careful about which archer first account of co-aboutness we adopt. Consider an extension of the hooded man cases discussed earlier. Suppose that in both cases (in the case that the man at the bar is a stranger and the case when he is Jill's brother), Jill also has a separate belief that her brother is excellent at table tennis. This belief is plausibly about her brother in both cases. But in one case Jill's belief concerning the man at the bar is co-intentional with her table tennis belief, while in the other it is not. If we adopt the straightforward causal view of co-aboutness, this would be because the two beliefs stand in different causal relations in the two cases. Jill may be unaware or mistaken concerning whether her beliefs are co-intentional. According to the co-aboutness first picture, which representations a representation is co-intentional with will determine its aboutness and she may be ignorant or mistaken about which representations are co-intentional. So if Jill is ignorant or mistaken about which representations her belief is co-intentional with, she is ignorant or mistaken about the intentionality of her belief.
Any archer first theory of co-aboutness worth its salt will allow for disagreement between co-intentional representations. Certainly, many archer first theories of co-aboutness do. The simple causal account certainly does. Which causal relations the representations stand in can vary freely with what properties are being ascribed to the intentional target, so there is nothing stopping representations being co-intentional and ascribing conflicting properties.

THE PUZZLES DISSOLVED
The co-aboutness first account does not face the underdetermination puzzles or puzzles concerning empty representations discussed earlier. There is no mystery about how representations that appear to be about things that do not exist have aboutness. When they have intentionality, they will often stand in co-aboutness relations and, as long as we adopt an archer first account of co-aboutness, the explanation of this co-aboutness will not involve identifying some common intentional object. If our explanation of intentionality does not appeal to intentional objects, it should not worry us that in some cases, there appear to be too few intentional objects to go around.
Traditional underdetermination puzzles do not arise either. The co-aboutness first explanation of the aboutness of a given representation will not involve identifying its intentional object. So the fact that there are too many candidate intentional objects need not concern us. Consider the case of Jack learning to add. I propose that the explanation of how he is thinking about the same function as his teacher does not involve both Jack and his teacher selecting the same function from the many. Rather, there is some explanation of how their representations are about the same thing that does not involve their intentional objects, and this directly explains the fact that Jack and his teacher can represent the same function. If we eschew intentional objects as an explanatory resource, our explanation of intentionality is not threatened by the fact that there are too many candidate intentional objects.
These are not solutions but dissolutions of the puzzles. The proposal does not yield guidance on how representations get to refer to one object on the mat rather than another, or to one mathematical function rather than another.

Objections
I will now consider some objections to the co-aboutness first approach. Because the co-aboutness first proposal is the central topic of this paper, I will limit myself to objections to the co-aboutness first approach taken as a whole and set aside objections to this or that archer first theory of co-aboutness.

LONELY REPRESENTATIONS
One might be tempted to object to the co-aboutness first approach as follows: suppose Robyn is looking out into a paddock at a horse. Suppose Robyn forms a belief that the horse in the paddock is gray. There is no one else around. Robyn's representation seems to be about the horse. Yet there is no one else around and, we can suppose, there might not be any representations of the horse other than Robyn's. How can this intentionality be explained by an appeal to the belief's being co-intentional with other representations?
First, it is plausible that Robyn has more than one representation of the horse. For instance, her belief about the horse might be about the same thing as her visual representation of the horse. If this is true, the aboutness of Robyn's belief can be captured partly in terms of its being co-intentional with some of her other representations.
But this response does not really address the spirit of the objection. What if Robyn had no other representations and there are no other representations of the horse? What if the representation is 'lonely'? Isn't the belief about the horse even if it is the only representation of the horse in the scenario? How could an account of aboutness that rests on relations of co-aboutness explain this?
I respond that there is another representation of the horse, even if we insist that there are no other representations of the horse in the scenario. The objector presenting the case is herself representing the horse.
But does this not make the intentional features of Robyn's belief too dependent on how it is described or on its relationship to us qua theorists? I do not think so. Recall that the aboutness of a belief can be distinguished from its role in the agent's narrowly construed psychology. The belief described in the case may only have its aboutness partly in virtue of its being about the same thing as the representation of the theorist considering the case, but its psychological role is independent of that fact. She may reason, talk, and behave in accordance with the belief. These beliefs will guide Robyn's behavior and cognition in a way that does not depend on its aboutness. Recall that aboutness is for tracking objects across representations. Aboutness allows us to track that horse (what the belief is about) across representations. In lonely representation cases, there are no other representations across which to track the intentional object. In these cases, the aboutness of the representation in question is idle, in a sense, except inasmuch as the person describing the case and their representations goes. Within the scenario, there is no other representation across which that horse, qua intentional target, needs to be tracked.

MOVING THE BUMP UNDER THE RUG
Another objection is that the co-aboutness first proposal merely moves the puzzling underdetermination around. After all, for many pairs of representations, it will be underdetermined whether they are co-intentional. Am I not trying to explain away puzzling underdetermination with something that is itself underdetermined in the same puzzling way?
Co-aboutness will be somewhat underdetermined. Indeed, it would be suspicious if our account of co-aboutness did not allow for some underdetermination. Subject matter identification just is a somewhat messy business. However, this kind of underdetermination is importantly different from the kind of radical underdetermination at play in traditional underdetermination puzzles.
Suppose Harriet and Meg walk into a room and, in response to what they see, form beliefs to the effect that Tibbles is on the mat. In line with the traditional underdetermination puzzle, we might wonder how each of these beliefs come to be about Tibbles, rather than one of the other candidate objects. According to the target first understanding of aboutness and coaboutness, for these two beliefs to be about the same thing, the underdetermination has to be resolved, and it has to be resolved such that both Harriet's belief and Meg's belief are about the same object. They both need to uniquely pick out the same object. If we adopt the target first approach to aboutness, the kind of underdetermination tied to the traditional underdetermination puzzles gets in the way of delivering the correct verdicts about co-aboutness in simple cases like this. The kind of underdetermination that remains within a co-aboutness first story does not get in the way of these beliefs being co-intentional. If my proposal is right, what matters is that the representations are co-intentional. The Harriet and Meg case is a clear case of co-aboutness according to all the leading archer first theories of coaboutness. Maybe Harriet and Meg disagree about where, exactly, Tibbles ends (spatially, temporally, or even modally), and this might make a difference to which representations their respective representations are co-intentional with. But this sort of underdetermination is confined, on my picture, to the disputed cases of co-aboutness and does not threaten the clear cases of co-aboutness; the underdetermination is correctly confined to borderline cases.

Concluding Remarks
The co-aboutness first approach is attractive and avoids some serious, influential, and stubborn puzzles that threaten its rivals. I have only presented the view in broad outline, and there are many important details to be filled in and refinements to be made. Nonetheless, I hope I have done enough to suggest that the co-aboutness first approach to aboutness is worth taking seriously and that there is worthwhile work to be done refining the view, getting clear on its limitations, and exploring the theoretical opportunities it offers. 12 Department of Historical, Philosophical and Religious Studies Umeå University NOTES 1 I prefer the 'aboutness' label because intentionality is often confused with intensionality. 2 I prefer the latter two labels because 'intentional identity' suggests that the relation must be explained in terms of identity relations among intentional objects. As we will see, this treatment of co-aboutness should not be taken as given.
3 In this way, my proposal differs from other archer first theories of aboutness defended by Farkas (2008), Kriegel (2008), Montague (2016), Mendelovici (2018), and others. These views, which are typically grouped under the umbrella of 'phenomenal intentionality theories', center on the intrinsic phenomenal features of individual representations in their treatment of intentionality. For a recent discussion of how phenomenal intentionality theories relate to questions of coaboutness, refer to Clutton and Sandgren (2019). 4 For a discussion of the view that aboutness is narrow, refer to Farkas (2008). 5 Underdetermination puzzles have an ancient pedigree. An underdetermination puzzle takes center stage in Plato's Cratylus (385a-390e) in the form of an argument against the conventionalist view attributed to Hermogenes. 6 For a recent excellent discussion of this kind of plenitude, refer to Fairchild (2019). 7 What if one adopts a relatively sparse object ontology such that most of these fine-grained entities do not exist (e.g., the ontology of ordinary objects defended by Korman, 2015)? Isn't one out of the woods here, at least as regards the Tibbles case? In presenting the problem, we seemed to be coherently talking and thinking about the different fine-grained entities. If one has a sparse ontology, one is committed to treating those representations as empty so by making this move, one has turned a problem of too many into a problem of too few. This might be advisable as far as it goes, but the puzzles discussed in Section 2.2 come in full force. 8 Puzzles involving empty representations also have an ancient pedigree. For instance, cases of this sort are central to the discussion in Plato's Sophist (236d-364b). 9 Note that this does not mean that they do not involve intentional objects at all. Rather, the idea is that if intentional objects are part of the story, they do not explain the intentional features of representations. They are archer first, not necessarily archer only. 10 Donnellan's view runs parallel with a causal theory of the semantics of proper names. The debate between purely causal theories of co-aboutness and the causal descriptivist theory of