Acquaintance, mental files and mental graphs Jim Pryor, NYU Section 1 --------- Suppose I know there to be some, but finitely many, spies. Suppose there is also what I know to be some linear ordering of spies: say, spy x counts as short'er than spy y iff spy x is shorter, or if they're the same height but spy x was born earlier, or if they're born at the same time but spy x was born closer to the equator, and so on. Then I'm in a position to know that there is a short'est spy. Am I in a position to have singular knowledge, of the person who is in fact the short'est spy, that he or she is a spy? Am in a position to even *consider* that singular thought? Depending on my circumstances, this second question might not be easy to answer. To adapt an example of Robin Jeshion's, it may turn out that, unbeknownst to me, *she* is a spy and in fact is the short'est spy. (Spies tending to be rather tall.) And I certainly *can* consider the hypothesis, concerning Robin, that she is a spy. Now fans of singular thoughts sometimes think of them as "Russellian": any "way" of thinking singularly about someone who is in fact the short'est spy is equivalent. On such views, it turns out that I *can* at least *consider* the singular thought of the short'est spy that she is a spy. But presumably I'm not in a position to *know* that thought, since I have so much doubt that Robin is a spy. And presumably also I'm not in a position to *know that I can consider* that singular thought; at least, not as so-described. Other fans of singular thought think of them as finer-grained: different ways of thinking about Robin can yield different singular thoughts about her being a spy. On such views, the kind of singular thought I had in mind---when I asked whether I could consider the singular thought, of the person who is in fact the short'est spy, that he or she is a spy---this kind of singular thought, I may not be in a position to consider. Whether I am depends on how easy it is to have singular thoughts. Or if my circumstances are different, and the short'est spy is in fact someone I've never laid eyes on, heard testimony about, and so on, in that case even some Russellians will deny I'm in a position to consider this singular thought. Whether I am depends again on how easy it is to have singular thoughts. Fans of "acquaintance" constraints on singular thought say that in these cases, no, I can't even consider the singular thought. In the second case, I'm not acquainted at all with the short'est spy, and so I can't have *any* attitudes towards singular thoughts about him or her. In the first case, where we think of singular thoughts as fine-grained, then although it's true I am acquainted with Robin, and she is in fact the short'est spy, I'm not acquainted with her *as* being such. In this case too, what singular thoughts I'm in a position to have is constrained by what things I'm acquainted with---and how I'm acquainted with them. What exactly counts as "being acquainted" is something theorists have different views about, so let's leave this open for the time being. Minimally, we should expect this relation to exclude my being acquainted with the short'est spy, just by virtue of being in the epistemic position I described. Foes of "acquaintance" constraints fall into two groups, what we might call "direct" foes and "meta" foes. The "direct" foes directly disagree with the view just expressed. They think whenever you're in a position to know that there's a unique F, you *are* in a position to consider singular thoughts about it: for instance, the thought that you've ever crossed paths with it. Perhaps also you're in a position to *know* some singular thoughts about it, for instance, the thought that it is F. The "meta" foes disagree in a less direct way. What they in the first place doubt is that the notion of "acquaintance" that we haven't yet tried to sharply pin down *can* be pinned down in any rigorous and definite way, while still doing the work the fans of "acquaintance" want it to. These theorists might hesitate to say unequivocally that one *can* always consider or know the singular thought, of the short'est spy, that he or she is a spy. That may depend ineliminably on the dialectical setting in which the question is raised. Section 2 --------- I used to count myself a fan of acquaintance. I was liberal about the constraints I believed singular thoughts were subject to, in respects that not every fan of acquaintance agrees with. But I still thought there were genuine and explanatorily important constraints. What I mean here by "explanatorily important" is that there are some philosophical theories that give singular thought a distinctive explanatory role: for instance, Evan's views on immunity to error through misidentification, Peacocke's views on perceptual knowledge in The Realm of Reason (2003; but perhaps I'm misremembering material from Being Known 1999), Brewer's views on perceptual content in his Perception and Reason (2002), some views on the role of intention in action, and so on. I'm not myself a subscriber to any of these theories; but they are all premised on a kind of distinctiveness to singular thought that would be illusory if it weren't constrained in the way the acquaintance theorist envisages. And it seemed to me that this is a legitimate premise to rely on. There are four ways in which I was "liberal" about acquaintance constraints. First, my confidence in definite and explanatorily important constraints was limited to *subjects having* certain kinds of mental states, not to *the correctness of ascribing* mental states in certain ways. I thought there was *a kind of thought* about the short'est spy that I'm not in a position to have. I doubt that there are the same kinds of constraints on *ordinary folk ascriptions*. If I'm not acquainted with the short'est spy, as such, but you are, it's not obviously incorrect for you to go up to her and say "Jim is trying to establish whether you work for China." Or, at least, ascriptions of this sort wouldn't always be incorrect. Some acquaintance theorists do think there are acquaintance constraints on the correctness of ascriptions as well; many of them find it unintelligible for our theories of thought and our theories of folk thought-ascription to come apart in the way I suspect they do. I'm inclined to sympathize with the "meta" doubts about any definite acquaintance requirements on ascription. But I can still get my head around a kind of thought that may be harder to have than our folk ascriptive practices directly reveal. ("Latitudinarianism" is sometimes used as name for anti-acquaintance theory. This term was introduced in the 1970s; I think by Sosa but I haven't verified that he wasn't following someone else's usage. In my mind, though, I associate this term more with the denial of acquaintance constraints on the correctness of folk ascriptions, which I am sympathetic to, than to the denial of acquaintance constraints on thought. When Sosa was writing these weren't yet being sharply distinguished.) Second, I was pretty relaxed about what it took to be acquainted with something. I didn't see any difficulty with becoming acquainted with something by hearing testimony from someone else who was so acquainted (it needn't even be sincere testimony). I didn't see any difficulty with becoming acquainted with something by seeing its shadow, especially if the shadow was moving. If we have to make sense, not just of being acquainted with someone, but with, say, being acquainted with Robin *as* the short'est spy, it becomes more difficult to say what does and doesn't count. But my inclinations here were clearly different than Russell's, who thought you couldn't be acquainted with anything unless it was epistemically certain for you that the thing existed. In fact, and this is a third sort of liberality, I was open to the idea of there being singular thoughts without referents. Consider three cases, in each of which I know I've never yet perceived something to be a leprechaun. In case (i), I then do come to perceive something to be a leprechaun, and know myself to do so. In case (ii), I undergo a hallucination indiscriminable from case (i), but in fact there is nothing I am perceiving---not even something I'm misperceiving to be a leprechaun. However, I wrongly take myself to be in case (i). In case (iii), I neither perceive nor seem to perceive a leprechaun, but I'm in a position to know I someday will. (I'm an immortal leprechaun hunter, and I know they're out there.) Now suppose in each case I attempt to frame to myself a singular thought, about the first leprechaun I'll ever see, that I'm now perceiving it. In the third case, I'm not disposed to believe this thought, but we're asking whether I can even consider it to reject it. In the first case, presumably I can frame this thought. An acquaintance theorist will say the third case is importantly different; in that case this thought isn't even available for consideration. But now what about the middle case? All acquaintance theorists should count this case as like case (iii) with respect to whether I can have singular thoughts about the object which is *in fact* the first leprechaun I'll ever see---some as-yet-unmet leprechaun. But plausibly I do here manage to do *something* with my mind that I'm not also in a position to do in case (iii). I do contort my mind in a way that *feels like* having the singular thought we agree I do have in case (i). There are interesting differences between case (ii) and case (i), but there are interesting similarities as well. An an important theoretical choice is whether one theorizes with a notion of "singular thought" that includes both of these cases---as interestingly different species---or whether one theorizes with a notion that only includes case (i). My third sort of liberality was in prefering the more inclusive notion. I regarded some thoughts that have no genuine object, as in case (ii), as having an interesting theoretical unity with thoughts that do. Perhaps "singular thought" and "object-dependent thought" and "de re" thought aren't the best labels for this notion; yet I thought of this view as continuous with the views that spawned those labels. We might more perspicuously describe what you have in case (i) and case (ii) as "object-directed" thought: a contortion of the mind that aims to be, and feels like being in, the relation to an object you're only genuinely in in case (i). I was a fan of acquaintance constraints on these kinds of thoughts. Fourthly, I was receptive to individuating thoughts more fine-grainedly than "Russellians" do. So I was inclined to think there were multiple singular thoughts concerning the individual Robin Jeshion who is in fact the short'est spy, to the effect that she is a spy. Some of these thoughts I am in a position to consider, and others I'm not. Here's another kind of example I used to discuss. It's possible to have dreams about particular people, say your mother. It's part of the dream that this is X, the person who is fact your mother (which isn't the same as being someone who the dream says mothered you). It's also possible for there to be characters in your dream who aren't any particular people you've ever met. Suppose you have a dream of the second sort about a woman with certain distinguishing features, features you've in fact never before perceived. Suppose it's also part of what the dream says that this is the first person you ever met who looks like this. Now suppose that years later you do in fact, knowingly, meet in real life a woman who looks just like you dreamt. Was your long-ago dream in fact about this person, in the way that other dreams were about your mother? It's intelligible that it was; perhaps your dream was some kind of prescient revelation of the future. I don't believe that kind of thing happens in reality, but I find it an intelligible possibility. But *must* that be what happened? Must your dream have been about this future person who you now know perfectly matches it, even to the extent of being the first person you met who looks like this. It's a strange kind of case. We might talk in ways that sound like they do count the dream as being about the future woman; but acquaintance theorists will want to say that the kind of "aboutness" they're theorizing about---the kind that obtains between your dreams about your mother and her---won't in fact obtain between the other dreams and the future woman. At least, not in the cases where the dream isn't a prescient revelation. So that was the sort of position I had worked myself to in thinking about singular thought. I don't now want to talk so much *about* that position as about the trajectory my thinking has taken from that starting point. I don't expect my intellectual biography as such has much interest for you. But I thought that articulating where I came from might help you better understand and appreciate the view that I've now come to, and am going in the rest of this talk to develop. Section 3 --------- Anyone who is sympathetic, as I am, to singular thoughts being finer-grained with respect to their objects than just the identity (or existence) of their object, faces a certain challenge. This challenge arises because we theorists already countenance a notion of going-together-in-some-fine-grained way that may hold or fail between thoughts in general, not just singular thoughts. For example, a preorder is a kind of mathematical relation, and some preorders are symmetric. The notions of a symmetric preorder and an equivalence relation are logically equivalent. Suppose I have some semantically simple way of thinking about symmetric preorders---let me coin the word "simpro." Then the thought that every simpro has the diamond property (look this up if you're curious, the details don't matter here) will be of the form "Every S is D," where S and D aren't cognitively structured. This is a general thought, not a singular thought. It is structurally the same as the thought that every equivalence relation has the diamond property; and moreover those two thoughts are logically equivalent. However, it is intelligible for me to be unaware that, or to have momentarily lost track of the fact that, simpros are identical to equivalence relations. So it's possible that for me, these are two different fine-grained thoughts. So if a theorist can point to some thoughts (or perhaps point in different ways to the same thought), a question she can ask is: are these the same fine-grained thought for a given subject, or not? She can also ask further questions. For instance, she can catch me saying to myself, on one occasion, "Every simpro has the diamond property," and on a different occasion, "No equivalence relation is asymmetric." These are clearly different thoughts, for the one is of the form "Every __ is D," and the other is of the form "No __ is A." But the gap in each case is filled by a way of thinking about a single class of relations. And our theorist can ask whether these thoughts are about that class in the same fine-grained way. Now, when we turn to singular thoughts and the debate about acquaintance requirements, one way of structuring the issues is like this. First, we identify some "privileged" set of thoughts---what the acquaintance theorist would deem as including at least one of your singular thoughts about each thing you can singularly about, and no non-singular thoughts. Second we ask the question what other thoughts go together with these in some fine-grained way. The debate will have a different character about these two questions. Fans and foes of acquaintance might agree about how to go about answering the second question. This is just Frege's problem, they'll say. What they'll disagree about is whether there is any interesting basis for selecting a "privileged" set of thoughts to be interested in, in the first place. The foes of acquaintance might be happy to allow that there is a well-defined notion of thoughts that go together in the way we're imagining with all the thoughts you formed on the basis of perception. Or with all the thoughts you formed on the basis of testimony. Or with all the thoughts you deduced from what you know about short'ness. What they doubt is whether there's any theoretically distinctive, unified way of identifying one of these starting sets as explanatorily special. One thing I've come to realize is that I'm much less interested in the first question---the question of which sets of thoughts to use as starting points---and more interested in the second question---given some selected set of starting thoughts, the question of which other thoughts should be grouped together with them. We might put it as: which other thoughts involve the same fine-grained "concepts" or ways of thinking deployed in the starting set. But the use of the term "concept" here is hazardous, for we shouldn't prejudge the question of whether the Fregean phenomena we're discussing are limited to thought contents that fall on one side of the fence in debates about "conceptual" vs "non-conceptual" content. Perhaps they are so limited; or perhaps they're not. (Or perhaps we shouldn't be comfortable with the way the debates about "conceptual" vs "non-conceptual" content divide the field, in the first place.) I'd like to leave that to settled separately. I'd prefer to talk instead this way: there's a partial content involved when you think to yourself "Robin is a spy." That partial content is also involved when you think to yourself "Robin doesn't have the diamond property," and may also be involved in dreams you have about Robin at an APA meeting on the moon. It may or may not also be involved when you see Robin, never having met her before or knowing who she is. (Perhaps the partial content involved in the latter case is interestingly different, because "non-conceptual.") I'm myself happy to regard our thoughts as being structured, but I think we can make some sense of this notion of "partial content" even if we don't. Proceeding in this way, the kinds of questions we were asking earlier in the talk can be rephrased as: there's one set of thoughts, that involve all the partial contents deployed in seeing Robin and other people, discussing their work and so on; and another set of thoughts, that involve the partial contents deployed when you say to yourself, "The short'est spy is a spy," "The short'est spies work for China," and so on. (Let's ignore the singularity of "China.") Am I in a position to consider any thoughts, about the short'est spy as such, that go together in a fine-grained way with the first set of thoughts rather than with the second. Or not. The acquaintance theorists say no. The anti-acquaintance theorists might agree with that, and just contest whether there is any theoretically principled basis for starting with sets of thoughts divided like that, rather than with other sets. As I said, I find myself now less interested in the question of which divisions should we use as starting points, and more interested in the question of which thoughts reuse the same partial contents and which don't. So am I in the end just interested in Frege's problem, and not any more with questions about distinctive constraints on singular thought? Perhaps that's right. However, for a long time I resisted thinking of these questions in Fregean terms. I think we *can* characterize them in "Fregean" terms, but the kind of "Fregeanism" that's involved here may come apart from what some Fregeans regard as essential commitments. One issue is that I'm interested in when a subject is, and when she isn't, thinking in the same fine-grained way that she is in my leprechaun case (ii), where there is no genuine object she's thinking about. If this is a question with a Fregean answer, it'll have to be a Fregeanism which deals in "referentially empty" ways of thinking. Some who call themselves Fregean are happy with that, others aren't. More difficult is the case I described earlier of the dream about the future woman. I'm still inclined to think that it's possible for the dream to be non-prescient, not even illusorily prescient in being about some woman you'll later meet but saying some false things about her. I'm inclined to think it's also possible (and overwhelmingly more likely) for the dream not to be about the future woman. That is, it's possible for the subject to say later, when he meets the future woman, "You're just like the woman I dreamt about, but I didn't dream about you." It's possible for him to say other things as well, which might invite other theoretical conclusions. I'm not proposing to take what he says at face value and unanalyzed. But I am disposed to think, on reflection, that the characterization just offered is a correct one. And this might be hard to reconcile with some forms of Fregeanism. Why? Because as I described the case, the future woman satisfies all the properties you dreamt about a woman having. These will even include many properties which you're in no position to linguistically articulate, such as a precise look. And they include uniquely identifying properties, like being the first person you ever meet who looks like this. Now certainly aspects of the later presentation may go beyond what was present in the original: you may when you meet the future woman be more vividly aware of how she smells than you were in the dream. But *that* is no reason to conclude that the partial content involved in your dream representation isn't being reused in the later perception. It's just that if it is, now your experience is attributing additional properties onto that content. What would be more probative is the question whether there were details of the original, dream representation that are absent later. In that case, one could argue that the later representation doesn't completely match the original, and so these needn't be thought of as a single fine-grained way of thinking about the woman, that evolves in attributional richness. Perhaps you're not inclined to agree with me that your later experiences can fail to fine-grainedly go together with your remembered dream experience. Perhaps you're happy to say that if you meet someone who perfectly matches what was qualitatively present in the dream, if that information was uniquely identifying, and if the dream didn't furthermore say something like "and this woman is Robin"---where Robin is someone who doesn't in fact match the dream---perhaps in that case you're happy to say that a single way of thinking is involved. Ok. But this is something we can intelligibly dispute. And if I'm going to intelligibly dispute it, then I can't do it in Fregean terms if we understand Fregeanism to commit itself to there being only a single way of thinking here. What I'm looking for is a theoretical framework that would permit there to be ways of thinking that are distinct, but which qualitatively match in the way my dream case is meant to illustrate. Perhaps this can also be regarded as a kind of Fregeanism, but I think it rejects some theses that *some* who call themselves Fregean regard as indispensable. *Could* the later presentation really qualititatively wholly match the earlier dream presentation (where we grant that "matching" permits more specificity)? Mustn't there be aspects of the dream presentation that *must* be absent from the later experience? I don't see why there must be. Certainly it needn't be part of the dream presentation that you are dreaming. Moreover, I think the pattern displayed here can arise in a variety of cases. Kit Fine describes a case that might be glossed as one where you have two distinct but qualitatively identical ways of thinking of a single person you call "Bruce." I've sometimes talked about a person enumerating numbers that 17 is indivisible by, and "losing track" of the fact that it's 17 they're thinking of, and including 17 in the enumeration. There's a kind of rational defect involved in thinking "17 is indivisible by 23 and by 3 and by 17"; but it's a different defect than is involved in thinking "17 is indivisible by 23 and by 3 and by itself, 17." This suggests that there are two different cognitive positions to be in: one in which you think of the number 17 twice, but unknowingly, and the other in which you don't. When you're in the first situation, the normal Fregean strategy will be to posit two ways of thinking of the number 17. But there's no reason to think that there needs to be any qualitative difference between these ways of thinking. Ok, some subjects may reflect on what they're doing and at the beginning of their thinking think "17, which is the number whose indivisibity I'm now considering," and at the end of their thinking think "17, which I'm now thinking something is indivisible by." Those are qualitatively different ways of thinking of the number 17. But I see no reason to think that the subjects in my example *have to be* doing that. Losing track of logical relations in your thinking doesn't *have to be* accompanied by qualitative differences in your thinking of this sort. Some may point out that the subject is in a position, if she reflects ideally, to figure out that she is thinking of the same number 17 twice, in both of our cases. Perhaps so, but what of it? I thought Fregean differences in ways of thinking were meant to explain differences in the thoughts subject actually have, not just what differences can survive ideal reflection. And it looks like the cognitive position of thinking "17 is indivisible by 17," where you've "lost track," is actually a different position than that of thinking "17 is indivisible by itself, 17." So if the kind of view I'm looking for is a form of Fregeanism, it would be a Fregeanism which allows ways of thinking to differ *solo numero*. That is, it would allow there to be distinct ways of thinking, even though all the qualitative (that is, non-numerical) aspects of those ways of thinking coincide. I think some Fregeans would be happy to count this as Fregeanism, and others wouldn't. Even if we do choose to count this as a form of Fregeanism, though, there are aspects of this theoretical strategy which still strike me as unsatisfying. These will come out as we proceed. I want to change gears a bit now and talk about "mental file folder" models of the mind. You might think of this as happily going together with Fregeanism, or you might think of it as diverging. I'm not going to try to settle that. Section 4 --------- I like the image of mental file folders. I think it's a good start to thinking about the mind in a fine-grained way. The way I'm inclined to deploy this imagery, it's quite easy to open a new file folder. If I say to you: No man who owns a wolf taller than he is ever came into my bar. and you consider the thought I've testimonially presented you with, I'd say that while you're thinking "man who owns a wolf taller than he is", you use a short-lived file folder, even though there is no particular man this folder is about. The fact that one and the same file folder is associated with "man" and "he" is what distinguishes you from someone who thinks "man who owns a wolf taller than it is," where the file folder associated with "it" is the one associated with "wolf" rather than the one associated with "man." We can make sense of these two patterns of file-folder re-use even if you've read too much contemporary teen fiction, and think many people are both man and wolf, and perhaps sometimes own themselves. Similarly, if you think: No critic who likes and is liked by another critic lasts long in this business. I'd say you are, when thinking the restrictor of the quantifier, using two file folders associated with the sortal "critic." A fan of acquaintance constraints might well embrace this theoretical model, and just say that in her view, some file folders are "special", perhaps because they were deployed in perceptual experience, and the singular thoughts are just the thoughts that re-use those folders, rather than the folders involved in the previous examples, or the folders involved when you try to work out, from general principles, what country the short'est spies work for, Sometimes advocates of the mental file folder imagery also like to talk about files or directories on a computer system. They shouldn't do that. When you know enough about computer filesystems, you can list a whole bunch of ways in which a user or a program might be dealing with the same file, or the same directory, twice without knowing it. But the whole point of the mental file folder imagery is that this shouldn't be possible. It shouldn't be possible to deploy the same mental file folder twice while thinking you're deploying two mental file folders. Actually, we should be more careful than I just was. We might want to distinguish between (i) the cognitive position of "thinking doubly," as was illustrated in my example of thinking 17 is divisible by 17 while "losing track" of whose indivisibility you were thinking about; and (ii) the cognitive position of *thinking you are* "thinking doubly." What I'm primarily interested in is the first. On some views, the structure of a subject's own thinking will always be transparent to the subject, and it won't be possible to be thinking doubly without knowing it, or to think you are when you aren't. I don't think that, myself. I think these two can come apart. What I want to say is that mental file folders are supposed to be such that you can't ever *think doubly* by using the same file folder twice. Whether you might come to have mistaken views about the structure of your own thinking is a separate question that I don't want to dwell on here. Ok, and the point about computer filesystems is that they do in fact permit a user or a program to be in a thinking-doubly kind of situation, while in fact only engaging with a single file or directory. In a variety of ways, which I'll be glad to enumerate, but the details don't matter here. Instead of that, we want to think of mental file folders as ones where taking hold of or using the same file folder twice always goes together with thinking singly, rather than with thinking doubly. Of course, you might have some thoughts which think singly in some aspects but think doubly in others. As when you think: Lex is weaker than Superman, but he isn't weaker than Clark. you are thinking singly with respect to Lex, but doubly with respect to the individual who is both Superman and Clark. This complicates some of the things I've been saying, but I'm trusting you can make the necessary corrections in your head. Ok, so if we think of mental file folders in the right kind of way, this should look quite appealing, and it'd be consistent with both an acquaintance-friendly elaboration and with being elaborated in other ways, that don't underwrite any special class of folders as being the ones which are distinctively and interestingly "genuinely singular." However, I have three reservations about the mental file folder imagery, which prompts me to prefer a somewhat different paradigm. In fact, it's not so clear whether the changes I'll recommend really do diverge from the core of the mental file folder model. I think they do diverge from what some proponents of that model have thought, but others may see what follows as a particular development of the mental file folder model, rather than an alternative to it. That's fine by me. As with Fregeanism, I think there's indeterminacy in what this kind of view is essentially committed to. Section 5 --------- My first reservation about the mental file folder model is this. As some of our preceding examples have suggested---the case of the dreamt woman and the future woman, the two ways of thinking about 17, and the hypothetical critic about which all you can assume is he reciprocally likes another critic---it's possible sometimes to "think doubly" even when there's no qualitative, non-numerical difference between the two ways of thinking. So if we're going to explain the difference between thinking singly and thinking doubly in terms of how many mental file folders your thoughts deploy, it should be possible for there to be pairs of file folders whose qualitative contents are the same, but which are numerically distinct. I expect many fans of mental file folders will be happy to allow this; but in conversation, I've found that some are not. These latter think of file folders as just a metaphor for bundles of information, and they identify those bundles with their qualitative content. The view I have of what the genuine mental possibilities and differences are requires more fine-grainedness than such views allow for. If we're going to work with the idea of mental file folders that might differ merely numerically, then it seems that's what's important, at least for the purposes at hand, is not what information we associate with each folder, but rather the folder's intrinsic identity, which underwrites the difference between thinking with the same file folder twice, and thinking with two folders that merely happen to qualitatively coincide. It might help for the moment to think of the folders as coming with unique serial numbers. I don't suppose these are anything the thinker herself has access to; they'll just be a handy prop to make it easier for theorists to talk about different scenarios. I will be arguing that this prop is fundamentally *in*appropriate to a good model of the mind. But it is a natural one to try to help ourselves to; and I think the mental file folder imagery invites it. So let's take it on board and see what happens. Take any of the examples where I've proposed you think doubly but without any qualitative difference. For example, the case where you "lose track" of its being the same number you're thinking of as indivisible and as putative divisor. In such a case, we should think you're deploying two mental file folders, say with serial numbers "alpha" then "beta." Contrast the case where you think, perversely, that 17 is indivisible by itself, 17. In this case, you're deploying only a single file folder, say the one with serial number "alpha." --- Or was it rather the one with serial number "beta"? --- And might the first case have been one where instead of thinking with "alpha" first and then with "beta", you instead used "beta" first then "alpha"? I'm not asking these questions to pose an epistemic difficulty, about how the subject or anyone else would know which situation would obtain. Rather, I'm trying to provoke discomfort with the idea that there *should be* any mental difference between the situations I'm describing. Consider some region of spacetime. Now consider whether there could be a different scenario, exemplifying all the same spatiotemporal structure, but where the points from the first scenario have been permuted in some way. Does that describe a genuinely different way for a region of spacetime to be? I'm attracted to the answer no, but I think both answers to this question are intelligible metaphysical views. What we're confronting here is the mental analogue of that. On the face of it, once we start paying attention to the intrinsic identity of mental file folders, rather than just their qualitative contents, we make room for merely permutational differences, where mental folders with different intrinsic identities switch places, without making any qualitative difference. It seems like this is a difference our theoretical model is now representing as genuine. At the same time, there doesn't seem to me to be anything in the phenomena we're using the model to explain to underwrite that difference. Whatever you may think about the possibility of permuting spacetime points, I submit that you don't have any idea what the mental difference would be between thinking of 17 twice using file folder "alpha" versus thinking of it twice using file folder "beta." And so on. So what I hanker for is something like the mental file folder picture, where things can get more fine-grained than is determined by the folders' qualitative contents, but not so fine-grained that permuting qualitatively equivalent folders makes any difference. We want the *number* of file folders with a given qualitative content to be significant, but not their "serial number" or intrinsic identity, which might be meaningfully permuted. This reservation also applies to the kind of "Fregeanism" we had worked ourselves to at the end of Section 4. If I'm going to work in a framework with senses, I want them to be senses that can differ solo numero---but the senses shouldn't have intrinsic identities that our framework allows to be meaningfully permuted. My third reservation about the mental file folder model arises when we look beyond the unary information we associate with the folders---information like being faster than a speeding bullet, being a defender of truth and justice, and so on. Let's think instead of binary and ternary and so on information---information like Lex standing in the weaker-than relation to it. When I consider (and endorse) the thought that Lex is weaker than Superman, I somehow associate this information with a Superman folder and a Lex folder. In a different way than if I thought that Superman was weaker than Lex. When I consider (and reject) the thought that Lex is weaker than Clark, I somehow associate this hypothesis with a different Superman folder, and the same Lex folder. But now how should we think about the difference between the two ways the Lex folder is associated with the hypothesis of being weaker than another object---one in which this hypothesis looks credible, and the other in which it doesn't? One answer would be to say that in one case, the Lex folder contains a pair of the relation of being weaker than, and a body of qualitative information about the object this hypothesis says is weaker---that he's a superhero, a defender of truth and justice, and so on. But this threatens to duplicate our whole universe of file folders inside the content of what each of them says. That's intelligible, but it posits a complexity we might well shy from. Additionally, it's not clear whether the file folders themselves, as opposed to the information they contain, would on this strategy retain any explanatory power. Another answer would be to say that in one case, the Lex folder contains a pair of the relation of being weaker than, and the serial number of one of your Superman folders---the folder you in fact associate with being a superhero and so on. In the other case, it contains a pair of the relation of being weaker than, and the serial number of another of your Superman folders---the folder you associate with being a mild-mannered reporter. This is a natural strategy for a proponent of mental file folders to adopt. However, it isn't satisfying, for two reasons. The first reason is just an echo of my second reservation, voiced above. If in fact your "defender of truth and justice" information is in file folder number "gamma", and your "mild-mannered reporter" is in file folder number "delta", then on this proposal your Lex folder looks like this: (is weaker than, file folder "gamma"): plausible (is weaker than, file folder "delta"): implausible But now consider a different scenario, where instead your "defender of truth and justice" information is in folder "delta," and "mild-mannered reporter" is in folder "gamma," and your Lex folder instead looks like this: (is weaker than, file folder "delta"): plausible (is weaker than, file folder "gamma"): implausible This doesn't seem to correspond to any difference in mental reality. But it is a difference the model permits. Moreover, the model seems to say these are not just genuine *global* differences, but that they are different bodies of information *you might associate with Lex.* All of this strikes me as misguided. Our model should abstract away from these kinds of differences. A different reason to be dissatisfied with the present strategy is that it seems to commit to a level of linguistic representation---the one used in referring to folders as "gamma" and so on---where Frege cases are presumed to be impossible. This is in a way reminiscent of Russell's strategy for explaining cognitive difference, by piggybacking on a body of representation where existence and identity mistakes can't arise. I have no argument that this strategy is incoherent or anything. But I think many of us will be reluctant to take on a commitment to any such magical, Frege-immune level of representation. If our file folders refer to each other by serial number, what's to prevent some single file folder from turning out to be labeled with multiple serial numbers? Section 6 --------- So I have a different model I'd like to offer in place of the mental files picture. It may be that some proponents of the mental file folder picture are happy to see this as a version of what they meant all along. As I said before, that's fine with me. What I care about is that we have a framework with the right properties, not whether it does or doesn't merit some familiar label. This model uses something like the mathematical notion of a graph. Not a graph in the sense of a Cartesian graph or the graph of a function, but a graph in the sense that includes mathematical trees as one species. In fact what we want is not precisely the notion of a graph, but an extension of this, that doesn't seem to have a standard name. We'll begin with the orthodox notion of a graph, first. Key to this notion are the vertices or nodes of the graph, on the one hand, and the edges that connect the nodes on the other. In some mathematical applications, the adjancency relation represented by an edge is symmetric or undirected; in other applications it has a direction and needn't always (but may) hold symmetrically. We need the latter kind of graph, with directed edges. In some mathematical applications, all that's important is the structure of nodes and edges. In others, it's important to annotate or label the nodes or the edges with additional information. For instance, edges are often annotated with a positive "cost" or "distance." We'll think of the nodes as taking on the jobs of our mental file folders. What they'll be annotated with will include the objects in the world (if any) that they are representations of. We'll want to add more things to our annotations of the node in a moment. We'll annotate the edges with something like the relations you believe to hold between different objects, thought of in the way that a given node stands for. So the thought that Lex is weaker than Superman (thought of as a superhero) and the thought that he is weaker than Superman (thought of as a mild-mannered reporter) will involve edges annotated with "being weaker than" leading from a single Lex node to two different Superman nodes. In fact, we'll need to complicate this proposal in a moment. But this should give you a feel for the basic approach. Before we go further, let me emphasize the difference between the nodes and what we annotate them with. It can be one and the same individual---Superman---who annotates multiple nodes. But the nodes themselves cannot both be "multiple" and be one and the same object. The nodes will be numerically distinct, though they may have annotations that are numerically the same. In the Superman case, your different nodes annotated with that one object will presumably differ in other respects; for instance, whether they're also associated with defending truth and justice, and whether "is loved by" edges lead from them to a node representing how you think of Lois. But in other cases I've mentioned, plausibly you can have two ways of thinking of a single object that differ solo numero. In these cases, the nodes will be the same in all their graph-theoretic respects. But there will nonetheless be two of them, not one. Another thing to emphasize now is the difference between the core mathematical notion of a graph, and the set-theoretic way in which graphs are typically "defined" in mathematical texts. The typical mathematical presentation takes nodes to have an intrinsic identity, independent of their place in the graph. So, as with mental file folders, these presentations seem to make it meaningful to talk of graphs which are different only in having some of their nodes permuted (without affecting the rest of their graph-theoretic structure, or how that structure is annotated). These mathematical presentations then typically propose, as a further step, to abstract away from the intrinsic identity of the nodes by working with equivalence classes of graphs under the natural isomorphisms. For our explanatory purposes, it would be better to work with a notion of a graph that could be understood as giving no meaning to permutations of the nodes in the first place. There are ways to mathematically "define" or build graphs that are more hospitable to this way of thinking. I don't propose to go into the details of this. I just wanted to acknowledge that a typical textbook "definition" of a graph will have some of the same deficiencies I accused the mental file folder picture of having. But I'm proposing to use the core mathematical notion of a graph, that doesn't *have to be* understood in the way textbooks typically "define" it. With the understanding I prefer, this: node -------------------> node annotated with a \ annotated with b \-----------> another node annotated with b is a different graph than this: node -------------------> node annotated with a annotated with b even though the b-labeled nodes of the first graph have no identity apart from their role in the graph. There is no such thing as a graph distinct from the first, but with its nodes permuted. Ok, now let's go through the ways in which the picture I've so far presented is too simple. First, let's think about how we're annotating the edges. I suggested that if you believe Lexis weaker than Superman (thought of in one way), that'd be represented by an edge from a Lex node to a Superman node with the annotation "is weaker than." But of course you don't just have *beliefs* about Lex's relation to Superman. You also have desires, and intentions, and deliberate withholdings of belief, and credences which are stronger than not but fall short of belief, and so on. We ought to be modelling all of this. So let's think of the edge annotations as not just being believed relations like being weaker than, but pairs of attitudes and such relations. Second, of course there are many relations you believe Lex to stand in to Superman. So it's natural to expect our model to have multiple edges leading from Lex to Superman. There would be other ways to proceed. Instead of multiple edges, we might instead annotate a single edge with *a set* of pairs of attitudes and relations. But there's nothing wrong with using multiple edges. In some ways that's conceptually simpler. It's just that if we do that, we're no longer using the orthodox mathematical notion of a graph. That orthodox notion excludes structures like this: node -------------------> single node annotated with Lex \____________> annotated with Superman There's nothing wrong or unintelligible with such structures; they're just not what mathematicians typically count as a graph. But mathematicians do sometimes work with these structures; sometimes they call them "multigraphs" though there isn't a consensus about the nomenclature. A related issue is that we believe (and desire, and intend, and so on) Lex to stand in relations to himself. The orthodox mathematical notion of a graph permits there to be "cycles" of edges like this: belief, dislikes node -------------------> node annotated with Lex annotated with Lois <------------------- belief, dislikes That would represent you believing that Lex and Lois dislike each other. However, what if you believe Lex dislikes himself? We'd want to represent that like this: node --------\ belief, dislikes annotated with Lex <-------/ and the orthodox mathematical notion of a graph excludes "loops" of this sort. As with multiple edges from the same source node to the same destination, there's nothing wrong or unintelligible with such structures; they're just not what mathematicians typically count as a graph. But they do sometimes work with these structures; sometimes they call graphs with such loops (or graphs with such loops and potentially multiple edges from the same source to the same destination) "pseudographs." But there isn't a consensus about the nomenclature here either. Now you may have noticed we've so far only been talking about binary relations you believe (or desire, or intend, or so on) to hold between Lex and other people or himself. But what about unary properties, like being diabolical? What about ternary relations, like having denounced __ to __? Don't we mentally attribute properties and relations like that to Lex as well? Let's consider unary relations first. This invites a simple fix to the picture we've given so far: instead of just annotating the nodes with the objects they represent, we might annotate them with a pair of that object and a set. The set would contain pairs of attitudes and unary properties you attribute with that attitude to Lex. Hence if you believe Lex to be diabolical and to dislike himself, you'd have: node --------\ belief, dislikes annotated with <-------/ Lex, { (belief, being diabolical) } Ternary relations are more difficult, and call for a more radical revision, which in the end permits a more elegant treatment of the unary case too. To model the belief that Lex denounced Superman to Lois, what we want is something like this: belief, denounced to node --------\/---------------------> node annotated with Lex node annotated with Lois annotated with Superman What we have here is kind of edge that starts at a source, and has an intermediate stop before reaching its final destination. It's an edge of length 2: to be distinguished from a "path" consisting of two edges of length 1. Such paths are common staple in the orthodox theory of graphs. Single edges that are themselves of lengths greater than 1 are more exotic, and are excluded from the orthodox theory. As before, though, they're perfectly intelligible, they're just not what mathematicians typically deal wih or count as graphs. Sometimes they do work with these structures, and sometimes call them "hypergraphs." But here too there doesn't seem to be a consensus about the nomenclature. If we permit a kind of graph (or hypergraph or whatever we call it) with edges of length 2, we can of course have ones with edges of length 3 and so on. And we can also make sense of edges of length 0; in fact we might identify nodes with such edges. And then our treatment of unary beliefs (that is, beliefs about the having of unary properties) would look more continuous with our treatment of binary and ternary beliefs. So this is the theoretical model of the mind that I prefer to (some understandings of) the mental file folder picture. Your mind isn't a file cabinet; rather, it's a kind of hypergraph. Section 7 --------- What I've been developing so far is a proposal for how we theorists can best think about the mind. There's a further question, how folk discourse can be understood so as to comport with this picture. It'd be nice if the ways we folk ascribe beliefs about Lex and Lois and Clark could be coordinated with the theoretical picture of hypergraphs that I'm recommending. I believe it can, and this is a good way to understand some recent semantic proposals. Now some philosophers think of contents as having a tree-like structure, mirroring the syntactic structure of the sentences we'd express those contents with. But as we mentioned before, trees are just one kind of graph. There'd be no principled obstacle to our permitting more complex kinds of graphs in our syntax. Or, if not in our syntax, then in the structured contents we might posit in semantics. And in that case, we might expect the graphlike content of a belief-ascription, when the ascription is correct, to map onto the mental graph that models the ascribee's entire state of mind. I said there's no obstacle to semantics proceeding that way; but this is not in fact the way working semanticists proceed. They prefer contents with graph-theoretically simpler structures, in part for some legitimate reasons and in part just from custom. In fact, most semanticists in linguistic departments won't even want to work with tree-like structures; they'll prefer semantic contents to be *built up* in a tree-like way, but they'll prefer to think of *what* has been built at each stage to be graph-theoretically "flat." So let's think in terms that respect these contemporary mores. If the semantics of folk ascriptions of belief are to capture any of the graph-theoretic complexity of an ascribee's state of mind, it'll have to do it in a way that "linearizes" or "flattens" the graph into a kind of content that doesn't itself look graphlike. One prospect here is that patterns of anaphora and variable binding in an ascription might communicate something about an ascribee's graphlike state of mind. For example, we might say that the ascription: Sam believes that 17 is indivisible by itself. communicates something different about Sam's state of mind than the ascription: Sam believes that 17 is indivisible by 17. In the former case, the ascription requires for its truth that Sam's state of mind include something like this: node --------\ belief, indivisible by annotated with 17 <-------/ whereas the latter ascription permits but does *not* require that. It also permits Sam's state of mind to be only like this, instead: belief, indivisible by node -------------------> node annotated with 17 annotated with 17 This looks like an appealing treatment of the present case. However, looking at a range of cases shows that patterns of anaphora and variable binding (as displayed in the use of terms like "itself") only imperfectly correspond to when an ascriber is trying to communicate that an ascribee is thinking singly rather than (definitely, or possibly) thinking doubly. One issue is that when the variables are *bound by a quantifier outside the complement* of an attitude verb, the ascription needn't require the ascribee to be thinking singly. Sam Cumming discusses a case from Love's Labor Lost, where Rosaline, Maria and Katherine dance in turns with Biron and each fools him into thinking she is one of the others. It seems we might correctly report the case as one where: Each girl persuaded Biron that she wasn't herself. Without the proper dialectical context, that ascription may be misunderstood, but it does seem a permissible way to describe what has happened. However, we are not here thinking that Biron was persuaded to be in this state of mind: node --------\ belief, non-self-identical annotated with one <-------/ of the girls So perhaps when the binding is done by a quantifier, we should think it's *only when the quantifier is inside the complement* of the attitude verb that we communicate that an attitude is held via a single node. However, what of the case where these binding patterns occur without a quantifier. For example, what if I say: All along, I was hoping to punch myself. You might understand me to be saying that I was hoping to arc my fist upward and inward towards the center of my own visual field. But this report also seems like it coud accurately describe a case where I didn't realize until just now that it was me who I was all along hoping to punch. Maybe I've been seeing furniture in my bedroom rearranged every morning, and I've been planning to wake and catch the culprit and give him a good punch in the nose. One night I set up a video camera. Reviewing the footage the next morning, I discover that I've been rearranging the furniture myself, while sleepwalking. I might then make the ascription above. In this case, I'm not trying to ascribe a state of mind like this: node --------\ hope, punch annotated with me <-------/ but rather one like this: hope, punch node -------------------> node annotated with me annotated with me There are also difficulties in thinking that even when variables *are* bound by a quantifier inside a verb's complement, this perfectly tracks an ascription being of a thinking singly rather than of a thinking doubly. (Discuss example.) Suppose I observe Abe having a thought he would express as: "Beatrice and Charles each prefer her to him." Now I want to ascribe this thought to Abe, in a way that communicates that he's thinking singly about the set of preferrers and the set of people the preferences concern. How might I do it? Well, I could say something whose semantic structure is like this: Abe believes that: Beatrice is an x where: x prefers x to Charles, and Charles is a y where: y prefers Beatrice to y. If we suppose that variable binding corresponds with thinking singly, then this will capture the fact that in Abe's thinking, it's one and the same person who prefers herself to Charles, and one and the same person who prefers Beatrice to himself. However, it leaves out that it's the same person Beatrice who prefers herself to Charles, and whom Charles prefers to himself; and similarly for Charles. It also leaves out that it's one and the same property that Abe's thinking attributes to each of Beatrice and Charles. This latter fact is better conveyed by something with the structure: Abe believes that: Beatrice and Charles are each a z where: z prefers Beatrice to Charles. However, this no longer captures the fact that it's a single person who prefers herself to Charles, at least not by a mechanism involving variable binding. You can play around with various ways of restructuring this ascription, but I don't think any of them are fully satisfying, on the assumption that thinking singly is communicated only by anaphoric variable binding. Moreover, this example can be extended to cases where the source of the anaphor is not a name like "Charles" but a quantifier phrase like "three men." Abe believes that Beatrice and three men each prefer her to him. Hence, even if we restrict our attention to cases where the binding quantifier occurs inside the complement of the ascription, it's not going to be easy to get patterns of variable binding to correspond perfectly to when Abe is and when he isn't being said to think singly. If any semantic mechanisms are able to play this communicative role, they'll have to be somewhat more exotic. And in fact there are semantic mechanisms that look promising for doing this, which are well-understood in computer science and some of which have become prominent in linguistics over the past 30 years. These latter mechanisms are for example the notion of a "discourse referent" as appealed to in dynamic semantics. This is in the neighborhood of being the kind of novel semantic structure that might communicate that an ascription concerns a thinking-singly rather than a thinking-doubly. In fact, however, for technical reasons that I'd be glad to discuss but aren't the topic of the present paper, this is not exactly what we need. The notion of a discourse referent is what corresponds in computer science to a mutable non-local variable. What we need instead is something customarily only used in tandem with that, but which is conceptually distinct, and is known in computer science as passing an argument by reference rather than by value. Some philosophical proposals are well-understood to be making use of this latter notion. Mark Richard floated such a proposal in 1983 and 1990; Fiengo and May have defended an analogous view; and most recently and prominently, Kit Fine has advocated such a view, which he calls "semantic relationism." Fine presents a package with various inter-connected components. I don't think these are all essential to the core proposal; and in fact I don't think his insistence that the semantics be "relational" rather than one with novel intrinsic semantic structure is part of the core. Understanding his core proposal in the way I do makes the analogies between his proposal and Richard's and Fiengo and May's more salient, and also makes it easier to talk about the way in which the same semantic structure is present in some computer languages. I think this is a good way to think about how folk ascriptions might communicate in a "linearized" way that an ascribee is thinking singly rather than doubly. This is a topic I'm keenly interested in these days and have a lot more to say about. But for now I just wanted to point in the right direction.