139 ISSN 2341-1465 LEAP 2 (2014): 139-152 Reply to Persson: Intransitivity and the Internal Aspects View L ARRY TEMKIN Rutgers University Abstract This article responds to Ingmar Persson’s article “Internal or External Grounds for the Nontransitivity of ‘Better/Worse than’”. In his article, Persson argues in favor of an account of supervenience that would be compatible with both an Internal Aspects View, and the nontransitivity of the “better or worse than” relations. This article points out that the Internal Aspects View that Persson favors would fail to capture many features of practical reasoning that most advocates of an Internal Aspects View favor, and that the version of the Internal Aspects View that I discuss in Rethinking the Good does capture. I note, however, that Persson’s view would not only be compatible with my book’s main claims and arguments, it would substantially buttress my results. Accordingly, I would welcome it if Persson could successfully develop and defend his view. Unfortunately, however, my article raises a number of worries about Persson’s view. I consider various different ways of understanding Persson’s position, and argue that none of them ultimately succeed in establishing a plausible version of a genuinely Internal Aspects View that would be compatible with the nontransitivity of the “better or worse than” relations. I acknowledge that if Persson can ultimately make good on his claims, he will have made a substantial contribution to our understanding of the good and the nature of ideals. However, as matters now stand, I am not moved by his arguments to revise the claims I made in Rethinking the Good, correlating the nontransitivity of the “better or worse than” relations with the Essentially Comparative View, rather than the Internal Aspects View. Keywords: Transitivity, Nontransitivity, Internal Aspects View, Essentially Comparative View, Practical Reasoning, Better than, Supervenience. I’d like to thank Ingmar Persson for his response to Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning (Temkin 2012). I have long admired Persson, and I have learned much from him over the years. 140 Larry Temkin LEAP 2 (2014) Persson’s work typically displays a rare combination of insight, good sense, and importance. Not only do I usually find his claims interesting and plausible, I usually find myself in agreement with them. I confess, however, that while I find his central claims in “Internal or External Grounds for the Nontransitivity of ‘Better/Worse than’” (Persson 2014) interesting and important, I don’t find them plausible. Indeed, I’m not really sure how to make sense of them. In this article, I’ll mainly try to show why I find his claims puzzling and unconvincing. Perhaps Persson will be able to adequately answer my concerns in a way that will give his claims the clarity, plausibility, and defensibility typical of his work. If so, I believe he will have made a significant contribution to our understanding of the good and the nature of ideals. But as matters now stand, I am not moved by his remarks to revise the claims I made in Rethinking the Good. 1. Before presenting Persson’s central claims, and my response to them, it will be useful to start with a brief recapitulation of some of Rethinking the Good’s key claims. I do this both as useful background for Persson’s position and, as importantly, to illustrate that I could, in principle, accept everything Persson contends without significant revision of my own views. Indeed, if correct, Persson will have provided a new and important argument which not only fits comfortably with my larger views, but which, in fact, provides independent support and further vindication of those views. In my book, I noted that many people make certain standard assumptions about practical reasoning. For example, most people assume various Axioms of Transitivity, believing, for instance, that the “all-things-considered better than”, the “all-things-considered equally as good as”, and the “all-things- considered at least as good as” relations are all transitive. Most people also assume an Independence of Irrelevant Alternatives Principle, believing that if one wants to know how any two outcomes O1 and O2 compare, it is sufficient to compare them directly. On such a view, how O1 and O2 compare to each other all things considered, won’t depend in any way on how either or both compare to some third outcome O3, or some alternative set of outcomes, Ok to On. Similarly, most people assume a Principle of Like Comparability for Equivalents, believing that if two outcomes, O1 and O2, are equally good, then however O1 compares to any third outcome O3, that is precisely how O2 will compare to O3. I showed that there is one way of thinking about ideals, which I called the Internal Aspects View, which had great intuitive plausibility and which, if true, would explain why each of the above principles held. More specifically, Reply to Persson 141 LEAP 2 (2014) I gave a particular characterization of the Internal Aspects View which would account for such principles, one according to which the goodness of each outcome would depend solely on in the internal features of that outcome, and where an outcome’s goodness could be accurately represented by a number or range of numbers on the real number line (Temkin 2012: sec. 11.3). However, in my book I also pointed out that there is an alternative way of thinking about ideals, which I called the Essentially Comparative View, that also has great intuitive plausibility. On this view, the factors that are relevant and significant for assessing an outcome’s goodness may vary depending on the alternative outcome(s) with which it is compared. I argued that many of the ideals people care most about, including a Narrow Person-Affecting View, the Pareto Principle, and particularly plausible versions of Maximin and Utility, are best captured by an Essentially Comparative View of ideals rather than an Internal Aspects View (Temkin 2012: ch. 12). I then argued that given the nature and structure of Essentially Comparative ideals, many of the common assumptions about the nature of practical reasoning may fail to hold or apply across different sets of outcomes, including the various Axioms of Transitivity, the Independence of Irrelevant Alternatives Principle, and the Principle of Like Comparability for Equivalents. In my book, I also pointed out that many important principles are limited in scope, in the sense that they are thought to be relevant and significant for comparing certain outcomes but not others. I noted that this is true of the Pareto Principle as it is commonly interpreted (Temkin 2012: sec. 12.5), it is true of John Broome’s Principle of Personal Good, as he presents it in Weighing Goods (Broome 1991: sec. 8.1), and it is true of John Rawls’s two principles of justice as he presents them in A Theory of Justice (Rawls 1971: 63). I then showed that whenever it is true for such a principle that there can be three outcomes, O1, O2, and O3, such that the principle would apply when comparing O1 and O2, but would not apply when comparing O1 and O3, then such “limited scope” principles are Essentially Comparative in the sense I am employing that notion, and this opens up the possibility that the common assumptions about practical reasoning discussed above, including the Axioms of Transitivity, may fail to hold or apply across different sets of outcomes. I suggested that one important set of cases where principles that were limited in scope came into play was in my Spectrum Arguments; where one such argument involved a Spectrum of outcomes where the first outcome involved a very long life with 15 mosquito bites per month and two years of excruciating pain, the second outcome involved a very long life with 15 mosquito bites per month and four years of pain almost as bad as that obtaining in the first outcome, the third outcome involved a very long life with 15 mosquito bites per month and eight years of pain almost as bad as that obtaining in the second outcome, and so on, where the last outcome of the Spectrum merely involved a very long life with 16 mosquito bites per 142 Larry Temkin LEAP 2 (2014) month but no torture. I claimed that (1) in accordance with a position I called the First Standard View, which reflected an additive-aggregationist approach to comparing outcomes, most people would judge that for each adjacent pair of outcomes along the Spectrum, n and n + 1, the earlier outcome, n, would be better than the later outcome, n + 1, all things considered, that (2) in accordance with a position I called the Second Standard View, which reflected an anti-additive-aggregationist approach to comparing outcomes, most people would judge that the Spectrum’s first member was worse than its last member, all things considered, and (3) that together, these plausible and widely-held judgments are incompatible with the Axiom of Transitivity for the “all-things-considered better than” relation (Temkin 2012: ch. 5; and Temkin 2014: sec. 1). A key part of my analysis of what is going on in my Spectrum Arguments was to emphasize that the First and Second Standard View are both limited in scope, so that we regard the First Standard View as relevant and significant for comparing adjacent outcomes along my Spectrum, but not for comparing outcomes at opposite ends of the Spectrum, and vice versa with respect to the Second Standard View. This implies that most people are implicitly relying on an Essentially Comparative View of ideals in making the judgments they do regarding my Spectrum’s outcomes, rather than an Internal Aspects View, and I claimed that this accounts for why the Axiom of Transitivity for the “betterness” relation fails, or fails to apply, across the different outcomes in my Spectrum cases. Having distinguished between the Internal Aspects View and the Essentially Comparative View in the way that I did, I acknowledged in a note that there may be alternatives ways of thinking about an Internal Aspects View that might allow for the non-transitivity of the “all-things-considered better than” relation (Temkin 2012: ch. 11, note 32). However, I don’t pursue this as, in fact, I believe that the best explanation of the various cases where the Axioms of Transitivity seem questionable lies in our implicitly accepting an Essentially Comparative View in thinking about those cases. Similarly, my motivation for focusing on the version of the Internal Aspects View that I did is that I think such a view is intuitively plausible, widely assumed in many contexts, and would account for many standard assumptions about practical reasoning, including the various Axioms of Transitivity, the Independence of Irrelevant Alternatives Principle, and the Principle of Like Comparability for Equivalents. Now Persson accepts that certain ideals people attach great weight to in assessing outcomes are Essentially Comparative. He also accepts that many ideals people value may be limited in scope, in a way that supports an Essentially Comparative View of ideals. So, he is prepared to grant that in a range of cases, people may be committed to a set of judgments that are incompatible with the Axioms of Transitivity because of essentially comparative considerations. Furthermore, he doesn’t deny the intuitive appeal of an Internal Aspects View Reply to Persson 143 LEAP 2 (2014) of the sort I characterized, nor does he deny that, if true, my version of the Internal Aspects View would support, and explain, many of the standard assumptions about practical rationality that I discuss. However, Persson is keen to defend the possibility that I broached in a note. More specifically, he believes that in the case of my Spectrum Arguments, we can explain the non-transitivity of the goodness of the Spectrum’s outcomes solely on Internal Aspects grounds. That is, Persson believes the non-transitivity of most people’s judgments about the goodness of the different outcomes in my Spectrum cases can be explained in a way that is wholly consistent with the view that, all-things-considered, an outcome’s goodness depends solely its internal features. Moreover, importantly, Persson believes that unlike some of the other cases of non-transitive goodness that I discuss, the best explanation of the non-transitivity of outcome goodness in my Spectrum cases will rest on Internal Aspects grounds rather than Essentially Comparative grounds. Naturally, in developing his position, Persson is committed to an alternative version of the Internal Aspects View than the one I offered in my book, since my version entails the various Axioms of Transitivity. This is partly what makes Persson’s suggestion so intriguing and important. If the best way of understanding the Internal Aspects View differs from the one I offered, in that it also supports the non-transitive “all-things-considered better than” judgments that most people make about my Spectrum Arguments, this will make it even harder to deny my book’s central conclusion that we need to significantly revise our understanding of the good, moral ideals, and the nature of practical reasoning. 2. In light of the foregoing, it should be clear that I would welcome the success of Persson’s project. Indeed, I would regard it as a friendly amendment that is clearly within the spirit of my own views, and one which would add significant weight to my book’s main claims. But despite that, I am not persuaded that Persson has provided a better account of people’s judgments in my Spectrum Arguments than my own. Indeed, to be completely honest, I don’t even understand Persson’s view, finding his claims about the Internal Aspects View and how it is supposed to support the rejection of the various Axioms of Transitivity deeply puzzling. In what follows, I will present my main worries about his position. Persson’s account of how best to understand what is going on in Spectrum Arguments rests on his views about supervenience. He assumes that any given supervenient property, V, could supervene on two distinct bases. Thus, it could be the case that a given base, B1, gave rise to a given supervenient property, V1, and that a slightly, or even wholly, different base, B2, could give 144 Larry Temkin LEAP 2 (2014) rise to a perfectly similar supervenient property (Persson 2014: 126). I accept this view, which might be expressed in several ways. One might say that B1, gives rise to V1, and that B2 gives rise to V2, where V1 and V2 are qualitatively indistinguishable even if they are numerically distinct. In this case, V1 and V2 might be thought of as two tokens of the same type, perhaps type V. If the supervenient properties are values, which is the class Persson is concerned with, then we can express this by saying that V1 and V2 have exactly the same value, which would then mean that B1 and B2 were exactly equally as good as each other. Another way of expressing the same idea is simply to say that two partially or wholly distinct bases, B1 and B2 can give rise to the very same supervenient value, V1. As the latter way of putting the point is simpler for purposes of exposition, that is how I’ll often put it in what follows. If this is right, then Persson contends that we should accept his principle Simp: If S is a property of objects that supervenes upon their having B, then, for all objects X, Y, and Z, even if both X and Y, and Y and Z, are perfectly similar or the same with respect to S, it’s logically possible that there are differences with respect to B between both X and Y, and Y and Z (Persson 2014: 126). As stated, there is every reason to accept principle Simp. But this is because if, as seems plausible, two distinct base objects could give rise to the very same supervenient property (or “perfectly similar” supervenient properties), then presumably three distinct base objects could also give rise to the very same supervenient property (or “perfectly similar” supervenient properties). So, where the supervenient property is a value, V1, Simp will be true as long as there could be three distinct base objects, B1, B2, and B3, each of which gave rise to V1, and there is good reason to accept that possibility. However, Persson claims something much stronger, and more controversial, than what I readily grant regarding principle Simp. He contends that the differences between the bases of objects X and Y, and the bases of objects Y and Z, could be such that we should accept his principle Add: Even if there are differences in respect of B between X and Y, and be- tween Y and Z, neither of which are sufficient for differences in respect of S between X and Y, or between Y and Z, but X is perfectly similar to Y, and Y to Z, with respect to S, it’s logically possible that there are differences in respect of B between X and Z that are sufficient for a difference with respect to S between X and Z (Persson 2014: 127). Now I can see how principle Add could be true on an Essentially Comparative View of ideals. After all, on such a view it could be the case that the factors that are relevant and significant for comparing outcomes X Reply to Persson 145 LEAP 2 (2014) and Z, might be different from the factors that are relevant and significant for comparing outcomes X and Y, or outcomes Y and Z. (Here, and in what follows, I have put Persson’s views in terms of “outcomes” rather than “objects”. This does not affect the substance of his views or my claims.) Hence, as principle Add contends, on the Essentially Comparative View, it could well be the case that the supervenient values of X and Y might be the same when they are compared, and the supervenient values of Y and Z might be the same when they are compared, and yet the supervenient values of X and Z might not be the same when they are compared. But I fail to see how principle Add can be made coherent on an Internal Aspects View, where the goodness of a given outcome depends solely in the internal features of that outcome. Regarding the kind of situation principle Add is supposed to be addressing, Persson seems to believe that the two bases corresponding to outcomes X and Z, call them Bx and Bz, differ sufficiently that they would give rise to supervenient properties that were not perfectly similar or the same. Since we are interested in the case where the supervenient properties are values, let’s say that the base properties of outcome X, Bx give rise to, or account for, the value of outcome X. I shall represent this as “Bx → Vx”. Further, suppose that, however the notion of value is ultimately understood, the letter K represents the value of outcome X. I will represent this as “Vx = K”. We can then use the notation “Bx → K”, to represent the fact that the bases of value in outcome X that determine X’s value are such, or make it the case, that outcome X’s value is K. We can then similarly write that “Bz → Vz”, “Vz = M” (where the letter M represents the value of outcome Z), and hence “Bz → M”. By hypothesis, in the cases covered by principle Add, K ≠ M, since, by hypothesis, the base objects of outcomes X and Z differ sufficiently that the values for outcomes X and Z differ. Now, as noted previously, on an Internal Aspects View, the value of an outcome depends solely on the internal features of that outcome. So, the value of outcome Y will supervene solely on the relevant internal features of Y that constitute the base, By, for Y’s value. Assume, in accordance with principle Add, that while By is distinct from Bx, they both give rise to perfectly similar, or the same, values. I have already granted, in accepting principle Simp, that this might be the case. This means that Vx = Vy, and thus, By → K. But since, by hypothesis, K ≠ M, it follows that it is not the case that By → M, and so, contrary to principle Add, outcome Y’s value will not be the same as outcome Z’s value. Alternatively, suppose that although the bases of value for outcomes Y and Z differ, they give rise to the same values for the two outcomes (as might be the case, in accordance with Simp). Since, by hypothesis, Bz → M, it follows that it will also be the case that By → M. But in that case it could not also be the case that By → K, since, by hypothesis, K ≠ M. 146 Larry Temkin LEAP 2 (2014) Putting the preceding together, since, on the Internal Aspects View, an outcome’s goodness depends solely on the internal features of that outcome, it seems clear that on that view the object bases for Y’s value should give rise to, or account for, exactly the same value for Y whatever alternative it is compared with. Accordingly, given that X’s value, K, is different from Z’s value, M, it seems clear that, on the Internal Aspects View, Y’s value could be equal to X’s, or it could be equal to Z’s, but it could not be equal to both! More specifically, if, in fact, Y’s internal features are such that By → K, then, indeed, X and Y will have the same value, but Y and Z will not; while if, on the other hand, Y’s internal features are such that By → M, then, indeed, Y and Z will have the same value, but X and Y will not. It seems, then, that if we adopt an Internal Aspects View, we should reject Persson’s principle Add. Why does Persson think otherwise? It isn’t clear. Perhaps Persson has something like the following picture in mind. The value bases for outcome X, Bx, determine X’s value, K, the value bases for outcome Y, By, determine Y’s value, L, and the value bases for outcome Z, Bz, determine Z’s value, M. So, on the notation used above, Bx → K, By → L, and Bz → M. Now it might be that K and L are so “close”, that we can’t distinguish them intuitively or phenomenologically. In that case, we might well regard them as “perfectly similar” or “the same”. Likewise, it might be that L and M are so “close”, that we can’t distinguish them intuitively or phenomenologically. In that case, too, we might well regard them as “perfectly similar” or “the same”. But it is perfectly consistent with those two facts that K and M are sufficiently far apart that we can distinguish them, and so rightly recognize them as different. Such a picture might account for any intuitive appeal that principle Add might have, even on an Internal Aspects View. Unfortunately, however, it would not justify or vindicate Add. I have three related worries about the picture in question. My first worry is that such reasoning is reminiscent of familiar arguments for the intransitivity of the indifference relation concerning alternatives involving vagueness or imperceptibly small differences. It is well known that presented with three alternatives A, B, and C, two at a time, many people might be indifferent between A and B because the differences between them are imperceptibly small, and they might similarly be indifferent between B and C because the differences between them are imperceptibly small, and yet they may not be indifferent between A and C. This is because together the imperceptibly small differences between A and B, and between B and C, might add up to a difference between A and C that is large enough to be perceptible and is one about which they would be concerned. But cases of this sort are like the notorious Sorites Paradoxes, such as those purporting to show that a heap of sand is the same as a single grain, or that hairiness is the same as baldness. Now there is much to be said about standard Sorites Paradoxes, but here I shall simply note that in my book I argued that my Spectrum Arguments Reply to Persson 147 LEAP 2 (2014) are not related to the standard Sorites Paradoxes (Temkin 2012: sec. 9.2), and Persson agrees with me about that. My Spectrum Arguments do not rely on vagueness, nor do they trade on a series of imperceptible differences which together add up to a perceptible difference. Rather, my Spectrum Arguments rely on differences of quality and number which are clearly perceptible, and which seemingly combine in one way for making certain comparisons, but in a different way for making other comparisons. Specifically, as noted previously, most people follow (something like) the additive-aggregationist approach of the First Standard View for comparing the outcomes of my Spectrum that are adjacent to each other. This generates a clear ranking between such outcomes where the “earlier” outcome is better than the “later” outcome, so that most would clearly prefer the former to the latter and would not be indifferent between them. Likewise, most people follow (something like) the anti-additive-aggregationist approach of the Second Standard View for comparing those outcomes that are at the opposite ends of my Spectrum. This also generates a clear ranking between such outcomes, so that most would clearly judge the last outcome as better than the first, and so would not be indifferent between them. But then, I submit that the proper explanation of what is going on with my Spectrum Arguments, and the root of their challenge to the transitivity of the “betterness” relation, has everything to do with the Essentially Comparative View of ideals, and nothing to do with the vagueness or accumulation of imperceptible differences which underlies the standard Sorites Paradoxes and which accounts for the intransitivity of the “indifference” relation in such contexts. Thus, if, as Persson claims, he is hoping to offer a better explanation of the Spectrum Arguments than the one I offered —one that is compatible with both the Internal Aspects View and the rejection of the transitivity of the “betterness” relation— it won’t do for him to rely on the sort of picture sketched above. As indicated, that picture mirrors the standard Sorities Paradoxes, but it does not mirror what is going on in the Spectrum Arguments. Second, even if one claims that the values of outcomes X and Y are so close as to be indistinguishable, and likewise that the values of outcomes Y and Z are so close as to be indistinguishable, there is good reason to believe that there are circumstances in which we’d be able to distinguish between at least one of the two sets of values, K and L, or L and M. More particularly, even if it were true that were we confronted only with outcomes X and Y, we might discern no difference in value between them, and were we confronted only with outcomes Y and Z, we might discern no difference in value between them, it seems likely that if we were confronted with all three alternatives at once we would discern a difference between at least two of the supposedly “indistinguishable” values. Suppose, for example, that we were presented with all three outcomes, X, Y, and Z, at the same time. Suppose, as before, that on the Internal Aspect 148 Larry Temkin LEAP 2 (2014) View, Bx → K, and Bz → M, where the difference in value between K and M was sufficiently great that we clearly recognized X’s value to be different than Z’s. In that context, as we were considering all three outcomes at once, how would we assess Y’s value? It seems there are only three possibilities here that we need to consider. It might be that in that context, Y’s internal features were such that By → K. If that were so, then X and Y would have the same value, but Y and Z would not, and so principle Add would not apply. Alternatively, it might be that in that context, Y’s internal features were such that By → M. If that were so, then Y and Z would have the same value, but X and Y would not, and so once again principle Add would not apply. Or, it might be that in that context Y’s internal features were such that By → L, where L was an intermediate value between K and M. In that case, Y’s value, L, will either be clearly distinguishable from one or both of K and M, or it will not. If it is clearly distinguishable from one or both of K and M, then once again principle Add would not apply. But similarly, if it is not clearly distinguishable from both K and M, then in that context we will have good reason to be confident that Y’s value is not perfectly similar to, or the same as, X or Z’s values, since, by hypothesis, those values, K and M, are clearly distinguishable from each other. Hence, again, principle Add won’t apply. In sum, for any three outcomes to which we might have thought principle Add would be applicable, if we considered those outcomes two at a time, we can see that principle Add would not apply to those three outcomes if we considered all three of them at once. Insofar as the latter result seems firmly grounded, and I believe it is, this suggests one of two appropriate responses to the initial judgment. First, we might decide that the initial judgment that principle Add applied to the three outcomes when they were considered two at a time was mistaken. In essence, we might conclude that the judgment in question was akin to a perceptual illusion, which is only revealed as such when we consider all three outcomes at once. This might be like the predicament of someone confronting the famous Muller-Lyer illusion, who was convinced when looking at two side-by-side line segments, alone, that the one with the “outward” pointing arrows ( ) was longer than the one with the “inward” pointing arrows ( ), until a ruler was placed between them revealing that, in fact, the two line segments were the exact same length. Alternatively, we might retain our conviction in our initial judgment, that X and Y really do have the same value, K, when they are compared with each other, and that Y and Z really do have the same value, M, when they are compared with each other, but that X and Z have different values, K and M, when they are compared with each other, even as one grants that Y can have one or neither of the values, K and M —but not both— when all three outcomes are considered at once. But in that case, it is clear that Y’s value depends not solely on its internal features, and the particular value bases corresponding to those internal features, By, but in part on the alternatives with which it is compared. Thus, either the intransitivity of the “equally as good as relation” suggested by Add Reply to Persson 149 LEAP 2 (2014) is an illusion, or it is based on an Essentially Comparative View of ideals, and not on an alternative version of the Internal Aspects View as Persson suggests. Next, let me discuss a related way of thinking about the kinds of cases that Persson may have in mind. To do this, it will help to consider Diagram One. Diagram One Diagram One represents the values of our three standard outcomes, X, Y, and Z. In accordance with the Internal Aspects View, the value of outcome X is determined by the relevant bases for value that obtain in X, and these bases are a function solely of X’s internal features. However, Diagram One represents a situation where the value of X, which we again represent by the letter K, does not correspond to a single number, rather it has a number of varying elements reflecting the ways in which and extent to which X is good. For simplicity, we have assumed that the different aspects of X’s value can be accurately represented by the two connected rectangles of different color and pattern in the top left portion of the diagram. Similarly claims might be made regarding outcomes Y and Z and their values, where the different aspects of Y’s value are represented by the two connected rectangles of different color and pattern in the bottom portion of the diagram, and the different aspects of Z’s value are represented by the two connected rectangles of different color and pattern in the top right portion of the diagram. As represented, there is considerable overlap in the nature and extent of value between outcomes X and Y, represented by the fact that X’s right rectangle, and Y’s left rectangle have the exact same color and pattern. Similarly, there is considerable overlap in the nature and extent of value between outcomes Y and Z, represented by the fact that Y’s right rectangle, and Z’s left rectangle have the exact same color and pattern. But there is no overlap in the nature and extent of value between outcomes X and Z, represented by the fact that X’s two rectangles, and Z’s two rectangles have completely different colors and patterns. The following might then be phenomenologically accurate. If someone were asked to compare the outcomes X and Y, he might naturally focus on the significant respects in which their values were the same, and thus “perceive” or judge that they had the same value. Likewise, if someone were asked to compare the outcomes Y and Z, he might naturally focus on the significant X, Bx = K Y, BY = L Z, BZ = M 150 Larry Temkin LEAP 2 (2014) respects in which their values were the same, and thus “perceive” or judge that they had the same value. But if someone were asked to compare the outcomes X and Z, he might naturally focus on the fact that their values were not the same at all, and hence “perceive” or judge that they had different values. Thus, considering the outcomes two at a time, one might naturally be drawn to judge that X and Y were equally good, and Y and Z were equally good, but that, contrary to the purported transitivity of the “equally as good as relation”, X and Z were not equally as good. Here, we might have three outcomes where the judgments people might actually make regarding their value would seem in accordance with principle Add. Moreover, importantly, the values we would be responding to in making our judgments about the different outcomes would be determined solely by the internal features of those outcomes, so it might seem that we can give an account of a violation of the transitivity of the “equally as good as” relation consistent with an Internal Aspects View of ideals. So should we accept Persson’s view, after all? I don’t think so; at least not on the basis of the foregoing. My reaction to this kind of case is similar to my reaction to the previous one. My first reaction, and my main one, would be to acknowledge that people might, in fact, react phenomenologically to the different outcomes in the way suggested, but to contend that when they did so they were mistaken, and caught in the equivalent of a normative optical illusion. Comparing outcomes X and Y, we might well find the respects in which their values are the same especially salient, and this may lead us initially to judge them as equally good. However, once we are clear about what is going on in such cases, it seems clear that X and Y are not equally good (or perfectly similar regarding value). There are, undoubtedly, respects in which their values are the same, represented by the two rectangles that they each have of exactly the same color and shape, but there are also, undoubtedly, respects in which their values are different, represented by the two rectangles that they each have of completely different color and shape. Absent a plausible story that we have not been given for why it is permissible to completely ignore the respects in which X and Y differ in the ways and extent to which they are good, it seems hard to stick with the intuitive judgment that X and Y have exactly the same value, all things considered. Similar points might be made, of course, about our initial intuitive judgment that Y and Z have the exact same value. My second reaction to this kind of case would be to point out that, while it would be true that whatever aspects of Y’s value that we find ourselves responding to arise from Y’s internal features, the particular features that we focus on in assessing Y’s value will not solely be a function of Y’s internal features. Instead, it will be a function of the alternative outcome with which we compare Y. So, contrary to the Internal Aspects View, we cannot first determine Y’s value, considering Y just by itself, do the same for X and Z, and then find out how Y compares with X and Z by comparing them directly Reply to Persson 151 LEAP 2 (2014) in terms of the independent answers we came up with. Rather, in assessing Y’s value, we focus and rely on the ways and extent to which Y is good that are represented by the bottom left rectangle in Diagram One when we are comparing Y with X, but we focus and rely on the ways and extent to which Y is good that are represented by the bottom right rectangle of Diagram One when we are comparing Y with Z. Thus, here too, the factors that are relevant and significant for assessing Y’s value vary depending on the alternative outcome with which it is compared, and hence it is an Essentially Comparative View, after all, that would account for the plausibility of principle Add and the intransitivity of the “equally as good as” relation, not a rival Internal Aspects View to the version that I presented. Let me make one final point. In presenting his view, Persson makes it clear that if one is going to have an Internal Aspects View that would be compatible with the rejection of the various Axioms of Transitivity, then we have to reject the natural and plausible model for thinking about the goodness of outcomes that I present in my book, where goodness is understood as a property that can, in principle, be quantified and accurately represented by a real number, or a range of real numbers. 1 I agree with Persson about this. Moreover, as I point out in my book, there are various important problems with the “numerical” model in question (see for example Temkin 2012: ch. 10, note 10). But recognizing this, it is not enough to note that we need something other than my numerical model if we are to explain violations of the Axioms of Transitivity in a way that is compatible with an Internal Aspects View. We need an account of what the alternative way of thinking about the Internal Aspects View looks like. So far, we don’t have even the broadest sketch of such an account —beyond the simple assertion that it can’t be like my numerical model. How, exactly, are we to understand this rival, non-numerical, conception of the Internal Aspects View, so as to capture the various features that Persson and I both agree need to be captured? Here, as elsewhere, the devil is in the details, and I think the burden of proof lies on Persson to further develop and defend the conception he has in mind. Perhaps he thinks he has already done this. But if he has, I am afraid I have missed it. And if I have, perhaps others have as well. 1. Parfit has often made similar claims during our discussion about these issues. He eschews thinking about goodness in terms that can be represented by a real number. However, it is not clear to me what the coherent alternative to thinking about goodness in such terms is supposed to be, which fits with the underlying intuitions that motivate the Internal Aspects View in the first place. 152 Larry Temkin LEAP 2 (2014) 3. Persson’s article presents a striking and intriguing suggestion. He suggests that even on an Internal Aspects View the Axioms of Transitivity should be rejected. Moreover, he contends that this position offers the best way of interpreting what is going on in my book’s Spectrum Arguments. Unfortunately, I don’t find Persson’s claims convincing. As I try to make sense of Persson’s view, I keep thinking that either his normative judgments are mistaken —caused, perhaps, by a cognitive illusion— or the real explanation for them is provided by an Essentially Comparative View. In sum, while I welcome further reasons to challenge some of our standard assumptions about practical reasoning, I am not yet persuaded that Persson can deliver on the promissory note that his article offers us. Specifically, I am not yet convinced that there is a plausible rival account of an Internal Aspects View that both fully reflects the position that an outcome’s goodness depends solely on its internal features, and is compatible with the rejection of the Axioms of Transitivity. Moreover, even if such a view could be defended, I’m not convinced that it would provide the best explanation for what is going on in my Spectrum Arguments, rather than the one that I suggested in terms of an Essentially Comparative View. But I look forward to learning more from Persson regarding all of this on another occasion. BIBLIOGRAPHY Broome, J., 1991: Weighing Goods, Oxford: Basil Blackwell. Persson, I., 2014: “Internal or External Grounds for the Nontransitivity of ‘Better/ Worse than’”, Law, Ethics and Philosophy 2: 120-138. Rawls, J., 1971: A Theory of Justice, Cambridge (Mass.): Harvard University Press. Temkin, L., 2012: Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning, Oxford: Oxford University Press. — 2014: “Rethinking the Good - A Small Taste”, Law, Ethics and Philosophy 2: 58-86.