The End-Relational Theory of 'Ought' and the Weight of Reasonsdltc_1235 405..418 Daan Evers† Abstract Stephen Finlay analyses 'ought' in terms of probability. According to him, normative 'ought's are statements about the likelihood that an act will realize some (contextually supplied) end. I raise a problem for this theory. It concerns the relation between 'ought' and the balance of reasons. 'A ought to F' seems to entail that the balance of reasons favours that A F-es, and vice versa. Given Finlay's semantics for 'ought', it also makes sense to think of reasons and their weight in terms of probability. In this paper, I develop such a theory of weight. It turns out, however, that it cannot explain the entailments. This leaves Finlay with a challenge: to explain these entailments in some other way consistent with his theory, or to show why the appearances deceive and there are no such entailments. 1. Introduction In a recent series of papers, Stephen Finlay develops a remarkable theory of normative discourse (Finlay 2004, 2005, 2006, 2008, 2009, forthcoming a, forthcoming b). It is remarkable for its reductive aspirations in the face of Moore's objection to any such attempt. Moore argued as follows: let 'N' be a nonnormative expression denoting some object, property or relation (like being pleasant). Then take the statement (a) 'X is N'. Intuitively, the question whether X is good is not settled by its being N. One can master 'good' and all the terms in (a) and still ask: 'is X good?'. This should not make sense if 'good' just meant the same as 'N'. Since the question is open for all values of 'N', no definition of 'good' in nonnormative terms can work (1903, ch. 1, section 12). Moore was primarily concerned with 'good', but his Open Question Argument could have been applied to words like 'ought' and 'reason' too. It had a great influence on twentieth-century metaethics and made many philosophers wary of analysing normative words in nonnormative vocabulary. In spite of this, Finlay proposes to reduce normative 'ought's to statements about the likelihood that an act will realize some end. He shows how this hypothesis reveals remarkable unity both within normative language, and between it and related nonnormative con- † Faculty of Philosophy, University of Oxford, 10 Merton Street, Oxford, OX1 4JJ, UK; Email: daan.evers@philosophy.ox.ac.uk dialectica dialectica Vol. 64, N° 3 (2010), pp. 405–417 DOI: 10.1111/j.1746-8361.2010.01235.x © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. Published by Blackwell Publishing Ltd., 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA structions. I believe his theory is a strong contender for the truth in normative semantics. It is for this reason that I wish to raise a problem, hoping that it might be solved. My problem concerns the relation between 'ought' claims and claims about the balance of reasons. 'A ought to F' seems to entail that there are reasons for A to F. Furthermore, 'A ought to F' seems to entail that the collective weight of the reasons for A to F is greater than the collective weight of the reasons for A to not-F.1 And vice versa: from 'the balance of reasons favours that A F-es' it seems to follow that A ought to F. I will formulate the most natural theory of weight for a semantics like Finlay's. It turns out, however, that it cannot explain the latter entailments. This leaves Finlay with a challenge: to explain these entailments in some other way consistent with his theory, or to show why the appearances deceive and the entailments don't exist. 2. The end-relational theory of 'ought' Finlay's (2009) theory unifies both the semantics of different normative terms, and the semantics of normative terms with their nonnormative counterparts. In these respects, it borrows from Aaron Sloman (1970) and Angelika Kratzer (1977, 1981). The English language contains several nonnormative modal terms, including 'must', 'have to', 'may', 'might', 'can' and 'could'. The conceptual apparatus of possible worlds provides a plausible way of making sense of their semantics. For example: Modal Must: It must be the case that p = (df.) Every possible world in which circumstances/laws C obtain is such that p, and Modal May: It may be the case that p = (df.) At least one possible world in which circumstances/laws C obtain is such that p (Finlay 2009, 319). Different modalities are accounted for by varying the circumstances/laws of the worlds with which compatibility is stated: Logical modality addresses compatibility (of representations) of worlds with the laws of logic alone; metaphysical modality addresses compatibility with metaphysical laws, nomic modality addresses compatibility with scientific laws, and epistemic modalities address compatibility with what is believed or known by some subjects, or knowable independent of other beliefs (Ib.). Nonnormative modal terms like 'may' and 'must' seem to have normative counterparts. For example: 'you may (are permitted) to show him the pictures' and 'he 1 By 'not-F' I mean any action incompatible with F that is part of a class of relevant alternatives. Daan Evers406 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. must not treat you like that'. Finlay believes that all (or at least most2) normative modals can be understood as ordinary modals under an 'in order that . . .' modifier. So when we say things like 'I have to sentence you to death', what we really mean is that I have to do this relative to some (contextually supplied) end, such as discharging my duty as a judge. If the latter end is the one relevant in the context of my utterance, its meaning is (roughly) as follows: Every possible world in which I perform my duty as a judge is such that I sentence you to death. And similarly for other normative modals. More formally (for normative uses of 'must' and 'may'): Muste: In order that e it must be the case that p = (df.) Every possible world in which circumstances/laws C obtain, including its being the case that e, is such that p; Maye: In order that e it may be the case that p = (df.) At least one possible world in which circumstances/laws C obtain, including its being the case that e, is such that p (Ib., 320). So Finlay suggests that normative modals are ordinary modals under an 'in order that . . .' modifier. That is: everything we may, must, can, could, have to (etc.) do is relative to some (contextually supplied) end. This hypothesis provides a straightforward way to accommodate 'relativized' normativity: the phenomenon that requirements and permissions can be relative to goals or types of consideration. Some things one is morally permitted to do are not prudentially allowed (such as self-sacrifice). So far, I've discussed modals like 'may', 'can', 'have to', etc. Finlay suggests that a similar story unifies normative and nonnormative uses of 'ought' (itself a modal auxiliary verb). The principal nonnormative use of 'ought' is the predictive use, as in 'It ought to rain tomorrow': Arguably both ordinary and normative 'oughts' concern the greater likelihood of some state of affairs over the likelihood of the members of a comparison class R. I propose the following account of the ordinary 'ought': Modal Ought: It ought to be the case that p = (df.) It is more likely, given circumstances C, that p than that any member of R obtains. Hence ['It ought to rain tomorrow'] is true just in case it is more likely given C that it will rain tomorrow than any relevant alternative (Ib., 322). Normative uses of 'ought' are also understood as statements about likelihoods. Finlay claims that normative 'ought's are end-relational just like other normative modals. So, in order to represent the truth conditions of 'A ought to F', we need 2 There may not be a nonnormative use of 'need to', as an anonymous referee for this journal pointed out. The End-Relational Theory of 'Ought' and the Weight of Reasons 407 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. to state an end relative to which A ought to F. According to Finlay, every utterance of the form 'A ought to F' is understood as elliptical for an utterance of the form 'A ought to F in order that e'. In the case of the predictive 'ought', what is said to be most likely given C is rain. So to preserve uniformity, we have to say that in case of the normative 'ought', what is said to be most likely is F (the means) given e (the end), rather than e (the end) given F (the means).3 This explains Finlay's definition of the end-relational normative 'ought': Oughte: In order that e it ought to be the case that p = (df.) It is more likely, given circumstances C including its being the case that e, that p than that any other member of  obtains (Ib., 323; my italics).4 The suggestion that 'ought' statements are about the likelihood of means seems counterintuitive: normative 'ought's don't appear to be preor retrodictions of the agent's actions (not even given that s/he has achieved some end). But Finlay believes that context determines that the circumstances relative to which the means are likely do not include facts about the agent's psychological dispositions (Finlay 2009, 323 and forthcoming a). Context determines that it is part of the relevant circumstances that any course of action is as likely to be taken as any other (Finlay calls this assumption symmetry of choice in his forthcoming a). This should not be taken to mean that C contains a false assumption: namely that the agent is equally likely to take any of the means. Rather, we should think of C as silent on particular properties of the agent. Perhaps it merely stipulates that the agent is human and capable of doing any of the actions in R. That is ordinarily true. Finlay claims that given symmetry of choice, if F is the most effective means of achieving e, then, given that e obtains, it is most likely that F was taken as a means (2009, 323).5 3 Actually, there are several important reasons to prefer Finlay's direction of conditionalization. One is that sometimes even the best means fails to make the end more likely than not. Another is that 'You must F' (arguably) entails 'you ought to F', but not the other way around. Furthermore, 'you ought to F' entails 'you may F', but not the other way around. Finlay's conditionalization of means on ends predicts this, but it is not clear how to get the same results if we reverse the order of conditionalization. 4 Although in this definition 'in order that' is treated much like 'given that', this is not the whole story. In his (forthcoming b), Finlay argues that normative statements involve a certain temporal and metaphysical ordering of ends and means. I will ignore these complexities here, since they do not affect the main argument. 5 Even though there are technical reasons to prefer the conditionalization of means on ends, it is not terribly intuitive. Finlay argues that, insofar as we include and exclude the right kind of information from the conditions relative to which the means are likely, we (necessarily) capture the same result as when we make statements about the likelihood of the end's being achieved given the means. So the most effective means will as a matter of necessity be the means most likely taken given that the end obtains. This may be true. But even if it is, it's still counterintuitive to say that normative 'ought's are about the likelihood of means given that some end has been achieved. Two propositions that are necessarily equivalent in terms of truth value may nonetheless have distinct content. (This does, of course, depend on one's take on proposiDaan Evers408 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. But I think there is still a worry: assume that F and Y are two acts which are conducive to e. C is a specification of the circumstances of the agent (it includes information about the laws of nature, but no information about the agent which is specific to that agent). Now assume that it is highly unlikely that any agent would succeed in F-ing if s/he tried (perhaps because of something to do with the laws of nature or something general about agents which is entailed by C). Also assume that F is far more conducive to e than Y is. In other words: if one manages to F, then one is more likely to realize e than if one manages to Y. Given the assumption that anyone is very unlikely to succeed in F-ing (unlike Y-ing), we cannot infer from Pr(e|C&F) > Pr(e|C&Y) that Pr(F|C&e) > Pr(Y|C&e). This shows that it is not enough that C is silent about particular properties of the agent. Sometimes asymmetries in the likelihood of means are due to something other than psychological dispositions of the agent. In response to this, Finlay suggested modifying symmetry of choice as follows: 'end-relational 'ought's are conditionalized on circumstances in which the performance of each means (rather than simply the pursuit of each) is equally likely' (personal communication). The fix seems to entail that the truth of 'ought' judgments may after all sometimes depend on a false assumption (though only in rare cases). Take: 'you ought to win the lottery'.6 According to Finlay this should mean that the agent is more likely to have won the lottery than that another relevant alternative transpired (given, say, the end that she becomes very rich). But it is hard to find an alternative which is less likely than having won the lottery. So it seems that Finlay's truth conditions for 'you ought to win the lottery' must involve a false assumption: an assumption which entails that the odds of winning the lottery are far greater than they are in fact. Could this be remedied in the same way as before? Instead of building a false assumption into C (the circumstances relative to which the likelihoods are determined), couldn't C be silent about some facts? This may seem dubious, since information about the likelihood of succeeding in one's aims is relevant to deliberation about which means to take. However, if such information is relevant and one is very unlikely to win the lottery, then the 'ought' statement may well seem false (as opposed to the statement: 'you ought to try to win the lottery').7 And that is exactly what Finlay's analysis predicts if C does not contain a false assumption. tions. I do not accept that propositions are sets of possible worlds.) So even if the probability of F given C and e is necessarily the same as the probability of e given C and F, it does not follow that we state the same thing with either formula. However, although the order of conditionalization is counterintuitive, it needn't be a knock-down problem. Most philosophical theories have some surprising consequences, and Finlay's theory has considerable linguistic evidence in its favour. 6 I owe this example to Stephen Finlay in personal communication. 7 This discussion has benefited from comments by an anonymous dialectica referee. The End-Relational Theory of 'Ought' and the Weight of Reasons 409 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. If the above is correct, only a slight worry remains. Instead of addressing 'ought' statements to agents ('you ought to win the lottery'), we can also say 'everybody ought to win the lottery some time'. Instead of expressing a requirement that it is an agent's (or some agents') duty to fulfill, this statement might express what would be good to happen. Such a statement need not sound false. That may be problematic if the only way to make it true is to include some false information into C (information which entails that the odds of winning the lottery are greater than they are). Isn't it odd to make the truth of such judgments depend on false assumptions? However, this problem is not insurmountable. If someone says 'everybody ought to win the lottery some time', there is a strong tendency to interpret it nonliterally. For example, we may take it to mean: 'everybody ought to have good fortune some time'. The truth of this statement does not appear to require the insertion of false information into C. 3. The end-relational theory of reasons and their weight Finlay's theory of normative discourse is promising, but I think it faces problems too. Many of them are successfully addressed in his (2009), but I want to raise a new one. It seems that 'A ought to F' entails that there are reasons for A to F. But, more importantly, it seems to entail that the collective weight of the reasons for A to F is greater than the collective weight of the reasons for A to not-F. And vice versa: from 'the balance of reasons favours that A F-es', it seems to follow that A ought to F. This matters for normative semantics. If the appearances are veridical, an adequate semantics for 'ought' and 'reason' should explain why these entailments hold. If a theory fails to explain them, we have some reason to reject it. In this section I want to do two things, one constructive, the other critical. The first aim is to suggest a natural extension of the end-relational theory of 'ought' to a theory of the weight of reasons. The second is to show why this theory cannot explain the relevant entailments. I will briefly reflect that what appears to be missing makes it hard to see why these entailments would hold. And so Finlay faces a challenge: either to explain the entailments in some other way consistent with his theory; or to explain why the appearances deceive. In an article that predates his theory of modals, Finlay proposes the following theory of normative reasons: [. . .] a fact is a reason for [F]-ing, relative to a system of ends [e], iff it explains why [F]-ing is conducive to [e] (2006, 8). But the question that is left unanswered is the following: what is it to judge that a reason is stronger than another reason? Even if we grant that judgments about what Daan Evers410 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. we ought to do and judgments about reasons are end-relational, some reasons for F-ing are stronger than others. What makes this the case? This question is not easy to answer, but it is prima facie even more difficult to see what the truth conditions are of judgments about the relative strength of reasons that derive from different ends. For instance, in a situation where one cannot do both, one may have a reason to keep one's promise and a reason to help someone out, where these reasons derive from different sources. What makes the one stronger than the other? In this section, I want to explore a possibility. Finlay says that a fact is a reason for F-ing, relative to a system of ends e, iff it explains why F-ing is conducive to e. What is it for an act to be conducive to an end? Given Finlay's treatment of 'ought', it is natural to think of conduciveness in terms of probability, i.e. an act F is conducive to an end e iff it raises the probability that e.8 So we can say the following: Conducive: F is conducive to e iff Pr(e|C&F) > Pr(e|C&not-F). So a reason to F is a fact which explains why the probability of e given C and F is greater than the probability of e given C and not-F. 'To explain why' is to be read as 'to be part of an explanation of why'. Several facts may be involved in the explanation. We have now arrived at the following view of reasons: Reason: a fact is a reason to F (relative to e) iff that fact explains why Pr(e|C&F) > Pr(e|C&not-F).9 Let me illustrate this definition. We're playing pool and you want to pocket the ball (your end e). Given this end, you have a reason to chalk the cue tip: chalking prevents the tip from slipping when it makes contact with the ball. This is a reason because it explains why you have a better chance of pocketing the ball if you chalk the tip than if you don't. Slightly more formally: the fact that chalking prevents the 8 This is in fact what Finlay says in footnote 19 of his (2006): "I suggest that A is conducive to E, approximately, iff (and to the degree that) E is more likely in the presence of A than it would be in the absence of A". 9 There is an alternative way of thinking about reasons. Reasons to F can also be thought of as facts which raise the probability that one ought to F (something like this is defended in Kearns and Star, 2009). But this approach is problematic in the context of Finlay's theory. It is plausible that 'A has most reason to F' entails that A ought to F. But according to Finlay, 'ought' judgments are themselves judgments about conditional probability. So, on this alternative way of thinking about reasons (and given a suitable analogue of Most Reason; see below in the main text), the judgment 'A has most reason to F' will be a judgment to the effect that it is most probable that it is most probable that F given e. But from 'It is most probable that it is most probable that p', it does not follow that it is most probable that p. And, if so, it won't follow from 'A has most reason to F' that A ought to F. This problem can be solved only if one can explain why it is necessarily the case that if one has most reason to F, then the probability that one ought to F is 1. The End-Relational Theory of 'Ought' and the Weight of Reasons 411 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. cue tip from slipping explains why the Pr(pocketing the ball | C & chalking the cue tip) > Pr(pocketing the ball | C & not chalking the cue tip). A small problem arises: the fact that chalking the cue tip increases your chances itself seems a reason to do it. But the fact that chalking increases your chances of pocketing the ball does not explain why chalking increases your chances of pocketing the ball. And so it wouldn't be a reason on Finlay's definition. There are two ways to solve this problem. (1) The fact that chalking increases the chances of pocketing the ball can be a reason in virtue of a further end, like that of winning the game.10 (2) In cases where there is no further end, Finlay can take a buck-passing view: the fact that F-ing increases the chances of e inherits its status as a reason to F from whatever facts make this the case (it is a kind of shorthand). After all, the fact that F-ing increases the chances of e is not a reason to F in addition to the facts which explain why F-ing increases the chances of e. So what about the strength of reasons? On Finlay's theory, a fact acquires its status as a reason to F in virtue of the fact that it explains why F-ing increases the chances of e. If what matters is the eventuation of e, we have most reason to do the act on the supposition of which e is most likely. Since 'most reason' means 'weightiest reason' (not 'greatest number of reasons'), the collective strength of reasons is correlated with how likely the act is to realize the end. But what about the weight of individual reasons? If we can think of reasons as facts which raise the probability of e, we can correlate the strength of individual reasons with the value to which they raise that probability. This seems compatible with Finlay's theory, according to which reasons are facts which explain why an act raises the probability of e. For note that facts which explain why a probability is raised are themselves things which raise that probability (at least in the sort of contexts we are dealing with)11: if tectonic movements explain why the chances of an earthquake have increased, then those movements are themselves (part of) what raises the chances of an earthquake. Similarly for reasons: the fact that taking the taxi is the only way to escape is not only what explains why taking it raises the chances of escaping, but it is also (part of) what raises the chances of escape. 10 I owe this solution to an anonymous dialectica referee. 11 It might seem that facts about probability theory partly explain why probabilities are raised. But they are not facts which themselves raise the probabilities (the fact that Bayes's theorem is true does not by itself raise the probability of an earthquake). However, I take it that what counts as explanatory depends on context. In mathematics classes, facts about probability can explain why probabilities are raised, without themselves raising probabilities. But if a geologist say that the chances of an earthquake have increased, it would be odd to mention Bayes's theorem in answer to the question why. In the latter context, things like probability theory, the laws of logic (etc.) are presupposed. They are part of the background assumptions relative to which facts acquire explanatory roles. I submit that when it comes to reasons for action, the context of explanation will confer explanatory status only on facts which themselves raise the probabilities. Daan Evers412 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. But what does it mean to say that a fact raises the conditional probability of e?12 This amounts to saying that the probability of e given C including that fact & F is greater than the probability of e given C without that fact & F.13 For example: pocketing the ball after chalking the cue tip has a certain probability without taking into account the fact that chalking prevents the tip from slipping (this probability is presumably equal to the probability of pocketing the ball without chalking the cue tip). But if we add the fact that chalking prevents the tip from slipping to our background information, the probability of pocketing the ball is higher, i.e. this fact raises the probability of e given C&F. Since the collective weight of reasons is correlated with how likely F is to realize e, we might suggest that an individual fact is stronger reason to F than another individual fact iff (a) both are reasons14 and (b) the first raises the probability of e given C&F more than the last. For example: returning a wallet (F) may raise the probability of happy feelings (e) because (1) it is in accordance with one's own principles and (2) one might get a reward. (1) by itself might raise the probability of happy feelings more than (2) does, since acting in accordance with one's principles nearly always makes one happy, whereas wallet owners only rarely give rewards. If so, then (1) would be the stronger reason to return the wallet. Formally, (1) and (2) would be part of C, so that we can establish their relative weights by comparing the probability of e given C including (1) but not (2) & F with the probability of e given C including (2) but not (1) & F. Of course, the foregoing only works for reasons for the same act F. But we can formulate a general principle of weight: More Reason: a fact is stronger reason to F than another fact is a reason to Y (relative to e) iff (a) both are reasons for some act in  and (b) the first raises the probability of e given C&F to a value higher than the last raises the probability of e given C&Y (where 'Y ' can take any value in , including the same value as 'F'). More Reason allows comparisons of the strength of reasons for the same and different acts. Whatever act a fact F1 is a reason for, it is stronger reason than another fact F2 (relative to e) just in case F1 raises the probability of e given C & the act F1 is a reason for to a value higher than the last raises the probability of e 12 Thanks to an anonymous dialectica referee for pressing me on this issue. Of course, C is to be read as a variable for a set of propositions, not any particular set (in which case it couldn't both contain and not contain the relevant fact). 13 Of course, this makes sense only if C does not entail the relevant fact. So we'll have to assume that the context will always supply an appropriate set of background assumptions, via a principle of accommodation (thanks to Ralph Wedgwood). 14 This condition is required since a reason was defined as a fact which explains why the Pr(e|C&F) > Pr(e|C&not-F). If a fact meets condition (b), it does not follow that the probability of e given C&F is greater than the probability of e given C&not-F. And so it does not follow that it is a reason in the first place. The End-Relational Theory of 'Ought' and the Weight of Reasons 413 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. given C & the act F2 is a reason for. More Reason says that this is so even if the act for which F1 is a reason is the very same as the act for which F2 is a reason. Given More Reason, we can state the truth conditions of 'A has most reason to F' as follows: Most Reason: 'A has most reason to F' (relative to e) iff the reasons to F collectively raise the probability of e given C&F to a value higher than the reasons to Y raise the probability of e given C&Y (for all Y in  non-identical to F).15,16 So is this theory of weight any good? One good feature of the account is the following: Most Reason entails that if A has most reason to F (relative to e), then A ought to F. Recall that 'A ought to F' means that, given C&e, F is more likely than any relevant alternative. Given symmetry of choice, this is indeed the case if the reasons to F collectively raise the probability of e to a value higher than the reasons for any relevant alternative. Symmetry of choice guarantees that if the probability of e given C&F is greater than the probability of e given C&Y, then the probability of F given C&e is greater than the probability of Y given C&e. So if the reasons to F make e more likely than the reasons for any relevant alternative, then, given that e obtains, F will also be more likely chosen as a means than any relevant alternative. Conversely, Most Reason also predicts that if A ought to F, then A has most reason to F (relative to e). After all (given symmetry of choice), if it is more likely that F given C&e than any relevant alternative, then the reasons to F collectively raise the probability that e given C&F more than the reasons for any alternative collectively raise the probability that e given C and that alternative. So Most Reason generates intuitively plausible results for the weights of reasons relative to a common end. However, our reasons derive from many different ends, and a theory of weight should allow for comparisons of the strength of reasons derived from different ends. As I will argue now, Most Reason fails here.17 Suppose we have two reasons F1 and F2 for an action F. And suppose we have two ends, e1 and e2. F1 raises the probability that e1 given C&F, but F2 raises the probability that e2 given C&F (henceforth I will omit 'C'). If we want to know which reason is weightier, it won't do to compare the values to which F1 and F2 15 So what we are comparing is the probability of e given C including the reasons to F & F with the probability of e given C including the reasons to Y & Y. 16 It is clear that the collective weight of reasons to F cannot be a matter of adding up the amounts by which they individually raise the probability of F given C&e. For there may be 1,000 reasons to F, but the probability of F given C&e cannot be greater than 1. I have nothing to say about the function which determines the collective weight of reasons. I will simply assume that such a function can be devised. 17 In fairness, Finlay acknowledges that his semantics faces problems when we go beyond a single end. See his (2009, 336–339) and (forthcoming a). Daan Evers414 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. respectively raise (1) the probability that e1 given F and (2) the probability that e2 given F. After all, it may be that F2 raises the probability that e2 given F to a lower value than F1 raises the probability that e1 given F, even though F2 is the stronger reason. This is the case if e2 is a more important end than e1. The obvious response seems to be the following: it's true that when two facts derive their status as reasons to F from different ends, their strengths are incommensurable without a further common end to which we can relate them. Once this is supplied (call it 's' for superend), we are in a position to determine their relative strengths by comparing the values to which they raise the probability that s given F. Finlay may be attracted to this response, since he also believes that judgments about different ends (and whether to pursue them) may themselves be indexed to some other (or in limiting cases the same) end(s) (2009, 336–339). So why not say that judgments about what we have more reason to do (and which reasons are stronger than which) are also relative to some further end? But there is a problem. Two facts can derive their status as reasons to F from two distinct ends. We are now considering the idea that their relative weights are determined by a further end. But it is not a priori that the speaker is always committed to a further end s such that both F1 and F2 raise the probability that s given F. (If the speaker is committed to a further end at all. Consider a conflict between requirements of prudence and requirements of morality. It is not clear on the basis of what further end we are to assess which one of these to follow.)18 Nor is it clear that, even if we could always find a further end, the respective values to which F1 and F2 raise its probability will always correspond to our intuitive assessments of their weights. At this point, there are two ways to save the theory of weight discussed: we can either deny that reasons with comparative weights ever derive their status as reasons from different ends, or we can try to show that whenever two reasons F1 and F2 (derived from two ends e1 and e2) have comparative weights, there is always a further end s such that the respective values to which F1 and F2 respectively raise the probability that e1 and e2 given F is always mirrored by the values to which they raise the probability that s given F. I take it that neither option is feasible. It will not work to combine e1 and e2 into a complex superend (a conjunctive end). If we grant that F1 and F2 can derive their status as reasons from different ends, then we presumably also grant that F2 can be weightier than F1 despite the 18 Some people may object to the idea that the speaker needs to be committed to a further end. Perhaps it would suffice if such a further end exists. Two points in response: first, I take it that a plausible assignment of truth conditions to normative statements will at least in some cases be constrained by the speaker's commitments. It would be odd to assign utilitarian truth conditions to moral judgments by a Kantian. But it is important to bear in mind that the notion of commitment is not supposed to entail conscious commitment. Speakers needn't be able to articulate the ends to which their judgments are indexed. Second, it is not at all clear that a further end can always be found, as I point out in the main text. The End-Relational Theory of 'Ought' and the Weight of Reasons 415 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. fact that the latter raises the probability that e1 given F to a value higher than F2 raises the probability that e2 given F. But simply combining e1 and e2 into a superend won't guarantee that F2 is such that it raises the probability that s given F to a greater value than F1 does. After all, F2 may not in any way raise the probability that e1 given F. Furthermore, e1 and e2 may be incompatible, in which case the probability of s is not defined at all. I think the above considerations show that our judgments about the relative weight of facts which derive their status as reasons to F from different ends cannot (always) be understood as judgments about the relative values to which they raise the probability of some further end. This result poses a challenge for Finlay's end-relational theory of 'ought', for that theory is most naturally paired with a probabilistic theory of weight. But I've argued that such a theory (a bare probability theory) cannot explain why 'A ought to F' entails that the balance of reasons favours that A F-es, nor why the latter entails the former. What appears to be missing from the account is something which determines the importance of an end. And it seems this cannot be understood in terms of probabilities. That, however, makes it unclear how 'A ought to F' (which is merely a statement of conditional probability) could entail information about relative importance. Suppose, for example, that importance for a subject is a matter of that subject's preferences. Since the meaning of 'A ought to F' does not involve anyone's preferences, there is no semantic entailment from 'A ought to F' to 'The balance of reasons favours that A F-es'. This does not mean that the end-relational theory is hopeless. Much depends on the possibility of analysing 'importance' in reductive terms, and on whether the entailments between 'ought' and the balance of reasons exist, or need be thought of as semantic. 4. Conclusion I have argued that, given Finlay's semantics, the most natural theory of reasons is one in which reasons to F are facts which raise the probability that e given F. And, likewise, a natural theory of a reason's weight is one where the weight of a reason depends on the value to which it raises the probability that e given F. However, I have argued that such a theory cannot explain why 'A ought to F' entails that the collective weight of the reasons for A to F is greater than the collective weight of the reasons for A to do an alternative. Nor can it explain, conversely, why it follows from the fact that the balance of reasons favours that A F-es that A ought to F. I have indicated that what appears to be missing from the truth conditions of statements about weight is something which determines the importance of an end. But 'importance' is itself a normative word, and requires analysing. Furthermore, Daan Evers416 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica. if 'ought' statements do not convey information about importance, it is unclear how they could entail statements about the balance of reasons. These considerations form a challenge for the end-relational theory of 'ought'.* References Finlay, S. 2004, 'The Conversational Practicality of Value Judgement', The Journal of Ethics 8, pp. 205–223. Finlay, S. 2005, 'Value and Implicature', Philosophers' Imprint 5, pp. 1–20. Finlay, S. 2006, 'The Reasons that Matter', Australasian Journal of Philosophy 84, pp. 1–20. Finlay, S. 2008, 'The Error in the Error Theory', Australasian Journal of Philosophy 86, pp. 347–369. Finlay, S. 2009, 'Oughts and Ends', Philosophical Studies 143, pp. 315–340. Finlay, S. forthcoming a, 'What Ought Probably Means, and Why You Can't Detach It', Synthese. Finlay, S. forthcoming b, 'Normativity, Necessity, and Tense. A Recipe for Homebaked Normativity', Oxford Studies in Metaethics vol. 5. Kearns, S. and Star, D. 2009, 'Reasons as Evidence', in: R. Shafer-Landau, ed., Oxford Studies in Metaethics vol. 4, Oxford: Oxford University Press, pp. 215–242. Kratzer, A. 1977, 'What "Must" and "Can" Must and Can Mean', Linguistics and Philosophy 1, pp. 337–355. Kratzer, A. 1981, 'The Notional Category of Modality', in: H. J. Eikmeyer and H. Rieser, eds, Words, Worlds, and Contexts, Berlin: Walter de Gruyter, pp. 38–74. Moore, G. 1903, Principia Ethica, Cambridge: Cambridge University Press. Sloman, A. 1970, 'Ought and Better', Mind 79, pp. 385–394. * I am grateful to Ralph Wedgwood, Stephen Finlay and two anonymous dialectica referees for extremely helpful comments on this paper. I would also like to thank the Stichting Fundatie van de Vrijvrouwe van Renswoude te 's Gravenhage, the Arts & Humanities Research Council, the Prins Bernhard Cultuurfonds, The Royal Institute of Philosophy, Jesus College, Oxford and the Deutscher Akademischer Austausch Dienst (who gave me the Michael Foster Memorial Scholarship) for financial support. The End-Relational Theory of 'Ought' and the Weight of Reasons 417 © 2010 The Author. dialectica © 2010 Editorial Board of dialectica.