Incommensurability of Value

According to influential arguments from several branches of philosophy, there exist some gradable natural language expressions that violate the following principle: if x and y are both F to some degree, then either x is at least as F as y or y is at least as F as x. Dorr, Nebel and Zuehl (2022) (DNZ), who refer to this principle as ‘Comparability’, respond to these arguments and offer a systematic case in support of Comparability. In this paper, I respond (...) to DNZ and develop an opposing case against Comparability that (i) buttresses previous criticisms of the principle, (ii) identifies two new arguments against the principle, and (iii) rebuts DNZ’s prospective arguments in favour of the principle. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative (...) Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

This is just an initial draft, which I hope to work on over the next year in light of comments. If you think I left off a big question, or left on a boring one, please email me! (Thanks to Brian Hedden and Harvey Lederman for some initial comments.).

I present a new puzzle about choice under uncertainty for agents whose preferences are sensitive to multiple dimensions of outcomes in such a way as to be incomplete. In response, I develop a new theory of choice under uncertainty for incomplete preferences. I connect the puzzle to central questions in epistemology about the nature of rational requirements, and ask whether it shows that preferences are rationally required to be complete.

In this article I try to elucidate the concept of human dignity by taking a closer look at the features of a paradigmatic torture situation. After identifying the salient aspects of torture, I discuss various accounts for the moral wrongness of such acts and argue that what makes torture a violation of human dignity is the perverted moral relationship between torturer and victim. This idea is subsequently being substantiated and defended against important objections. In the final part of the chapter (...) I give a (qualified) defense of the methodology employed in the previous sections. (shrink)

A moral requirement R1 is said to be lexically prior to a moral requirement R2 just in case we are morally obliged to uphold R1 at the expense of R2 – no matter how many times R2 must be violated thereby. While lexical priority is a feature of many ethical theories, and arguably a part of common sense morality, attempts to model it within the framework of decision theory have led to a series of problems – a fact which is (...) sometimes spun as a ‘decision theoretic critique’ of lexical priority. In this paper, I develop an enriched decision theoretic framework that is capable of modelling lexical priority while avoiding all extant problems. This will involve introducing several new ingredients into the standard decision theoretic framework, including multidimensional utilities, de minimis risks, and the means to represent two different conceptions of risk. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

This article presents a new argument against many forms of moral and prudential value incompleteness. The argument relies on two central principles: (i) a weak "negative dominance" principle, to the effect that Lottery 1 is better than Lottery 2 only if some possible outcome of Lottery 1 is better than some possible outcome of Lottery 2, and (ii) a weak form of ex ante Pareto, to the effect that, if Lottery 1 gives an unambiguously better (stochastically dominant) prospect to some (...) individuals than Lottery 2, and equally good prospects to everyone else, then Lottery 1 is better than Lottery 2. Given modest auxiliary assumptions, these two principles rule out incompleteness in the prudential ranking of individual lives, and many forms of incompleteness in the moral rankings of outcomes and lotteries. (shrink)

Critical-set views avoid the Repugnant Conclusion by subtracting some constant from the welfare score of each life in a population. These views are thus sensitive to facts about biographical identity: identity between lives. In this paper, I argue that questions of biographical identity give us reason to reject critical-set views and embrace the total view. I end with a practical implication. If we shift our credences towards the total view, we should also shift our efforts towards ensuring that humanity survives (...) for the long term. (shrink)

This entry explains what the issue of weighing reasons is about and then discusses a number of theories concerning weighing reasons. The general issue concerns how reasons (or considerations or pros and cons) systematically interact to determine the normative status of some action, belief, or attitude. For example, it concerns how reasons determine whether an action is permissible, required, or what ought to be done. The general issue also concerns how reasons aggregate or themselves result from systematic interactions with the (...) broader context. Along the way, the entry considers whether reasons can be incommensurable (e.g., be on a par); whether reasons have more than one weight value (e.g., justifying, requiring, and commending); the relation between reasons for and reasons against; conditions (enablers, disablers); modifiers (amplifiers, attenuators); exclusionary reasons; higher order evidence; what happens when, say, morality and epistemic rationality conflict; and so on. (shrink)

We can often permissibly choose a worse self-interested option over a better altruistic alternative. For example, it is permissible to eat out rather than donate the money to feed five hungry children for a single meal. If we eat out, we do something permissibly partial toward ourselves. If we donate, we go beyond the call of moral duty and do something supererogatory. Such phenomena aren’t easy to explain, and they rule out otherwise promising moral theories. Incommensurability and Ruth Chang’s notion (...) of parity can explain certain small improvement puzzles, but they can’t explain permissible partiality and supererogation. On the other hand, Josh Gert’s distinction between justifying and requiring weight can explain all three phenomena: permissible partiality, supererogation, and the relevant small improvement puzzle. Indeed, this chapter provides a reason to endorse the justifying/requiring weight distinction by showing that it provides the only extant explanation of all three phenomena. (shrink)

Historically, philosophers who thought our world unsurpassable, like Leibniz, thought it the uniquely best of all possible worlds. But recent developments in value theory and philosophy of religion make clear that our world could be unsurpassable, but not uniquely best—because other worlds are still as good as or incomparable with it. In particular, the world may contain infinities that result in incomparability with many other worlds. This chapter advances the recent philosophical debate over whether it is tenable to hold that (...) our world is unsurpassable, given that it may contain an infinite number of people with lives that go infinitely well. I argue that while recent innovations in formal axiology offer prospects for comparing many worlds with these kinds of infinities, many infinite worlds are genuinely incomparable with each other. Consequently, whether there is another world better than our own ends up turning on substantive metaphysical and normative questions: metaphysical questions about personal identity across possible worlds, and normative questions about what makes for a valuable life. (shrink)

This chapter will amount to a detailed exposition and exploration of one of the most prominent arguments against the existence of an unsurpassable world: the argument from addition. Endorsed by a variety of thinkers such as St. Thomas Aquinas, Alvin Plantinga, and William Rowe, the argument from addition uses the possibility of adding good things to a candidate unsurpassable world to argue that every world is surpassable. While widely endorsed, the argument has come under recent criticism. By carefully working through (...) a targeted version of the argument, I set out to establish the following: (i) that a world can always contain more good things; (ii) that a suitably restricted additive aggregation principle allows us to say that adding more good things in a certain way is an improvement, and (iii) that objections to the argument from widespread value incomparability fail. (shrink)

Parfit (Theoria 82:110–127, 2016) responded to the Sequence Argument for the Repugnant Conclusion by introducing imprecise equality. However, Parfit’s notion of imprecise equality lacked structure. Hájek and Rabinowicz (2022) improved on Parfit’s proposal in this regard, by introducing a notion of degrees of incommensurability. Although Hájek and Rabinowicz’s proposal is a step forward, and may help solve many paradoxes, it can only avoid the Repugnant Conclusion at great cost. First, there is a sequential argument for the Repugnant Conclusion that uses (...) weaker and intuitively more compelling assumptions than the Sequence Argument, and which Hájek and Rabinowicz’s proposal only undermines, in a principled way, by allowing for implausible weight to be put on the disvalue of inequality. Second, if Hájek and Rabinowicz do put such implausible weight on the disvalue of inequality, then they will have to accept that a population A is not worse than another same sized population B even though everyone in B is better off than anyone in A. (shrink)

Pareto principles are at the core of ethics and decision theory. The Strong Pareto principle says that if one thing is better than another for someone and at least as good for everyone else, then the one is overall better than the other. But a host of famous figures express it differently, with ‘not worse’ in place of ‘at least as good.’ In the presence of parity (or incommensurability), this results in a strictly stronger Pareto principle, which I call Super‐Strong (...) Pareto. Super‐Strong Pareto, however, yields cyclic betterness and is therefore false. I point out a number of influential arguments—concerning population ethics, collective action problems, and decision‐making in the face of parity and uncertainty—that crucially rely on Super‐Strong Pareto and are therefore unsound. I then turn to the most influential argument against the possibility of parity—Broome's collapsing argument—and argue that it likewise relies on Super‐Strong Pareto reasoning and is therefore question‐begging. Finally, I turn to the much‐neglected question of how to justify Strong Pareto. The answer I arrive at, which emphasizes tie‐breaking, yields a striking insight, namely that Super‐Strong Pareto amounts to the denial of insensitivity to mild sweetening. That is what makes it problematic in the presence of parity. (shrink)

Value pluralists believe in multiple dimensions of value. What does betterness along a dimension have to do with being better overall? Any systematic answer begins with the Strong Pareto principle: one thing is overall better than another if it is better along one dimension and at least as good along all others. We defend Strong Pareto from recent counterexamples and use our discussion to develop a novel view of dimensions of value, one which puts Strong Pareto on firmer footing. We (...) conclude by defending Dimensionalism, the hypothesis that overall value relations are determined solely by how things compare along value dimensions. These are first steps towards a more systematic value pluralism. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

After 50 years of debate, the ethics of aggregation has reached a curious stalemate, with both sides arguing that only their theory treats people as equals. I argue that, on the issue of equality, both sides are wrong. From the premise that “each counts for one,” we cannot derive the conclusion that “more count for more” or its negation. The familiar arguments from equality to aggregation presuppose more than equality: the Kamm/Scanlon “Balancing Argument” rests on what social choice theorists call (...) “(Positive) Responsiveness,” Kamm’s “Aggregation Argument” assumes that “equal” lives are fungible, and Hsieh et al. have it that spreading goods broadly best approximates equality. In each case, the crucial premise is not equality itself but a further idea that Taurek, I argue, can safely reject. I conclude with a conjecture: there is no theory-neutral argument that settles the question of whether the numbers count. (shrink)

The foundation of natural law ethics is a set of basic human goods, such as life and health, knowledge, work and play, the appreciation of beauty, friendship, and religion. A disputed question among natural law theorists is whether the basic goods can be measured or compared in terms of their value. Proponents of New Natural Law Theory, the best-known version in the contemporary literature, hold that basic goods are both incommensurable and incomparable. Proponents of Classical Natural Law Theory, the historically (...) mainstream version, maintain that basic goods are incommensurable but comparable. I make a case for the comparability of basic goods, arguing that commonsense moral intuitions about human flourishing and analysis of how we resolve moral conflicts provide good reasons to affirm that basic goods are comparable and that some goods are more valuable than others. (shrink)

In this paper, I reply to Ruth Chang’s ‘What is so Hard about Hard Choices’.

The book develops, defends, and applies a "Dual Scale" model of weighing reasons to resolve various issues in ethics. It tells you everything you ever wanted to know about weighing reasons and probably a lot of stuff you didn't want to know too. It addresses, among other things, what the general issue of weighing reasons is; what it is to weigh reasons correctly; whether reasons have more than one weight value (e.g., justifying, requiring, and/or commending weight); whether weight values are (...) context sensitive; how to tell what the weights of reasons are; how reasons for are related to reasons against; and how the weights of reasons aggregate. After addressing such issues, it explains a number of puzzling phenomena in ethics, such as the All or Nothing Problem, the normative significance of small improvements, and the intransitivity of the makes-it-permissible-to-act-against relation. (shrink)

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (shrink)

It is natural to assume that every value bearer must be good, bad, or neutral. This paper argues that this assumption is false if value incomparability is possible. More precisely, if value incommensurability is possible, then there is a fourth category of absolute value, in addition to the good, the bad, and the neutral.

The aim of this paper is to provide a detailed characterisation of some ways in which our preferences reflect our reasons. I will argue that practical reasons can be characterised along two dimensions that influence our preferences: their balance and their weight. This is analogous to a similar characterisation of the way in which probabilities reflect the balance and weight of evidence in epistemology. In this paper, I will illustrate the distinction between the balance and weight of reasons, and show (...) how this is crucial for an adequate account of preference and choice. The upshot is a more complete picture of a particular kind of decision, labelled by Isaac Levi and, more recently, Ruth Chang as ‘hard choices’. These are choices in which one option is better than another in some ways, the other is better than the first in some ways, but neither seems better overall. The distinction between the balance and weight of reasons presents a new way of understanding how hard choices vary by degree and what it is that makes them so hard. (shrink)

Why should ‘better than’ be transitive? The leading answer in ethics is that values do not change with context. But this cannot be the entire source of transitivity, I argue, since transitivity can fail even if values never change, so long as they are complex, with multiple dimensions combined non-additively. I conclude by exploring a new hypothesis: that all alleged cases of nontransitive betterness, such as Parfit’s Repugnant Conclusion, can and should be modelled as the result of complexity, not context-relativity.

The much-discussed ‘Argument from Small Improvement’ has been advanced both as a reason to reject (tripartite) Completeness, one of the standard axioms of decision theory, and to accept the possibility of rationally incomparable choices. But this form of argument cannot be an effective basis for either of these conclusions, unless one already has some prior, independent reason to prefer Transitivity to Completeness as a constraint on rational preferences (or rational values). In particular, I show how a reverse argument from small (...) improvement can be constructed, starting from the assumption of tripartite Completeness, to the conclusion that Transitivity fails. I conclude that this form of argument as it has been standardly presented in the literature is a kind of ‘red herring’. We can only make progress here by evaluating the reasons independent of either such argument to prefer one or other of Transitivity or Completeness. (shrink)

The foundation of natural law ethics is a set of basic human goods, such as life and health, knowledge, work and play, appreciation of beauty, friendship, and religion. A disputed question among natural law theorists is whether the basic goods are “incommensurable.” But there is widespread ambiguity in the natural law literature about what incommensurability means, which makes it unclear how this disagreement should be understood and resolved. First, I clear up this ambiguity by distinguishing between incommensurability and incomparability. I (...) show that proponents of New Natural Law Theory hold that basic goods are both incommensurable and incomparable, whereas proponents of Classical Natural Law Theory hold that basic goods are incommensurable but comparable. Second, I critique the leading New Natural Law arguments for the incomparability of basic goods. Throughout the article, I explain why value incommensurability is an essential feature of natural law ethics but value incomparability is not. (shrink)

Many people find comparisons of the value of persons distasteful, even immoral. But what can be said in support of the claim that persons have incomparable worth? This chapter considers an argument purporting to show that the value of persons is incomparable because it is so great—because it is infinite. The argument rests on two claims: that the value of our capacity for valuing must equal or exceed the value of things valued and that our capacity for valuing is unbounded (...) in a very strong sense. After laying out this argument, I consider its implications for how we should regard each other. In particular, I suggest that it complicates efforts to understand morality as a system of principles. Instead, I propose that an aesthetic attitude, not unlike our experience of the sublime, is an apt response to humanity’s infinite value. -/- . (shrink)

Sometimes one can prevent harm only by contravening rights. If the harm one can prevent is great enough, compared to the stringency of the opposing rights, then one has a lesser-evil justification to contravene the rights. Non-consequentialist orthodoxy holds that, most of the time, lesser-evil justifications add to agents’ permissible options without taking any away. Helen Frowe rejects this view. She claims that, almost always, agents must act on their lesser-evil justifications. Our primary task is to refute Frowe’s flagship argument. (...) Secondarily, it is to sketch a positive case for nonconsequentialist orthodoxy. (shrink)

Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

John Taurek argues that, in a choice between saving the many or the few, the numbers should not count. Some object that this view clashes with the transitivity of ‘better than’; others insist the clash can be avoided. I defend a middle ground: Taurek cannot have transitivity, but that doesn’t doom his view, given a suitable conception of value. I then formalize and explore two conceptions: one context-sensitive, one multidimensional.

Totalism is the view that one distribution of well-being is better than another just in case the one contains a greater sum of well-being than the other. Many philosophers, following Parfit, reject totalism on the grounds that it entails the repugnant conclusion: that, for any number of excellent lives, there is some number of lives that are barely worth living whose existence would be better. This paper develops a theory of welfare aggregation—the lexical-threshold view—that allows totalism to avoid the repugnant (...) conclusion, as well as its analogues involving suffering populations and the lengths of individual lives. The theory is grounded in some independently plausible views about the structure of well-being, identifies a new source of incommensurability in population ethics, and avoids some of the implausibly extreme consequences of other lexical views, without violating the intuitive separability of lives. (shrink)

ABSTRACT I consider paradoxical spectrum arguments involving transitive relations like ‘better than’. I argue that, despite being formally different from sorites arguments, at least some spectrum arguments arise from vagueness, and that vagueness might often be the most natural diagnosis.

This chapter presents several arguments related to Parfit's notion of evaluative imprecision and his imprecisionist lexical view of population ethics. After sketching Parfit's view, it argues that, contrary to Parfit, imprecision and lexicality are both compatible with thinking about goodness in terms of positions on a scale of value. Then, by examining the role that imprecision is meant to play in defusing spectrum argument, it suggests that imprecision should be identified with vagueness. Next, it argues that there is space for (...) robust moral realists to think of evaluative vagueness as a semantic phenomenon, illustrating this view with a version of conceptual role semantics on which the precisifications of betterness are correctness conditions for the precisifications of preference. Finally, it gives a probability-based argument against the imprecisionist lexical view. (shrink)

The (moral) permissibility of an act is determined by the relative weights of reasons, or so I assume. But how many weights does a reason have? Weight Monism is the idea that reasons have a single weight value. There is just the weight of reasons. The simplest versions hold that the weight of each reason is either weightier than, less weighty than, or equal to every other reason. We’ll see that this simple view leads to paradox in at least two (...) ways. We must complicate the picture somehow. I consider two candidate complications. The first, Parity Monism, is inspired by Ruth Chang’s suggestion that parity is a fourth comparative beyond the traditional three (>, <, =). This view complicates the single weight relation by allowing that the weights of reasons can be on a par. Unfortunately, Parity Monism resolves only one of the two paradoxes that afflict simple versions of Weight Monism. To resolve both paradoxes, we need our second candidate complication, Weight Pluralism. This view holds that reasons have at least two weight values (e.g., justifying weight and requiring weight) and these two values aren’t always equivalent. Parity is no substitute for Pluralism. (shrink)

Politics, Philosophy & Economics, Volume 21, Issue 4, Page 347-371, November 2022. We sometimes have to choose between options that are seemingly incomparable insofar as they seem to be neither better than, worse than, nor equal to each other. This often happens when the available options are quite different from one another. For instance, consider a choice between prioritizing either criminal justice reform or healthcare reform as a public policy goal. Even after the relevant details of the goals and possible (...) reforms are filled in, it is plausible that neither goal is better than, worse than, nor equal to the other. Such seemingly incomparable options present a problem for rational choice since it is unclear how an agent might rationally choose between them. What we need are some principles to help govern rational choice when faced with seemingly incomparable options. I here present three such principles. While each principle is individually compelling, I show that they are jointly incompatible. I then argue that the correct response to this inconsistent triad is to reject the principle that rationally censures performing a sequence of choices one knows will result in a suboptimal outcome. The upshot is that when seeming incomparability is involved, an agent can money pump themselves without being less rational for it. (shrink)

A number of Christian theologians and philosophers have been critical of overly moralizing approaches to the doctrine of sin, but nearly all Christian thinkers maintain that moral fault is necessary or sufficient for sin to obtain. Call this the “Moral Consensus.” I begin by clarifying the relevance of impurities to the biblical cataloguing of sins. I then present four extensional problems for the Moral Consensus on sin, based on the biblical catalogue of sins: (1) moral over-demandingness, (2) agential unfairness, (3) (...) moral repugnance, and (4) moral atrocity. Next, I survey several partial solutions to these problems, suggested by the recent philosophical literature. Then I evaluate two largely unexplored solutions: (a) genuine sin dilemmas and (b) defeasible sinfulness. I argue that (a) creates more problems than it solves and that, while (b) is well-motivated and solves or eases each of the above problems, (b) leaves many biblical ordinances about sin morally misleading, creating (5) a pedagogical problem of evil. I conclude by arguing that (5) places hefty explanatory burdens on those who would appeal to (b) to resolve the four extensional problems discussed in this paper. So Christian thinkers may need to consider a more radical separation of sin and moral fault. (shrink)

How should you evaluate your choices when you’re unsure what their outcomes will be? One popular answer is to rank your options in terms of their expected utilities. But what should you do when you think that the value of their respective outcomes might be incommensurable? In the face of incommensurable values, it no longer makes sense to speak of ranking your options according to expected utility. Are there any general principles to guide us when facing decisions of this kind? (...) If only! This chapter develops an impossibility result: it holds that there are a handful of independently plausible constraints that no such decision theory can jointly satisfy. The result, while depressing, can be used to helpfully classify extant approaches based on which of the constraints they violate. (shrink)

We defend three controversial claims about preference, credence, and choice. First, all agents (not just rational ones) have complete preferences. Second, all agents (again, not just rational ones) have real-valued credences in every proposition in which they are confident to any degree. Third, there is almost always some unique thing we ought to do, want, or believe.

Ruth Chang and Joseph Raz have both drawn far-reaching consequences for agency from the phenomenon of incommensurability. After criticizing their arguments, I outline an alternative view: if incommensurability is vagueness, then there are no substantial implications for agency, except perhaps a limited form of naturalistic voluntarism if our reasons are provided by desires.

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...) is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...) is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

The concept of natural otherness can be found throughout the environmental ethics literature. Drawing on this concept, this article pursues two aims. For one, it argues for an account of individual natural otherness as stable difference as opposed to accounts of natural otherness that put more emphasis on independence for the purpose of differentiating individual natural otherness from the concept of wildness. Secondly, this account of natural otherness is engaged to argue for a particular way of theorising the moral standing (...) of individual nonhuman entities. While individual natural otherness in itself does not provide an account of whether an entity matters morally in itself (that is, whether it is morally considerable); it points to an account of incommensurable moral significance for all entities which are attributed moral considerability. That is an often-overlooked alternative to egalitarian or hierarchical accounts or moral significance. Individual natural otherness understood in this way in turn provides another explanatory story for why relational accounts of environmental ethics that strongly emphasise the importance of concepts such as wildness are particularly salient. (shrink)

Amartya Sen’s critique of the concept of need and his case for the superiority of capability as a measure of advantage have been highly influential. However, Sen perpetuates a caricature. Needs are not necessarily mere instrumental resource requirements for the achievement of ends; the valuable ends of people’s lives can themselves constitute needs, as can freedoms. Indeed, these ideas are already present in basic needs theory. Moreover, official disavowals notwithstanding, expansive notions of need are implicitly present in certain important theories (...) of capabilities and other advantages. Objections to need can be undermined in part by showing how this is the case. Aversion to need is unfortunate, because the concept offers powerful theoretical resources that could be better exploited if negative preconceptions were overcome and need were explicitly embraced. However, this proposal is friendly. It is not that need should replace, but that it can augment, other concepts. Drawing on need may assist with: selecting important capabilities or dimensions of advantage; marking a distinction of seriousness between these and relatively trivial advantages (and buttressing claims to the ethical or political priority of the former); explaining the incommensurability/non-substitutability of certain capabilities and dimensions of advantage, and; defining notions of sufficiency. (shrink)

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

According to the person-affecting restriction, one distribution of welfare can be better than another only if there is someone for whom it is better. Extant problems for the person-affecting restriction involve variable-population cases, such as the nonidentity problem, which are notoriously controversial and difficult to resolve. This paper develops a fixed-population problem for the person-affecting restriction. The problem reveals that, in the presence of incommensurable welfare levels, the person-affecting restriction is incompatible with minimal requirements of impartial beneficence even in fixed-population (...) contexts. (shrink)

Sometimes, when comparing a pair of items, it appears that neither is better than the other, nor that they are equally good, relative to a certain value that they bear. Cases of this kind have come to be referred to as superhard comparisons. What grounds superhard comparisons? On the dominant views, held by Joseph Raz and Ruth Chang, they are grounded, at least partially, in the failure of the three classic value relations—‘better than’, ‘worse than’, and ‘equally good’. On an (...) alternative view, which might be called the vagueness view, first developed by John Broome, they are grounded in vagueness about which of the classic value relations holds between the items. In this paper, I pay special attention to superhard comparisons in the context of choice and develop a novel argument against the dominant views on the basis of an account of decision-making under vagueness in ‘better than’. The upshot is that a new vagueness view emerges. (shrink)