We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (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)

According to the Competing Claims View we decide between alternatives by looking at the competing claims held by affected individuals. The strength of these claims is a function of two features: how much they stand to benefit by each alternative, and how badly off they would be in its absence. The view can be, and is, endorsed by both egalitarians and prioritarians. For the former the second condition will concern looking at how badly off the person is relative to others, (...) whereas for the latter it will be how badly off she is in absolute terms. In this paper I want to argue that neither should be endorsed. The egalitarian version of CCV breaks down when attempting to assess the competing claims of possible persons who may never exist. Also, the view, on at least one plausible interpretation, leads to intransitive judgements. The prioritarian version of CCV, in turn, is vulnerable to its own unique objection, namely delivering an anti-prioritarian and rather implausible verdict in certain Single Person Cases. (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.

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...) assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (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.

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.

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This sorites analogy is (...) here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (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)

The topic of this thesis is axiological uncertainty – the question of how you should evaluate your options if you are uncertain about which axiology is true. As an answer, I defend Expected Value Maximisation (EVM), the view that one option is better than another if and only if it has the greater expected value across axiologies. More precisely, I explore the axiomatic foundations of this view. I employ results from state-dependent utility theory, extend them in various ways and interpret (...) them accordingly, and thus provide axiomatisations of EVM as a theory of axiological uncertainty. (shrink)

It is notoriously difficult to find an intuitively satisfactory rule for evaluating populations based on the welfare of the people in them. Standard examples, like total utilitarianism, either entail the Repugnant Conclusion or in some other way contradict common intuitions about the relative value of populations. Several philosophers have presented formal arguments that seem to show that this happens of necessity: our core intuitions stand in contradiction. This paper assesses the state of play, focusing on the most powerful of these (...) ‘impossibility theorems’, as developed by Gustaf Arrhenius. I highlight two ways in which these theorems fall short of their goal: some appeal to a supposedly egalitarian condition which, however, does not properly reflect egalitarian intuitions; the others rely on a background assumption about the structure of welfare which cannot be taken for granted. Nonetheless, the theorems remain important: they give insight into the difficulty, if not perhaps the impossibility, of constructing a satisfactory population axiology. We should aim for reflective equilibrium between intuitions and more theoretical considerations. I conclude by highlighting one possible ingredient in this equilibrium, which, I argue, leaves open a still wider range of acceptable theories: the possibility of vague or otherwise indeterminate value relations. (shrink)

In 'Rethinking the Good', Larry Temkin makes two core claims. First, the goodness of a distribution is sometimes ‘essentially comparative’ – it sometimes depends on which alternative distribution(s) it is compared to. Second, such cases threaten the transitivity of ‘all things considered better than’. I argue that the goodness of a distribution may indeed depend on what other distributions are feasible. But contrary to Temkin, I also argue that transitivity holds even when the goodness of a distribution depends on the (...) feasible set of which it is a member. (shrink)

Should we be time-biased on behalf of other people? 'Sometimes yes, sometimes no'—it is tempting to answer. But this is not right. On pain of irrationality, we cannot be too selective about when we are time-biased on behalf of other people.

Larry Temkin famously argues that what he calls spectrum arguments yield strong reason to reject Transitivity, according to which the ‘all-things-considered better than’ relation is transitive. Spectrum arguments do reveal that the conjunctions of independently plausible claims are inconsistent with Transitivity. But I argue that there is very strong independent reason to reject such conjunctions of claims, and thus that the fact that they are inconsistent with Transitivity does not yield strong reason to reject Transitivity.

In Better Never to Have Been, David Benatar argues that existence is always a harm. His argument, in brief, is that this follows from a theory of personal good which we ought to accept because it best explains several ‘asymmetries’. I shall argue here that Benatar's theory suffers from a defect which was already widely known to afflict similar theories, and that the main asymmetry he discusses is better explained in a way which allows that existence is often not a (...) harm. (shrink)

John Harsanyi has offered an argument grounded in Bayesian decision theory that purports to show that John Rawls's original position analysis leads directly to utilitarian conclusions. After explaining why a prominent Rawlsian line of response to Harsanyi's argument fails, I argue that a seemingly innocuous Bayesian rationality assumption, the continuity axiom, is at the heart of a fundamental disagreement between Harsanyi and Rawls. The most natural way for a Rawlsian to respond to Harsanyi's line of analysis, I argue, is to (...) reject continuity. I then argue that this Rawlsian response fails as a defence of the difference principle, and I raise some concerns about whether it makes sense to posit the discontinuities needed to support the other elements of Rawls's view, although I suggest that Rawls may be able to invoke discontinuity to vindicate part of his first principle of justice. (shrink)

Although the thesis that the moral better than relation is transitive seems obviously true, there is a growing literature according to which Parfit’s repugnant conclusion and related puzzles reveal that this thesis is false or problematic. This paper begins by presenting several such puzzles and explaining how they can be used in arguments for the intransitivity of better than. It then proposes and defends a plausible alternative picture of the behavior of better than that both resolves the repugnant conclusion and (...) preserves transitivity. On the threshold-based model of lexicality defended here, hedonic episodes whose intensity is above a certain point are lexically greater than those whose intensity is below it. The final sections argue that this model is independently plausible and can be defended from several important objections. (shrink)

Consider the following claim: given the choice between saving a life and preventing any number of people from temporarily experiencing a mild headache, you should always save the life. Many moral theorists accept this claim. In doing so, they commit themselves to some form of ‘moral absolutism’: the view that there are some moral considerations that cannot be outweighed by any number of lesser moral considerations. In contexts of certainty, it is clear what moral absolutism requires of you. However, what (...) does it require of you when deciding under risk? What ought you to do when there is a chance that, say, you will not succeed in saving the life? In recent years, various critics have argued that moral absolutism cannot satisfactorily deal with risk and should, therefore, be abandoned. In this paper, we show that moral absolutism can answer its critics by drawing on—of all things—orthodox expected utility theory. (shrink)

Should we allow grave harm to befall one individual so as to prevent minor harms befalling sufficiently many other individuals? This is a question of aggregation. Can many small harms ‘add up’, so that, collectively, they morally outweigh a greater harm? The ‘Close Enough View’ supports a moderate position: aggregation is permissible when, and only when, the conflicting harms are sufficiently similar, or ‘close enough’, to each other. This paper surveys a range of formally precise interpretations of this view, and (...) reveals some of the problems they face. It also proposes a novel interpretation which avoids these problems. (shrink)

Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...) of what else that future contains, while minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. But sequence arguments are usually formulated in classical logic. One might therefore wonder if they work if we instead adopt many-valued logic. I show that, in a common many-valued logical framework, the answer depends on which versions of transitivity are used as premises. We get valid sequence arguments if we grant any of several strong forms of transitivity of 'is at least as bad as' and a notion of completeness. Other, weaker forms of transitivity lead to invalid sequence arguments. The plausibility of the premises is largely set aside here, but I tentatively note that almost all of the forms of transitivity that lead to valid sequence arguments seem intuitively problematic. Still, a few moderately strong forms of transitivity that might be acceptable lead to valid sequence arguments, although weaker statements of the initial value claims avoid these arguments at least to some extent. (shrink)

Larry Temkin challenged what seems to be an analytic truth about comparatives: if A is Φ-er than B and B is Φ-er than C, then, A is Φ-er than C. Ruth Chang denies a related claim: if A is Φ-er than B and C is not Φ-er than B, but is Φ to a certain degree, then A is Φ-er than C. In this paper I advance a context-sensitive semantics of gradability according to which the data uncovered by Temkin and (...) Chang leave both statements intact. (shrink)

According to the Internal Aspects View, the value of different outcomesdepends solely on the internal features possessed by each outcome and theinternal relations between them. This paper defends the Internal AspectsView against Larry Temkin’s defence of the Essentially Comparative View,according to which the value of different outcomes depends on what isthe alternative outcome they are compared with. The paper discusses bothperson-affecting arguments and Spectrum Arguments. The paper doesnot defend a person-affecting view over an impersonal one, but it arguesthat although there (...) are intuitive person-affecting principles that entail anEssentially Comparative View, the intuitions that support these principlescan also be acommodated by other principles that are compatible with theInternal Aspects View. The paper also argues that the rejection of transitivityand the Internal Aspects View does not help us to solve the challengespresented by Spectrum Arguments. Despite this, the arguments presentedby Temkin do succeed in showing that, unfortunately, our intuitions arechaotic and inconsistent. The paper argues that this has metaethicalconsequences that will be unwelcome by a moral realist such as Temkin,since they challenge the idea that our intuitions may track a moral realityexisting independently of our preferences. (shrink)