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)

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)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter, we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter, we review these different answers, with a special focus on the latter answer and the debate it has generated. (shrink)

Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.

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)

According to asymmetric comparativism, it is worse for a person to exist with a miserable life than not to exist, but it is not better for a person to exist with a happy life than not to exist. My aim in this paper is to explain how asymmetric comparativism could possibly be true. My account of asymmetric comparativism begins with a different asymmetry, regarding the (dis)value of early death. I offer an account of this early death asymmetry, appealing to the (...) idea of conditional goods, and generalize it to explain how asymmetric comparativism could possibly be true. I also address the objection that asymmetric comparativism has unacceptably antinatalist implications. (shrink)

I present a new argument for the repugnant conclusion. The core of the argument is a risky, intrapersonal analogue of the mere addition paradox. The argument is important for three reasons. First, some solutions to Parfit’s original puzzle do not obviously generalize to the intrapersonal puzzle in a plausible way. Second, it raises independently important questions about how to make decisions under uncertainty for the sake of people whose existence might depend on what we do. And, third, it suggests various (...) difficulties for leading views about the value of a person’s life compared to her nonexistence. (shrink)

In Reasons and Persons, Parfit (1984) posed a challenge: provide a satisfying normative account that solves the Non-Identity Problem, avoids the Repugnant and Absurd Conclusions, and solves the Mere-Addition Paradox. In response, some have suggested that we look toward person-affecting views of morality for a solution. But the person-affecting views that have been offered so far have been unable to satisfy Parfit's four requirements, and these views have been subject to a number of independent complaints. This paper describes a person-affecting (...) account which meets Parfit's challenge. The account satisfies Parfit's four requirements, and avoids many of the criticisms that have been raised against person-affecting views. (shrink)

Many real-world agents recognise that they impose harms by choosing to emit carbon, e.g., by flying. Yet many do so anyway, and then attempt to make things right by offsetting those harms. Such offsetters typically believe that, by offsetting, they change the deontic status of their behaviour, making an otherwise impermissible action permissible. Do they succeed in practice? Some philosophers have argued that they do, since their offsets appear to reverse the adverse effects of their emissions. But we show that (...) they do not. In practice, standard carbon offsetting does not reverse the harms of the original action, nor does it even benefit the same group as was harmed. Standard moral theories hence deny that such offsetting succeeds. Indeed, we show that any moral theory that allows offsetting in this setting faces a dilemma between allowing any wrong to be offset, no matter how grievous, and recognising an implausibly sharp discontinuity between offsettable actions and non-offsettable actions. The most plausible response is to accept that carbon offsetting fails to right our climate wrongs. (shrink)

In Rabinowicz (2008), I considered how value relations can best be analysed in terms of fitting pro-attitudes. In the formal model of that paper, fitting pro-attitudes are represented by the class of permissible preference orderings on a domain of items that are being compared. As it turns out, this approach opens up for a multiplicity of different types of value relationships, along with the standard relations of ‘better’, ‘worse’, ‘equally as good as’ and ‘incomparable in value’. Unfortunately, the approach is (...) vulnerable to a number of objections. I believe these objections can be avoided if one re-interprets the underlying notion of preference: instead of treating preference as a ‘dyadic’ attitude directed towards a pair of items, we can think of it as a difference of degree between ‘monadic’ attitudes of favouring. Each such monadic attitude has just one item as its object. Given this re-interpretation, permissible preferences can be modelled by the class of permissible assignments of degrees of favouring to items in the domain. From this construction, we can then recover the old modelling in terms of the class of permissible preference orderings, but the previous objections to that model no longer apply. (shrink)

Multidimensional adjectives are ubiquitous in natural language. An adjective F is multidimensional just in case whether F applies to an object or pair of objects depends on how those objects stand with respect to multiple underlying dimensions of F-ness. Developing a semantics for multidimensional adjectives requires us to address the problem of dimensional aggregation: how do the application conditions of an adjective F in its positive and comparative forms depend on its underlying dimensions? Here we develop a semantics for multidimensional (...) adjectives that incorporates aggregation functions. We then explore an analogy between dimensional aggregation and preference aggregation, bringing results from social choice theory to bear on the number and kind of aggregation functions that are admissible in a context. These results suggest that, for any given adjective, there will often be multiple aggregation functions admissible, meaning that multidimensional comparatives are often vague. (shrink)

Even philosophers of religion working on the problem of non-human animal suffering have ignored the suffering of creatures like insects. Sensible as this seems, it’s mistaken. I am not sure whether creatures like these can suffer, but it is plausible, on both commonsensical and scientific and philosophical grounds, that many of them can. If they do, their suffering makes the problem of evil much worse: their vast numbers mean the amount of evil in the world will almost certainly be increased (...) by many, many orders of magnitude, the fact that disproportionately many of them live lives which are nasty, brutish, and short means that the proportion of good to evil in the world will be drastically worsened, and their relative lack of cognitive sophistication means that many theodicies, including many specifically designed to address animal suffering, would apply to their suffering only with much greater difficulty, if at all. Philosophers of religion should therefore more seriously investigate whether these beings can suffer and what, if anything, could justify God in allowing as much. (shrink)

This paper examines a puzzle about whether truth is a valuable property: Valuable properties, like beauty and moral goodness, come in degrees; but truth does not come in degrees. Hence, the argument concludes, truth is not valuable. This result is puzzling since it seems to conflict with a deep intuition that truth is valuable. It is suggested that a roughly Platonic theory, on which truth is distinguished into two different concepts, gives a satisfying answer to the puzzle. One of these (...) concepts can be had in degrees, which, it is suggested, may be determined by the true proposition's explanatory power. (shrink)

This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of ‘better than’, (...) ‘worse than’, and ‘equally good’. Imprecise comparability, which can be understood in terms of the more familiar notions of cardinality and incommensurability, rejects only the first claim while parity rejects both claims of the standard view. -/- I then argue that insofar as those attracted to imprecise comparability assume that all rankings are trichotomous, as Parfit appears to, the view should be rejected. This is because imprecise equality is not a form of equality but is a sui generis ‘fourth’ basic way in which items can be ranked. We should, I argue, understand imprecise equality as parity, and imprecise comparability as entailing ‘tetrachotomy’ – that if two items are comparable, one must better than, worse than, equal to, or on a par with the other. Thus those attracted to the idea that cardinality can be imprecise should abandon trichotomy and accept parity and tetrachotomy instead. -/- Finally, I illustrate the difference between Parfit’s trichotomous notion of imprecise comparability and parity by examining how each notion might be employed in different solutions to the problem posed by the Repugnant Conclusion in population ethics. I suggest that parity provides the arguably more ecumenical solution to the problem. (shrink)

This short paper states a new objection against “spectrum arguments” for nontransitive betterness. It is shown that defenders of such arguments must reject one of two very plausible principles.

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)

Comparative judgments abound in sports. Fans and pundits bandy about which of two players or teams is bigger, faster, stronger, more talented, less injury prone, more reliable, safer to bet on, riskier to trade for, and so on. Arguably, of most interest are judgments of a coarser type: which of two players or teams is, all-things-considered, just plain better? Conventionally, it is accepted that such comparisons can be appropriately captured and expressed by sports rankings. Rankings play an important role in (...) sports arguably because of the conventional acceptance that rankings capture and express all-things-considered relations between the ranked teams or players. Standard ranking practices rely on a number of widely held assumptions. I discuss three of the most important and argue that at least one of them must be false. If this is right, the strong and growing commitment to using rankings to determine participation in tournaments and the awarding of championships is mistaken. At the least, given the conventional wisdom about rankings, my argument provides good reasons to be skeptical that any particular ranking ‘gets it right’. At the limit, it suggests that our most basic assumptions about all-things-considered athletic quality are wrong. (shrink)

This article criticises one of Stuart Rachels' and Larry Temkin's arguments against the transitivity of 'better than'. This argument invokes our intuitions about our preferences of different bundles of pleasurable or painful experiences of varying intensity and duration, which, it is argued, will typically be intransitive. This article defends the transitivity of 'better than' by showing that Rachels and Temkin are mistaken to suppose that preferences satisfying their assumptions must be intransitive. It makes cler where the argument goes wrong by (...) showing that it is a version of Zeno's paradox of Achilles and the Tortoise. (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)

Is the relation ‘is a morally permissible alternative to’ transitive? The answer seems to be a straightforward yes. If Act B is a morally permissible alternative to Act A and Act C is a morally permissible alternative to B then how could C fail to be a morally permissible alternative to A? However, as both Dale Dorsey and Frances Kamm point out, there are cases where this transitivity appears problematic. My aim in this paper is to provide a solution to (...) this problem. I will then investigate Kamm’s justification for rejecting the transitivity of the ‘is a permissible alternative to’ relation. Next, I will look at Dorsey’s solution, which involves a reinterpretation of the intuitions used to generate the problem. I will argue that neither of these solutions are fully satisfying before going on to provide my own solution to the problem and arguing that it avoids these problems. (shrink)

When people must either save a greater number of people from a smaller harm or a smaller number from a greater harm, do their choices reflect a reasonable moral outlook? We pursue this question with the help of an experiment. In our experiment, two-fifths of subjects employ a similarity heuristic. When alternatives appear dissimilar in terms of the number saved but similar in terms of the magnitude of harm prevented, this heuristic mandates saving the greater number. In our experiment, this (...) leads to choices that are inconsistent with all standard theories of justice. We argue that this demonstrates the untrustworthiness of distributive judgments in cases that elicit similarity-based choice. (shrink)

A phenomenon called perspectival disagreement is laid out and modelled on the basis of modifications to known consensus measures for qualitative representations of preferences and transitive values by binary relations. Cases of perspectival disagreement are of general philosophical interest, because they allow for the possibility that two or more agents judge the value positions of other agents differently even when their assessments are based on the same evidence. Various examples of perspectival disagreement are given, generalizations are discussed, and it is (...) argued that any representation by cardinal utilities also gives rise to some form of perspectivity. Although the examples strongly suggest that this phenomenon occurs in real life, it is concluded in the end that it does not pose any fundamental threat to representations of preferences and values as binary relations. Instead, position‐sensitive measures of disagreement ought to be taken as a modelling option for cases in which the relative importance of preference changes matters to an agent. (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)

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)

Numerous papers have investigated the transitivity principle of ‘better-than.’ A recent argument appeals to the principle of mereological dominance for transitivity. However, writers have not treated mereological dominance in much detail. This paper sets out to evaluate the generality of mereological dominance and its effectiveness in supporting the transitivity principle. I found that the mereological dominance principle is vulnerable to a counterexample based on Simpson’s Paradox. The thesis concludes that the mereological dominance principle should be revised in certain ways.

Larry Temkin has shown that Derek Parfit’s well-known Mere Addition Paradox suggests a powerful argument for the intransitivity of the relation “better than.” The crux of the argument is the view that equality is essentially comparative, according to which the same inequality can be evaluated differently depending on what it is being compared to. The comparative view of equality should be rejected, I argue, and hence so too this argument for intransitivity.

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)

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.

Contemporary ‘Fitting Attitude’ axiological frameworks – defining value in terms of having properties that provide reasons for pro-attitudes – struggle with the so-called Wrong Kind of Reasons problem. That is, they fail to offer a coherent account as to what reasons are fitted to enter our evaluative endeavors in the first place. Furthermore, WKR opens FA to charges regarding intransitivity of value ordering. I argue that revisiting Josiah Royce’s ‘plan of life’ mediating principle offers a promising reasons’ aggregation recipe, and (...) thus safeguards the transitivity axiom under FA. (shrink)

Parfit’s Repugnant Conclusion argues, against intuition, that for any world A, another world Z with higher population and minimal well-being is better. That intuition is incorrect because the argument has not considered resources that support well-being. Z must have many more resources supporting well-being than A does. Z is repugnant because it spreads those resources among too many people; another world with Z’s resources and fewer people, if available, would be far superior. But Z is still better than A; it (...) is worth accepting its very large population to get the resources needed to support their well-being. (shrink)

According to the mixed lexicographic/additive account of ‘better than’ and similar aggregative value comparatives like ‘healthier than’, values are multidimensional and different aspects of a value are aggregated into an overall assessment in a lexicographic way, based on an ordering of value aspects. It is argued that this theory can account for an acceptable definition of Chang’s notion of parity and that it also offers a solution to Temkin’s and Rachels’s Spectrum Cases without giving up the transitivity of overall betterness. (...) Formal details and proofs are provided in an “Appendix”. (shrink)

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)

I defend these claims: (1) 'Pleasure' has exactly one English antonym: 'unpleasure.' (2) Pleasure is the most convincing example of an organic unity. (3) The hedonic calculus is a joke. (4) An important type of pleasure is background pleasure. (5) Pleasures in bad company are still good. (6) Higher pleasures aren't pleasures (and if they were, they wouldn't be higher). Thesis (1) merely concerns terminology, but theses (2)-(6) are substantive, evaluative claims.

In Reasons and Persons, Derek Parfit cannot find a theory of well-being that solves the Non-Identity Problem, the Repugnant Conclusion, the Absurd Conclusion, and all forms of the Mere Addition Paradox. I describe a “Quasi-Maximizing” theory that solves them. This theory includes (i) the denial that being better than is transitive and (ii) the “Conflation Principle,” according to which alternative B is hedonically better than alternative C if it would be better for someone to have all the B-experiences. (i) entails (...) that Quasi-Maximization is not a maximizing theory, but (ii) ensures that its evaluations will often coincide with such theories. (shrink)

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.

Is there some large number of very mild hangnail pains, each experienced by a separate person, which would be worse than two years of excruciating torture, experienced by a single person? Many people have the intuition that the answer to this question is No. However, a host of philosophers have argued that, because we have no intuitive grasp of very large numbers, we should not trust such intuitions. I argue that there is decent intuitive support for the No answer, which (...) does not depend on our intuitively grasping or imagining very large numbers. (shrink)

Seemingly every theory of population ethics is confronted with unpalatable implications. While various approaches to the subject have been taken, including non-consequentialist approaches, this area has been dominated by utilitarian thought. The two main approaches to population ethics have been total utilitarianism () and average utilitarianism (). According to TU, we should seek to bring about the state of affairs that maximizes the total amount of happiness. According to AU, we should seek to bring about the state of affairs that (...) maximizes average per capita happiness. Both theories have been afflicted by seemingly strong objections, and as a result, numerous variations and hybrids have been introduced. Despite the widespread disagreement in the field, though, a near consensus has developed in rejecting AU as an absurd view. In this article, however, I will go against the grain and argue that AU is the theory of population ethics that we should endorse. (shrink)

Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous (...) to a question that has exercised ethicists over the past thirty years. How do we weigh a population consisting of some number of exceptionally happy and satisfied individuals against another population consisting of a much greater number of people whose lives are only just worth living? This is the question that occasions population ethics. In this paper, I go in search of the correct population ethics for credal states. (shrink)

Suppose that each of the following four conditions obtains: 1. You can save either a greater or a lesser number of innocent people from (equally) serious harm. 2. You can do so at trivial cost to yourself. 3. If you act to save, then the harm you prevent is harm that would not have been prevented if you had done nothing. 4. All other things are equal. A skeptic about saving the greater number rejects the common-sensical claim that you have (...) a duty to save the greater number in such circumstances. (shrink)

One of the currently popular dogmata of anti-consequentialism is that consequentialism doesn't respect, recognize, or in some important way account for what is referred to as the The charge is often made, but rarely explained in any detail, much less argued for. In this paper I explain what I take to be the most plausible interpretation of the separateness of persons charge. I argue that the charge itself can be deconstructed into at least two further objections to consequentialist theories. These (...) objections amount to (i) the rejection of axiological aggregation, and (ii) the rejection of deontic aggregation. Of these two objections, I argue that the first one, though often made, is untenable. I also argue that the second objection, in its various forms, relies on distinctions whose moral significance is vigorously denied by almost all consequentialist theorists. I thus argue that the separateness of persons objection poses no special threat to consequentialism. (shrink)

Carson Strong has recently argued that wide reflective equilibrium (WRE) is an unacceptable method of justification in bioethics. In its place, Strong recommends a methodology in which certain foundational moral judgments play a central role in the justification of moral beliefs, and coherence plays a limited justificatory role in that the rest of our judgments are made to cohere with these foundational judgments. In this paper, I argue that Strong’s chief criticisms of WRE are unsuccessful and that his proposed alternative (...) is in fact just another version of WRE. In the course of doing so, I specify which theses are central to WRE and which are not, and thus, provide a response to an additional objection, advanced by Peter Singer, that WRE is vacuous. I conclude by arguing that there may be better prospects for advancing the debate regarding methodology in bioethics if we focus on restricted epistemic and methodological theses rather than broad approaches, such as WRE, that come in many different varieties. (shrink)

The Rachels–Temkin spectrum arguments against the transitivity of better than involve good or bad experiences, lives, or outcomes that vary along multiple dimensions—e.g., duration and intensity of pleasure or pain. This paper presents variations on these arguments involving combinations of good and bad experiences, which have even more radical implications than the violation of transitivity. These variations force opponents of transitivity to conclude that something good is worse than something that isn’t good, on pain of rejecting the good altogether. That (...) is impossible, so we must reject the spectrum arguments. (shrink)

Is well-being the kind of thing that can be summed across individuals? This paper takes a measurement-theoretic approach to answering this question. To make sense of adding well-being, we would need to identify some natural "concatenation" operation on the bearers of well-being that satisfies the axioms of extensive measurement and can therefore be represented by the arithmetic operation of addition. I explore various proposals along these lines, involving the concatenation of segments within lives over time, of entire lives led alongside (...) one another or in sequence, and of evaluatively basic propositions via conjunction. All of these proposals turn out to carry highly controversial commitments about the good. I do not claim that these commitments are unacceptable. But they suggest that we cannot simply take for granted, as many philosophers do, that there is any such thing as the sum of well-being. (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.

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)

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)