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)

Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. Therefore, Arrhenius’s theorems (...) fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them. (shrink)

According to Critical-Level Views in population axiology, an extra life improves a population only if that life’s welfare exceeds some fixed ‘critical level.’ An extra life at the critical level leaves the new population equally good as the original. According to Critical-Range Views, an extra life improves a population only if that life’s welfare exceeds some fixed ‘critical range.’ An extra life within the critical range leaves the new population incommensurable with the original. -/- In this paper, I sharpen some (...) old objections to these views and offer some new ones. Critical-Level Views cannot avoid certain Repugnant and Sadistic Conclusions. Critical-Range Views imply that lives featuring no good or bad components whatsoever can nevertheless swallow up and neutralise goodness or badness. Both classes of view entail that certain small changes in welfare correspond to worryingly large differences in contributive value. -/- I then offer a view that retains much of the appeal of Critical-Level and Critical-Range Views while avoiding the above pitfalls. On the Imprecise Exchange Rates View, the quantity of some good required to outweigh a given unit of some bad is imprecise. This imprecision is the source of incommensurability between lives and populations. (shrink)

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up on lexicality, (...) problems of the same kind remain. (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.

Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we (...) interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology. (shrink)

We argue that all gradable expressions in natural language obey a principle that we call Comparability: 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. 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)

Variable-Value axiologies propose solutions to the challenges of population ethics. These views avoid Parfit's Repugnant Conclusion, while satisfying some weak instances of the Mere Addition principle (for example, at small population sizes). We apply calibration methods to Variable-Value views while assuming: first, some very weak instances of Mere Addition, and, second, some plausible empirical assumptions about the size and welfare of the intertemporal world population. We find that Variable-Value views imply conclusions that should seem repugnant to anyone who opposes Total (...) Utilitarianism due to the Repugnant Conclusion. So, any wish to avoid repugnant conclusions is not a good reason to choose a Variable-Value view. More broadly, these calibrations teach us something about the effort to avoid the Repugnant Conclusion. Our results join a recent literature arguing that prior efforts to avoid the Repugnant Conclusion hinge on inessential features of the formalization of repugnance. Some of this effort may therefore be misplaced. (shrink)