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.

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.

Act consequentialism states that an act is right if and only if the expected value of its outcome is at least as great as the expected value of any other act’s outcome. Two objections to this view are as follows. The first is that act consequentialism cannot account for our normative ambivalence in cases where agents perform the right act out of bad motives. The second is that act consequentialism is silent on questions of character: questions like ‘What are the right motives to have?’ and ‘What kind of person ought I be?’. These objections have been taken to motivate a move to global consequentialism, on which acts are not the only subjects of normative assessment. Motives and decision-procedures (amongst other things) are also judged right or wrong by direct reference to their consequences. In this paper, I argue that these objections fail to motivate the move from act to global consequentialism.

According to Neutral-Set Views in population axiology, some number of lifetime welfare levels are contributively neutral. Adding a life at these levels to a population makes that population neither better nor worse. If just one welfare level is neutral, the view counts as a Neutral-Level View. Adding a life at this level leaves the new population equally good as the original. If more than one welfare level is neutral, the view counts as a Neutral-Range View. Adding a life within this range renders the new population incommensurable with the original. In this paper, I sharpen some old objections to these views and offer some new ones. Neutral-Level Views cannot avoid certain Repugnant and Sadistic Conclusions. Neutral-Range Views imply that lives featuring no good or bad components whatsoever can nevertheless swallow up and neutralise goodness and badness. Both classes of view entail that certain small changes in welfare correspond to worryingly large differences in contributive value. I then offer a new view that retains much of the appeal of Neutral-Set 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.

No abstract