This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

This paper is the introduction to the volume. It gives an argumentative view of the philosophical landscape concerning incommensurability and incomparability. It argues that incomparability, not incommensurability, is the important phenomenon on which philosophers should be focusing and that the arguments for the existence of incomparability are so far not compelling.

Many believe that we ought to save a large number from being permanently bedridden rather than save one from death. Many also believe that we ought to save one from death rather than a multitude from a very minor harm, no matter how large this multitude. I argue that a principle I call “Aggregate Relevant Claims” satisfactorily explains these judgments. I offer a rationale for this principle and defend it against objections.

According to the Repugnant Conclusion: Compared with the existence of many people who would all have some very high quality of life, there is some much larger number of people whose existence would be better, even though these people would all have lives that were barely worth living. I suggest some ways in which we might be able to avoid this conclusion. I try to defend a strong form of lexical superiority.

Argues that there is no one it is irrational to love, that it is rational to act with partiality to those we love, and that the rationality of doing so is not conditional on love. It follows that Anscombe and Taurek are right: you are not required to save three instead of one, even when those you could save are perfect strangers.

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)

(No abstract is available for this citation).

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

Following an introductory classification of prescriptive language that emphasizes the parallel between imperatives and moral language, this chapter distinguishes between the indicative and imperative moods of language. It then dismisses various attempts to account for imperatives, particularly their reduction to indicatives as well as expressivist theories like Ayer's and Stevenson's.

Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a headache rather than saving one person from death? Many people answer ‘yes’ and ‘no’, respectively. They therefore accept a partially aggregative moral view. Patrick Tomlin has recently argued that the most promising partially aggregative views in the literature have implausible implications in certain cases in which there are additions or subtractions to (...) the groups of people that we can save. Several philosophers have begun responding to this argument by developing partially aggregative views that avoid the relevant implications. In this paper, I extend Tomlin’s argument to create a dilemma that no partially aggregative view can avoid. I conclude that we should accept a fully aggregative moral view. (shrink)

This paper presents an argument against the widespread view that ‘hard choices’ are hard because of the incomparability of the alternatives. The argument has two parts. First, I argue that any plausible theory of practical reason must be ‘comparativist’ in form, that is, it must hold that a comparative relation between the alternatives with respect to what matters in the choice determines a justified choice in that situation. If comparativist views of practical reason are correct, however, the incomparabilist view of (...) hard choices should be rejected. Incomparabilism about hard choices leads us to an implausible error theory about the phenomenology of hard choices, threatens an unattractive view of human agency, and leaves us in perplexity about what we are doing when we choose in hard choices. The second part of the argument explores the main competitor to comparativist views of practical reason, noncomparativist view, according tow which a choice is justified so long as it is not worse than any of the alternatives. This view is often assumed by rational choice theorists but has its best philosophical defense in work by Joseph Raz. On Raz’s view, incomparabilism about hard choices avoids the problems faced if comparativism is correct, but it faces different difficulties. I argue that Raz’s noncomparativist view mistakenly assimilates practical reason to more restricted normative domains such as the law. (shrink)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that none of these (...) strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

It is widely accepted that the ethical supervenes on the natural, where this is roughly the claim that it is impossible for two circumstances to be identical in all natural respects, but different in their ethical respects. This chapter refines and defends the traditional thought that this fact poses a significant challenge to ethical non-naturalism, a view on which ethical properties are fundamentally different in kind from natural properties. The challenge can be encapsulated in three core claims which the chapter (...) defends: that a defensible non-naturalism is committed to the supervenience of the ethical, that this commits the non-naturalist to a brute necessary connection between properties of distinct kinds, and that commitment to such brute connections counts against the non-naturalist’s view. Each of these claims has recently been challenged. Against Nicholas Sturgeon’s recent doubts about the dialectical force of supervenience, this chapter defends a supervenience thesis as deserving to be common ground among ethical realists. It is then argued that attempts to explain supervenience on behalf of the non-naturalist either fail as explanations, generate near-identical explanatory burdens elsewhere, or appeal to commitments that are inconsistent with core motivations for non-naturalism. The chapter concludes that, suitably refined, the traditional argument against non-naturalism from supervenience is alive and well. (shrink)

Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a migraine rather than saving one person from death? Many people answer “yes” and “no,” respectively. The aim of partially aggregative moral views is to capture and justify combinations of intuitions like these. In this article, I develop a risk-based reductio argument that shows that there can be no adequate partially aggregative view. (...) I then argue that the only plausible response to this reductio is to accept a fully aggregative view. (shrink)

Geach and Thomson have argued that nothing is just plain good, because ‘good’ is, logically, an attributive adjective. The upshot, according to Geach and Thomson, is that consequentialism is unacceptable, since its very formulation requires a predicative use of ‘good’. Reactions to the argument have, for the most part, been uniform. Authors have converged on two challenging objections . First, although the logical tests that Geach and Thomson invoke clearly illustrate that ‘good’, as commonly used, is an attributive, they don’t (...) show that ‘good’ lacks an intelligible predicative interpretation. Second, even if the English word ‘good’ fails to express the property of goodness, we can just stipulate that ‘good*’ expresses goodness and thus formulate consequentialism accordingly. The second objection is one way of voicing skepticism about the method of drawing substantive philosophical conclusions from considerations about ordinary language. In this essay, we present an argument, inspired by Geach and Thomson, which isn’t susceptible to the same objections but which supports the same conclusion. The significance of our argument for ethics is obvious; it challenges the intelligibility of standard consequentialism, and even certain forms of non-consequentialism. One might be inclined to think that a more sophisticated consequentialism, which relies on ‘good {possible world/state of affairs/outcome}’ instead of just ‘good’, evades the criticism. But we explain why the criticism can’t be so easily evaded. (shrink)

The small-improvement argument is usually considered the most powerful argument against comparability, viz the view that for any two alternatives an agent is rationally required either to prefer one of the alternatives to the other or to be indifferent between them. We argue that while there might be reasons to believe each of the premises in the small-improvement argument, there is a conflict between these reasons. As a result, the reasons do not provide support for believing the conjunction of the (...) premises. Without support for the conjunction of the premises, the small-improvement argument for incomparability fails. (shrink)

After providing a novel taxonomy of lottery procedures for fairly distributing scarce goods, I defend a new weighted lottery theory. This taxonomy is necessary because the debate between unweighted and weighted lottery theorists overlooks a range of cases, overlap cases, in which conducting an unweighted lottery is impossible or implausible. Therefore, to account for all such cases, lottery theorists must adopt a weighted lottery. However, while no extant weighted lottery is adequate in overlap cases, my new weighted lottery theory is. (...) I conclude by discussing my theory’s practical implications. (shrink)

John Taurek has argued that, where choices must be made between alternatives that affect different numbers of people, the numbers are not, by themselves, morally relevant. This is because we "must" take "losses-to" the persons into account (and these don't sum), but "must not" consider "losses-of" persons (because we must not treat persons like objects). I argue that the numbers are always ethically relevant, and that they may sometimes be the decisive consideration.

The ‘standard interpretation’ of John Taurek’s argument in ‘Should the Numbers Count?’ imputes two theses to him: first, ‘numbers scepticism’, or scepticism about the moral force of an appeal to the mere number of individuals saved in conflict cases; and second, the ‘equal greatest chances’ principle of rescue, which requires that every individual has an equal chance of being rescued. The standard interpretation is criticized here on a number of grounds. First, whilst Taurek clearly believes that equal chances are all-important, (...) he actually argues for a position weaker than the equal greatest chances principle. Second, the argument Taurek gives for the importance of equal chances ought to commit him to being more hospitable to the significance of numbers than he seems to be. Third, and as a result, Taurek should not have dismissed the significance of numbers but embraced a form of pluralism instead. Fourth, this result should be welcomed, because pluralism is more plausible than either the equal greatest chances principle or the saving the greater number principle. (shrink)

In this paper, I concentrate on two themes: to what extent numbers bear on an agent's duties, and how numbers should relate to social policy. In the first half of the paper I consider the abstract case of a choice between saving two people and saving one, and my focus is on the contrast between a duty to act and a reason which merely makes an action intelligible. In the second half, I turn to the issue of social policy and (...) investigate how if at all numbers can have a bearing there, if there is no obvious duty on individuals to save the greater number. My proposal is that it is not the bare numbers themselves which explain our intuitions in such cases, but rather considerations of the extent to which each of us can make a reasonable claim on others. In short, I argue: numbers don't count, people do. (shrink)

Parfit has argued for the revolutionary thesis that personal identity does not matter in ordinary survival, only the R-relation does. “Reconciliationists,” such as Lewis, have tried to stop this revolution, arguing that both personal identity and the R-relation matter. The disagreement has been between those who hold that only the R-relation matters and those who hold that, in addition, personal identity matters. But there is a third option. I argue that Parfit is right that personal identity does not matter but (...) he is wrong that the R-relation matters, and the reconciliationists are wrong to think both matter since neither does. (shrink)