I begin by reconsidering the arguments of John Taurek and Elizabeth Anscombe on whether the number of people we can help counts morally. I then consider arguments that numbers should count given by F. M. Kamm and Thomas Scanlon, and criticism of them by Michael Otsuka. I examine how different conceptions of the moral method known as pairwise comparison are at work in these different arguments and what the ideas of balancing and tie-breaking signify for decision-making in various types of cases. I conclude by considering how another moral method that I call virtual divisibility functions and what it helps reveal about an argument by Otsuka against those who do not think numbers count.

According to critics such as Bernard Williams, traditional ethical theories render it impossible to lead good and meaningful lives because they emphasize moral duty or the promotion of external values at the expense of the personal commitments that make our lives worth living from our own perspective. Responses to this criticism have not addressed the fundamental question about the proper relationship between a person's commitments to moral values and her commitments to non-moral or personal values. In this article, I suggest that we think about this relationship by reflecting on the way that a prudentially virtuous person who has commitments to both moral and non-moral values would regard these commitments. I argue that people with the virtue of balance do have reasons to act in accordance with their moral commitments, but that whether or not these reasons are overriding depends on the type of commitment in question.

Doubts about the origin of Bentham's formula, ‘the greatest happiness of the greatest number’, were resolved by Robert Shackleton thirty years ago. Uncertainty has persisted on at least two points. (1) Why did the phrase largely disappear from Bentham's writing for three or four decades after its appearance in 1776? (2) Is it correct to argue (with David Lyons in 1973) that Bentham's principle is to be differentially interpreted as having sometimes a ‘parochial’ and sometimes a ‘universalist’ bearing? These issues are reopened here with particular reference to textual evidence overlooked in earlier discussions and contextual evidence on the development of Bentham's radicalism in the last two decades of his life. In conclusion some broader issues are raised concerning the character of Bentham's understanding of ‘happiness’ itself.

Perhaps the most impressive environmental ethic developed to date in any detail is Robin Attfield's biocentric consequentialism. Indeed, on first study, it appears sufficiently impressive that, before presenting any alternative theoretical approach, one would first need to establish why one should not simply embrace Attfield's. After outlining a seemingly decisive flaw in his theory, and then criticizing his response to it, this article adumbrates a very different theoretical basis for an environmental ethic: namely, a value-pluralist one. In so doing, it seeks to give due weight to anthropocentric, zoocentric, biocentric and ecocentric considerations, and argues that the various values involved require trading off. This can be accomplished by employing multidimensional indifference curves. Moreover, after considering a three-dimensional indifference plane superimposed upon a three-dimensional possibility frontier, it becomes apparent that a moral-pluralist environmental ethic is, contrary to widespread assumptions, capable, in principle at least, of providing determinate answers to moral questions.

My theory of biocentric consequentialism is first shown not to be significantly inegalitarian, despite not advocating treating all creatures equally. I then respond to Carter's objections concerning population, species extinctions, the supposed minimax implication, endangered interests, autonomy and thought-experiments. Biocentric consequentialism is capable of supporting a sustainable human population at a level compatible with preserving most non-human species, as opposed to catastrophic population increases or catastrophic decimation. Nor is it undermined by the mere conceivable possibility of counter-intuitive implications. While Carter shows that value-pluralism need not be riddled with contradictions, his version still introduces some, and faces further problems. Thus consequentialist theories may be needed to sift our values, at least if our values are commensurable. Carter's apparent suggestion that monistic theories such as biocentric consequentialism can never be harnessed to rich theories of value and must each myopically give undue prominence to a single value is questioned.

The Slogan holds that one situation cannot be worse (or better) than another unless there is someone for whom it is worse (or better). This principle appears to provide the basis for the levelling-down objection to teleological egalitarianism. Larry Temkin, however, argues that the Slogan is not a plausible moral ideal, since it stands against not just teleological egalitarianism, but also values such as freedom, rights, autonomy, virtue and desert. I argue that the Slogan is a plausible moral principle, one that provides a suitable moral basis for the levelling-down objection to teleological egalitarianism. Contrary to Temkin, freedom, autonomy, virtue, and rights can all be understood in person-affecting terms, while equality of outcome cannot. Moreover, the Slogan is open to a variety of different ideas about how we should weight or rank people's gains and losses. This flexibility allows the Slogan to accommodate ideals such as prioritarianism and desert.