¹ See Nelson, Mark, ‘Utilitarian Eschatology”, American Philosophical Quarterly, xxviii (1991), 339–46.Google Scholar Bennett, Jonathan, ‘The Necessity of Moral Judgments”, Ethics, ciii (1993), 458–72CrossRefGoogle Scholar, has recently pointed out that this same criticism was earlier sketched in Quinton, Anthony, Utilitarian Ethics, London, 1973.CrossRefGoogle Scholar

² A moral theory (such as utilitarianism) is applied when its account of obligation is conjoined with the judgements that some particular action is permissible or that some action is impermissible. See Nelson, , 341.Google Scholar

³ The difficulty confronting the utilitarian becomes greater when utilitarianism is conceived as directing agents or critics to prefer those actions that will instantiate the possible world with the greatest net or average utility. For if, no matter what I do, human existence will go on forever and will contain infinite amounts of utility and disutility, then utilitarianism will be unable to discriminate morally among my alternatives. (Judith Thomson suggests thinking of utilitarianism as requiring the action that instantiates the best among available possible worlds in ‘Goodness and Utilitarianism”, American Philosophical Association Proceedings, lxvii (1993), 145–59CrossRefGoogle Scholar, and in conversation Peter Vallentyne has expressed thoughts along similar lines. On the desirability of employing a conception of consequences that goes beyond causal effects, see Sen, Amartya, ‘Utilitarianism and Welfarism”, Journal of Philosophy, lxxvi (1979), 463–89.)CrossRefGoogle Scholar

⁴ This point militates against indirect utilitarianism and other forms of sum-ranking consequentialism, not just against act utilitarianism. Indeed, it will cause trouble for direct and indirect forms of egalitarian consequentialism as well, in so far as they require a comparison of the total amount of goods that all affected parties will ultimately receive. One reason for this is that it may go on forever that people's holding of goods is affected by a particular action. For the sake of simplicity, however, we will limit our discussion to standard act utilitarianism.

⁵ See Vallentyne, Peter, ‘Utilitarianism and Infinite Utility”, Australasian Journal of Philosophy, lxxi (1993), 212–17.CrossRefGoogle Scholar

⁶ However, the claim, advanced by Frances Howard-Snyder and Alastair Norcross in ‘A Consequentialist Case for Rejecting the Right”, Journal of Philosophical Research, xviii (1993), 109–25CrossRefGoogle Scholar, that ‘consequentialism is best conceived as a theory of the good, and not as a theory of the right” seems to constitute a rejection of (1) by some thoughtful young consequentialist thinkers.

⁷ Vallentyne does mention the possibility of discounting the value of future pains and pleasures but does not pursue it as a possible solution to his problem. See Vallentyne, , 214.Google Scholar

⁸ See Parfit, Derek, Reasons and Persons, Oxford, 1984, p. 480.Google Scholar

⁹ Some economists think that temporally discounting for the future is a requirement of rationality. Without it, they argue, it might, for example, turn out at every moment to be better to invest than to spend so that, in the end, one never spends the money invested. Even if that is sufficient to show that discounting is a requirement of rationality, however, it remains to be shown that it fits with what Vallentyne calls ‘the spirit of utilitarianism”. In so far as utilitarianism is aggregative, it is easy to see why a longer benefit is to be preferred to a shorter one, a more intense one to a less intense one, and a more probable one to a less probable one. However, the aggregative nature of utilitarianism does nothing to justify preferring a benefit that comes sooner to one that comes later when the sooner one is not also more probable. (This error is, it must be admitted, an attractive one. It ensnared Bentham himself, who included temporal ‘propinquity” (along with probability, duration, and intensity) as a ‘dimension” in which pleasures and displeasures were to be measured in his hedonic calculus.)

¹⁰ Vallentyne, , 212–13.Google Scholar

¹¹ The utilitarian theorist might resort to a filtering device (such as Brandt's ‘rational psychotherapy”) in order to justify ignoring the selfish preferences of the people in our scenario. However, this strategy is problematic for those who insist that only the preferences of those now alive should count in determining utility. How could a theorist of this sort justify using such a filter? After all, what the filter would serve to do is to direct us to impute to the people in our scenario a concern for the (probable) interests of people not yet alive, while the theory itself tells those of us who apply it not to attend to the probable interests of people not yet alive.

¹² Actually, there is another way in which (4) might be challenged. As Jordan Howard Sobel in private correspondence 28 August 1992, has pointed out, even if the experience of pleasure and pain need not come to an end or dwindle, there could be what could reasonably be seen as a uniquely maximal alternative. Here are two cases to this point (there are others): There might be just two alternatives, one of which leads to pleasure on balance at each moment forever, and the other to pain on balance. And there might be just two alternatives, one which leads to pleasure on balance at each moment forever, and the other to a cessation on December 31 of this year of all experience of pleasure and pain. Also, we are assuming throughout a standard analysis of infinite and infinitesimal numbers and quantities. Sobel also suggested that (3) may also be rejected if a Robinsonian non-standard analysis of infinities and infinitesimals is permitted, since such an analysis makes it possible to discriminate between larger and smaller infinite numbers, without the cardinality problems of Cantorian infinite sets. The details and implications of such an approach are not widely understood, and we make no claim to have grasped them, but they may deserve further attention from mathematically-minded defenders of utilitarianism. For an introduction to such non-standard analyses, see Henle, J. M. and Kleinberg, E. M., Infinitesimal Calculus, Cambridge, Mass., 1979.Google Scholar We are indebted to Jordan Howard Sobel for this reference.

¹³ See Vallentyne, , 214–15.Google Scholar

¹⁴ Ibid., 217.

¹⁵ Ibid., 215.

¹⁶ When we say that this is not a maximizing principle, we mean that it does not maximize the result—the number of books read. It does, of course, maximize the rate at which they are read, as we allow by saying that, on it, the agent does read books faster.

¹⁷ Ibid., 216.

¹⁸ See Sen, , ‘Utilitarianism and Welfarism”, 463–4, 468–71Google Scholar; Sen, , ‘Well-Being, Agency, and Freedom”, Journal of Philosophy, lxxxii (1985), 169–84, especially 175.Google Scholar See also Sen, and Williams, ed., Introduction, Utilitarianism and Beyond, Cambridge, 1982, pp. 1–21.CrossRefGoogle Scholar

¹⁹ For ease of exposition, we have followed Sen in taking utilitarianism to be essentially committed to ranking distributional schemes by their sums. This may be a little too simple. Some utilitarians have found it appealing to treat average utility, rather than total, as the maximand. (See, for example, pp. 33–4 of Smart, ‘An Outline of a System of Utilitarian Ethics”, in Utilitarianism: For and Against, ed. Smart, J. J. C. and Williams, Bernard, Cambridge, 1973, pp. 3–74.)CrossRefGoogle Scholar This is not, strictly speaking, sum-ranking. However, it is a sum-determined ranking principle. What is important for our purposes is that an infinite future of ramifying good and bad effects raises problems not only for sum-ranking in the strict sense but for any principle that works upon a mathematical function of the action's total good and bad effects. Thus, it poses difficulties for average-utility utilitarians as well as for total-utility utilitarians, and also for equalitarians inasmuch as the equalitarian proceeds in two stages: first determining what an equal distribution would be like, and then using some principle to rank various achievable distributional patterns according to how much they deviate from this standard. The equalitarian's will still be a sum-determined ranking principle if someone using it determines what an equal distribution would be like by first totaling everyone's holdings of benefits and harms, and then dividing that total by the number of persons affected. When there is no finite sum, then this procedure will prove unfeasible.

²⁰ Vallentyne, , 217.Google Scholar

²¹ We cite Bennett here in order to explore how a suggestion he makes might be adapted to the defence of utilitarianism. We should not be taken to imply that Bennett himself accepts utilitarianism or wishes to defend it.

²² See Bennett, , ‘The Necessity of Moral Judgments”, 461Google Scholar, and Bennett, private correspondence 22 December 1991.

²³ This very helpful analogy was suggested to us by Alastair Norcross.

²⁴ The controversial suppositions we have in mind are that human beings do not eternally survive after death and that the species will become extinct.

²⁵ This paper is based, in part, on Jorge Garcia's comments on Peter Vallentyne's ‘Utilitarianism and Infinite Utility” at the Chicago meeting of the American Philosophical Association, Central Division, April 1993. We would like to thank Hampden-Sydney College, Georgetown University, the National Endowment for the Humanities, and Harvard's Programme in Ethics and the Professions for financial support, and to express our gratitude to Jonathan Bennett, Laura Garcia, Glenn Loury, Alastair Norcross, Frederick Schick, Jordan Howard Sobel, and Peter Vallentyne for helpful comments, correspondence, discussion, and instruction. The mistakes we make are our fault, not theirs. We also thank Mary Buchanan for help in preparing the manuscript.