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Published online by Cambridge University Press: 26 January 2009
Suppose that time is infinitely long towards the future, and that each feasible action produces a finite amount of utility at each time. Then, under appropriate conditions, each action produces an infinite amount of utility. Does this mean that utilitarianism lacks the resources to discriminate among such actions? Since each action produces the same infinite amount of utility, it seems that utilitarianism must judge all actions permissible, judge all actions impermissible, or remain completely silent. If the future is infinite, that is, the prospects for utilitarianism look bleak.
1 Nelson, Mark, ‘Utilitarian Eschatology”, American Philosophical Quarterly, xxviii (1991), 339–47.Google Scholar
2 Vallentyne, Peter, ‘Utilitarianism and Infinite Utility”, Australiasian Journal of Philosophy, lxxii (1993), 212–17.CrossRefGoogle Scholar
3 Garcia, Jorge and Nelson, Mark, ‘The Problem of Endless Joy: Is Infinite Utility Too Much for Utilitarianism”, Utilitas, vi (1994), 183–92.CrossRefGoogle Scholar
4 See, for example, Von Weizsacker, Carl Christian, ‘Existence of Optimal Programs of Accumulation for an Infinite Time Horizon”, Review of Economic Studies, xxxii (1965), 85–104CrossRefGoogle Scholar; Diamond, Peter, ‘The Evaluation of Infinite Utility Streams”, Econometrica, xxxiii (1965), 170–7CrossRefGoogle Scholar; Gale, David, ‘On Optimal Development in a Multi-Sector Economy”, Review of Economic Studies, xxxiv (1967), 1–18CrossRefGoogle Scholar; Koopmans, Tjalling C., ‘Representation of Preference Orderings Over Time”, Decision and Organization, ed. McGuire, C. B. and Radner, Roy, Amsterdam and London, 1972, pp. 79–100Google Scholar; Campbell, D. E., ‘Impossibility Theorems and Infinite Horizon Planning”, Social Choice and Welfare, ii (1985), 283–93CrossRefGoogle Scholar; Epstein, L. G., ‘Intergenerational Preference Orderings”, Social Choice and Welfare, iii (1986), 151–61CrossRefGoogle Scholar; Lauwers, Luc, ‘Intertemporal Objective Functions: Strong Pareto Versus Time Neutrality”, (1993)Google Scholar, unpublished; and Liederkerke, Luc Van, ‘The Weight of Future Generations in an Infinite Growth Model: A Normative Exercise”, (1994)Google Scholar, unpublished. Thanks to John Broome for bringing the existence of this literature to my attention.
5 Cain, James, ‘Infinite Utility”, Australasian Journal of Philosophy (1995)CrossRefGoogle Scholar, forthcoming.
6 Vallentyne, Peter, ‘Infinite Utility: Anonymity and Person-Centredness”, (1995)CrossRefGoogle Scholar, unpublished.
7 The claim that more books are read by the two book per day policy is even easier to defend if one assumes that the books are numbered, and that each day the two book policy involves reading the next two unread books, whereas the one book policy involves reading the next even-numbered unread book. For in this case, the two book policy involves reading every book that the one book policy does, but not vice-versa.
8 Economists have recognized the incompatibility of infinite impartiality and some sort of monotonicity principle. See, for example, Liederkerke, Luc Van, ‘Should Utilitarians Bother About an Infinite Future”, Australasian Journal of Philosophy, (1995)Google Scholar, forthcoming; and Lauwers, Luc, ‘Intertemporal Objective Functions: Strong Pareto Versus Time Neutrality”, (1993)Google Scholar, unpublished. I take the example and the statement of the incompatibility directly from the former.
9 Thanks to Brad Hooker and Mark Nelson for helpful comments.
