Skip to main content

Who Is Afraid of Numbers?

  • S. MATTHEW LIAO (a1)

In recent years, many non-consequentialists such as Frances Kamm and Thomas Scanlon have been puzzling over what has come to be known as the Number Problem, which is how to show that the greater number in a rescue situation should be saved without aggregating the claims of the many, a typical kind of consequentialist move that seems to violate the separateness of persons. In this article, I argue that these non-consequentialists may be making the task more difficult than necessary, because allowing aggregation does not prevent one from being a non-consequentialist. I shall explain how a non-consequentialist can still respect the separateness of persons while allowing for aggregation.

Hide All

1 For an excellent overview of this topic, see Wasserman D., and Strudler A., ‘Can a Nonconsequentialist Count Lives?’, Philosophy and Public Affairs 31.1 (2003), pp. 7194.

2 Roger Crisp has noted though that even consequentialism may not always require one to save the greater number in the tsunami case, as such a requirement assumes that the population before the tsunami is optimal, but we may just have no clue regarding whether saving more lives will produce the best state of affairs.

3 Taurek J., ‘Should the Numbers Count?’, Philosophy and Public Affairs 6 (1977), pp. 293316.

4 Taurek, ‘Should the Numbers Count?’, p. 307.

5 Taurek, ‘Should the Numbers Count?’, p. 303.

6 Kamm F., Morality, Mortality, vol. 1: Death and Whom to Save from It (New York: Oxford University Press, 1993), pp. 101, 114–21; Scanlon T., What We Owe to Each Other (Cambridge, Mass.: Belknap Press, 1998), pp. 228–41; and Timmermann J., ‘The Individualist Lottery: How People Count, but Not Their Numbers’, Analysis 64.2 (2004), pp. 106–12.

7 See, e.g., Otsuka M., ‘Scanlon and the Claims of the Many versus the One’, Analysis 60 (2000), pp. 288–93.

8 Kamm, Morality, Mortality, p. 101; Scanlon, What We Owe to Each Other, p. 232.

9 Scanlon, What We Owe to Each Other, p. 232.

10 F. Kamm, ‘Owning, Justifying, and Rejecting’, Mind 111 (2002), pp. 323–54.

11 Otsuka, ‘Scanlon and the Claims of the Many versus the One’.

12 Kamm F., ‘Aggregation and Two Moral Methods’, Utilitas 17.1 (2005), pp. 1112. See also Hirose I., ‘Saving the Greater Number without Combining Claims’, Analysis 61 (2001), pp. 341–42. For an insightful comment on Hirose's argument that the Kamm–Scanlon Argument does not aggregate or combine claims, see Brooks T., ‘Saving the Greatest Number’, Logique et Analyse 177–8 (2002), pp. 55–9.

13 Michael Otsuka has helpfully noted that the conclusion of this argument is not that one should save the greater number. Instead, the conclusion is that saving the greater number is better. According to Otsuka, one needs an additional premise – such as the consequentialist premise that one should bring about the best outcome – to get to the conclusion that one should save the greater number.

14 See, e.g., Hirose I., ‘Aggregation and Numbers’, Utilitas 16.1 (2004), pp. 6279.

15 Kamm, ‘Aggregation and Two Moral Methods’, pp. 12–15.

16 Kamm, ‘Aggregation and Two Moral Methods’, p. 13; Kamm, Morality, Mortality, vol. 1, p. 103.

17 Kamm, ‘Aggregation and Two Moral Methods’, p. 15.

18 John Broome first considered the weighted lottery, though he did not endorse it. See Broome J., ‘Selecting People Randomly’, Ethics 95 (1984), pp. 3855. See also Timmermann, ‘The Individualist Lottery’; Brock D., ‘Ethical Issues in Recipient Selection for Organ Transplantation,’ Organ Substitution Technology: Ethical, Legal, and Public Policy Issues, ed. Mathieu Deborah (Boulder: Westview Press, 1988), pp. 8699. For a perceptive analysis of different versions of the weighted lottery, see Wasserman D., ‘Let Them Eat Chances’, Economics and Philosophy 12 (1996), pp. 2949; I. Hirose, ‘Weighted Lotteries in Life and Death Cases’, Ratio (forthcoming). See also Lang G., ‘Fairness in Life and Death Cases’, Erkenntnis 62 (2005), pp. 321–51 for a different way than a weighted lottery by which fairness could matter.

19 Timmermann, ‘The Individualist Lottery’, pp. 110–11; Kumar R., ‘Contractualism on Saving the Many’, Analysis 61 (2001), pp. 165–70.

20 Timmermann, ‘The Individualist Lottery’, p. 111.

21 I thank an anonymous referee for this point.

22 See Hirose, ‘Weighted Lotteries in Life and Death Cases’ for other arguments against the Weighted Lottery Argument.

23 Rawls J., A Theory of Justice (Oxford: Oxford University Press, 1971); Nagel T., ‘Equality’, Mortal Questions (New York: Cambridge University Press, 1979), pp. 122–7.

24 Kamm F., ‘Precis of Morality, Mortality? Vol. I: Death and Whom to Save from It’, Philosophy and Phenomenological Research 58 (1998), pp. 940–1.

25 See, e.g., Raz J., The Morality of Freedom (Oxford: Clarendon Press, 1986), ch. 13, for an account of incommensurability as incomparability and not ‘rough equality’. See also Wasserman and Strudler, ‘Can a Nonconsequentialist Count Lives?’, p. 90, for a discussion of incommensurability as incomparability. Note that I am describing here what I think is one common-sense notion of the separateness of persons rather than Rawls's specific conception of it, which he used to criticize classical utilitarianism (in A Theory of Justice); and where John Harsanyi has argued that average utilitarianism is not susceptible to Rawls's objection (‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Journal of Political Economy 61 (1953), pp. 453–5). Throughout the article, I will be exploring various other competing senses of this notion, but not specifically Rawls's particular conception.

26 Taurek, ‘Should the Numbers Count?’, p. 302. It should be noted that Taurek goes on to say that: ‘There may well come a point, however, at which the difference between what B stands to lose and C stands to lose is such that I would spare C his loss. But in just these situations I am inclined to think that even if the choice were B's he too should prefer that C be spared his loss’ (Taurek, ‘Should the Numbers Count?’, p. 302). This further remark may spare Taurek from holding the view that persons are incommensurable, but his position may become confused. In particular, why could someone not say that the point at which one should spare C his loss is precisely when C is in a larger group than B, and that even if the choice were B's he too should prefer that C be spared his loss, that is, the greater number should be saved? Michael Otsuka has suggested though that Taurek can reject this line of thought by drawing a distinction between pairwise comparisons (which do not involve any appeal to groups) and those comparisons that involve appeals to groups. Let me preface by noting that I do not think that the existence of the view that each person is incommensurable necessarily depends on Taurek's having held this view. Indeed, as I proceed to point out in the main text, other people have also held this view. This said, let me express some reservations regarding this interpretation of Taurek. In particular, elsewhere, Otsuka has argued that the anti-number position leads to a choice-defeating intransitivity as a result of endorsing the principle of non-aggregation and affirming pairwise comparisons (‘Skepticism about Saving the Greater Number’, Philosophy and Public Affairs 32 (2004), pp. 413–26). Given this, interpreting Taurek as holding instead the view that persons are incommensurable may enable Taurek to reach his anti-number position while avoiding Otsuka's charge of choice-defeating intransitivity. See, however, Meyer K., ‘How to be Consistent without Saving the Greater Number’, Philosophy and Public Affairs 34.2 (2006), pp. 136–46, for the argument that Taurek's position does not lead to choice-defeating intransitivity even if it affirms pairwise comparisons. As I shall shortly argue though, from the perspective of the view that persons are incommensurable, the method of Pairwise Comparison is itself also problematic.

27 See, e.g. Murphy M., Natural Law in Jurisprudence and Politics (Cambridge: Cambridge University Press, 2006).

28 Nagel, ‘Equality’, pp. 122–7; Kamm, Morality, Mortality, p. 87.

29 See Otsuka, ‘Scanlon and the Claims of the Many versus the One’, pp. 290–1, for this interpretation of the anti-number position.

30 Taurek, ‘Should the Numbers Count?’, p. 303.

31 Scanlon, What We Owe to Each Other, p. 232.

32 Nozick R., Anarchy, State and Utopia (Oxford: Blackwell, 1974), pp. 32–3; Rawls, A Theory of Justice, secs. 5, 6, 30. I thank an anonymous referee for prompting me to pursue this line of inquiry.

33 Rawls, A Theory of Justice, p. 30.

34 For the proposal of using reflective equilibrium in this context, see M. Otsuka, ‘Saving Lives, Moral Theory, and the Claims of Individuals’, Philosophy and Public Affairs 34.2 (2006), pp. 109–35. Note that one difference between my proposal of the Standard Picture and Otsuka's proposal of reflective equilibrium is that the Standard Picture explicitly permits aggregation, whereas it is not clear whether reflective equilibrium would permit aggregation.

35 Another difference between consequentialism and non-consequentialism may be whether the theory has a maximizing structure or not. See, e.g., Broome John, Weighing Goods: Equality, Uncertainty and Time (Oxford: Blackwell, 1991).

36 See, e.g., Parfit D., Reasons and Persons (Oxford: Oxford University Press, 1984).

37 Scanlon, What We Owe to Each Other, p. 235.

38 This Principle is stated in a way that B has lexical priority over A. If this is too strong, one could state it in a discontinuity form, which would say that if some benefits, A, are too trivial when compared to others benefits, B, then enough of B should outweigh any amount of A. See Griffin J., Well-Being (Oxford: Oxford University Press, 1986), pp. 85–6, for the notion of discontinuity. See Parfit D., ‘Justifiability to Each Person’, Ratio 16 (2003), pp. 368–90, for the Triviality Principle, which he does not endorse. See Scanlon, What We Owe to Each Other, p. 240; Scanlon T. M., ‘Replies’, Ratio 16 (2003), pp. 424–39, for an affirmation of the Triviality Principle.

39 Similarly, non-consequentialists arguably have resources to address the repugnant conclusion without rejecting aggregation. For example, they could employ something like Griffin's principle of discontinuity. See also Temkin L., Inequality (Oxford: Oxford University Press, 1993), for discussions of these paradoxes of transitivity.

40 I would like to thank Michael Otsuka, David Wasserman, Roger Crisp, John Broome, Rahul Kumar, Iwao Hirose, Joseph Shaw, Wibke Grutjen, Thom Brooks, and the two anonymous referees at Utilitas for very helpful comments on earlier versions of this article. Thanks are also due to Frances Kamm for valuable discussions on this topic.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0953-8208
  • EISSN: 1741-6183
  • URL: /core/journals/utilitas
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 7
Total number of PDF views: 61 *
Loading metrics...

Abstract views

Total abstract views: 319 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th January 2018. This data will be updated every 24 hours.