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Millian Superiorities and the Repugnant Conclusion

Published online by Cambridge University Press:  01 September 2008

KARSTEN KLINT JENSEN
KARSTEN KLINT JENSEN*
Affiliation:
University of Copenhagen, [email protected]
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Abstract

James Griffin has considered a form of superiority in value that is weaker than lexical priority as a possible remedy to the Repugnant Conclusion. In this article, I demonstrate that, in a context where value is additive, this weaker form collapses into the stronger form of superiority. And in a context where value is non-additive, weak superiority does not amount to a radical value difference at all. These results are applied on one of Larry Temkin's cases against transitivity. I demonstrate that Temkin appeals to two conflicting notions of aggregation. I then spell out the consequences of these results for different interpretations of Griffin's suggestion regarding population ethics. None of them comes out very successful, but perhaps they nevertheless retain some interest.

Type
Research Article
Information
Utilitas , Volume 20 , Issue 3 , September 2008 , pp. 279 - 300
Copyright
Copyright © Cambridge University Press 2008

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References

1 Mill, John Stuart, Utilitarianism, 1861, quoted from Utilitarianism, On Liberty, Considerations on Representative Government (London, 1993), p. 9Google Scholar.

2 Parfit, Derek, Reasons and Persons (Oxford, 1984), pp. 338, 419–41Google Scholar.

3 A ‘reasonable’ principle of distribution, in this context, is a principle which implies that if one of two outcomes with the same people has a greater total of welfare and it has welfare more equally distributed, then it is better.

4 Griffin, James, Well-Being: Its Meaning, Measurement and Moral Importance (Oxford, 1986), p. 340 (n. 27)Google Scholar.

5 Roger Crisp, ‘Ideal Utilitarianism: Theory and Practice’ (DPhil. Thesis, Oxford University, 1988), pp. 177–8.

6 Parfit, Reasons and Persons, p. 188.

7 Griffin, Well-Being, pp. 83–6.

8 Arrhenius, Gustaf and Rabinowicz, Wlodek, ‘Millian Superiorities’, Utilitas 17 (2005), pp. 127–46CrossRefGoogle Scholar.

9 It is assumed that concatenation is associative, which means that we get the same whole from concatenating any three objects, regardless of the order in which they are concatenated.

10 That is: e is better than e′, if and only if e is at least as good as e′, and e′ is not as least as good as e; and e is equivalent to e′ if and only if e is at least as good as e′, and e′ is at least as good as e.

11 That is: for all objects e, e′, e″: if e is at least as good as e′, and e′ is at least as good as e″, then e is at least as good as e″.

12 That is: for all objects e, e′, either e is at least as good as e′ or e′ is at least as good as e.

13 Cf. Krantz, David H.., Luce, R. Duncan, Suppes, Patrick and Tversky, Amos, Foundations of Measurement, vol. 1: Additive and Polynomial Representations (San Diego, 1971), pp. 73–4Google Scholar.

14 Arrhenius and Rabinowicz only assume the ‘only if’ − part in their Independence-condition – that is all they need for their Observation 2.

15 Krantz et al., Foundations of Measurement, vol. 1, p. 74 (Theorem 1).

16 Cf. Krantz et al., Foundations of Measurement, vol. 1, pp. 271–2.

17 Griffin, Well-Being, p. 85.

18 Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 134 (Observation 2). The proof is in Appendix 1, p. 138.

19 Arrhenius and Rabinowicz, ‘Millian Superiorities’, pp. 131–2 (Observation 1).

20 Cf. Krantz et al., Foundations of Measurement, vol. 1, p. 39 (Theorem 2.1).

21 From Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 131 (Observation 1).

22 Arrhenius and Rabinowicz, ‘Millian Superiorities’, pp. 136–7 (Observation 3).

23 From Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 134 (Observation 2).

24 See here also Arrhenius, Gustaf, ‘Superiority in Value’, Philosophical Studies 123 (2005), pp. 97–114CrossRefGoogle Scholar.

25 Arrhenius, ‘Superiority in Value’, pp. 108–9.

26 Temkin, Larry S., ‘A Continuum Argument for Intransitivity’, Philosophy & Public Affairs 25–3 (1996), 174–210Google Scholar.

27 Temkin, ‘A Continuum Argument for Intransitivity’, p. 179.

28 Temkin, ‘A Continuum Argument for Intransitivity’, p. 190.

29 Temkin, ‘A Continuum Argument for Intransitivity’, p. 191.

30 From Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 134 (Observation 2).

31 From Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 136 (Observation 3).

32 Cf. the list in Griffin, Well-Being, p. 67.

33 Griffin, Well-Being, pp. 86–7.

34 Cf. Krantz et al., Foundations of Measurement, vol. 1, pp. 245–315 (ch. 6).

35 In the standard framework, it is assumed that the set of possible lives, L, is a product set. This means that the values in a life are independently realizable, i.e. that that the domain contains every possible combination of degrees of realization of values. However, this is not a condition which is necessary for the additive representation as such.

36 To be sure this can be done, we need to assume a solvability condition, cf. Krantz et al., Foundations of Measurement, vol. 1, p. 301. This is another structural condition, which is not necessary for the additive representation.

37 In other words, if a numerical representation were possible (which I have not yet assumed), we would have wP(p 2) = 2wP(p 1), wP(p 3) = 3 wP(p 1), . . . .

38 Note that these standard sequences are not defined relative to each other.

39 Cf. Krantz et al., Foundations of Measurement, vol. 1, p. 253.

40 From Arrhenius and Rabinowicz, ‘Millian Superiorities’, p. 134 (Observation 2).

41 Alternatively, we could imagine that welfare is measured on two dimensions, cf. Hausner, M.: ‘Multidimensional Utilities’, Decision Processes, ed. Thrall, R. M., Coombs, C. H. and Davis, R. L. (New York, 1954), pp. 167–80Google Scholar.

42 There is a rigorous treatment in Robinson, Abraham, Non-Standard Analysis, rev. edn. (Amsterdam: North-Holland, 1974)Google Scholar. As for measurement, see Narens, Louis, ‘Measurement without Archimedean Axioms’, Philosophy of Science 41 (1974), pp. 374–93Google Scholar; Narens, Louis, ‘Minimal Conditions for Additive Conjoint Measurement and Qualitative Probability’, Journal of Mathematical Psychology 11 (1974), pp. 404–30Google Scholar; and Skala, Heinz J., Non-Archimedean Utility Theory (Dordrecht, 1975)Google Scholar.

43 I owe this interpretation to a communication from John Broome.

44 Cf. Broome, John, Weighing Lives (Oxford, 2004), p. 138CrossRefGoogle Scholar. This point is largely overlooked.

45 Griffin, Well-Being, pp. 130–1, 345 (n. 12).

46 Conceptually, however, these are two different questions. Cf. Broome, Weighing Lives, pp. pp. 199–214 (ch. 14).

47 Griffin, Well-Being, p. 340 (n. 27), my italics.

48 However, in this case, the framework described so far does not provide a cardinal scale that would allow summing up welfare.

49 Cf. Griffin, Well-Being, pp. 88, 98–102.

50 This is how Arrhenius, Gustaf: Future Generations. A Challenge for Moral Theory (Uppsala, 2000), pp. 96–7Google Scholar, understands Griffin. The interpretation is also apparent in Crisp, Roger, ‘Utilitarianism and the Life of Virtue’, The Philosophical Quarterly 42 (1992), pp. 139–60Google Scholar.

51 Arrhenius, ‘Future Generations’, pp. 97–100.

52 Cf. Parfit, Reasons and Persons, pp. 419–42 (ch. 19).

53 In fact, it is a weak statement of the requirement I mentioned in n. 3.

54 Glover, Jonathan, Causing Death and Saving Lives (Harmondsworth, 1977), pp. 70–1Google Scholar.

55 Parfit, Derek, ‘Overpopulation and the Quality of Life’, Applied Ethics, ed. Singer, P. (Oxford, 1986), pp. 161–3Google Scholar.

56 Parts of this article were presented at the John Stuart Mill Bicentennial Conference in April 2006, London. I am indebted to Statens Räddningsverk for financial support. I should like to thank Gustaf Arrhenius, John Broome, Roger Crisp, James Griffin, Nils Holtug and Wlodek Rabinowicz for helpful discussion on this subject, which I have worked with on and off for many years. A very early version appeared in my PhD thesis. A rather recent version of the article appeared in the electronic Festschrift for Wlodek Rabinowicz on his sixtieth birthday.