¹ See Raz, Joseph, The Morality of Freedom, Oxford, 1986, pp. 330–3Google Scholar and ‘Value Incommensurability: Some Preliminaries’, Proceedings ofthe Aristotelian Society, lxxxvi (1986)Google Scholar. Griffin's most comprehensive discussion is in Griffin, James, Well-Being: Its Meaning, Measurement and Moral Importance, Oxford, 1986, p. 81 and pp. 95–8Google Scholar. I discuss Griffin's arguments at length in section III.

² For a useful introduction see Chang, Ruth, ‘Introduction’, Incommensurability, Incomparability and Practical Reason, ed. Chang, R., Harvard, 1997Google Scholar.

³ Griffin's discussions of the topic are to be found in ch. 5 of Well-Being as well as in Griffin, James, ‘Are there Incommensurable Values?’ Philosophy and Public Affairs, xlvii (1977)Google Scholar; ‘Mixing Values’, Aristotelian Society, lxv (1991)Google Scholar; ‘Incommensurability: What's the Problem?’, Incommensurability, Incomparability and Practical Reason; and ‘Replies,’ Well-Being and Morality: Essays in Honour of James Griffin, ed. Crisp, R. and Hooker, B., Oxford, 1999Google Scholar.

⁴ See ‘Incommensurability: What's the Problem’, pp. 37 f.and p. 40.

⁵ See Well-Being, p. 79; much the same picture of (in)commensurability is implicit in ‘Incommensurability: What's the Problem?’, p. 35. Ruth Chang has recently defined incommensurability in such a way that it differs from incomparability, as well as ‘noncomparability’, but her distinctions are not relevant to the content of this paper. See Chang, Ruth, ‘Introduction’, pp. 2 fGoogle Scholar.

⁶ I am using the exclusive ‘or’ here, and in the conditions which follow; if it were the inclusive ‘or’, the addition of ‘or both’ in(Cl) and in later conditions would not be necessary.

⁷ This condition differs from a similar condition which might be termed (following Raz, Joseph, The Morality of Freedom, p. 324)Google Scholar ‘indeterminacy’ of prudential values. This occurs when it is neither true nor false that AGB, or BGA or both. Broome discusses indeterminacy at length in John Broome, ‘Is Incommensurability Vagueness?’, Incommensurability, Incomparability and Practical Reason.

⁸ See The Morality of Freedom, pp. 322 f.

⁹ See Broome, John, ‘Incommensurable Values’, p. 22Google Scholar.

¹⁰ ‘Incommensurable Values’, p. 31; the passage from Griffin quoted here is from Well-Being, p. 80.

¹¹ Broome may have meant instead that some sort of lexical relation holds between options which realize values, so that the slightest increase in one value may be worth more than any amount of some other value. His text is ambiguous.

¹² I have made this argument at greater length in ‘Needs, Incommensurability and Well-Being’, Review of Political Economy, ix (1997)Google Scholar, though my views about the subject have altered considerably since I wrote that paper.

¹³ Well-Being, p. 80.

¹⁴ ‘Replies’, pp. 286 f.

¹⁵ Well-Being, pp. 80 f., 96–8.

¹⁶ Well-Being, p. 81.

¹⁷ Well-Being, p. 79.

¹⁸ ‘Introduction’, pp. 23–7.

¹⁹ I am relying here on Griffin's clarification of his position in a series of conversations on the subject.

²⁰ On this see Well-Being, p. 97.

²¹ Keefe, Rosanne and Smith, Peter (ed.), Vagueness. A Reader, Cambridge, Mass., 1996, pp. 17–22Google Scholar make this point about the epistemic account of vagueness, though what I am calling epistemic vagueness differs from Williamson's account of vagueness which they discuss.

²² Regan classifies Griffin as a ‘rough egalitarian’ and distinguishes Griffin's position from the one he himself advocates, which involves ‘complete comparability’; see ‘Value, Comparability and Choice’, Incommensurability, Incomparability and Practical Reason, pp. 129 f. Broome, similarly, thinks that, on Griffin's view, there are incommensurate cases and so, for Broome, Griffin does not support ‘commensurabilism’, and, for this reason, Broome terms Griffin a ‘rough commensurabilist’. See ‘Incommensurable Values’, p. 36.

²³ See Raz, Joseph, ‘Incommensurability and Agency’, in Incommensurability, Incomparability and Practical Reason, p. 273Google Scholar.

²⁴ The Morality of Freedom, p. 322; ‘Value Incommensurability: Some Preliminaries’, 117. Much the same definition is to be found in ‘Incommensurability and Agency’, p. 110. In Raz's writings ‘equal to’ seems to mean ‘precisely equal to’ (so that rough equality might involve incommensurability).

²⁵ The Morality of Freedom, pp. 322–33.

²⁶ Well-Being, pp. 95 f.

²⁷ Well-Being, p. 96.

²⁸ Part of the problem also relates to confusions about ‘rough equality’: in a recent discussion Griffin argues that one of Raz's definitions of incomparability in fact focuses on rough equality, which, for Griffin, is a type of comparability. See ‘Incommensurability: What's the Problem?’, pp. 262 f.

²⁹ Well-Being, pp. 80 f.

³⁰ James Griffin explained to me in conversation that this is actually how he often uses ‘equal to’; so (Cl) clearly misrepresents his position.

³¹ ‘Introduction’, pp. 23–7.

³² See Keefe and Smith for a discussion.

³³ See, amongst others, Machina, Kenton, ‘Truth, Belief and Vagueness’, Journal of Philosophical Logic, v (1976), and repr. in Keefe and Smith. This approach has also been applied in economics particularly in the context of poverty and inequality rankings. This literature includesGoogle ScholarBasu, Kaushik, ‘Axioms for a Fuzzy Measure of Inequality’, Mathematical Social Sciences, xiv (1987)Google Scholar, and Cheli, Bruno and Lemmi, Achille, ‘A “Totally” Fuzzy and Relative Approach to the Multidimensional Analysis of Poverty’, Economic Notes, xxiv (1995)Google Scholar.

³⁴ This point is often made. See Keefe and Smith, p. 43.

³⁵ James Wood Bailey also thinks that vagueness can be invoked in defence of comparability, though he does not develop this thought much. See Bailey, James Wood, ‘Is it Rational to Maximize?’ Utilitas, x (1998), 204 fGoogle Scholar.

³⁶ I am grateful to James Griffin for pointing this out to me.

³⁷ See ‘Mixing Values’, 107 f.

³⁸ ‘Incommensurability: What's the Problem?’ p. 38, where Griffin writes: ‘if it is not clear that they are examples of comparability, it is not clear for the same reason that they are examples of incomparability either.’

³⁹ I am very grateful to James Griffin for his comments at different stages of the development of this paper, for his encouragement, for clarifying his position on a number of points, and for allowing me to look at his reply to John Broome, in its unpublished form. I must also thank John Broome for sending me his original paper in its unpublished form. The earliest version of this paper was presented at a conference on development ethics at Queen Elizabeth House, Oxford in April 1998. I would like to thank Sabina Alkire, Nigel Dower, Des Gasper and Charles Gore for their comments there, as well as Roger Crisp, Alan Hamlin and Jonathan Aldred, all of whom commented on various earlier versions of paper. Any error is mine.