Equality, Clumpiness and Incomparability

Utilitas

Volumn 17, Issue 2, 2005, Pages 180-204

  Hsieh, Nien Hê ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

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EID: 85008566280     PISSN: 09538208     EISSN: 17416183     Source Type: Journal    
DOI: 10.1017/S0953820805001512     Document Type: Article

References (57)

1. See Derek Parfit, Reasons and Persons (Oxford, 1984, paperback edn. with corrections 1987), p. 431
2. James Griffin, Well-Being (Oxford, 1986), pp. 80-1, 96-8, 104
3. James Griffin, 'Incommensurability: What's the Problem?', Incommensurability, Incomparability, and Practical Reason, ed. R. Chang (Cambridge, 1997), pp. 38-9. Parfit, to be clear, refers to the relation in terms of 'rough comparability'. Two other accounts of rough equality can be found respectively in Thomas Hurka, Perfectionism (Oxford, 1993), p. 87, and George Harris, 'Value Vagueness, Zones of Incomparability, and Tragedy', American Philosophical Quarterly 38 (2001). This article analyses Parfit's account and Griffin's account. The analysis applies to Hurka's account. I do not take up Harris's account because he examines comparisons in terms of making choices and relies on an epistemic and psychological conception of vagueness in the context of choice. I take choice to be a distinct problem from comparison. Joseph Raz also argues that two items can be 'roughly equal'. Raz, however, uses the term not as a distinct comparative relation, but rather to describe situations in which the choice between two incommensurable items bears little significance. See Joseph Raz, The Morality of Freedom (Oxford, 1986), p. 330.
4. Ruth Chang, 'The Possibility of Parity', Ethics 112 (2002)
5. Ruth Chang, 'Introduction', Incommensurability, ed. R. Chang, pp. 25-7.
6. Chang, 'Parity', p. 666.
7. A 'range property' according to Waldron, 'may be understood in terms of a region on a scale. The idea is that although there is a scale on which one could observe differences of degree, still once a range has been specified, we may use the binary property of being within the range, a property which is shared by something which is in the center of the range and also by something which is just above its lower threshold' (Jeremy Waldron, God, Locke, and Equality: Christian Foundations in Locke's Political Thought (Cambridge, 2002), pp. 76-7
8. John Rawls, A Theory of Justice (Cambridge, 1971), p. 508
9. Chang, 'Introduction', p. 24.
10. The Trichotomy Thesis states that 'if two items A and B are evaluatively comparable, then A must be better or worse than B, or A and B must be equally good'. See Chang, 'Parity', p. 660.
11. 'Parity', p. 661.
12. The thesis advanced in this article provides only partial support for the Trichotomy Thesis, for two reasons. First, the thesis that I advance is silent with regard to whether items can be related by a relation other than 'better than' or 'worse than' when they are not equally good. Second, the thesis that I advance invokes two modes of comparison, both of which can be incorporated into the Trichotomy Thesis, but are not distinguished in the original statement of the thesis. For a defence of the Trichotomy Thesis, see the work of Donald Regan. Where I differ from Regan is that he argues against the possibility of incomparability. See Donald Regan, 'Value, Comparability, and Choice', Incommensurability, ed. R. Chang, pp. 129-50.
13. See Raz, Morality, ch. 13.
14. Chang has argued that incomparability, rather than incommensurability, ought to be the focus of attention. See Chang, 'Introduction', pp. 1-3.
15. By this I mean to distinguish the kind of rational choice theory under consideration from a revealed-preference approach in which a preference can be established ex post on the basis of the choice made by a rational agent. For a discussion of the revealedpreference approach, see Amartya Sen, Choice, Welfare and Measurement (Cambridge, 1982), pp. 41-53. Comparative judgements can be interpreted as including both holistic comparisons and determinate component comparisons.
16. This is the standard definition of completeness in the rational choice literature. To avoid confusion, it should be pointed out that Harris refers to completeness as 'exhaustiveness', reserving completeness to express the idea that the Trichotomy Thesis is true. See Harris, 'Value Vagueness', p. 160.
17. I draw inspiration from a teacher who said that she graded in terms of clumps. I thank Alan Strudler for relating this anecdote to me.
18. T. K. Seung and Daniel Bonevac make a similar distinction. They distinguish between algorithmic comparisons and non-algorithmic comparisons, which correspond, roughly, to component comparisons and holistic comparisons. Where their account differs is that the authors consider all non-algorithmic comparisons to be based on intuition. On the account in this article, holistic comparisons can be well-defined. See T. K. Seung and Daniel Bonevac, 'Plural Values and Indeterminate Rankings', Ethics 102 (1992), p. 801.
19. G. A. Cohen, in personal conversation, has raised the point that this understanding of the way in which covering considerations function commits one to the view that an item which is worse than another item in a component comparison might nevertheless be better from the perspective of the covering consideration. I am not certain that this is the case, and even if it were, I see no reason why a covering consideration cannot operate as such.
20. I thank Joseph Raz for pressing me to clarify this point and for helpful suggestions for ways in which to do so.
21. I owe the example of architectural design to Joseph Raz who put to me the example of symmetry.
22. Chang, 'Parity'
23. Chang, 'Introduction'.
24. Chang, 'Parity', p. 673.
25. Chang refers to this principle as the 'Small Unidimensional Difference Principle' ('Parity', p. 674).
26. Chang, 'Introduction', pp. 26-7.
27. Chang adapts an illustration from Adam Morton, Disasters and Dilemmas (Oxford, 1991), pp. 34-5.
28. This position might be thought of as the projection of the item on the vertical axis.
29. 1captures the idea that the comparison between Michelangelo and Talentlessi does not require any respects that are associated with creativity in musical composition. Whether or not one makes this change to the image does not affect the analysis.
30. Chang, 'Introduction', pp. 14-15.
31. See Parfit, Reasons, p. 431
32. Griffin, Well-Being, pp. 80-1, 96-8, 104
33. Griffin, 'Incommensurability', pp. 38-9
34. Hurka, Perfectionism, p. 87.
35. Parfit, Reasons, p. 431.
36. Griffin, for example, writes that a feature of two items, A and B, being roughly equal is that 'C's being clearly better than B does not allow us to conclude that C is better than A' (Griffin, Well-Being, p. 81). Hence although Parfit does not name this relation that he describes, I use the term 'rough equality' to encompass the relation that Parfit describes.
37. Raz, Morality, pp. 325-6.
38. Parfit, Reasons, p. 431.
39. I thank Joseph Raz for raising this objection and for pressing me to clarify my response to it.
40. Amore general point to consider is the assumption of the transitivity of 'equally good' as a comparative relation. The assumption that comparative relations are transitive is held, in part, that otherwise a person may be a 'money pump'. This, for example, is Chang's concern. The problem of the money pump, however, is a problem of choice, which is distinct from the problem of comparison. Only when choices are exclusively governed by comparisons is the assumption of transitivity of comparative relations necessary to avoid the possibility that a person may be a money pump. The view that choices are exclusively governed by comparisons, however, is not an uncontroversial view. Joseph Raz, for example, challenges this view in 'Incommensurability and Agency', Engaging Reason: On the Theory of Value and Action, ed. J. Raz (Oxford, 1999).
41. See Chang, 'Introduction'.
42. Waldron, God, pp. 76-7.
43. Similarly, consider the practice in American paediatric medicine of classifying newborn babies as 'small', 'average' or 'large' relative to their gestational age at birth. For example, for babies born at forty weeks, those who weigh less than 2.5 kilograms are 'small', those who weigh more than 4.0 kilograms are 'large', and those whose weight falls between these two categories are 'average'. Let us call the designation that a baby is assigned by this practice her 'paediatric birth weight'. Suppose that Zoe weighs 3.0 kilograms and Zachary weighs 3.5 kilograms, and that they are both born at forty weeks. In terms of paediatric birth weight, they are equal; they are equally 'average'. It might strike some as mistaken, however, to call them equal because they differ in terms of their actual birth weight. Zachary, in fact, weighs more than Zoe. However, even though they are not the same in terms of the covering consideration on which they are normally compared, there is nothing inherently unequal between them as measured by the covering consideration of paediatric birth weight. Comparisons, to reiterate, are made with respect to a covering consideration. It would be mistaken to say that Zachary and Zoe are equal with respect to actual birth weight. However, this should have no bearing on their comparison with regard to paediatric birth weight, even when paediatric birth weight is comprised by actual birth weight. Note that the categories are defined in terms of standard deviations within the population of babies born. Although they use the same categories of weight, some classification schemes name the categories differently. I thank Sara Toomey for this example.
44. Raz, Morality, p. 332.
45. 'To be indifferent to this kind of choice', as Raz writes, 'is not to have proper respect for oneself'.
46. There are situations in which a person is not indifferent to a choice between items that are equally good. Suppose that I am driving in my two-seater car and come across two victims of a hit-and-run accident at the side of the road. I am confident in my belief that each victim will be made better off to an equal degree by my taking the victim to the hospital in my car. Given the nature of their injuries, I can take only one victim if I am to help either of them at all. From the perspective of the value of well-being, it is equally good which victim I take to the hospital. Nevertheless, it is inappropriate to adopt an attitude of indifference with regard to the choice of which victim I elect to take in my car, even if I take my decision solely with regard to the covering consideration of well-being. As such, the fact that a person is not indifferent to the choice between the legal career and the musical career in itself need not count against the possibility that the two careers can be understood as being equally good. This example highlights the differences between a generic comparison between two items and a choice between two items. One difference is that choice requires us to think of the items not only in terms of reasons for their choice but also in terms of reasons not to choose them. For discussion of some of the differences between comparison and choice, see Ian Carter, 'Choice, Freedom, and Freedom of Choice', Social Choice and Welfare 22 (2004).
47. Joseph Raz has noted in personal conversation that the addition of $1000 is not necessarily an improvement with respect to the covering consideration of goodness of career, but rather an improvement with respect to another value, namely, having a higher salary. For purposes of discussion, let us take it to be an improvement with respect to goodness as a career.
48. Chang labels this case for incomparability, the 'Small Improvement Argument'. Chang takes this argument to be an argument for the failure of one of the standard trichotomy of relations to obtain, rather than as an argument for incomparability. See Chang, 'Parity', pp. 667-73
49. 'Introduction', pp. 23-6.
50. Others, as Chang points out, take this argument to be an argument for incommensurability. In particular, she cites Raz, Morality
51. Ronald de Sousa, 'The Good and the True', Mind 83 (1974)
52. Walter Sinnott-Armstrong, Moral Dilemmas (Oxford, 1988), p. 67.
53. Raz, Morality, pp. 325-6.
54. Morality, p. 326.
55. Chang, 'Parity', p. 667. I do not address Donald Regan's argument against incomparability. See Regan, 'Value'.
56. Chang, 'Parity', p. 661.
57. In writing this article, I would like to thank Ian Carter, G. A. Cohen, Rahul Kumar, Eric Orts, Joseph Raz, Alan Strudler, Sara Toomey, Alec Walen, Ralph Wedgwood, Andrew Williams, and the editor and referees of Utilitas. For providing a hospitable working environment, I thank the Department of Politics and International Relations at Oxford University where I was a Visiting Research Fellow while writing this article. For funding this research, I thank the Wharton Legal Studies Research Program. All remaining errors are my own.