1. Hampshire, Stuart, ‘Russell, Radicalism, and Reason’ 15:6 The New York Review of Books (8 October 1970) at 4 Google Scholar. I owe this reference to Griffin, James, ‘Are There Incommensurable Values?’ (1977) 7 Phil. & Pub. Affairs 39.Google Scholar

2. See Hampshire, Stuart, Morality and Conflict (Oxford: Basil Blackwell, 1983) at 82–100 Google Scholar.

3. See Kuhn, Thomas S., ‘Theory Change as Structure Change: Comment on the Sneed Formalism’ in Butts, Robert E. & Hintikka, Jaakko, eds., Historical and Philosophical Dimension of Logic, Methodology and Philosophy of Science (Dordrecht: D. Reidel, 1977) at 301.Google Scholar Note, however, that contrary to a mistaken (though apparently quite frequent) understanding of the implication of the mathematical concept of incommensurability, it does not negate the possibility of comparison. Take again, for instance, the aforementioned classic example: the hypotenuse and sides of the triangle are unequivocally comparable. That is, we can certainly ascertain which is longer simply by placing them side by side; by comparing them to a third line; or even by conducting a simple measurement or calculation to any necessary (and of course, available) standard of accuracy. The mathematical argument about the incommensurability of the isosceles right triangle’s hypotenuse and sides points to the absence of any unit of measurement that can be used to indicate the difference in length between them. It does not suggest an inability to conduct an accurate and reliable comparison.

4. See Kuhn, Thomas S., The Structure of Scientific Revolutions (Chicago, IL: University of Chicago Press, 1962).Google Scholar

5. See Feyerabend, Paul K. ‘Explanation, Reduction, and Empiricism’ in Feigl, Herbert & Maxwell, Grover, eds., Minnesota Studies in the Philosophy of Science: Scientific Explanation, Space, and Time (Minneapolis: University of Minnesota Press, 1962) 28.Google Scholar

6. Both Kuhn and Feyerabend in presenting the incommensurability thesis, were in fact responding to the empiricist philosophy of science, which was dominant at the time, and especially (as far as the incommensurability thesis is concerned) to the idea that the meaning of the vocabulary used in observations is theory-neutral, i.e., that there exists an observational language, which is independent of theory and can be used as a common semantic ground as a shared vocabulary, for direct comparison between rival theories. For a comprehensive analysis see Sankey, Howard, The Incommensurability Thesis (Aldershot: Avebury, 1994) at 6–30 Google Scholar.

7. For the sake of clarity and convenience I will use the phrase ‘the incommensurability thesis’ to indicate the arguments about incommensurability within mathematics and within the philosophy of science, while referring to the idea of incommensurability of values in an explicit fashion as ‘the argument about the incommensurability of values’ or, alternatively, as the ‘incommensurability of values thesis’.

8. Cf. Raz, Joseph, ‘Incommensurability and Agency’ in Chang, Ruth, ed., Incommensurability, Incomparability and Practical Reason (Cambridge, MA: Harvard University Press, 1997) 110, n. 1 at 273.Google Scholar

9. Kuhn, supra note 3 at 301.

10. The most salient example of advocating the idea about the incommensurability of ethical theories is probably the case presented by MacIntyre, Alasdair (After Virtue, 2nd ed. (London: Duckworth, 1985) at 70–71 Google Scholar). (For a similar approach see Taylor, Charles, ‘The Diversity of Goods’ in Sen, Amartya & Williams, Bernard, eds., Utilitarianism and Beyond (Cambridge: Cambridge University Press, 1982) 129 at 132-5)CrossRefGoogle Scholar. The essence (at least in the present context) of MacIntyre’s argument is the inherent subservience of one’s moral perspective to her constituting history (her past contingencies and cultural provisos) and the inseparability of the two, which renders different moral perspectives incommensurate. Different societies are granted a legacy of ethical concepts which are moulded by the specific and distinct tradition and cultural circumstances of the society. As a result, says MacIntyre, different ethical views do not have a shared conceptual basis. For instance, to take an extreme example, a modern-Western-atheist society cannot have and does not have a shared conceptual basis with an ancient-Eastern-religious one (see James Griffin, ‘Incommensurability: What’s the Problem?’ in Chang, supra note 8 at 39). The fact that each society has its own particular moral heritage and rhetoric, and that no common conceptual basis(e.g., universal moral language) exists, means that there is no common basis for rational discussion and systematic comparison, and consequently their different moral concepts and ethical approaches are incommensurable. Thus, according to MacIntyre, moral philosophies present a case of incommensurability similar to the one characteristic of the philosophy of science: i.e., the different origin and theoretical context of different moral philosophies render impossible any attempt of a systematic, point-by-point, comparison (cf. Griffin, James, Well-Being (Oxford: Clarendon Press, 1986) at 336, n.12Google ScholarPubMed).

11. See Statman, Daniel, Moral Dilemmas (Amsterdam: Rodopi, 1995) at 60 Google Scholar and Chang, supra note 8 at 1. Cf. Nagel, Thomas, Mortal Questions (Cambridge: Cambridge University Press, 1979) 128.Google Scholar

12. Griffin, supra note 10 at 35. Since that is what nearly all of us mean, I will substitute henceforth ‘incomparability’ for ‘incommensurability’ and refer to the incomparability of values.

13. Chang (in her introduction to Chang, supra note 8) argues (at page 2, after indicating the pervasive disagreement about the meaning of incommensurability) that we should distinguish between ‘incommensurability’ (a concept to which she refers as indicating the impossibility of accomplishing exact measurement and as a result, of producing exact cardinal ranking) and ‘incomparability’ (a concept she employs to indicate the impossibility of ordinal ranking). One may quite reasonably challenge the necessity and reasonableness of introducing the distinction at all. Though there are clear and significant variations between the various arguments about the incommensurability of values, there is also much in common, and above all (as I have indicated in the main text) the fact that the gist of all arguments (even though some of them are mistaken) is the impossibility of comparison, i.e., incomparability. Accordingly, adopting Chang’s distinction might lead to confusion by conveying the wrong im Pression that some arguments about the incommensurability of values renounce the possibility of comparison, while others do not. It seems that the main possible claim in favour of introducing the concept of ‘incomparability’ is the fact that it better presents and manifests the essence, the result and primary design, of the argument about the incommensurability of values: i.e., the claim that incommensurable values are incomparable. However, if this is to be the case, then the claimed superiority cannot be used as an argument in favour of introducing the distinction, but rather as an argument in favour of substituting ‘incomparability’ for ‘incommensurability’.

14. Cf. Chang, supra note 8 at 1.

15. In The Concise Oxford Dictionary, 9th ed., for instance, ‘Incomparable’ is defined also as ‘without an equal; matchless’. Cf. Raz, supra note 8 at 110, n. 1 (at 273): ‘“How can you compare,” one may say, “Mozart and Salieri? Clearly Mozart is incomparably the better composer.” Which he is.’

16. The argument has been rightly dismissed as irrelevant by many. See, for example, Griffin, supra note 10 at 35.

17. From a practical point of view it does not matter whether the reason for the incomparability of X ‘s child and money is because money is simply not suitable for representing the intensity of X ‘s. feeling towards her child as many would tend to say, or because X regards (or should regard) her child as equals an infinite amount of money, as others would claim.

18. The reasons for our inability to compare will be discussed shortly.

19. Brown v. Board of Education, 347 U.S. 483 (1954).

20. Obviously, there is no clear cut distinction between the abstract and the concrete: there is no dichotomy between the abstract value and its concrete instantiation, but rather a continuous scale with the abstract case in one end and the infinitesimally concrete case in the other end.

21. Some might hold that certain values, in their abstract form, are always more important than others. For instance, one may hold that the value of human life is always more important than any other value. And yet, many will consider such a view, even when confined to the value of human life, to be rather extreme and contrary to common practices.

22. I will use hereinafter the term ‘option’ in order to indicate the specific instantiation of a value, and the term ‘choice’ in order to indicate the necessity to choose between the competing options.

23. Cf. Broome, John, Ethics Out of Economics (Cambridge: Cambridge University Press, 1999) at 146.CrossRefGoogle Scholar

24. I do not mean to imply that we can always actually compare, in a conscious and rational manner, the competing options. That is, it seems undeniable that there can indeed be cases (in reality, not only in our feverish philosophical imagination) of competing options that would defy, at least practically, any attempt for rational comparison. And note: we are sometimes compelled to reach a decision even in these kinds of practical incomparability situations. Reaching a decision in those cases is, however, akin to an arbitrary selection, ‘taking our pick’, and we must not confuse ‘taking our pick’ with making a choice based on rational and sophisticated comparison. For instance, we might, in a practical incomparability situation, take our pick based on tossing a coin. Now, this might very well be a rational thing to do in such a case, but it certainly cannot fully qualify as a comparison based choice (unless the reason for tossing the coin is a rational and conscious conclusion that the options are equally valuable).

25. The utilitarian doctrine has, of course, evolved over time, resulting in a variety of versions which differ, among other things, in their particular maximands. For simplicity, I will focus on the maximization of overall welfare version, though my arguments can be applied just as well to the other versions.

26. The choice in question may be between alternative lines of action (in the case of act utilitarianism) or between alternative rules (in the case of rule utilitarianism). The distinction between the two alternative versions of utilitarianism is of little significance in the present context.

27. The status and implications of being ‘roughly equal’ is discussed below.

28. Note that utilitarianism is not necessarily committed to the view that positive value relations can always be established between competing options and therefore can peacefully coexist with a certain notion of incomparability. It is, however, committed to the view that a choice cannot be justified unless positive value relation obtains.

29. It might be argued that positive value relations are necessary only if the content of the choice is to be justified whereas one might very well be justified in making a choice even when positive value relations between the options does not obtain. Suppose, for instance, that one has to choose between two alternative lines of action, X and Y, and suppose that no positive value relation can be established between the two. Under these circumstances the content of the choice, i.e., the choice of X over Y (or vice versa), cannot be justified and yet we might still be perfectly justified in making a choice, i.e., in opting for either X or Y. Supporters of the conventional view would rightly insist, however, that the move from justifying the content of the choice to justifying the making of the choice would not evade the need for establishing positive value relations if the choice is to be justified. The only way to justify the making of the choice is by establishing positive value relation between (X v Y) and (X v Y), i.e., between making a choice and not making a choice. Needless to say, failure to establish this ‘second order’ positive value relation does not prevent one from making a choice nonetheless. The choice, however, would not be a justified one.

30. Having a covering value is a formal, qualifying condition for comparison. Incomparability₁ is, therefore, rightly characterized by Chang as a formal failure of comparison (noncomparability in Chang’s terminology). See Chang, supra note 8 at 27.

31. Griffin, supra note 10 at 35.

32. See Adler, Matthew D., ‘Law and Incommensurability: Introduction’ (1998) 146(5) U. Pa. L. Rev. 1169 at 1177Google Scholar; and Statman, supra note 11 at 61. This is, of course, the analogue in the moral domain of the requirement for common denominator that characterizes the mathematical version of the incommensurability thesis.

33. See Chang, supra note 8 at 6. Cf. Meikle, Scott, Aristotle’s Economic Thought (Oxford: Clarendon Press, 1995) at 13–14 Google Scholar. Within his discussion of Aristotle’s notion of ‘exchange value’, Meikle indicates that ‘When things are commensurable, they are so in respect of some property they share, and if that property is measurable, they may be said to be equal or unequal in respect of it. Two things cannot simply be said to be ‘equal’ without qualification. They can be, and be said to be, equal in length, for example, provided they are both extended in space. But the possibility of a relation of equality holding between them rests on the fact that they are already commensurable in both being spatially extended.’

34. ‘Scale’, ‘ground of comparison’, and ‘covering value’ are used interchangeably in the relevant literature.

35. Meikle, supra note 33 at 14, suggests that ‘A sound cannot be said to be equal to a sausage, because there is no property in respect of which the two things are commensurable. What is a measurable property in one, intensity or length, is not a property possessed by the other, so they are not commensurable and cannot be equated.’ He is probably right, if by arguing for the lack of shared ‘property’ he refers to some tangible/physical property. However, sound and sausage may very well be comparable if the relevant property is defined, for example, as the pleasure X would experience as a result of being exposed to one or the other. It might, for instance, be the case that X is suffering at the moment from a horrific headache, as a result of not having anything to eat for the last 24 hours. It is quite conceivable that under these circumstances X would abhor the idea of being exposed to sound (any sound even music by Mozart) and at the same time, would yearn for some food (any food, even a sausage). Cf. Perry, Michael J., ‘Some Notes on Absolutism, Consequentialism, and Incommensurability’ (1984-1985) 79 Nw. U. L. Rev. 967 at 979.Google Scholar

36. Raz, Joseph, The Morality of Freedom (Oxford: Clarendon Press, 1986) at ch. 13Google Scholar. Raz uses the notions incomparability and incommensurability interchangeably (see 322).

37. The distinction (or lack of it) between incomparability and rough equality is discussed at length in section 6.

38. Raz, supra note 36 at 331. Some might wish to reserve indifference as the appropriate attitude towards (strictly) equals only, and deny the inference from ‘rough equality’ to indifference. Like most, I believe, I find that view objectionable. And yet, as I do not intend to argue for the veracity of that inference in the present essay, I will simply assume, as Raz rightly does, its truth.

39. Ibid. at 332.

40. Ibid.

41. How exactly ‘success’ should be defined and measured is not specified by Raz. I will not try to do so either.

42. Raz, supra note 36 at 333.

43. Let’s see him persuading my 7-year-old son who insists, adamantly, to use his personal taste as the only relevant covering value when bread is concerned: ‘white is undoubtedly better than brown.’

44. Without a covering value, comparison could not be made. Without a comparison, one would not be justified in designating one of the options as better than the other. Now, if we cannot specify one of the options as better than the other, then perhaps, the argument might go, we are justified in concluding that neither is.

45. It could after all, have been any of several other relevant covering values such as their relative taste, their relative price, their culinary value and so on.

46. See my second caveat regarding the reference and context of the phrase ‘incomparability of values’ in section 3 above.

47. It is important to emphasize that incomparability₁ (the lack of a common scale) does not result from some technical or epistemic difficulty in the process of comparison, but rather from a more basic concern regarding the existence of a covering value. It is in that sense, then, that the claims are on an ontological level: saying that we lack a covering value because such a value does not exist.

48. Perry, supra note 35 at 979-80.

49. See, in that context, Meikle’s example of comparing ‘sound’ and ‘sausage’: supra note 35. The covering value must, of course, be applicable to both sides of the equation.

50. Dworkin, Ronald, ‘Objectivity and Truth: You’d Better Believe It’ (1996) 25(2) Phil.& Pub. Affairs at 134 Google Scholar. The same difficulty characterizes, obviously, not only the comparison ‘among evident geniuses at the very highest levels of different genres’, but also any other comparison among representatives of different genres who enjoy (respectively, within the relevant genres) similar status. Hence, what applies to ‘evident geniuses’ would apply just as well to ‘evident failures’.

51. Dworkin’s argument, after all, is that we cannot rank Beethoven and Picasso, who are both, needless to say, evident geniuses of two different genres, because ‘no precise ranking makes sense among evident geniuses at the very highest levels of different genres’.

52. Chang, supra note 8 at 5.

53. To claim that the expected effect on overall welfare is not the appropriate covering value is to raise an external critique against utilitarianism, that is, a critique that rests on the assumptions of alternative normative theory and, therefore, begs the question against utilitarianism. In contrast, holding utilitarianism vulnerable to the incomparability₁ argument is an internal critique, according to which utilitarianism, taken on its own terms, suffers from internal inconsistency as a result of commanding a comparison based maximization of welfare without assigning a relevant/applicable common scale.

54. Raz, supra note 36 at 326.

55. Sinnott-Armstrong, Walter, Moral Dilemmas (Oxford: Basil Blackwell, 1988)Google Scholar. Similar examples are offered by Raz, supra note 36 at 332; Broome, supra note 23 at 151; Chang, supra note 8 at 23.

56. Based on Chang, supra note 8 at 24.

57. Ibid.

58. A commitment to the trichotomy principle implies, then, the rejection of ‘incomparability’ as ontologically distinct value relations.

59. Kramer, Matthew H., ch. 1 (draft) of a forthcoming book (Objectivity and the Rule of Law (Cambridge: Cambridge University Press)) at 16.Google Scholar

60. For a compelling discussion of the distinction between ‘uncertainty’ and ‘indeterminacy’ see Dworkin, supra note 50 at 129-39: ‘If I see arguments on all sides of some issue, and do not find, even after reflection, one set of arguments stronger than the others, then I am entitled without more to declare that I am uncertain, that I have no view of the matter. I do not need a further, more substantive, reason, beyond my failure to be persuaded of any other view, for claiming uncertainty. But in all these respects indeterminacy differs from uncertainty. … A belief in indeterminacy is a positive claim, and it needs a positive reason or assumption to support it’ (131).

61. ‘Incommensurability’; ‘Incomparability’; ‘Parity’; ‘Rough equality’.

62. ‘In my view, the Trichotomy Thesis is false; there is a fourth positive value relation—’on a par’—that, together with the traditional three, exhausts the logical space of comparability.’ (Chang, supra note 8 at 4-5).

63. Raz, supra note 36 at 322.

64. Ibid.

65. Ibid. at 329.

66. A valuation is ‘positive’, according to Raz, if it provides a clear indication of the relative value of the alternative options, i.e., if it results in a positive discernment of the option’s value relations. In that sense, ‘incomparability’ is indeed not a positive valuation.

67. Raz, supra note 36 at 328.

68. Similarly, no one would seriously maintain that the fact that a distinction can be made between ‘equality’ on the one hand and ‘worse than’ and ‘better than’, on the other (e.g., the fact that the first is ‘unbiased’ and the other two are), means that their ontological status is somehow different.

69. Surely, one might be wrong in finding the options incomparable; just as one might be wrong in finding one better than the other. And yet, a judgment of incomparability, in itself, does not imply error of any kind.

70. By defining the difficulty as ‘epistemic’, I do not mean to imply that the difficulty is necessarily surmountable; it might very well not be.

71. In a sense, then, it might be argued that the distinction is no more than academic. However, in fact there is a significant difference in message and tone. For a trichotomist the state of incomparability is, by definition, a state of error. It is an unwanted state. For the incomparabilist, the state of incomparability is just like any other state: if options are incomparable, then they just are. Not only there is nothing one can do about it; there is also nothing one should do about it. In a way, then, the incomparabilists have become almost ‘error-proof’ in the process of comparison. However, it is the wrong kind of ‘error-proofness’, as it is not the case that they cannot err anymore, but rather that they cannot identify an error; they have practically erased the possibility of identifying an error, because they necessarily have the tendency to fall back on incomparability.

72. See, once again, Dworkin, supra note 50 at 129-39.

73. A simple intellectual experiment with the nominal-notable test seems to drive this point home: whenever we are faced with a case of competing options that seem to be incomparable, a quantitative modification of the intensity of the values that are being realized by the options would serve to increase the interval beyond the resolution frontier and make the options comparable.

74. Indifference should, undoubtedly, characterize one’s attitude to the choice between equals. In that sense, indifference is obviously the consequence of equality: we ascertain the options equality and deduce that we should be indifferent between them. At the same time, however, there seem to be good reasons for holding the view that indifference is actually the defining feature of equality of options, or at least its most fundamental test/mark. That is, in many cases indifference would be the only independent sense in which the options equality can be identified and even defined.

75. Raz, supra note 36 at 328-35.

76. Ibid. at 330.

77. Ibid.

78. Ibid. at 331.

79. Ibid.

80. Ibid. at 328-29.

81. Ibid. at 331.

82. Ibid.

83. The magnitude of X is, obviously, context dependent.

84. Rough equality may be used in everyday speech to describe a case where (1) 0 < G < ≤ Y; and (2) we actually do know which way the gap goes. Thus, for instance, one may legitimately say that Carn Mor Dearg and Aonach Mor (two of the Scottish Munros) are roughly equal in height, even when one knows perfectly well that the latter is actually one meter higher. This everyday use does not, however, affect the aforementioned analysis.

85. Note that the demand on our ability to measure G is minimal, that is, we only have to be able to establish that 0 ≠ G ≤ X. We do not have to establish its actual measure.

86. Needless to say, stipulating that X ≤ e_r is indeed a constraint. It means that one would not be able to regard as roughly equal options between which the gap is bigger, even if just slightly, than the variation in measurement.

87. Raz, supra note 36 at 331.

88. Ibid. See again supra note 74 regarding the relations between equality and indifference.

89. Ibid.

90. Ibid. at 331-32.

91. Ibid. at 332.

92. Ibid.

93. Ibid.

94. Ibid.

95. Ibid.

96. Ibid.

97. Ibid. at 333.

98. This is, obviously, the relevant quote from Raz (ibid. at 332) in which I have substituted ‘event’ for ‘decision’ and ‘choice’ (the claim was properly quoted above: see main text for supra note 39).

99. Raz, supra note 36 at 328.

100. Chang, supra note 8 at 5.

101. Ibid. at 26.

102. ‘A difference is zero if it does not have extent. A difference is biased if it favors one item and correspondingly, disfavors the other. A zero difference, then, must be unbiased. … Why should we think nonzero, biased differences (better than and worse than) and zero (unbiased) differences (equally good) are the only kind of differences there are? In particular, why should we rule out the possibility of nonzero, unbiased differences?’ (ibid.).

103. Ibid. (italics added).

104. The only support offered by Chang is a dubious analogy to the mathematical notion of absolute value (ibid.), which clearly fails, and an equally dubious attempt to metamorphose a diagrammatic model into reality (ibid. at 27).

105. Ibid. at 27.

106. One can only speculate about the content of the intellectual process that lead both Chang and Raz to propose and insist on profoundly uncanny characterizations of incomparability₂ (Raz, as the reader would remember, maintains that incomparability₂ is a case where the gap between two alternative options is both zero and non-zero). My guess would be that both cases resulted from an unrelenting attempt to locate a logical space for a strongly held, though poorly justified, intuition. One is reminded of W. Somerset Maugham’s claim that the source of intuition is the same as the effect of advertisement: ‘tell a man ten thousand times that Pears Soap is good for the complexion and eventually he will have an intuitive certainty of the fact.’ (See Sherrin, Ned, A Dictionary of Humorous Quotations (Oxford: Oxford University Press, 1995 at 6)Google Scholar.

107. See Dworkin, supra note 50 at 129-39.

108. The career-choice case can be easily contrived so as to form an example for such a case.