Incomparability

Rather than focus on commensurability between abstract values, a number of authors focus on the comparability between concrete bearers of value, often in the context of choice (Broome 1997, 2000; Chang 1997, 2002; Griffin 1986; Raz 1986). Bearers of value sometimes appear incomparable in cases like Joseph Raz’s example of the choice between careers (described above in subsection 1.2).
The case for incomparability in such examples relies in part on what Ruth Chang calls the “Small Improvement Argument” (Chang 2002b, 667). As noted in the initial discussion of the example, if the legal and musical careers were of equal value, then a slightly improved version of the legal career would be better than the musical career, but this judgment appears incorrect. The Small Improvement Argument takes the following general form: “if (1) A is neither better nor worse than B (with respect to V), (2) A+ is better than A (with respect to V), (3) A+ is not better than B(with respect to V), then (4) A and B are not related by any of the standard trichotomy of relations (relativized to V)” where V represents the relevant set of considerations for purposes of the comparison (Chang 2002b, 667-668). In addition to Raz, Ronald de Sousa and Walter Sinnott-Armstrong are among those who have advanced the Small Improvement Argument (De Sousa 1974; Sinnott-Armstrong 1985).
Focusing on the incomparability of bearers of value has given rise to two lines of inquiry in the literature. The first concerns the relation between incomparability and vagueness. The second concerns the range of comparative relations that can hold between two items. This section summarizes debate within each line of inquiry. The relation between incomparability of bearers of value and incommensurability of values will be addressed in subsection 3.1.

2.1 Vagueness

Raz distinguishes incomparability from what he calls the “indeterminacy” of value. Recall that Raz defines two bearers of value as incomparable if and only if it is not true that “either one is better than the other or they are of equal value.” The indeterminacy of value is a case of vagueness: it is neither true nor false of two items that “either one is better than the other or they are of equal value.” Raz regards the indeterminacy of value to result from the “general indeterminacy of language” (1986, 324).
In contrast, other philosophers argue for interpreting incomparability as vagueness (Griffin 1986, 96; Broome 1997, 2000). For example, Broome introduces what he calls a “standard configuration” (1997, 96; 2000, 23). Imagine the musical and legal careers from Raz’s example. Fix the musical career as the “standard.” Now imagine variations in the legal career arranged in a line such that in one direction, the variations are increasingly better than the standard and in the other direction, the standard is increasingly better than the variations. There is an intermediate zone of legal careers that are not better than the standard and such that the standard is not better than the legal careers. If this zone contains one item, Broome defines this legal career to be equally good with the standard. If this zone contains more than one item, the zone is either one of “hard indeterminacy” or one of “soft indeterminacy.” A zone cannot be both one of hard indeterminacy and one of soft indeterminacy. In a zone of hard indeterminacy, it is false that the legal careers are better than the standard and false that the standard is better than the legal careers (1997, 73, 76). In a zone of soft indeterminacy, it is neither true nor false that the legal careers are better than the standard and neither true nor false that the standard is better than the legal careers (1997, 76). The latter is a zone of vagueness. Broome argues that indeterminate comparatives, including “better than” are softly indeterminate, thereby arguing for interpreting incomparability in terms of vagueness.
By understanding incomparability to entail vagueness, Broome disagrees with Raz (Broome 2000, 30). Raz defines incomparability so that it is compatible with vagueness, but not so that it entails vagueness. Griffin also argues that incomparability entails vagueness (1986, 96). Where Broome disagrees with Griffin is with regard to the width and significance of the zone of soft indeterminacy. Broome takes Griffin to suggest that if there is a zone of soft indeterminacy, it is narrow and unimportant. Broome argues that vagueness need not imply either narrowness or lack of importance (2000, 30-31). Erik Carlson (2004) provides one response to Broome’s account.

2.2 “Roughly Equal” and “On a Par”

The second line of inquiry concerns the set of possible comparative relations that can obtain between two items. The small improvement argument for the incomparability of the musical career and the legal career in Raz’s example assumes what Chang calls the “trichotomy thesis.” The trichotomy thesis holds that if two items can be compared in terms of some value or set of values, then the two items are related by one of the standard trichotomy of comparative relations, “better than,” “worse than,” or “equally good” (2002b, 660). A number of authors have argued that these three comparative relations do not exhaust the space of comparative relations. If they are correct, the musical career and the legal career may, in fact, be comparable.
James Griffin and Derek Parfit argue that items may in fact be “roughly equal” and hence comparable (Griffin 1986, 80-81, 96-98, and 104; 1997, 38-39; 2000, 285-289; Parfit 1987, 431). As an illustration, Parfit imagines comparing two poets and a novelist for a literary prize (1987, 431). Neither the First Poet nor the Novelist is worse than the other and the Second Poet is slightly better than the First Poet. If the First Poet and the Novelist were equally good, it would follow that the Second Poet is better than the Novelist. This judgment, according to Parfit, need not follow. Instead, the First Poet and the Novelist may be roughly equal. The intuition is that even though three items display the respects in virtue of which the comparisons are made, some comparisons are inherently rough so that even though two alternatives are not worse than one other, they are not equally good. In turn, the musical and legal careers in Raz’s example may be roughly equal.
“Roughly equal,” as used here, is to be distinguished from two other ways in which the term has been used: (1) to refer to a small difference in value between two items and (2) to refer to a choice of little significance (Raz 1986, 333). As used here, two items A and B are said to be roughly equal if neither is worse than the other and C’s being better than B does not imply that C is better than A when the comparisons are all in virtue of the same set of respects.
There is some debate as to whether “roughly equal” is in fact a fourth comparative relation to be considered in addition to the three standard relations, “better than,” “worse than,” and “equally good.” One way to conceive of “roughly equal” is as a “roughed up” version of “equally good.” On this interpretation, the trichotomy thesis basically holds; there are simply precise and rough versions (Chang 2002b, 661, fn. 5). Furthermore, “roughly equal” is a relation that can be defined only in virtue of three items, and as such, appears to be something distinct from a standard comparative relation. The standard comparative relations are binary; transitivity with respect to them is a separate condition (Hsieh 2005, 195).
A separate proposal for a genuine fourth relationship is Ruth Chang’s argument for “on a par” (Chang 1997; Chang 2002b). Two items are said to be on a par if neither is better than the other, their differences preclude their being equally good, and yet they are comparable. Whereas “roughly equal” is invoked to allow for comparability among alternatives that display the same respects (e.g., literary merit), “on a par” is invoked to allow for comparability between alternatives that are different in the respects that they display. Imagine comparing Mozart and Michelangelo in terms of creativity. According to Chang, neither Mozart nor Michelangelo is less creative than the other. Because the two artists display creativity in such different fields, however, it would be mistaken to judge them to be equally creative. Nevertheless, according to Chang, they are comparable with respect to creativity. Something can be said about their relative merits with respect to the same consideration. According to Chang, they are on a par.
Chang’s argument relies on invoking a continuum that resembles Broome’s standard configuration. Chang asks us to imagine a sequence of sculptors who are successively worse than Michelangelo until we arrive at a sculptor who is clearly worse than Mozart in terms of creativity. Chang then brings to bear the intuition that “between two evaluatively very different items, a small unidimensional difference cannot trigger incomparability where before there was comparability” (2002b, 673). In the light of this intuition, because Mozart is comparable to this bad sculptor, Mozart is also comparable to each of the sculptors in the sequence, including Michelangelo.
Whether “roughly equal” or “on a par” imply comparability is a matter of some debate. “Roughly equal” and “on a par,” for example, are intransitive, so to recognize them as distinct comparative relations would require us to reconsider the transitivity of comparative relations (Hsieh 2007). Some authors suggest that one of the three standard comparative relations obtains between all items that are claimed to be incomparable, roughly equal, or on a par (Regan 1997). In the case of “on a par,” Joshua Gert has argued that it can be defined in terms of the three standard comparative relations (2004). Another view is that values can be “clumpy,” meaning that the values sort items into clumps. According to this view, once we recognize the way in which the relation “equally good” functions in the context of clumpy values, items that appear to require “roughly equal” or “on a par” can be judged equally good (Hsieh 2005).

Incomparability

2.1 Vagueness

2.2 “Roughly Equal” and “On a Par”

Incomparability :: تعاليق

Incomparability