If one has a clear measurement, a scale, to relateAtoB,one does not have to deal with incomparability. It is obvious that the attendence at Trump’s inaugural lec-ture was far lower than Obama’s in 2013. Thus, incomparability, it is safe to say, belongs to the realm beyond (clear) measurement. However, it does not follow that everything that lacks a scale entails incomparability. Think, again, of friendship versus 1000 Dollars; for the vast majority it is perfectly clear what is ‘better’ (more valuable, more satisfying, etc.). All what we can infer from this might be that cases of comparative breakdown should be explained in terms of a certain kind of in-determinacy. Which kind? In the following passage I would like to distinguish four—alledged—sources of incomparability—plus an argument, to be refuted, that negates or mitigates the existence of incomparability:
Trichotomy and its failure (Joseph Raz) Repudiating to compare (Derek Parfit*)
Parity—instead of incomparability? (Ruth Chang) Indeterminacy of the covering value (John Broome)
Indeterminacy of (the meaning of) comparatives (John Broome)
Let’s go!
1. Trichotomy and its failure
The moral philosopher Joseph Raz has presented what one might call the standard view of incomparability. This view is based in the trichotomy assumption mean-ing that there are (see above) three comparative predicates exhaustmean-ing together the logical space of describing a comparison betweenAandB:better, worse, and equally good. Incomparability is, then, the breakdown of applying better, worse, and equally good to the relation betweenAandB.Is liberty or security preferable?
Here, Raz claims, we have not only to deal with the sense of comparison and its limits, but also with the truth of that very relationship.34
Now, one could imagine to improveAa bit compared toB.The claim implied by their being incomparable is that this slight improvement cannot trigger com-parability betweenAandBeither. So, if one takes again liberty and security while
‘improving’ the latter by giving everyone in the ‘secure(d)’ world 1000 Dollars on top, nothing has changed. Liberty and security remain in the mode of being incompara-ble, since the improvement suggestion elicits the notion that the countable element of money might introduce the scalability of the whole comparison—but it doesn’t.
34 Cf. Raz,The Morality of Freedom, 322-23.
Raz also underlines the difference between incomparability and equality. A judgment, Raz holds, concerning the relative value ofAandBis impossible in the case of them being incomparable—whereas equality is precisely such a judgment.
There is another difference, the case of transitivity: IfAandBare equal, and ifB andCare equal too, it follows thatAandCare equal as well. However, ifAandBare incomparable andBandCare too, it does not follow that one could not compareA andC(325). A similar response goes also for what has been coined as ‘rough equal-ity’ meaning thatAandBare in that relation when there difference is very small in such a way that all other options that are better (or worse) thanAare also better (or worse) thanB(330). In the case of rough equality one is, Raz adds, entitled to be indifferent concerning a preference betweenAandB.However, incomparability does not mean indifference and is not based on it either; it is rather the lack of sufficient reasons to go in one direction or the other.
Raz thinks that both elements just sketched—non-transitivity and non-im-provement—constitute together a test (not a definition) for incomparability (335).
That means: ifAandBare incomparable, and an optionCis better thanAbut not better thanB,and if an improvement ofA(orB) does not turnA(orB) better than B(orA) both,AandBare ‘truly’ incomparable.
This account has caused some protest since, for some, it is not clear whether tri-chotomy really exhausts the logical space of positive value relations. Especially Ruth Chang has suggested that some (or all?) cases that run under, in Raz, the heading of incomparability are, in reality, cases of ‘parity’ and, thus, of being comparable (see 7.3.).
2. Repudiating to compare
In part IV of his seminalReasons and PersonsDerek Parfit invites us to contemplate different and increasingly complicated scenarios of future states. The criteria are, for a good part, the amount of people who will populate the planet, the quality of their lives—combined with discussing what it means to speak of a life worth living (as a minimal standard of living) plus more specific conditions varying possible outcomes, for instance a higher standard of living for the next 100 years at the cost of a lower standard for the generations then to come—as part of ‘future ethics’—or the promise of health while accepting a crucial sacrifice such as a nearer death or having a minority of people living under poor conditions while all others having a good life—as part of ‘populations ethics’.35
Parfit starts off by introducing the picture you can see in figure 1 (on 385).
First of all, Parfit is not so much concerned with reflecting on comparisons (that’s why I added a (*) to his name above; an exception is what he calls ‘rough equality’ and ‘rough or partial comparability’, cf. 357 i.a.). However, heiscomparing 35 Cf. Derek Parfit,Reasons and Persons, Oxford 1984, 384-390.
Fig. 1
all the time scenarios likeA, B, C,…. ,Z—while the height of the columns signifies the quality of life and their width represents the amount of people living accord-ing to a specific scenario. Hence, inApeople enjoy an extremely high standard of living whereas the population is rather small; its amount is doubled inBin having a population with a slightly lower standard.
If one conceptualizes both parameters—quality and quantity of life—and if one presupposes, as utilitarians may have it, that qualitative judgments are eventually reducible to a scalable measurement, one is, henceforth, entitled to compare fu-ture states of affairs:Bis better thanA, Cis better thanB,…. Now, the scope of Parfit’s argument is the paradox that is waiting for us if we continue like this up the scenarioZ: here, we have an enormous amount of people living a life hardly worth living. That is, obviously, a “repugnant conclusion” (387).
It is astonishing that Parfit invests so much effort in elaborating on scenarios like the sketched one (and its far more complex sibblings) without paying heed to the question of the comparability of their outcomes or, more to the point, of our willing- and readiness to compare here in the first place. Hence, what might justify this reservation on our part? To begin with, there are two trivial while far-reaching assumptions that make these scenarios keep going, namely that quality of life is somehow measurable and that, even if it were, we can measure that quality of life on the same scale as the one we may use for the amount of people. Both assumptions are either plainly false or have first to be defended.
Putting these deliberations aside for a moment, one might ask why one could hesitate to compare here. I don’t think it is enough to refer again to the standard account by Raz and others saying that the comparative predicates ‘better than’,
‘worse than’ and ‘equally good’ remain out of business here since we do compare AandZto refute the latter. But why notAandBorC? One answer is that we are dealing here with what Raz called ‘constitutive incomparability’, i.e. it is, then, an intrinsic element ofA, B, C… not to be compared in the case of really valuing A, B, C.His own example is, as seen above, money versus friendship—but there,
we can compare in giving (usually) the privilege to friendship. However, what to do confronted byA, B,andC… is not that clear.36 Another way of explaining the difficulty at hand is to refer to the complex situation consisting of the mixture of quantitative and qualitative elements as well as divergent values that may come into the picture in evaluating the scenarios in question. By values (in a broad sense), I have in mind problems such as whether the notion to benefit a person by causing his/her existence, as Parfit holds (see 394 i.a.), has any sense. The way we answer that question influences our willingness to compareAandB(amounting to prefer B).
I stop here for a moment. For sure, there is more to be said concerning the phe-nomenology of these cases and our hesitation against a straightforward meeting these problems. However, one lesson that can be learnt from this here could be the direction in which we should go: the problems of comparability may be based on different kinds of indeterminacies effecting the elements constituting the compar-ison, i.e. the relata as well as the covering value by which these relata are set into a relation. We will come back to this in section 7.4. and 7.5.
3. Parity—Instead of incomparability?
A good deal of the debate concerning incomparability is, however, not dedicated to this notion itself, but to refuting the trichotomy thesis. Hence, it would be wrong to claim that comparingAandBmeans that one of them is better or both are equally good—since there is, it is argued, a forth logical relation possible that is called by the main proponent of this move, Ruth Chang, ‘being on a par’ or ‘parity’.37 This has obvious implications for the scope of incomparability, but it is not clear what exactly is meant to be achieved if the idea of parity could be established in the first place: sometimes it seems to entail the stronger claim according to which there is no room anymore for incomparability (of different values) by explaining these instances away in referring to parity;38sometimes, however, Chang is not attempting to replace incomparability but to reduce its scope, by correcting false characterisations of cases as allegedly being incomparable in describing these cases as being on a par.39
But what exactly is parity? Chang uses a particular kind of arrangement to sub-stantialize this somehow vague or surprising notion by attacking the trichotomy thesis and the standard view based on it. I quote the relevant passage at some length:
36 See also Lukes, Comparing the Incomparable, 184-195, 188 and 195.
37 Esp. in her influential paper “The Possibility of Parity”, and one might take that to be the starting point of trying to establish further logical relations beyond the classical trichotomy plus parity.
38 Cf. Chang,Making Comparisons Count, xix.
39 Cf. Chang, The Possibility of Parity, 662.
“[T]ake an arbitrary pair (X, Y ) of evaluatively diverse items. For at least some (X, Y ) we can create a continuum of X-items by successively adding or subtracting dollars (or pleasurable tingles, etc.) from X. If we add enough dollars, we get an X-item, X+, that is better than Y, and if we subtract enough dollars, we get an X-X-item, X-, that is worse than Y. Now according to our abstract intuition, adding a dollar, pleasurable tingle, and so forth cannot make a difference to whether one item is better or worse than another item evaluatively very different from it. Therefore, there must be some X-item, X*, in the continuum between X- and X+ that is nei-ther better nor worse than Y. But what relation holds between X* and Y? Suppose one of the trichotomy always holds. Then since X* is neither better nor worse than Y, it and Y must be equally good. According to our intuition that a dollar can’t make a difference, however, this is impossible. For if we add fifty cents to X*, we get an item that is better than Y; if we take away fifty cents from X*, we get an item that is worse than Y. And the difference between X* fifty cents, which is better than Y, and X* fifty cents, which is worse than Y, is a dollar. Thus X* and Y cannot be equally good. Therefore, we must reject the assumption that one of the trichotomy al-ways holds; X* is not better than Y, not worse than it, and the two are not equally good.”40
The less abstract, but structurally parallel version of the argument uses the com-parison between Mozart and Michelangelo in terms of creativity. What follows is the attempt to create a reductio: suppose the trichotomy holds and both Ms are incomparable, i.e. neither is better than the other and they are not equal either.
Now, imagine, there is a guy called Talentlessi, a very bad sculptor. Obviously, he is far worse than Mozart in terms of creativity. Now, imagine that we succes-sively improve Talentlessi to T+, T++, … and so on—in the end, we will have, again, Michelangelo. However, the standard view entails also, what is called the “small improvement argument” according to which, as we have seen in section 2., a tinily improved element in A—given thatAandBare taken to be incomparable—does not turnAbetter than B.41Hence, if Talentlessi is worse than Michelangelo and Mozart (and comparable with them), and if the small improvements (T+, T++, …) cannot make a crucial difference meaning not to be able to trigger incomparability, Tal-entlessi+++++++….. is Michelangelo and he is not comparable with Mozart without being better or worse or equal. In other words, insofar as Mozart is comparable with Talentlessi, he is comparable with Talentlessi+, since the difference between T and T+ is just a small one, and such a difference cannot cause incomparability between different items when we had before comparability. If Mozart is compa-rable with T+, then applying the principle anew, it follows that he is compacompa-rable
40 Cf. Chang, The Possibility of Parity, 672.
41 Cf. Raz,The Morality of Freedom, 328.
with T++, and so on. Comparability with Mozart is secured through the reapplica-tion of small differences, and hence we are lead to the conclusion that Mozart is, finally, comparable with Michelangelo. However, Mozart is not more or less cre-ative than Michelangelo, and nor are both equally crecre-ative. Yet it seems that they are nevertheless comparable; thus, there is a forth relation between them.
Chang thinks that those rejecting parity are committing the same mistake as potential dichotomists only allowing for being better or worse than; a trichotomist has, then, to show that there is indeed a third relation, being equal; and a par-allel discussion, Chang holds, we have between the standard view and defenders of parity.42Nevertheless, there is enough veil surrounding the notion of parity to maintain doubtful. First, one might try to explain what is captured by ‘parity’ in sticking to more common observations, such as indeterminacy and vagueness of the relation and relata in question.43Second, both arguments, the abstract and the Mozart/Michelangelo-form, seem to be based just on a sorites-argument—under-mining the transitivity of comparability through small improvements.44And third, one might come back to the unclarity mentioned at the beginning of discussing parity, namely the ambivalance of adding a forth relation to comparability and the stronger claim that parity substitutes all cases of incomparability between values.45 However, we in fact need a notion to express our comparing items under, let’s say, fuzzycircumstances, i.e. that these items are different in kind while, nevertheless, being compared. In the case considered, we, one might say, actually do compare Mozart and Michelangelo. Holding that it is hard to privilege one of them in terms of creativityisitself a comparative result.
4. Indeterminacy of the covering value
According to Raz there are two types of incomparability going back to the follow-ing versions: number one is the position Raz himself was concerned with, namely meaning by ‘being incomparable’ that, as we have seen, all three traditional compar-ative predicates fail; number two is the alterncompar-ative that John Broome, in criticizing Raz, was focussed on saying that it is neither true nor false that the traditional
42 Cf. Ruth Chang, Parity, Imprecise Comparability, and the Repugnant Conclusion, in:Theoria 82 (2016), 182-215, see 193.
43 For this option see Joshua Gert, Value and Parity, in:Ethics114 (3/2004), 492-510; a counter-defence of parity is to be found here: Mozaffar Qizilbash, The Mere Addition Paradox, Parity and Vagueness, in:Philosophy and Phenomenological Research75 (1/2007), 129-151.
44 Chang has tried to dispel the sorites appearance, but not in a convincing manner; see her The Possibility of Parity, 673 and 680; cf. also Erik Carlson, Parity Demystified, in:Theoria76 (2010), 119-128.
45 For a general critique of (the possibility of) parity see Ryan Wasserman, Indeterminacy, Igno-rance and the Possibility of Parity, in:Philosophical Perspectives18 ‘Ethics’ (2004), 391-403.
predicates apply. This second version puts the stress on the indeterminacy that is based on different candidates causing the vague character in question.46
This vagueness concerns either the covering value of the comparison or the ele-ments that are compared in regard to that value. Let’s begin with the first problem and take the example of baldness.47 This predicate belongs to the non-gradable ones, denoting properties that do not possess certain degrees. Hence, we are often dealing here with borderline cases in, again, two forms: whether a personAfalls under the extension of ‘baldness’ and whether it is possible to decide whetherAor Bis balder. Ghandi and Churchhill serve here as the prominent example. Who is balder? First of all, that might be a case of trivial vagueness that is accompanied by further circumstances typical for indeterminacy: tolerance meaning here that you could add or substract hairs from Churchhill without solving the question of who is balder; but also the sorites-danger we have encountered already that it leads to a paradox in applying that move too often.48Since Gandhi and Churchhill belong in terms of their hair to a particular range of applying the vague predicate ‘being bald’, it is, as Broome holds,49true that it is neither true nor false to state that one of them is balder than the other or that they are equally hairy.
To deepen that case a bit it might be helpful to recognize some differences in our predicates here. First, it is obvious that, for incomparability, we need predicates denoting non-countable elements; second, amoung these vague predicates (such as
‘tall’), some have sharp comparatives (such as ‘taller’ contrary to ‘bald’ and ‘balder than’);50third, one might analyse a predicate by referring to its properties on which that predicatesupervenes: for instance, one could hold that baldness is analysable by the amount of hairs, their distribution, their thickness. Now, these sub-features do not suffer from nonquantifiability, because amount and thickness are measur-able, and the distribution is determined insofar one stipulates a particular cluster.
However, measurement on the sub-level (amount of hair, distribution, thickness) does not bring about a measurement on the supervening level (baldness). And that move of having sub-layers is repeatable, of course.
Therefore, one might say that it is indeterminable whether Gandhi or Church-hill is balder. And this truly frustrating result might go back to two sources involved here: that being bald(er) is in this case a borderline application challenging a pre-cise comparative result including equality; and that we have, on the sub-lever, a
46 Hence, I do not distinguish further between ‘indeterminacy’ and ‘vagueness’.
47 See also Cristian Constantinescu, Vague Comparisons, in:Ratio29 (4/2016), 357-377, see 359.
48 If one hair does not make the difference, and if you repeat the substraction, you end up with the contradictive result that a completely bald guy has fine hair.
49 See John Broome, Is incommensurability vagueness?, in: Ruth Chang (ed.), Incommensurabil-ity, incomparabilIncommensurabil-ity, and practical reasoning, Cambridge/London 1997, 67-89.
50 Cf. again Constantinescu, Vague Comparisons, 365.
multidimensionality of different regards that entail precise comparatives while it still is not determinate how exactly to combine them.
Thus, the indeterminacy of the covering value challenging incomparability amounts to sub-cases: indeterminacy caused by the vague applicability of the predicate and the indeterminacy caused by the different regards of comparingA andBwithout knowing how to come to a comparative result betweenAandBin terms of a supervening regard. However, in both cases we can and we do compare, often enough by stipulation, by making the regard more concrete, by defining the relation between the sub-level and the covering value. If it is, then, still difficult to say who’s balder—Gandhi or Churchhill—we might hold that they are, in this respect, fuzzily equal.
5. Indeterminacy of (the meaning of) comparatives
Apart from the indeterminacy of the comparative regard there is also indeter-minacy possible—and widespread—concerning the items to be compared. Here, again, we have to distinguish two forms, one having to do with the application of a predicate, another one with its meaning, hence, a practical and a semantic version.
A somewhat weird but illustrative example for the first form is given in the following scenario:
“Suppose Aye measures 180 cm with the mole and 179.5 cm without it. Exactly how tall is Aye? This may be vague—the sentence ‘Aye is exactly 180 cm tall’ seems in-determinate. But the vagueness at play is not predicate vagueness: expressions of the form ‘exactly x cm tall’ are paradigmatic examples of sharp predicates. Rather, the vagueness seems to reside in the name.”51
So, the predicate ‚tall’ might itself be vague while its comparative form ‘taller than’
is not at all. Nevertheless, comparability is only possible by stipulation to solve the indeterminacy here. But speaking of incomparability in these rather simple cases might resemble a stipulative act as well.
A bit more sophisticated is the semantic form. Take, for instance, the predicate
‘virtuous’ and compare two people in this regard. Obviously, ‘virtuous’ is a vague predicate, and—contrary to ‘tall’ and ‘taller thwitan’—‘being more virtuous’ retains that vagueness. What precisely is meant here? Consider the following scenario: we attempt to determine whetherAorBis more virtuous. There are different dimen-sions that are relevant to our comparingAand B; think of the classical list of virtues such as justice, prudence, modesty, truthfullness, but also love and hope. Now, what about the cardinal virtue that is missing in this list: faith. Even among theologians it is highly debated whether we should includefideshere, not to speak of the
com-51 Cf. Constantinescu, Vague Comparisons, 363.