Value Vagueness, Zones of Incomparability, and Tragedy

American Philosophical Quarterly, April 2001, 155-176.

Comparative value judgments take the form x is better than y with respect to V, where V ranges over covering values. Such judgments are crucial, if, as many philosophers believe, practical reason tracks our ability to compare the importance of practical options. Call this the tracking thesis. According to another important thesis, the trichotomy thesis, the comparative value relations between any two value bearers are exhausted by three possibilities: one option is either better than, worse than, or equal to the other. Since the trichotomy thesis is a thesis in a debate concerning values and practical reasoning, the "better than" relation should be understood as asserting that one option is more worthy of choice than the other, the "worse than" relation that one option is less worthy of choice than the other, and the "equal to" relation that the options are equally worthy of choice. If both the tracking thesis and the trichotomy thesis are true, then all relations between value bearers are comparable in terms of some covering value, though the covering value might be different for different value bearers. The trichotomy thesis is therefore consistent with either value monism or value pluralism. Joseph Raz argues that for some value bearers it is false that one is either better than, worse than, or equal to the other. If so, he claims, incomparability exists between some value bearers. Call this the incomparability thesis. Ruth Chang argues that neither the trichotomy thesis nor the incomparability thesis is true. Rather, she argues, there is a fourth comparative relationship that can obtain between two value bearers, namely, that they are on a par. In what follows, it will be argued that the trichotomy thesis masks the existence of several value relations but that recognizing these other relations provides grounds for confirming the incomparability thesis. In each case, the source of incomparability is what will be called a zone of vagueness. The analysis promises to explain some important features of tragic choice. 

A good place to begin is with the question what might incomparability be if it does exist? The argument here is that it involves vagueness, but not in the way that current philosophers treat vagueness and value. Current debates about vagueness and incomparability treat the issue as largely an issue in the semantics and metaphysics of value. On this approach, arguments for incomparability go in one direction and those for vagueness in another, making the two kinds of arguments exclusive. Incomparability arguments claim that for some such pair of value bearers the trichotomy thesis is false, whereas, arguments from vagueness claim that for such a pair of value bearers, the trichotomy thesis is indeterminate in its truth values. Since the trichotomy thesis cannot in the same instance be both false and indeterminate in its truth values, the arguments are exclusive. Those who are metaphysically inclined on this issue then find themselves wondering what the semantic debate says about realism and value. The analysis given here is that there is another, less metaphysical way of conceptualizing the problem that combines a kind of argument from vagueness to the conclusion of incomparability without attempting to square the circle.

First, what is being asserted by the advocates of incomparability when they say that the trichotomy thesis is false and by the advocates of vagueness when they say that the trichotomy thesis is indeterminate in its truth values. The trichotomy thesis could be false without incomparability: there might be comparative relations besides the superiority, inferiority, and equality relations. If so, the trichotomy thesis is false because it does not state the full range of comparative relations that a properly revised thesis must assert. What the advocates of incomparability and vagueness assert is that no matter how the trichotomy thesis is revised and expanded in terms of the kinds of comparative value relations that might obtain, the thesis will not be true. Advocates of incomparability assert that such a thesis is not true because it is false relative to some value bearers, and advocates of vagueness assert that such a thesis is not true because it is indeterminate relative to those value bearers. The debate, then, between advocates of incomparability and advocates of vagueness does not turn on how many value relations are referred to in any proposed replacement of the trichotomy thesis. For this reason, assume for the moment that the trichotomy thesis is true just in case arguments from incomparability or vagueness fail. This is simply a way of putting some philosophical issues to the side for the time being in order to focus on others. Later the issue of the incompleteness of the trichotomy thesis can be taken up again.

For now, the task is to make sense of how incomparability could obtain because of vagueness. To perform this task, two notions of incomparability and a different notion of vagueness than the one employed by the advocates of indeterminacy will be used. The difference in this approach and the one currently reflected in the philosophical literature is that the approach in the literature frames the issue metaphysically and semantically, whereas the approach defended here frames the issue as being more empirical and psychological.

To motivate the need for such a view, suppose you believe, as the parties to this debate do, that the tracking thesis is true, that practical reason tracks comparability in the sense that an agent can make a rational decision only to the extent to which she can compare the options. Now suppose you believe that practical reason is ubiquitous, that there is no context in which if an agent deliberates properly under favorable epistemic circumstances that she cannot come to a rational choice in the sense that she has a comparative reason for doing what she does. (In some cases, this reason might be no more than that she has equally good reasons for doing one thing rather than another.) If you believe both the tracking thesis and the ubiquity thesis, you believe that rational choice is always possible because comparison is always possible. You should therefore have a view about the kinds of comparative relations that can obtain between options. The trichotomy thesis represents one such view, and we are momentarily assuming for the sake of argument that it is true unless either incomparability or semantic vagueness obtains. But suppose you believe that though the tracking thesis is true, the ubiquity thesis is false. Though more will be said about this later, the point here is that you will believe that practical reason sometimes fails because of a failure in the capacity to compare options, which is the position defended here.

What sense can be made of this?

First, there are two notions of incomparability, one semantic and the other psychological. Moreover, one explains the other. The more fundamental notion is the psychological one. Incomparabilists are right: the trichotomy thesis is false rather than true or indeterminate. So the account of vagueness as semantic indeterminacy is wrong. The crucial question is this: if the trichotomy thesis is false, what makes it false? The answer is that it is false just because in some cases rational agents cannot, even under favorable epistemic and psychological conditions, compare the value of options in a way that determines choice. Incomparability in this sense is not a semantic fact or a fact about normative language at all. It is a fact about our higher order valuing capacities. We care about things and value them in a variety of ways. We sometimes value one thing more than another; sometimes one thing less than another; and sometimes two things equally. But sometimes we value two things in a way that renders choice between them impossible. These are comments about our higher order valuing capacities, comments about our psychology. If the trichotomy thesis is true, it is true in virtue of some non-semantic fact about our higher order valuing capacities. Similarly, if it is false, it is so because of some non-semantic fact about those capacities. 

So, on the one hand, the trichotomy thesis, the ubiquity thesis, and the tracking thesis might be true because, when the higher order valuing capacities of practical reasoners fail to determine choice, this is only because of unfavorable epistemic or psychological conditions of choice. On the other hand, the tracking thesis might be true but the trichotomy thesis and the ubiquity thesis false because sometimes under favorable epistemic and psychological conditions, practical reasoners cannot determine choice. Just as the ubiquity of psychological comparability would explain the truth of the trichotomy thesis and the ubiquity thesis, the failure of psychological comparability would explain the falsity of the trichotomy thesis and the ubiquity thesis and establish the semantic point against vagueness as indeterminacy.

Before getting to the issue of vagueness as defended here, it is important to remove a source of confusion. As Chang has pointed out, there is a difference between incomparability and non-comparability. Non-comparability obtains when a covering value does not apply between two value bearers. Concepts and cookies do not compare in taste, simply because they are not both the sorts of things that can be tasted. This is non-comparability. But incomparability would have to involve a case in which the covering value applies but the value bearers cannot be compared. Incomparability in this sense just is the inability of a practical reasoner to determine choice under favorable epistemic and other psychological conditions. 

Think of love and its different forms. We sometimes love two people equally. Our children sometimes ask which we love most, and we usually have no trouble saying that we love them equally. Often this is also true about our love for our friends. But there are clear cases where we love two people unequally, and this sometimes because we love them in different ways. For example, we might love our friends but love our children more. All these are cases in which comparison is clear and unproblematic. Now consider choosing between saving the life of your spouse or the life of your child or parent. It might be very clear that you love one more than the other, but it is anything but clear that this would always be so or that you would love them equally. Most of us love for our children equally but our children more than our neighbors. But which is superior in general between our love for our children and our love for our spouses and our parents? This question is much harder to answer. If you dearly love your parents, your spouse, and your children, is it clear which you love more? Notice that life can put us in a position of having to answer this question. This means that the relation between the value bearers is not that of non-comparability. Moreover, the psychological anxiety the question generates when taken seriously presents at least a prima facie case for incomparability. Why so? Because it suggests that there are contexts in which we could not choose. If this occurs under propitious epistemic and psychological conditions, then this just is a case of incomparability in the psychological sense. It is not a case of non-comparability.

One consequence of this way of conceptualizing the matter is that the issue of incomparability should turn on evidence. And that evidence should be what our higher order valuing capacities are under favorable epistemic and psychological conditions, not on the semantics of normative language or metaphysical speculation.

Someone might worry that to have to make a choice between saving one=s child or one=s spouse would itself impose unfavorable psychological conditions. True, the worry might go, one might be unimpeded epistemicallyBone might know all the relevant facts--but the stress of the choice itself would count as an unfavorable psychological condition. 

Reflection shows that this cannot be the case. 

Not all forms of being under stress can count as a psychological encumbrance. The values that eventuate the choice are themselves such that they bring the stress. Important things are at stake. Which will it be? These are the very components of any important choice. It is only stress that blinds one to what is a stake or independent psychological factors that precede the choice situation that can count as unfavorable psychological encumbrances. The stress that is brought by the conflict of the values at stake cannot. 

Of course, other psychological forces may be at work besides stress. There may be character flaws like self-deception or weakness of will. Unlike the forms of stress that issue from the values at stake, these must count as encumbrances, the former with an epistemic dimension not found in the latter. But no one, on reflection, would want to claim that all cases of inability to decide are attributable to self-deception. To the contrary, self-deception often explains why people can decide. By blinding people to what is at stake, self-deception allows choice to proceed unproblematically where we would expect it to be problematic. 

There remains weakness of will. One might think that any person who does not suffer from a lack of relevant information, self-deception, or some other psychological condition that distorts what is a stake knows clearly how much she values one thing in regard to another and if she cannot decide she suffers from weakness of will. The difficulty is understanding why anyone would believe this. Is this supposed to be a conceptual truth? If so, what is the analysis that shows it to be? Of course, if practical reason is ubiquitous and these other conditions obtain, then she suffers from weakness of will, but whether practical reason is ubiquitous is the very issue at stake. So the only way that the ubiquity thesis could be falsified and the tracking thesis be true is for something to count against comparability. What must incomparability be? is the crucial question. The thesis here is that incomparability just is the inability to determine choice under favorable epistemic and psychological conditions. One cannot eliminate this possibility with an a priori commitment to the view that if a person cannot decide it must be because of a lack of information or a psychological encumbrance.

But what role can vagueness play? It cannot play the role assigned to it by the advocates of semantic indeterminacy. Otherwise, semantic incomparability could not obtain as the analysis here asserts that it does. The kind of vagueness that explains incomparability must explain why we cannot always, even under favorable epistemic and psychological conditions, determine choice. This will be value vagueness rather than vagueness as semantic indeterminacy. If it exists the trichotomy thesis is false as incomparabilists claim.

What kind of vagueness, then, is value vagueness?

Consider both an analogy and a disanalogy with a case involving perception. You are driving in a rainstorm that gets increasingly worse as you drive, making it more and more difficult for you to see well enough to continue. At first, but with some difficulty, you can make out what you are approaching as you drive ahead. For example, you can vaguely see a person on the side of the road, but you cannot tell whether it is a man or a woman. As the rain increases and as you continue to drive, you vaguely see something on the side of the road, but you cannot tell whether it is an animal or a person. Just a bit later you vaguely see an object but you cannot tell whether it is animate or inanimate or whether it is in the road or beside it. Finally, your vision is so impaired that you can vaguely tell where the road is and so you decide to pull over and wait for a change in the weather. 

Certainly, the vagueness in all these cases makes perfect sense; yet clearly none implies the linguistic vagueness of semantic indeterminacy. Suppose as you drove along you guessed at whether the first object was male or female, whether the second was an animal or a person, and whether the third was inanimate or animate or in the road or beside it. The guess expressions would all be straightforwardly true or false rather than indeterminate. Vagueness here is not a feature of language but of perception, a capacity of your cognitive psychology. When we are not in favorable conditions for perception, we sometimes perceive vaguely in the sense that we can determine some things about the object but not others. When the weather clears, so to speak, the vagueness evaporates with the clouds. Our perceptual capacities can then determine unproblematically beliefs about objects in the world.

With valuing, things are bit different. The similarity with the perception case is that if our ability to compare is impeded enough, we cannot choose, just as we cannot continue to drive when the rain impedes our perceptual abilities past a certain threshold. Sometimes our valuing abilities are impeded by unfavorable epistemic or psychological conditions. For example, sometimes we cannot compare one wine with another because we have not tasted one, or we have tasted both but with our palates under the influence of another powerful taste. Other times we cannot compare one wine with another because we are so preoccupied with problems that we cannot pay attention. These are cases of incomparability that are due to epistemic or psychological impediments: we cannot tell how important the options are to us because our higher order valuing capacities are not working under favorable conditions. Just as vagueness of perception is the inability to tell with enough precision what something is, vagueness of value is the inability to tell with enough precision how important something is to choice. In the cases in question, we value vaguely due to unfavorable epistemic and psychological conditions of choice, but when the conditions return to a favorable state, we can compareBwe can tell how important the options are--and make the choice. In these cases, the vagueness of value can be treated somewhat like the perception case of vaguely seeing something on the road ahead.

Now for the difference. Sometimes we value vaguely under favorable conditions. Despite the fact that we have adequate information and are not psychologically encumbered, we know that the options are important to our choice; we know why they are important to our choice; but we cannot tell how important they are to our choice. Moreover, not knowing how important two things are to choice is not so much a matter of knowing as feeling. It is simply the felt inability of one=s forms of caring about the objects of choice to resolve choice. Conversely, knowing how important two things are to choice is the felt ability of one=s forms of caring about the objects of choice to resolve choice. What one is doing in forming a practical decision is trying to resolve a problematic situation that has arisen in the context of one=s life in a way that allows one to proceed into the future. That is what practical reason is about. What makes the trichotomy thesis false is just this kind of psychological limitation on our higher order valuing capacities to resolve certain kinds of conflicts among the things we care about. The incomparability of values just is this feature of our higher order valuing capacities. 

If soBif this is what incomparability is--where does it arise among our values in a way that undermines practical reason? Four concepts will play a central role in the answer: the concept of the completeness of the trichotomy thesis, the concept of a comparison scale, the concept of comparability zones, and the concept of imprecise units of measurement.

First, the concept of completeness. There is a difference between the completeness of the trichotomy thesis and the exhaustiveness of the thesis. Those who want to defend the trichotomy thesis also want to defend both the tracking thesis and the ubiquity thesis. They believe (i) that practical reason tracks comparability, (ii) that the trichotomy thesis represents the complete set of value relations that can obtain between options, and (iii) that practical options are always comparable. If all these beliefs are true, the trichotomy thesis is not only complete in its specification of the kinds of comparative relations that can exist between options but also exhaustive in the sense that no other kind of relationBlike incomparabilityBcan exist between options. The trichotomy thesis is therefore true just in case it is both complete and exhaustive. What will be argued here is that the thesis is false because it is not exhaustive and it is not exhaustive because incomparability obtains. But there is still the issue of whether it is complete. Are there comparative relations that can exist among value bearers other than the superiority, inferiority, and equality relations?

In one sense, the answer is no. This may seem at odds with what was said earlier about the trichotomy thesis masking other important value relations, but it is not. The reason can be made clear by reference to the concept of a comparison scale.

An adequate concept of a comparison scale will have to be one in which all comparative relations relative to a kind of covering value find a place; otherwise, it is incomplete. (It will become clear that no one kind of scale applies to all kinds of covering values). According to the trichotomy thesis, all comparison scales can be graphed in terms of zones in the following preliminary way:

Preliminary Trichotomy Scale:

Superiority Zone (A is superior to B) Equality Zone (A is equal to B) Inferiority Zone (A is inferior to B) 

There are two reasons that this is preliminary: first, it leaves open the possibility that the three major zones might take different forms depending upon the kinds of values at stake, and, second, the borders between the zones are not graphically defined. Both issues are crucial. When it was said earlier that the trichotomy thesis is misleading, what was meant by the claim that it masks further important comparative relations is that the superiority, equality, and inferiority relations might take different forms. What follows will show that this is true. In the absence of a compelling reason to think that there is some other comparative relation, it will be argued that every comparative relation that can obtain among values takes some form of superiority, equality, or inferiority. There are at least two forms of each of these relations, and there may be more. But the argument here is that it is important to distinguish at least two forms of each of these relations, that as yet we lack good reasons for thinking that there are comparative relations that do not fall under these headings, and that understanding differences in these forms reveals that there is also incomparability. This amounts to a confirmation of the completeness of the trichotomy thesis.

There remains the issue of graphically defining the borders between the various zones and the exhaustiveness of the trichotomy thesis. If the trichotomy thesis is true, then there will be no cases in which there are gaps between the zones in which comparison cannot take place. If there are such gaps, they will be graphed as zones of incomparability. The argument here will be that there are such gaps and they are due to imprecise units of measurement reflected in the fact that we sometimes value vaguely in a way that prevents choice even under favorable circumstances.

Consider first the quality zone. Suppose A and B are strictly equal in terms of some covering value. What must the covering value be like, and how can we represent the comparison scale in terms of the borders between the equality zone and the superiority and inferiority zones? The answer to the first question is that the covering value must be such that it employs precise units of measurement, and the answer to the second that the borders between the zones must be non-vague to the epistemically well informed person valuing under psychologically favorable conditions of choice. Graphically, the comparison scale for two value bearers that can stand in the relation of strict equality would look like the following:

Strict Equality Comparison Scale:

A is superior to B | A is strictly equal to B| A is inferior to B

The straight vertical lines indicate non-vague borders between the zones, with the borders being clearly detectable to the epistemically informed and psychologically competent person. Something that has only monetary value fits perfectly on such a scale. 

The central thought behind the concept of strict equality is this: A and B are strictly equal just in case there is some state of A and B such that (i) any improvement in A makes A more worthy of choice than B and (ii) any diminishment in A makes A less worthy of choice than B (and vice versa). Whatever the smallest unit of difference the covering value admits of is the basic unit of measurement relative to that covering value. In American coinage, A and B are strictly equal in monetary value just in case adding a penny to A=s value would make A superior to B and subtracting a penny from A=s value would make A inferior to B. The question is whether all important covering values that yield equality relations employ precise units of measurement appropriate to a strict equality comparison scale. 

No. Some are rough. For example, imagine yourself laboring over a decision of which career to pursueBthat of a clarinetist or that of a lawyer. You have thought about this for some time, taking great pains to inform yourself of each option: what life will be like, how the choice will affect other things you care about, the probabilities of success in each career, your various talents, the relative contributions you might make, and so on. No relevant matter has been lost to your reflective consideration. Nothing suggests that your wavering is a function of some psychological malady affecting your judgment or your will. Still, the issue remains hard to resolve. A friend who sympathizes with your difficulty advises you to just flip a coin. Your extensive reflection on the matter, he urges, shows that there is no real difference between the options and that you should conclude that they are equal. Since you cannot have both, you must decide arbitrarily between them; so flip a coin and get on with your life. This strikes you as excellent advice. If after all this reflection, you cannot determine a difference between the options, they must be equal; so flipping a coin is as good a way as any to resolve the matter. Just as you are about to flip the coin another friend who happens to be a clarinetist and who overheard the advice from the other friend makes you the following offer. He will pay you as a kind of bonus $200 in real money adjusted for inflation to be spread out evenly over the career if you will decide in favor of becoming a clarinetist. Expecting each career to be thirty years before retirement, you can count on a $6.67 increase in real annual earning power from being a clarinetist than on your previous calculations. After a brief pause, all three of you break out into laughter, realizing that, of course, your second friend was only joking. Such a small improvement in one of the options would obviously not make any difference to your choice.

Examples of this sort are the basis for what philosophers have called arguments from small improvements and have been used to yield different conclusions. Some philosophers have taken arguments from small improvements to prove incomparability; others have taken them to be prove rough equality. They actually prove both.

Consider first the issue of rough equality. Relations of rough equality are best understood in contrast to relations of strict equality. Recall that A and B are strictly equal just in case there is some state of A and B such that (i) any improvement in A makes A more worthy of choice than B and (ii) any diminishment in A makes A less worthy of choice than B (and vice versa). In contrast, A and B are roughly equal just in case A and B are in a state in which (i) A and B are equally worthy of choice, and (ii) neither small improvements nor small diminishments in A would make A more or less worthy of choice than B (and vice versa), and (iii) the rational attitude toward A and B as practical options when there are these small improvements and diminishments is the same as that toward these options without them.

This notion of rough equality accurately describes the example above. If you were genuinely unable to find in full view of the facts a career as a clarinetist more or less worthy of choice than that of a lawyer, adding $200 of real income over the career as a clarinetist would make no difference to the choice. If to settle the issue you could flip a coin in the first instance, you could do so in the second. Moreover, there would be some zone of improvements in the one over the other that would make no difference to the choice. That there is such a zone establishes that there are relations of rough equality. Moreover, such relations are pervasive among our values, because few covering values yield precise measures.

Now to the issue of how arguments from small improvements and the examples that support them establish incomparability. The argument is not to the absurd conclusion that in the same instance two value bearers both stand in the relation of rough equality and are also incomparable. Rather, the argument is that in order for rough equality to be possible, so must incomparability. The way to see this is in determining how to represent the borders between the equality zone and the superiority and inferiority zones on a rough equality comparison scale. Recall that the strict equality comparison scale represents the borders between the superiority zone and the equality zone and the equality zone and the inferiority zone as clear and non-vague. This is because such a scale is appropriate to covering values that have precise units of measurement. The covering values that yield rough equality relations are not like this, however. The problem is how to reflect on the scale the difference between values that employ precise units of measurement and those that employ imprecise units of measurement. The difference will be in how the borders are represented. 

For the concept of rough equality to have application between two value bearers, there must be zones on the scale between the rough equality zone and the surrounding superior and inferior zones that are vague. Since judgments of strict equality are not possible for value bearers that stand in the relation of rough equality, there can be no sharp, non-vague boundary between the superiority zone and the rough equality zone. Nor can there be a clear non-vague boundary between the rough equality zone and the inferiority zone. How much improvement in A is sufficient to make A more worthy of choice than B or vice versa? And how much diminishment in A is sufficient to make A less worthy of choice than B or vice versa? The notion of rough equality requires that the answers to these questions are imprecise, whereas strict equality requires that they are precise. Where strict equality employs precision in unit of measurement, rough equality employs imprecision in a way that involves vagueness.

The following considerations will show how rough equality involves imprecision and vagueness.

Suppose we think of A as the career as a clarinetist and B as the career as a lawyer and that we have judged the options to be strictly equal in terms of all their contributory values save one, namely, their earning power. In this case, the covering value is value as a career and the contributory values that go into the covering value are things like intrinsic interest of the work, time consumption, consistency with non-professional interests, earning power, etc. Imagine that the career as a clarinetist is equal to that of the lawyer except in terms of earning power: the career as a clarinetist will pay $200 more over the career than the law career. According to the strict equality unit of measurement, the career as a clarinetist has 200 more units of a contributory value than that of the lawyer, but since we would not judge the career as a clarinetist to be more worthy of choice than that of the lawyer under these circumstances, the unit of measurement cannot be the same for judgments of rough equality as for judgments of strict equality. What, then, are the units of measurement for judgments of rough equality? 

Note that if we could answer this question, we could transform judgments of rough equality into judgments of strict equality. By hypothesis we know that adding $200 to the career as a clarinetist would not suffice to make it more worthy of choice than the career as a lawyer. But suppose instead of $200 $2M were added to the earning power of the music career over that of the lawyer and that all other contributory values were held constant. Surely, this would make the difference that the clarinetist career would be more worthy of choice than that of the lawyer. So there are some improvements in A that could make it more worthy of choice than B, and this is revealed in the notion of rough equality: $200 will not do, but $2M will. Now assume that there is some precise amount between $200 and $2M that tips the scale in favor of A over B, say $100K. We would then know that 100,000 units of the contributory value of earning power translate into one unit of the covering value of value as a career. We could then say precisely when the career as a clarinetist would be more worthy of choice than that of the lawyer. 

But this is not the notion of rough equality. If it were, it would not constitute a value relation distinct from strict equality. The very notion of rough equality as applied to our example requires that there is some zone between $200 and $2M where it is unclear whether a sum within that zone would be sufficient to determine the worthiness of choice of A over B. Within this zone, it will be true of A and B that A is neither more worthy of choice than B, less worthy of choice than B, strictly equally worthy of choice as B, nor roughly equally worthy of choice as B. This is the incomparability thesis with a revision that recognizes rough equality. In cases that lie within the zone of vagueness rather than within the zone of rough equality or the superiority or inferiority zones, we will not be able to make a rational practical judgment because of the vagueness of the covering value. When such vagueness does exist, we do not find ourselves clearly resorting to devices like flipping a coin or some other arbitrary decision mechanism. Rather, we find ourselves toiling over decisions, sometimes rather trivial ones, but especially over those of the magnitude of career choice. The kind of vagueness in question consists in the inability to judge precisely how difference in contributory value translates into difference in covering value. Thus, one form that vagueness of value might take and result in incomparability is where there is imprecision in regard to how to translate unit of measurement of contributory value into unit of measurement of covering value.

How do we graph the relation of rough equality on a comparison scale? The scale that graphs the choice as interpreted above is the following:

The Rough Equality Comparison Scale

A is better than B \\\vagueness\\\ A is roughly equal to B\\\ vagueness\\\ A is worse than B.

The multiple slashes represent the borders between the comparative zones as vague due to their imprecision, and the borders are thick enough to represent zones themselves. As such, they represent gaps in the scale of comparability and are, as such, incomparability zones. 

Somewhere between $200 and $2M the clarinetist career becomes superior to the law career, but there is no precise place where this happens. Moreover, the imprecision covers an indeterminate number of units of value. In moving up the scale from inferiority, there is a zone in which we can confidently say that the clarinetist career is inferior to the law career: the earning power, say, is just too low in comparison. In such a case, we value non-vaguely. Then there is a zone in which we are quite confident that there is no difference and we value non-vaguely: the earning power is exactly equal and other considerations are equal. When we are offered the $200 as a bonus for the career as a clarinetist, it makes no difference. Here despite the lack of precision, we nonetheless value non-vaguely, that is, we confidently value in a way that allows us to determine choice. So imprecision does not always result in the inability to choose. Only when it does are we valuing vaguely. There is, however, no precise place along the scale where we go from valuing A and B clearly to valuing A and B vaguely; just as there is no precise place on the scale where we go from valuing A and B equally to valuing one as superior and the other as inferior. Between the points on the scale where we value A and B equally and clearly are zones in which we value A and B vaguely because we cannot convert units of contributory value into units of covering value. 

Consequently, If we hold the other contributory values constant, we can isolate three comparability zones: (i) a zone in which the salary is clearly not enough to make the music career compare equally with the law career (some significant amount less, definitely $2M less would do); (ii) a zone in which the two salaries are clearly equal (somewhere between no difference between the salaries and more than $200 but not a large amount); and (iii) a zone in which the salary for the music career would be clearly superior (again, some large amount, definitely $2M more would do). Within these zones, we value non-vaguely because we are able to determine choice despite imprecise units of value. For these zones to have the characteristics they have, there must be areas bordering the equality zone that are vague in the relevant sense, namely, areas in which adding dollars to the salary of one of the careers neither is indifferent to choice nor determines choice; rather, it stultifies choice. These are incomparability zones along the rough equality comparison scale. They are incomparability zones due to vagueness because, even under favorable epistemic and psychological conditions of choice and within a range of value difference, we know that the options are important to our choice, we know why they are important to our choice, but we do not know how important they are to our choice. It is in this sense that the arguments from small improvements prove incomparability by way of vagueness.

The result is that anyone who endorses the tracking thesis and who admits that there are covering values that yield relations of rough equality must endorse incomparability and admit that the trichotomy thesis is false. It is hard to see a way around this. 

The opponents of incomparability could concede this and maintain that if this is all that incomparability comes to it does not come to much. The idea would be that as long as the zones of vagueness and incomparability are small, wherever they occur, the practical significance will be negligible and will not infect our capacities for practical reason. 

There are two conclusive reasons for rejecting this response. First, when vagueness occurs at this level, the issue just is whether the difference is negligible or significant. That is what cannot be resolved. If the values at stake are important values, rather than trivial ones like preferences in ice cream, this kind of inability to resolve whether the difference is significant can be maddening. The more important the values at stake, the more maddening the vagueness will be. Second, arguments from small improvements are not the only ones to reveal different value relations and different zones of vagueness. 

As long as we focus on arguments from small improvements, we will invoke only cases that support the notion of rough equality. The idea is that small improvements in one value do not add up to making a difference in worthiness of choice but moderate ones do. Indeed, this is the very form of judgments of rough equality. If neither small nor moderate improvements but only large ones make a difference, it is difficult to see in what sense the options are judged to be roughly equal. What would it be for a career as a clarinetist to be equally worthy of choice as that of a lawyer and yet it would take a large improvement of one to make it superior to that of the other? If we were willing to say that it would take a large improvement in the career as a lawyer to make it more worthy of choice than that of the clarinetist, we would not be judging them to be equal in either a rough or a strict sense. Rather, we would be judging that the career as a clarinetist is vastly more worthy of choice than a career as a lawyer.

One notion of vast superiority to be dispensed with in the argument over incomparability does not require a distinct superiority relation. $2M is vastly superior to $200 in earning power in the ordinary sense that there are vastly more units of earning power in the former sum than in the latter. This is ordinary vast superiority and is easily charted on a comparison scale that employs precise units of measurement. It is also easy to chart one kind of claim that a career as a clarinetist is vastly superior to that of a lawyer on the Rough Equality Comparison Scale. If $100K added to the career as a clarinetist will make that career roughly equal to a career as a lawyer, then adding $2M will make it vastly superior. Here the thought is that if adding superior numbers of precisely measured units of value can produce vast superiority, then adding superior numbers of imprecise units can achieve the same result. Neither of these, however, is the relevant notion of vast superiority.

The relevant notion of vast superiority is a form of a rough relation and is best understood in contrast with strict superiority. A is strictly superior to B just in case A is superior to B no matter what improvements are made in B and what diminishments in A. The stoic view of the value of virtue fits this definition. External goods like wealth, possessions, even family and friends, have the value of being preferred but not desired. No improvement in an external good can make it equal to or better than virtue. Virtue is strictly superior to any external good. Here the point is not to agree with the stoic claim but to understand the concepts it employs. Vast superiority, on the other hand, (of the relevant sort) is a rough relation in which there are improvements in B or diminishments in A that would make B superior to A but the improvements or diminishments must be very large to undermine the superiority of A over B. Mill=s claim that the intellectual and moral pleasures are superior to the physical pleasures seems to take this form. It is better to be Socrates dissatisfied than a fool satisfied, but only if Socrates is not starving. Some level of physical dissatisfaction will make the intellectual and moral life less valuable than the life of physical comfort. Though the intellectual and moral life is not strictly superior to the life of physical pleasure, it is vastly superior. The idea is that as long as some threshold level of physical comfort is secured, no amount of added physical pleasures will make a life without intellectual and moral pleasures equal to or superior to a life that contains a certain threshold of physical comfort and the intellectual and moral pleasures. Again, the point here is not to agree or disagree with Mill but to understand the concepts employed in the kind of comparison he was trying to make.

Both strict and vast superiority differ from ordinary superiority in that the first two relations mark out a difference in kind, whereas the latter only in degree. What is distinctive about both strict and vast superiority is that when either value relation is an appropriate form of comparison between two value bearers, the relations of either strict or rough equality cannot apply to the relation between those value bearers. This is what makes both strict and vast superiority relations distinct from ordinary superiority. Where ordinary superiority and ordinary inferiority are buffered, either by strict equality or by rough equality and zones of vagueness, strict superiority is bordered only by strict inferiority. No buffer zone of any sort exists between them. If A is strictly superior to B, then there is no context in which A is either strictly or roughly equal to B, nor is there any context in which it is vague as to whether A is superior to B. On the other hand, if A is vastly superior to B, while no small improvement in B or diminishment in A would make B either strictly or roughly equal to A, there is a zone of vagueness and incomparability. That zone is reflected in the imprecision of how much of a large improvement in B or diminishment in A will make B superior to A. There is then a buffer zone between vast superiority and vast inferiority, but that zone is not one of either strict or rough equality but of vagueness, a zone of incomparability, a zone in which the practical reasoner cannot tell how important the options are in a way that determines choice.

Like strict and rough equality, strict and vast superiority are distinguished by their precise and imprecise units of measurement. Because rough equality requires moderate improvements to make an improvement significant enough to render one option better than the other, there is a zone of vagueness and incomparability between small and moderate. With vast superiority, the zone of vagueness is located not between small and moderate but between large and very large. Within this zone, there is vagueness and incomparability, a zone in which A is neither more worthy of choice, less worthy of choice, strictly equally worthy of choice, nor roughly equally worthy of choice as B.

How do we graph these scales? 

It is clear that the scale for two value bearers where one value bearer is strictly superior to the other should be graphed as follows:

Strict Vast Superiority Comparison Scale:

A is better than B and B is worse than A.

But how are we to graph the scale of vast superiority? The answer is the following:

Vast Superiority Comparison Scale:

A is better than B\\\ VAGUENESS\\\ A is worse than B.

For this to work, the zone of vagueness must be construed as involving a border of only large, more than modest improvements in B, which is why vagueness is in capital letters. Because only large improvements in B over A can reverse the superiority relationship between A and B, there can be no zone of either strict or rough equality between value bearers that stand in the relationship of vast superiority.

Now, if there are cases of vagueness of this sort, they will be far more difficult for practical reason than cases of vagueness involved in rough equality. The reason is that if rough equality can exist between two conflicting value bearers of different kinds and we find ourselves trapped within a zone of vagueness at one of its borders, we have at least the thought that at most moderate differences in values are to be lost, no matter what our decision. If important values are at stake, this itself is no small matter. On the other hand, if vast superiority can exist between two conflicting value bearers and we find ourselves trapped within a zone of vagueness at its border, we know that the losses are going to be great rather than moderate or small, no matter what we decide. As long as we are clear that we are within the zone of vast superiority, we can give as a reason for incurring the loss of one kind of value the vast superiority of the other. But within the zone of vagueness, we cannot have this sort of reason for incurring the loss of one kind of value. When trapped within a zone of vagueness of this sort, we cannot give as a reason for selecting one option over the other a comparison of the options. And when the losses, either way, in terms of conflicting values are great, we are faced with a tragic choice of the most pressing sort. This is the grief of reason at it worst.

Note that when choice is between conflicting values that can be successfully compared and one is found to be strictly equal to the other, there is still going to be loss. This is what monism has trouble accounting for. But in these cases, even when we decide randomly for one of the options, we have the consoling thought that what was lost was equal to what was saved in terms of some covering value. And when it is clear that one option is vastly superior to the other, there is still loss, but we have the consoling thought that what was lost was not nearly so great as what was saved. Neither of these consoling thoughts is available within the kind of zone of vagueness under consideration.

Does practical reason ever face decision contexts of this sort? 

Suppose you must decide between favoring a dear friend or an esteemed stranger regarding some scarce resource. Without food, let us say, the friend or the esteemed stranger will not survive. Now assume that all factors are equal except for the difference in the character of your friend and the stranger. That is, assume that your friend and the stranger have the same health profile, that they are equally likely to survive with the food or to die without it, that they are both equally likely to make contributions to the world, and so on, but that there is a difference in their character. On any plausible view of the role of friendship in a loving and respectful life, friendship allows some favoritism toward a friend over an equally worthy stranger. All this is just to point out that love does not distribute itself in a way that is proportionate to perceived merit and that we admire and approve of friendships that involve some degree of favoritism. Anyone who would view the options as strictly equal in worthiness for choice when both the friend and the stranger were equal in all respects, even in regard to character, would not be a loving friend. To deny this is simply not to understand friendship.

But are there any improvements in the stranger=s character or diminishments in the friend=s character that could reverse the choice-worthiness of the options? To answer negatively is to endorse friendship as strictly superior to respect for persons and their character. This is not at all plausible. 

Consider what Ruth Chang calls nominal-notable comparisons. Nominal-notable comparisons establish at least two things: first, comparisons are often possible between items that seem incomparable at first and, second, there are covering values that do not have names (which makes them seem almost invisible in our practical deliberations). Regarding the first point: consider the difficulty involved in comparing two artists who work in different art forms. Who was the most creative artistically, Mozart or Michelangelo? One might conclude from the difficulty of making such an assessment that composers and painters are incomparable in regard to the covering value of artistic creativity. But surely this is false, at least at some level. Consider the comparison between Michelangelo and Average Joe Painter. Michelangelo is a notable painter, and Average Joe a nominal one. When compared in regard to creativity as an artist, Michelangelo is clearly better than Average Joe. But what about Mozart and Average Joe in regard to artistic creativity? If we assume that painting is Average Joe=s only artistic endeavor, surely we still want to say that Mozart is better in terms of artistic creativity than Average Joe, despite the fact that they work in different art forms. So what looked impossible at first turns out not to be. It may still be true that we cannot fine-tune a comparison between Mozart and Michelangelo in terms of artistic creativity, but it will not be for the general reason that incomparability prevents comparisons across art forms. A nominal-notable comparison has disabused us of that notion.

It does not follow from this, however, that covering values always allow us to compare. Why? Because vagueness might exist along the scale of the comparison. This is clear in the case of friendship and respect for persons. Suppose the friend is a nominal friend and the other person is a notable stranger. Perhaps the friend and the stranger have grown in opposite directions in regard to their character to the point to which the friend is due significantly less respect than the stranger. This could be a result of both a diminishment in the friend=s character and improvements in the stranger=s. Surely, even where you still love your friend, there is some widening of the gap that would make it clear that favoring the stranger would be more worthy of choice than favoring the friend. Imagine that your friend who had once been a reasonably respectful and sympathetic person and loyal in his personal relationships had over time changed into a person who was quite disrespectful and calloused and noticeably neglectful within his personal relationships. You still love him but are no longer able to respect him as you once did. In fact, you have now quite had it with him in many ways. You now see him as very nearly no friend at all and believe him to be incorrigible in his vices, yet you still love him and are committed to him to some degree. The stranger, on the other hand, has become one of the most notable people of whom you are aware. Though you do not stand in any loyalty relationship with him, you admire the deep loyalties he has with his loved ones, his commitment to justice and the relief of human suffering, as well as his commitment to excellence. Indeed, he is now a person who strikes you with a kind of moral awe. And now it is his life or your friend=s.

So construed, the choice situation now reveals that there is a great deal of room between what we might call entry level respect for a person and moral awe. In between is room for vagueness about the practical significance of these degrees, especially when weighed off against the value of those we love. But notice the difficulty in imagining a point at which flipping a coin would make any difference. As we move along the scale of comparison, there seem to be only points that favor the friend, the stranger, or leave one confused about whom to favor. Flipping a coin is simply out of the question. If the friendship example does not bring this point into focus, simply imagine a similar choice of a loving mother in regard to her nominal child and some such notable stranger. What imaginable context could make sense of her willingness to flip a coin? Yet it is not difficult to imagine confusion and indecision in some context, even where she is adequately informed.

There is also another way in which vagueness can show up, not in regard to degree of improvement in one person=s character over that of another, but in terms of the numbers of people who might have to be sacrificed or hurt in some deep way in order to accommodate the kind of favoritism that love involves. What is crucial here is that some forms of favoritism involve the notion of disproportionate sacrifice, a sacrifice of the many for the few. Many philosophers believe that such sacrifices are either irrational or only rational because of their indirect relationship to a relevant covering value, usually thought to be social utility. The argument here, however, is that disproportionate sacrifices are sometimes rational and when they are they are rational because of direct comparisons that yield judgments of vast superiority. Failure to recognize this value relation has led many philosophers to assume that indirection must be the rationale for cases of justifiable disproportionate sacrifice.

Can we compare the importance of one of our loved ones to the importance of others we respect but do not love when we judge our friends and these others individually as equally worthy of respect? From the perspective of respect alone, the friend is, let us assume, equal in worth as any other individual person. So if we take respect alone as the covering value for a choice in a situation involving decisions about the extent of sacrifice to be made by some for the sake of others, it is difficult to see how to make the choice in anything other than a maximizing way. Where everything else is equal, we have no way from the covering value of respect alone to favor a smaller number by requiring a disproportionate sacrifice. But friendship does involve the recognition of contexts in which disproportionate sacrifices, sacrifices that favor the few over the many, are in order. Assuming that we think some degree of such favoritism is justified, what are the grounds for the justification?

Advocates of the trichotomy thesis even with revisions that recognize strict and rough equality are limited in possible justifications for disproportionate sacrifice. If the justification is to be made in terms of direct comparisons, the only hope they seem to have is to appeal to judgments of rough equality. But that will not do, because value bearers that are roughly equal are to be treated just like those that are strictly equal, which means that judgments of rough equality could never justify disproportionate sacrifice. Since neither ordinary superiority or ordinary inferiority could directly justify disproportionate sacrifice, it is impossible to represent the reasoning behind such sacrifices as a direct comparative judgment. One is left, then, with thinking that they must either be irrational or indirectly justified. But this dilemma is forced on us only if no other comparative relation besides ordinary superiority and inferiority and strict and rough equality are possible. This is false. It is also false that strict superiority and inferiority will complete the list. Vast superiority is also a possibility (and there may be others). Failure to recognize that friends are taken by a person who is both a loving friend and a respectful person to be vastly more important than equally respectable strangers has led many to distort the place of friendship in our practical deliberations. Not only could there be a comparative relation that would directly justify disproportionate sacrifice, we actually make judgments that employ appeal to such a value relation. Nominal-notable comparisons prove this, as will be clear in what follows.

What, then, has been the misleading factor that has prevented many from seeing this? It might be the fact that the covering value is nameless. But something akin to a nominal-notable comparison reveals that there is a covering value. Suppose the choice involves saving one dear friend at the expense of one other equally respectable stranger and everything else is equal. Saving one=s friend does not involve a disproportionate sacrifice, a sacrifice of the many for the few. But what number of equally respectable strangers can be reasonably sacrificed for the sake of a dear friend? If we take choice situations involving one dear friend as a case of a nominal number of friends, we can represent a nominal-notable comparison as one in which there is some notable number of respectable strangers that would shift the priorities in favor of the strangers over the lone friend. Only those who endorse friendship as strictly more important than respect for others would think that any nominal-notable comparison would fail. Most of us do not believe this but that some disproportionate sacrifices are unjustified. Why? Because we do not believe that our friends are strictly more important than other people we respect but do not love. This is even true for some of us who believe that some disproportionate sacrifice for the sake of our friends is in order.

The fact that we can make such a nominal-notable comparison shows both that our judgments in these cases are comparative judgments and that there is a covering value. Since it does not have a name, what is it? When we say that our friends are Amore important than@ the respectable strangers, we are not employing either respect or love as the covering value. If we restricted our decision to friendship without consideration of the respectability of the strangers, we would always favor our friends, and we do not believe this. On the other hand, if we restricted our decision to considerations of respect, we would never find a reason directly justifying a disproportionate sacrifice. But the nominal-notable comparison shows that we do make comparisons between these kinds of value bearers. So there must be a covering value. We can make sense of Athe more important" relation in question by construing the relation as one of vast superiority in terms of the covering value of a meaningful life. For persons who are both loving friends and respectful persons, friends are vastly more important than respectable strangers in the overall meaning that both provide in the direction of their lives.

This explains why we struggle so much in trying to decide how much disproportionate sacrifice to tolerate for the sake of our friends. The truth is that within the psychology of a person who cares for others in two ways--she both loves her friends and respects others she does not love--the comparative value of friends and respectable others is at some point vague, and the vagueness is ineliminable. As we are forced by the conditions of choice to compare the relative importance of our friends and others we respect in the overall place they have in our lives, we are either clearly in a zone of vast superiority or vast inferiority, or we are in a zone of vagueness. When we are in the latter, we are in a zone of practical indeterminacy in which neither the love we have for our friends nor the respect we have for others is either more, less, or equally meaningful in the direction each provides to our lives. When we find ourselves within this zone of vagueness, we are trapped in a tragic situation of the worst sort, which is why we are crushed by it. These are cases in which we know that both our friends and respectable strangers are important to our choice; we know why they are important to our choice; but we do not know how important they are to our choice.

What we should realize is that failure to recognize vast superiority as a distinct superiority relation makes it very difficult to account for one of the most tragic dimensions of life. Lying between vast superiority and vast inferiority is a wasteland that some conceptual schemes render invisible. This is a decisive argument against these schemes, for tragedy unrecognized is all the more tragic for its concealment.

In her debate with the strict trichotomists who do not even recognize relations of rough equality, Ruth Chang takes them to task for not taking the phenomenology of our experience seriously. Our experience is in error or is misleading they say, revealing that their commitment to the trichotomy thesis is stronger than the allure of their experience backed by an alternative conceptual model. She says,

The strict trichotomist commits us to an error theory about our judgments. But the phenomenology is in tension with the theory; the greater occurrence of such judgments and the more widespread the thought that they are rational, the less reason there is to think that the judgments are in error. And it cannot be denied the phenomenology is very common.

The phenomenology Chang is referring to is our experience regarding rough equality. But our experience of the rationality of some forms of disproportionate sacrifice and our experience of some forms of tragedy are at least as strong as our experience of the rationality of rough equality. We should therefore apply Chang=s advice of giving priority to the conceptual scheme that better accounts for the phenomenology to the issue of whether vast superiority is a distinct superiority relation. We will then recognize vast superiority, because it accounts well for disproportionate sacrifice. In so doing, we will recognize the incomparability that comes with the vast superiority comparison scale, because the vagueness along that scale accounts well for some important forms of tragedy.

To conclude, consider two worries that might serve as a basis for eliminating incomparability. The first might appeal to a proposal by T.K Seung and Daniel Bonevac. Seung and Bonevac have defended a notion of indeterminacy that might be thought better suited to do the work that vagueness does in the present analysis. The notion of indeterminacy they defend is captured in the idea of an indeterminate ranking. For them, an indeterminate ranking applies where there is no covering value. Even if A and B cannot be compared by appeal to a covering value, they might nonetheless be ranked, according to Seung and Bonevac. Unlike Chang, these authors seem to take the need for recourse to a lexical ranking as evidence that there is no covering value that can rationalize the ranking. For the sake of argument, assume that this is sometimes true. In some cases, where there is no covering value, the rankings will be determinate; in others, the rankings will be indeterminate. Of indeterminate rankings, the authors say:

The ranking of A and B is indeterminate just in case it is reasonable to conclude that A is better than B, that A is worse than B, and that A and B are of equal value.

Though this sounds paradoxical, the idea is that where there is no covering value in terms of which items can be compared overall there might nonetheless be other values in play that produce alternate rankings. The creativity of the music career might provide a reason for ranking the music career over that of the legal one. The earning power of the legal career might provide a reason for thinking of the music career as inferior to the career in law. And the compatibility of the two careers with the value of community life might provide a reason for ranking them equally. If this is the case and there is no covering value that allows one to compare the importance of all these values to overall choice, then the overall ranking will be a conjunction of the rankings from the perspective of each of the values in play. When we conjoin these in the case under consideration, we get an overall ranking that is indeterminate in Seung and Bonevac=s sense. The conjunction of these values and their rankings gives us as a reason for favoring A over B the ways in which A is better than B, and as a reason for favoring B over A the ways in which A is inferior to B, and as a reason for arbitrarily favoring one over the other the ways in which they are equal. Now take the original conditions of choice between the career as a clarinetist and the career as a lawyer. Whatever we decide, we need not appeal to the notion of incomparability to explain the choice. If we decide to favor the career as a clarinetist, we can have as our reason the ways in it is superior to the legal career. If we decide in favor of the legal career, we can have as our reason the ways in which it is superior to the career in music. And if we decide to flip a coin and arbitrarily favor one career over the other, we can have as our reason the ways in which the careers are equal. Indeterminate rankings, then, provide us with reasons in contexts in which there are no covering values and in which whatever we do we can have reasons for doing it.

Whether this is a good analysis of the career choice is itself doubtful, but this is not the point that will be pushed here against taking Seung and Bonevac=s proposal as the basis for an eliminativist strategy against incomparability. To serve in this way, their proposal would require appeal to contexts in which we are able to choose. The appeal here is to cases in which we are not. What explains the stultification of practical reason? What explains tragic situations in which practical reason cannot proceed? If Seung and Bonevac=s analysis provided us with grounds for eliminating incomparability, then we would never be in a position in which we could not have as a consoling reason that A is better than B, or that A is worse than B, or that A is just as good but no better than B. But we are sometimes in a position in which we do not have such consoling reasons, which is revealed by the phenomenology of some experiences of tragedy. On the other hand, the analysis given here in terms of vagueness and incomparability accounts both for those cases in which we can have such consoling reasons and those in which we cannot. Nor do indeterminate rankings account well for disproportionate sacrifice. Those believing that disproportionate sacrifice is justified on the grounds of the vast superiority of one good over another do not believe that they also have reasons that would justify a reverse ordering of their priorities if only they chose that option. When we are fretting over whether such a sacrifice is in order, we might very well recognize that there are different reasons for different courses of action, but we are not fretting over which of several justifying reasons to act upon. It is the fact that they cannot each be justifying that explains the fretting.

The second concluding consideration that might provide a basis for eliminating incomparability is that the vagueness is an epistemic consideration and that this undermines the analysis. The thought is that the kind of practical inability to choose in the tragic circumstances central to this account is a function of some form of ignorance. If we knew enough, the objection goes, the phenomena at the heart of the analysis here would disappear. Those who believe in God, for example, might believe that God does not suffer from the maladies alluded to here. Perhaps it is because he is omniscient in regard to facts and values. 

It is hard to se the appeal of this view. You might know exactly how many lives of other people saving the life of your friend might cost, yet you might not be able to decide. If your inability to choose is not a function of weakness of will, what is the form of ignorance that applies? What fact or value of which you are ignorant is such that the relevant knowledge would remove the indecision? The reason God can always choose is not just that he is omniscient but that he cares only along one dimension, that is, he allegedly loves us all and equally so. If so, he does not have indeterminate rankings, but the reason for this is not his lack of ignorance but the manner of his caring. God does not have friends. He does not care for people in that way. For this reason he does not have to compare the value of his friends to the value of those he respects in order to make his practical decisions. But we do. Nor does God make comparisons of rough equality or vast superiority. But again, this is not because of his lack of ignorance but because of the manner of his caring. Caring like God allegedly does is what exempts him from the vagueness we experience, but as long as we care in the ways that we do--in the myriad ways that we do--we will remain vulnerable to tragedy. No increase in knowledge will change this; only a change in values and forms of caring. Of course, what is said here of God can be said for any attempt to construct an ideal conception of practical rationality in which all rankings are determinate and fully comparable. We can get such rankings, but we will have to make the ideal practical reasoner care in ways much different than we do. As we make him more sophisticated in his web of knowledge, we will have to simplify his forms of caring, rendering him far different from ourselves. Some will see in this an argument against this account and a recommendation that we become more ideal and Godlike; others will find in it an account of what is best in us and a reason either for thinking without God or thinking of God in other ways. For those in the latter group these considerations provide a strong argument against eliminativist strategies that have incomparability as their target.
 

Endnotes

1.See Ruth Chang, "Introduction," in Incommensurability, Incomparability, and Practical Reason, ed. Ruth Chang (Cambridge, Massachusetts: Harvard University Press, 1997), 5.

2.See Joseph Raz, "Incommensurability and Agency," in Incommensurability, Incomparability, and Practical Reason, ed. Ruth Chang (Cambridge, Massachusetts: Harvard University Press, 1997), 110-28 and The Morality of Freedom (Oxford: Clarendon Press, 1986), 321-68.

3.See Chang, "Introduction," 26, 27.

4. Joseph Raz is perhaps the leading advocate of this kind of argument. See his The Morality and Freedom, (London: Oxford University Press: 1986) and his AIncommensurability and Agency,@ in Incommensurability, Incomparability, and Practical Reason, 90-109.

5.John Broome is the leading advocate of the argument from vagueness. See his AIs Incommensurability Vagueness?,@ in Incommensurability, Incomparability, and Practical Reason, 67-89. See also his book, Weighing Goods, (Oxford: Basil Blackwell 1991) for further discussion of incommensurability.

6. Ruth Chang wants to defend the notion of parity, which she says is a comparative relation distinct from the usual three. See Chang, AIntroduction,@ 23-27. She defends this further in an as yet unpublished paper, ABeyond >Better Than,=>Worse Than,= and >Equally Good.'"

7. See Chang, AIntroduction,@ 27-34.

8. This is an embellishment of an example by Joseph Raz. See The Morality of Freedom, 332.

9. This assumes that the diminishments do not reach the point of destroying A as what it is.

10. One might worry that there are other relations akin to vast superiority but still not the same. Whether this is true is not clear. But the argument presented here does not turn on whether there are additional forms of rough relations, vast or otherwise. The point is that there is this kind of relation and this has important implications for some aspects of practical reason.

11. See Chang, "Introduction," 14-16 and 30-34.

12. Donald Regan believes in complete comparability and argues even against rough equality. He raises some difficulties for Raz=s analysis and the role that Raz assigns to the will in practical reason. But an argument for complete comparability could not assume that the success of nominal-notable comparisons insures completeness of comparability. The possibility of vagueness prevents such an inference. See Donald Regan, "Value, Comparability, and Choice," in Incommensurability, Incomparability, and Practical Reason, ed. Ruth Chang (Cambridge, Massachusetts: Harvard University Press, 1997), 129-50. It is also important to note that Regan is right to think of rough equality as a threat to complete comparability. Though Chang thinks she can have parity in her sense without incomparability, if the account here is correct, vagueness prevents the one without the other.

13. Certainly there are contexts in which respect prevents maximization strategies. There is no denying this. What can be denied is that respect can avoid maximization in some contexts. If you have equal respect for the agency of ten people and face a decision in which you can preserve the agency of nine by distributing scarce resources in one way and save only one by distributing them in another and everything else is equal, then you are left with nothing but a maximizing strategy to make sense of your values. For a discussion of how respect might require maximization, see David Cummiskey, Kantian Consequentialism (New York: Oxford University Press, 1996).

14. For a discussion of how the meaning of one=s life from one=s own point of view factors into practical reason, see my Agent-Centered Morality: An Aristotelian Alternative to Kantian Internalism (Berkeley: University of California Press, 1999).

15. Ted Kazinski was the famous letter bomber responsible for a rein of terror in the United States. He killed and wounded several people by mailing them letter-bombs. One can only wonder what his brother went through in coming to the decision to turn him into the authorities. Though this is a case of a family relationship rather than a friendship, the same kind of point applies. Also, for a discussion of how choice sometimes renders us vulnerable, see myDignity and Vulnerability: Strength and Quality of Character (Berkeley: University of California Press, 1997).

16. Some will object that certainly we do sometimes judge our friends and respectable strangers to be equal in regard to choice and that this undermines what has been said. Of course, we do sometimes make such judgments but not in terms of the covering value in question. When determining what the law should be, we often judge our friends and family to be equal to anyone else. But in the overall importance to the direction of our lives, we do not.

17. One of the best accounts of the role of incommensurability in accounting for tragedy is found in Henry Richardson=s work. However, even that account fails, at least for some forms of tragedy. Richardson believes, that incomparability is not necessary, only the kind of incommensurability defended by Stocker, namely, that values are plural and conflicting and cannot be commensurated along a single dimension. If the account here is right, vagueness, which brings incomparability with it, plays a role as well. Further work in progress develops an account of vagueness and its role in tragedy. See Henry S. Richardson, Practical Reasoning About Final Ends (Cambridge: Cambridge University Press, 1997) and my book manuscript in progress AReason=s Grief: An Essay on Tragedy and Value."

18. Chang, AIntroduction,@ 25.

19. T. K. Seung and Daniel Bonevac, "Plural Values and Indeterminate Rankings,"Ethics 102 (July 1992): 799-813. Seung and Bonevac do not themselves argue for the elimination of incomparability, but others might find grounds in what these authors say for an elimination strategy.

20. Seung and Bonevac, "Plural Values and Indeterminate Rankings," 802.

21. I would like to thank Douglas Browning, Ruth Chang, Paul Davies, Tom Seung, Laurence Thomas, and an anonymous referee for American Philosophical Quarterly either for comments on earlier drafts or for discussion of some of the ideas contained here.