Value and Parity

Value and Parity*

Joshua Gert

“Value and Parity,” Ethics, Vol. 114, No. 3 (2004), pp. 492-510. Please cite published version.

In “The Possibility of Parity,” Ruth Chang argues for the existence of a fourth value

relation, which she calls ‘parity’.1 The three traditional value relations are ‘better than’, ‘worse

than’, and ‘equal to’. In saying of one thing that it stands in one of these relations to a second

thing, one is making a positive assertion about the value relations between the two: one is not

merely denying that such a relation holds, as one would be doing if one merely said that A is not

better than B. In this sense, the three traditional value relations are positive value relations.2 An

assertion of parity between two items is not merely the denial that one or more of these

traditional relations obtain; in this sense parity is also a positive value relation. This paper agrees

with much of what Chang has to say, especially when she argues against a number of alternative

interpretations of the cases that she takes to support the existence of parity. Nevertheless, it is the

purpose of this paper to offer its own interpretation of the cases she makes use of. The suggested

interpretation is consistent with virtually all of Chang’s claims about the particular cases, but it

does not require us to posit a fourth positive value relation that has so far evaded the explicit

conceptual or linguistic notice of a species so prone to making comparisons.

The raw material out of which Chang constructs her arguments for the existence of parity

is primarily to be found in cases in which we are reluctant to say, of two items being compared in

a certain evaluative respect, that one is better than the other, or that they are equally good.

Following Chang, let us call these ‘hard cases’. Of course the mere existence of hard cases does

very little by itself to support the idea of a fourth positive value relation. Chang describes three

other possible interpretations of such cases: (a) one of the two items really is better, or they are

equally good, but we just don’t know it, (b) such cases represent failures of comparability, so that

no positive value relation whatever holds between the two items (this is what many philosophers

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mean by calling such items ‘incommensurable’ or ‘incomparable’) and (c) such cases represent

instances in which the vagueness of ‘better than’ and ‘equally good’ explains why there is no fact

of the matter whether one of the items is better than the other, even though it is also not true that

they are equally good. I will not discuss Chang’s remarks about (a) through (c), for even if she is

right in holding that they cannot account for all hard cases, this paper will argue that we do not

need a fourth positive value relation to account for them. I agree with Chang that each of these

three alternative interpretations assumes what she calls ‘the trichotomy thesis’. The trichotomy

thesis holds that if two items are comparable, it is because one of the items is better than the

other, or because they are equally good. In Chang’s terminology, the thesis holds that “the

conceptual space of comparability between two items is spanned by the trichotomy of relations

‘better than’, ‘worse than’, and ‘equally good’.”3 This paper will defend the trichotomy thesis, at

least in one important sense: it will hold that any other positive value relations that we might

wish to make use of can be defined in terms of the three traditional relations.4 Thus it will not

exactly deny the possibility of parity, if parity is understood in a certain derivative way. But

Chang’s idea seems to be that parity is a fourth value relation of the same sort as the three

traditional value relations.5 This is the idea that will be challenged.

The central piece of conceptual apparatus that will be exploited in this paper is the

distinction between the choices that a person is disposed to make, and the choices that a person is

disposed to regard as rationally permissible. The former may plausibly be taken to reveal a

person’s preferences, but a person’s valuations are more plausibly taken to be revealed by the

latter. That is, preference and valuation are not the same thing, and preference is most closely

related to choice, while valuation is more closely related to the assessment of choice. For

example, when faced with a choice between two items, and asked to choose between them (not:

to assess their relative value) based on beauty, talent, or something of that sort, it might be that I

would choose one item, but that I can see that the opposite choice might also have been made by

someone else without either of us failing to appreciate the “true value” of each item. Moreover, I

can often see that this might continue to be true even if the item I chose were improved to some

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degree. For on this picture of human choice and valuation, our valuations of two items are not

given by our dispositions to choose, but by our dispositions either to understand or to be puzzled

by certain choices: to regard them as rational or irrational, mistaken or not mistaken.6 Our

valuation of an item may, but need not be, interpreted as a belief. But however a valuation is

interpreted, it can be expressed by claims regarding the rationality of certain choices. This

interpretation of ‘valuation’ will form the basis for an explanation of all of the intuitions Chang

cites in favor of the possibility of parity.

The above distinction between preference and valuation allows for an easy explanation of

the following common phenomenon: often we claim that while we would prefer A over B if we

were choosing based on value V, this does not mean that we regard A as superior to B in respect

of that value. If one has linked preference to valuation too closely, one may wonder how

someone could prefer A to B – that is, not simply opt for A on a random basis – without

regarding A as superior to B, at least if that person were rational. But this worry will seem

theoretically motivated once one (a) distinguishes preference from valuation, (b) acknowledges

the plausibility of the idea that our valuations reflect our views regarding the rationality of

preference, and (c) notes that only very rarely do we think of our particular personal preferences

as the uniquely rational ones.7 This view of preference and value allows that two people in the

same epistemic situation, who have the same perfectly precise standards for assessing the value

of items with respect to V, and who take the same interest in whether or not something has value

V, could make different, but equally rational choices between two items, when the relevant value

is value V. It is the purpose of this paper to explain and defend this view of preference and

valuation.

It may initially seem that in refocusing the discussion from judgments of relative value to

judgments of the rational permissibility of choice, this paper has changed the subject. But, as

Chang acknowledges, the whole practical import of the discussion of incomparability – and

therefore of parity, which is Chang’s tool for arguing against incomparability – lies in its

implications for rationally justified choice. Chang first introduced us to the notion of parity in

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Incommensurability, Incomparability, and Practical Reason. There, after an isolated remark to

the effect that incomparability may have interesting implications for some unspecified

metaphysical questions about value, her six subsequent pages of discussion of the significance of

the topic are cast entirely in terms of justified choice.8 Moreover, Chang’s discussion makes it

clear that almost all the contributors to that volume share the same view of the extremely tight

connection between value and practical reason.9 And despite the fact that the comparison

between Mozart and Michelangelo, which plays such a large role in “The Possibility of Parity,”

may not seem to be a practical one, it is notable that the vast majority of the other illustrative

examples in Incommensurability, Incomparability, and Practical Reason and “The Possibility of

Parity” are examples of choice situations. On reflection, this should not be a surprise. The idea

that there could be value “out there,” independent of practical human questions is a very

suspicious one. And there does seem to be an analytic tie between value judgments and the

rationality of choice: if one is comparing items in terms of what Chang calls a ‘covering value’

such as philosophical talent – and Chang holds that all comparisons must take place relative to

some such value – then if one makes certain comparisons, one is rationally committed to making

certain corresponding choices.

Of course, the fact that value comparisons have implications for justified choice is

compatible with the idea that the scope of the value relations, including parity, is much wider

than the scope of our possible practical choices. Thus, we might discuss the relative merits of

Mozart and Michelangelo without suggesting anything about the justification of certain choices.

But given that virtually the whole discussion of the significance of comparability, and therefore

of parity, is given in terms of justified choice, it does not seem that this difference in scope could

be very great. Moreover, we can make an even stronger claim. Chang strongly suggests that the

limits of applicability of the comparable/incomparable distinction, and therefore the limits of

applicability of her notion of parity, coincide exactly with the limits of possible practical choice.

She writes:

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Even if there is never a failure of applicability [of value terms, so that one can sensibly

ask ‘How philosophically talented is the number five?’ and so can also sensibly compare

its level of talent with Wittgenstein’s], we would still want to make a distinction between

cases that practical reason might present to us and ones beyond its scope. So we have an

equivalent distinction, not made in terms of applicability and nonapplicability.10

It is clear that Chang does not see the notion of parity as sensibly applied to a pair of items unless

practical reason might actually be faced with a choice between them.

Chang’s Argument

Chang’s argument for the possibility of parity starts by drawing attention to the existence

of cases in which two items are not related by any of the three traditional value relations. For

example, suppose you are called upon to judge which of two items of clothing are more elegant:

say, some instance of Victorian ballroom dress, and a costume worn in eleventh-century Japan by

members of the imperial court. You are unwilling to say of either item that it is more elegant

than the other. So far that is consistent with their being equally elegant. But suppose now that

you would be willing to say that a certain alteration in the width of the silk belt in the Japanese

costume would increase its elegance. The alteration is made, and now you are asked the original

question again: which is more elegant, the Victorian ballroom dress, or the improved Japanese

court outfit? It may well be that you would still be unwilling to say that the improved Japanese

outfit is more elegant than the Victorian dress: their elegance is simply too different to allow

such a claim. If that is the case then it seems that we should not say that the two original items of

clothing were equally elegant. After all, if they had been, then the improvement in the elegance

of one should have made it the more elegant item. So none of the three traditional value relations

seems to have held between the two original items of clothing. If this particular case is not

convincing, Chang offers others, and cites many authors who offer still others.11 In any case,

Chang herself agrees that there are examples of this sort that do show that there can be pairs of

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items that are not related by any of the traditional three value relations. Doubting readers should

therefore grant this point for the sake of the debate.

So far this argument, which Chang calls “the small-improvement argument,” only

succeeds in showing that there can be pairs of items, neither of which are better with respect to

some value, even though they are also not equally good with respect to that value. What Chang

needs to do is to argue that not all of these cases are cases of incommensurability: cases in which

no positive value relation holds between the items. She attempts to do this with an argument she

calls “the unidimensional chaining argument,” which runs as follows. Suppose we have two

items that are not related by any of the three traditional value relations, when compared with

respect to a certain value. Let us say that the items are Michelangelo and Mozart, and that the

value is artistic creativity. Now, imagine a third artist, Talentlessi, who is quite uncreative

artistically, so that he is clearly comparable with Mozart: he is worse. It is possible (let us grant)

to imagine a sort of chain of artists, starting with Talentlessi, and ending with Michelangelo,

which has the following property. Between each two members of this chain, there is only a small

unidimensional change. The dimension of change need not be constant from adjacent pair to

adjacent pair, but each pair differs only in one respect, and not a great deal in that respect. Chang

argues that since Talentlessi is comparable with Mozart, and since no single small

unidimensional change could transform an artist from one who was comparable with Mozart into

one who was not, each member of the chain from Talentlessi to Michelangelo is comparable with

Mozart.12 Since Michelangelo himself is the last member of this chain, it follows that he is

comparable, in respect of artistic creativity, with Mozart. We have already granted that

Michelangelo and Mozart do not bear either of the traditional three value relations to each other,

with respect to artistic creativity. Thus, since they are nevertheless comparable, there must be a

fourth such relation. And this relation we call ‘parity’.

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The Argument Against Parity

Chang herself provides the central point that this paper will exploit in arguing against the

need to posit a fourth positive value relation. The unidimensional chaining argument makes

crucial use the following claim: “a small unidimensional difference [is not] powerful enough to

effect a switch from two […] items being comparable to their being incomparable.”13 Chang

calls this claim “The Small Unidimensional Difference Principle.” But she herself points out that

the Small Unidimensional Difference Principle, despite its “deep intuitive appeal,” is simply

false in some cases. The example Chang uses to illustrate its lack of full generality comes from

economics, and is the following. It is possible to hold that different people’s utilities simply are

incomparable. If that is so, then if I am better off in situation A than in situation B, and if you are

better off in situation B than in situation A, then, with respect to social well-being, situations A

and B cannot be compared. But this impossibility of interpersonal comparisons of utility does

not mean that it is always impossible to compare situations with respect to social well-being. For

we can apply a Pareto Rule.

Pareto Rule: Unless we are equally well-off in each of two states of affairs, one state is

better than another if at least one of us is better off than we would be in the

other state and none of us is worse off, otherwise the states are

incomparable.14

Let us use ordered pairs of the form (x, y) to represent states of affairs in which I have utility x

and you have utility y. Now consider states A, B, and C, which are given by the ordered pairs

(9a, 10b), (10a, 9b) and (10a, 10b).15 If we use the Pareto Rule given above, then a small

unidimensional change might make the difference between A not being comparable to B, and its

being comparable. For such a change might turn A, which is not comparable to B, into C, which

is comparable to B. Chang acknowledges that this falsifies the Small Unidimensional Difference

Principle.16 As she writes: “[t]he Small Unidimensional Difference Principle holds only when

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comparability and incomparability are not rule generated in this way.” The Pareto Rule works as

it does because the unified judgment it yields concerning a pair of social states is generated by

looking at two judgments of a simpler sort: judgments about whether each of the two people is

better or worse off in one of two states. If we assume the trichotomy thesis with regard to these

latter judgments, there are nine relevant ways in which the members of the ordered pairs can be

related to each other.17 In three cases the Pareto Rule says that the first ordered pair represents a

state that is better than the state represented by the second. In three cases it yields the opposite

judgment. In one case it claims that the states are equally good. This leaves a remainder of two

cases, and in those the rule yields its judgment of incomparability, at least if there is no further

standard to which we can appeal. This paper will propose a rule that shares certain formal

features with the Pareto Rule above, although it does not – in an important sense – yield

judgments of incomparability. And it will be argued that this rule can generally, and plausibly,

be used to describe the kinds of valuations that Chang makes use of in her arguments, without

any appeal to a fourth positive value relation.

What Are Valuations?

What does it mean to claim that one thing is better than another? The suggestion I would

like to make, which need be only roughly true to indicate how we can understand Chang’s hard

cases without having to posit a fourth positive value relation, is that we use the word ‘better’ to

mean something like the following: ‘to be chosen, on pain of having made a mistake’.

Correlatively, ‘worse’ can be taken to mean ‘not to be chosen, on pain of having made a

mistake’.18 What is it that makes it appropriate or true to claim that a particular choice a

mistake? It is important to see that no particular answer need be given here. This paper’s

proposal is consistent with the idea that judgments such as ‘that choice was a mistake’ or ‘that

choice was rationally permissible’ are merely expressions of certain non-cognitive attitudes. For

even a non-cognitivist needs to explain the patterns of judgment that Chang points to: e.g., how it

can be acceptable to judge that A is neither better nor worse than B, and that this would remain

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true even if A were improved somewhat. This paper’s proposal offers the non-cognitivist a

straightforward means for providing the required explanation. Alternately, however, this paper’s

proposal is perfectly consistent with the idea that judgments about the rationality of choices are

robust beliefs, and that they have cognitive content and can be literally true or false. I favor such

a cognitivist position, which I explain and defend elsewhere in terms of an overwhelming

agreement in a relevant attitude toward practical choices (both one’s own and those of others).19

For when there is such overwhelming agreement in response or attitude, then the processes of

ostensive language teaching and learning can parlay it into a concept with an objective referent in

the same way that they do in the case of color terms such as ‘yellow’ and ‘red’: statistical outliers

are identified by the linguistic community as inappropriate applications of the term, allowing

both for the identification of an objective referent, and also for the correlative notions of color-

blindness and other visual dysfunctions. If some such story is correct, then an overwhelming

agreement that a certain patch is yellow is (to put it mildly) very strong evidence that it is yellow.

For such agreement is very strong evidence that the patch has the property that plays the

appropriate role in the teaching and learning of the meaning of the word ‘yellow’. And this is

true even though the claim that something is yellow is very different from the claim that the

overwhelming majority of people see it as yellow.20 In the case of a choice being a mistake, the

relevant response is something like puzzlement about someone making the trade-off in question.

The claim that there is such overwhelming agreement may initially seem unlikely if it is confused

with the claim that there is such agreement in the trade-offs people are actually disposed to make.

But this is to confuse preference with valuation. Once one is clear on this distinction, it should

seem much more plausible that despite a great variation in the choices we are disposed to make,

we nevertheless tend to understand (not be puzzled by) the overwhelming majority of practical

choices made by other people.

Given the meaning of ‘better’ that I am claiming is the relevant one here – one that can be

translated into claims about whether or not certain choices are rationally permissible or not – and

assuming, for the moment, the response-dependent account of rational permissibility that I have

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briefly suggested, we have (again, to put it mildly) very strong evidence that B is better than W if

a sufficiently overwhelming majority of people would be puzzled by the choice of W over B.

And we have very strong evidence that one item is not better than another if a similar majority

would not be puzzled in the same way. There may of course be cases in which there is no

majority of either sort: many people would be puzzled, but many would not. Similarly, there are

plenty of cases in which many people would call something ‘blue’ while many others would call

it ‘green’. When this happens, this counts as evidence that we have a borderline case, and that

the meanings of the relevant terms are not sufficiently precise to yield a determine truth-value.

There is no need to deny the existence of such borderline cases. But what is not a borderline case

is the case in which one item is clearly not better than another, and also clearly not worse. And

we have strong evidence that we have such a case when the vast majority of people would not be

puzzled by either choice.21 Moreover, when this happens it may often be that the two items

would continue to have this relation even if one item were improved a bit, although sufficient

improvement would make one item better than the other.22 These are the “hard cases” that

Chang claims her notion of parity is required to explain. This paper claims that all that is

required are the same positive value relations that we have always been familiar with – although

it is true that we need to understand these notions themselves in terms of the still more basic

notion of a practical mistake in choice: a choice that is irrational or doesn’t make sense. But this

latter notion is much less obscure than the notion of parity. I have gestured at a response-

dependent account of this basic notion, but any other account could be substituted in its place: a

Platonic account, or even a non-cognitivist account, although in that case Chang’s data might

have to be reinterpreted slightly. Both the non-cognitivist account and my own favored response-

dependent account appeal to the idea of explaining the meaning of value claims in terms of what

does and does not make sense to human beings, rather than explaining what makes sense for

human beings in terms of the values of various items – values, the origins of which remains a

mystery.

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Now consider the following thought experiment. A series of people are placed in

situations in which they must choose one of two evils, which they will then suffer. And for each

pair, we can say whether or not we would regard it as a mistake, or a symptom of irrationality, if

the first evil were chosen over the second evil, and whether or not we would make a similar

judgment if the second evil were chosen over the first evil. The following table sets out a

plausible pairing of choice pairs with our assessments of the two respective choices. ‘R’

indicates ‘rationally permissible’, and ‘I’ indicates ‘irrational’. ‘Dental visit’ indicates the pain

and discomfort typically caused by getting a filling at the dentist’s, including the pain of a

Novocain injection in the upper palate.

1) [One second of nausea, Dental visit] [R, I]

2) [One minute of nausea, Dental visit] [R, I]

3) [One day of poison ivy, Dental visit] [R, R]

4) [One week of poison ivy, Dental visit] [R, R]

5) [One month of poison ivy, Dental visit] [R, R]

6) [Six months of anxiety, Dental visit] [I, R]

7) [One year of anxiety, Dental visit] [I, R]

8) [Five years of anxiety, Dental visit] [I, R]

Given our understanding of ‘worse’, we can read the following valuations off of this table. First,

rows 1 and 2 indicate that the pain and discomfort of a dental visit is worse than a minute or less

of nausea. Second, rows 6, 7 and 8 indicate that six months or more of anxiety is worse than the

pain and discomfort of a dental visit. Some readers will be tempted to claim that one’s

preferences regarding such things as pain, itch, and anxiety are not subject to rational criticism.

Indeed, one surprisingly popular Humean view claims that none of one’s basic preferences are

subject to rational criticism, unless they are based on irrational beliefs. Criticizing such views is

beyond the scope of this paper. But those who profess a Humean open-mindedness with regard

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to the preferences at issue should ask themselves what they would think if their son or daughter

refused a treatment for an anxiety disorder that promised to last, without treatment, for six

months or a year, when that treatment involved roughly the same pain and discomfort as a trip to

the dentist. Such a refusal is enough, by itself, to show that a person is suffering from a phobia

or some other mental illness. It cannot plausibly be interpreted merely as the expression of an

unusual preference. Perhaps it is the philosopher’s focus on reasoning that makes it seem as

though all mental illnesses must be cognitive. But there are affective disorders as well, and one

characteristic feature of such disorders is the possession of irrational basic preferences.23

Now, for the same reasons that were employed in the small-improvement argument, rows

3, 4 and 5 show that one week of the itch of poison ivy (or one day, or one month) is not equal in

badness to the pain and discomfort of a dental visit. Is this failure of equality merely an

epistemic matter, or a matter of vagueness? Well, let us eliminate these two potential

explanations for purposes of argument, and see if there is some alternative interpretation of the

data that still allows all of our judgments to be literally true. This will be enough to show that we

need not embrace parity even if Chang’s arguments against appeals epistemic problems or to

vagueness go through.

Our strategy will therefore be to make some very strong assumptions about comparability,

including the elimination, for purposes of argument, of any relevant vagueness or epistemic

problems. Nevertheless, we will come up with a rule of valuation for the evils in the above

thought experiment that is consistent with all of Chang’s claims, and yet does not require us to

posit a fourth positive value relation. It is important here to realize that the strength (and

probable falsity) of our assumptions about comparability, lack of vagueness, and so on, do not

weaken, but rather strengthen, the argument against Chang. For the argument will show that

even if we accept Chang’s arguments against various alternative explanations of the phenomena,

we can still explain those phenomena without appeal to a fourth value relation. So suppose the

following: that the strengths of any given person’s preferences can be compared so precisely that

they admit of real-number values, indexed to some standard. That is, when a person is faced

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with a choice between two alternatives, then, unless some sort of irrationality is involved,

knowledge of those numbers would allow us to predict which option that person was going to

choose. One way of accounting for the judgments in the second column of the above list is to

assign to each evil a range that indicates the strengths of the preferences (to avoid that evil) that

we would not consider to be irrational or mistaken. For example, we might assign the following

ranges of ‘strength of preference to avoid’ to each of the evils involved.

Dental visit [50, 140]

One second of nausea [2, 4]

One minute of nausea [6, 15]

One day of poison ivy [20, 60]

One week of poison ivy [70, 120]

One month of poison ivy [130, 250]

Six months of anxiety [200, 400]

One year of anxiety [450, 700]

Five years of anxiety [800, 2000]

These ranges allow us to explain why it is not a mistake to prefer a day of poison ivy to the pain

and discomfort of a dental visit: it is rationally permissible to have a preference of strength 70 to

avoid the dental pain (for any preference strength between 50 and 140 is rationally permissible)

and a preference of strength 35 to avoid the day of itching (for any preference strength between

20 and 60 is rationally permissible). Similarly, it is not a mistake to prefer the dental pain in this

case, since it is rationally permissible to have a preference of strength 50 to avoid the pain and of

60 to avoid the itch. In fact, our interpretation of these ranges entails that whenever there is any

overlap in the two ranges associated with two evils, then it will not, by itself, be a mistake to

choose either option. This is what is happening in cases 3, 4 and 5. On the other hand, not even

the strongest rationally permissible preference to avoid a minute’s nausea (here, a preference of

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strength 15) is enough to overcome the weakest rationally permissible preference to avoid the

dental pain (here, a preference of strength 50), so that is would be a symptom of irrationality to

select the dental pain over the minute’s nausea. This is the reasoning behind the judgments in the

second column of rows 1 and 2 above. Similarly, not even the strongest rationally permissible

preference to avoid the dental pain would be sufficient to overcome the weakest rationally

permissible preference to avoid six months or more of anxiety. This is the reasoning behind the

judgments in the second column of rows 6, 7 and 8 above.

Now, if there are no restrictions placed on consecutive choices, we will get into trouble

making the blanket claim that overlapping ranges indicate the rational permissibility of choosing

either item. For, on the ranges given above, it would be rationally permissible to prefer a trip to

the dentist to a day of poison ivy, and to prefer a month of poison ivy to a trip to the dentist,

although it is irrational to prefer a month of itching to a day of itching.24 But the fact that the

ranges given above for the dental pain, the day of itching, and the month of itching are,

respectively, [50, 140], [20, 60], and [130, 250], should not be taken to mean that the very same

agent might rationally have preferences of strengths 50 and 60 when considering the first two of

these evils, but have preferences of strengths 140 and 130 when considering the first and third.

Rather, the ranges reflect the fact that there is a rationally permissible latitude in the strengths of

the preferences that humans can have for avoiding the dental pain, and for avoiding itching. But

there must be a certain consistency in the preferences a given agent has for items that bear the

very same value in differing degrees. Given the ranges above, someone whose preference to

avoid a day of itching has strength 60 should not have a strength of preference to avoid a week of

itching that deviates from 120 by any great amount. And someone who prefers the trip to the

dentist to the day of itching cannot have a preference to avoid the dental pain that is greater than

60; thus such a person would not be rational to prefer the month of itching to the trip to the

dentist. These kinds of restrictions do not argue in any way against the proposal being made

here, however, since the strength of the agent’s preference for an item is a very different thing

from his valuation of that item. It is possible for an agent who is, relatively speaking, very averse

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to pain, to recognize this fact about himself, and thus to acknowledge that while it would be

rationally permissible to be quite a bit less averse, it would not be rationally permissible to be

very much more averse. The ranges used here should be understood as indicating which

preferences would be irrational or mistaken simply in virtue of the values of the relevant items.

But of course preferences can be irrational for other reasons, having to do with their relations to

the other preferences of the agent. The fact that preference is different from valuation means that

the proposal offered here is even consistent with the idea that the preferences of individual

rational agents must satisfy the axioms of rational choice theory. Of course, agents should be

able to change their preferences over time, and this will result in intransitive preferences, but this

is not a problem specifically for the proposal here.

Of course we do not explicitly think of the disvalue of a minute’s nausea in terms of an

interval of rationally permissible strengths of preferences to avoid it. But the intuitive idea

behind the formalization is an appealing and plausible one. This is the idea that when presented

with pairs of items between which we must make a choice, we can understand (regard as

rationally permissible, or as not being a mistake) many choices that are different from the choices

that we would make, even though we also regard our choices as rationally permissible. But there

are limits to how far this ability to understand extends, and these limits vary from case to case.

The ranges we have been using are simply a formal way of expressing how wide these limits are

in particular cases. If we think of our valuations as given by our dispositions to regard certain

choices as rationally permissible, and others as mistakes, then it makes sense formally to

represent our valuations of items with ranges.

Since ranges are represented by two numbers, it should be no surprise that our valuations

do not lend themselves to comparisons as if they were represented by a single number. In fact,

because two numbers will be required to represent a valuation, there will be a general rule of

comparison that we can use to make ‘better than’ and ‘worse than’ judgments that has a structure

rather similar to the Pareto Rule discussed above. This rule is the following:

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Range Rule: One item is better than another in a certain respect if the lower bound of the

range of the strengths of its relevant rationally permissible preferences is

higher than the upper bound of the other’s; otherwise the items are not

traditionally comparable.

More roughly put, one item is better than another in a certain respect if and only if their relevant

ranges are disjoint. This rule allows us to say that the pain and discomfort of a dental visit is

worse than a minute’s nausea, but not as bad as six months of anxiety. Now, in claiming that

items with overlapping ranges are not traditionally comparable it may seem that I am simply

assuming the trichotomy thesis.25 But I use the phrase ‘traditionally comparable’ advisedly here,

to mean ‘not comparable by one of the three traditional value relations’. This leaves it open that

our normal sense of ‘comparable’ includes more than this, and so I am not begging any questions

against Chang. Again, I am not assuming the trichotomy thesis. Rather, I am seeking to show

that we do not need to posit any additional positive value relations to describe what is going on in

the cases in which two items are not traditionally comparable.

It is worth noting that the Range Rule, unlike the Pareto Rule, does not falsify the Small

Unidimensional Difference Principle. For the Range Rule only entails that small unidimensional

changes can make the difference between two items being traditionally comparable and their not

being traditionally comparable. Chang could still hope to argue that when a small

unidimensional difference causes traditional comparability to disappear, the items are

nevertheless still comparable, because they are on a par. But this claim is almost certainly much

too simple. Ordered pairs that represent ranges can be related in nine ways that can be explained

simply in terms of the three traditional value relations that hold between their members. If we

identify one of these ways with ‘better than’ and one with ‘worse than’ – as the Range Rule does

– then it should be clear that using the single term ‘parity’ to refer to the remaining seven (or six,

if we allow exact equality – see case 2 below) will lose important information.26 The existence

of overlapping ranges for two items, A and B, only entails the following: that it is not a mistake,

17

or irrational, to choose A over B, or B over A, and that this may continue to be true even if one of

the items is slightly improved. But this truth is consistent with all of the following cases (and

more):

1) That A and B have exactly the same range. Thus, for any third item, C, the rational status

of choosing A over C, or vice versa, will always be the same as the rational status of

choosing B over C, or vice versa. This case might plausibly be called ‘parity’.

2) The same as case 1, but the ranges are stipulated to be quite narrow. Such a case

approximates the case in which there is a unique rationally permissible degree of

preference shared by both: the case of exact equality of value. Because of this, it seems

very unhelpful to call the items ‘incomparable’. ‘Rough equality’ seems much more

informative.

3) That A and B have overlapping ranges because they share a lower bound, but the range

for B has an upper bound that is significantly higher than the range for A. In such a case

there will be many items of which the following will be true: it would be a mistake to

choose A over that item, but not a mistake to choose B over that item. Thus this case

does not seem usefully described as one of parity or rough equality.

4) B’s range has higher upper and lower bounds than A’s, but B’s lower bound is

nevertheless marginally lower than A’s upper bound. That is, the ranges for A and B are

almost, but not quite, disjoint. This does not seem usefully described as a case of parity

or rough equality for the same reasons as in case 3. Moreover, in this case it also seems

clearly to be a mistake to describe A and B as incomparable, since a small improvement

to B would make the ranges actually disjoint, so that B would be simply better than A.

18

It is very important to note that a small unidimensional difference that changes two items from

being traditionally comparable to not being traditionally comparable can be expected to yield

items of the sort described in 4. For before the small unidimensional change their ranges were

disjoint: this is why one was better than the other. And cases of this sort simply do not seem

appropriately described as cases of parity or incomparability, for the reasons given above.

Despite this, it may seem that I have conceded at least the possibility of parity to Chang by

granting the reasonable application of the term ‘parity’ to case 1. But if we are to be charitable to

Chang, we should not hold that in arguing for the existence of a fourth positive value relation she

means to be doing nothing more than putting a label to a phenomenon that can be easily

explained in terms of the three traditional relations. Moreover, if this is what Chang had in mind,

then it is mysterious why she did not mention or give a name to any of the other kinds of case.

Finally, Chang has claimed in earlier work that parity, together with the three traditional positive

value relations, exhausts the logical space of comparability.27

Now, Chang might protest at this point that the phenomena that I claim can be “easily

explained” in terms of the three traditional relations can only be so explained by a model that

interprets value in terms of ranges of rationally permissible strengths of preference. And she

might go on to claim that while ranges provide one model for understanding value and parity,

there are other models. Thus the notion of parity is distinct from and independent of any of these

models, and cannot be “explained away” by any given one of them. But the use of ranges is

simply an efficient formal way of representing our dispositions to regard certain choices, in the

light of certain values, as mistakes or not. This paper is not making the controversial – though

plausible – claim that the value of an item should actually be understood as a range of rationally

permissible strengths of preference. It is making the less controversial claim that ‘better in

respect R’ can usefully be understood as ‘rationally to be preferred, when choosing based on R

alone’. All the above use of ranges can be recast in terms of claims of the following sort:

‘Although in a choice between A and B, one could rationally choose either, A would have to be

improved more than B, before it was no longer a mistake to choose it over C’. We can express

19

this claim in terms of ranges by saying that the ranges for A and B overlap, but B’s upper bound

is higher than A’s, and C’s lower bound is higher than either. And we can efficiently summarize

large numbers of claims of this last sort by assigning ranges to the items with which we are

concerned. But talk of ranges, and of degrees of preference, is clearly dispensable. And this

means that all the phenomena that Chang takes to support the existence of parity can be

explained in terms of the everyday notion of ‘better than’, and the idea of greater or lesser

improvements.

Some Philosophical Advantages

Chang holds that the existence of parity would be of importance for views of practical

reason, in the following way. It is a common view, which Chang herself endorses, that ‘the

possibility of justified choice between two alternatives depends on their being comparable; if the

alternatives cannot be compared, practical reason fails to determine at least one of the

alternatives as justified’.28 Parity is therefore important, on Chang’s view, because it may

provide a way to increase the number of cases in which one can make justified choices: cases in

which practical reason yields the status ‘rationally permissible’ to at least one of the options.29

But the interpretation of valuation offered in this paper also has this implication, and does not

wait on an explanation of how the parity of items might be relevant to rational choice between

them. For example, if we assign Aye the range [3,6] with respect to philosophical talent, and

assign Bea the range [4,8], this means that it is rationally permissible to prefer Aye to Bea when

selecting one of them based on philosophical talent, but also that it would not be a mistake to

select Bea over Aye. This explains the rational permissibility of either choice without requiring

us to assert that they are equally talented, and without any appeal to vagueness.

One worry that the above example is likely to suggest is the following. If it is permissible

to prefer Bea to degree 8, while it would only be permissible to prefer Aye to degree 6, and if,

similarly, the lowest degree that one could be motivated to choose Bea is higher than the lowest

for Aye, what could explain this other than the fact that Bea is more philosophically talented?

20

The answer to this question is that it does not take sufficiently seriously the independently

plausible idea that there are ranges of rationally permissible degrees of motivation to choose

items. And why should there not be such ranges? After all, ‘rationally permissible’ is very

closely related to ‘normal’ (‘irrational’ and ‘abnormal’ are terms of criticism, though ‘rationally

permissible’ and ‘normal’ are not typically terms of praise) and there are normal ranges of height,

weight, intelligence, and so on. Once one concedes this point, situations like the Aye and Bea

comparison will arise. It can be admitted that there is a difference, relevant to evaluations,

between Aye and Bea. Indeed this is one way of explaining Chang’s otherwise obscure notion of

an ‘evaluative difference’, which she uses to explain the notion of incomparability. According to

Chang, all the positive value relations assert the existence of some evaluative difference between

compared items: even ‘equal to’ does this, by asserting that the difference is zero. Of

incomparables, one cannot even say that the difference is zero.30 Now, of Aye and Bea one

cannot say that Bea is simply better than Aye. For to say this would imply that it would be a

mistake to choose Aye over Bea. But if one likes, one can characterize the evaluative difference

(difference in valuations) between the two candidates by saying that Bea is “better in a sense”

than Aye. This sense is the following: even though Bea is not simply better than Aye, there are

other possible candidates – Cee for example, with range [7, 9] – who are simply better than Aye,

but who are not simply better than Bea.31 And there are many other ways in which the valuations

of items can be related that we could call ‘evaluative differences’ (cases 3 and 4 above, for

example) even though one item is not simply better than the other.

A final advantage our strategy of representing valuations with ranges is that we can save

standard decision and rational choice theory from Chang’s claim that ‘the basic assumptions of

standard decision and rational choice theory [are] mistaken: preferring X to Y, preferring Y to X,

and being indifferent between them do not span the conceptual space of choice attitudes one can

have toward alternatives’.32 In the first place, the suggestion of this paper makes it very clear that

choice attitudes need not be taken to reflect valuations of the sort that Chang is concerned with.

That is, Chang’s criticism of standard decision and rational choice theory is misplaced unless our

21

preferences should be taken as completely revealing our valuations. Since only very rarely do we

think of our choices as the uniquely rational option, this assumption is unwarranted. And in the

second place, it is possible to do decision theory and rational choice theory while assigning

ranges in place of scalar values for desirability indices. Indeed, the idea of using a range to

characterize subjective probability estimates is already familiar in expected-utility theory.33 In

this way, the techniques of decision and rational choice theory could be brought to bear directly

on the logic of value.

22

FOOTNOTES

* Many thanks to Ruth Chang for her extremely speedy and helpful criticisms of the first draft of

this paper. Thanks also to a number of anonymous referees from Ethics, and to Maria Victoria

Costa, for comments on the penultimate version.

1 Ruth Chang, “The Possibility of Parity,” Ethics 112 (2002): 659-688.

2 For more on the distinction between positive and negative value relations, see Chang, “The

Possibility of Parity,” p. 663.

3 Ibid, p. 661.

4 In fact, fewer will suffice, for ‘better than’ can be used to define ‘worse than’, and vice versa.

But, for reasons given below, the interdefinability of these two terms should not lead us to

conclude that parity is equally basic.

5 For example, elsewhere she puts her thesis in the following way: ‘there is a fourth positive

value relation – ‘on a par’ – that, together with the traditional three, exhausts the logical space of

comparability’. See Chang’s introduction to Incommensurability, Incomparability, and Practical

Reason (Cambridge MA: Harvard University Press, 1997), pp. 4-5.

6 I do not mean to conflate these three dichotomies, but only to give more of an idea of the sort of

yes/no distinction that might suffice to account for the same phenomena that Chang believes

requires the postulation of a fourth positive value relation.

7 Indeed, Humeans often hold that there are no rational bounds at all on basic preferences. Such

an attitude makes it difficult to enter into a discussion such as the present one, in which it is

assumed that some items are better than others in certain respects. The proposal in this paper

accommodates the existence of wide bounds on the rationality of basic preferences without

abandoning the idea that there are any such bounds. It therefore represents a compromise, in

some ways, between Humeans and those who hold value to be more objective.

23

8 Chang, Incommensurability, pp. 7-13.

9 In her Ethics article, Chang also gives a list of philosophers who ‘have understood

incomparability in terms of unresolved conflict between the considerations relevant to choice’.

See Chang, “The Possibility of Parity,” p. 660, fn. 2.

10 Chang, Incommensurability, p. 30.

11 Chang, “The Possibility of Parity,” pp. 668-669 inc. fns. 12, 13 and 16.

12 Chang is certainly aware that this argument has the form of a sorites, and would be invalid if

‘comparable’ were a vague predicate. In this paper I do not address her arguments that

‘comparable’ is not vague, because they are irrelevant to my main suggestion. However, it

should be clear that on the view offered below, ‘comparable’ will be roughly as vague as

‘irrational’, ‘mistaken’, or ‘puzzling’. My view that ‘comparable’ is vague is entirely

compatible with Chang’s claim that the specific failure of Michelangelo to be better than, worse

than, or equal to Mozart, with respect to artistic creativity, is not a result of the vagueness of the

predicates used to express these relations.

13 Chang, “The Possibility of Parity,” p. 674.

14 Ibid, p. 676.

15 The ‘a’s and ‘b’s here are included to remind us that we cannot compare the first item in any

given ordered pair with the second.

16 Chang, “The Possibility of Parity,” pp. 676-677.

17 Of course Chang might say that we should not assume the trichotomy thesis. But the point

here is to see whether, in this and other cases, we can say everything we wish to say without

abandoning the trichotomy thesis. If we can, then this constitutes an argument against parity, not

an assumption that there is no such thing.

18 Despite superficial grammar, these accounts of ‘better’ and ‘worse’ clearly do not exhaust the

evaluative space. For our account of ‘worse’ means only that if one chooses a worse item, one

has made a mistake. It does not follow from something’s not being better, in the sense given

24

above, that it is worse, in this sense. However, on these definitions, A’s being better than B does

imply, as it should, that B is worse than A.

19 See my Brute Rationality, (Cambridge: Cambridge University Press, 2004), chapter seven. My

view has much in common with Philip Pettit’s “genealogical” account of response-dependent

notions. See Philip Pettit, “Realism and Response-Dependence,” Mind 100 (1991): 587-626,

esp. p. 600. Pettit, however, does not emphasize the role of language acquisition.

20 Indeed, these claims could even have different truth values under sufficiently strange

circumstance.

21 These are cases in which the failure of ‘better than’, ‘worse than’, and ‘equal to’ is not to be

explained by appeal to vagueness, since it is determinate that none of these apply.

Unsurprisingly, such cases can be used to explain the phenomena that Chang uses in her

arguments against appeals vagueness.

22 ‘Improvement’ is to be understood in the same general framework: improving an item is a

matter of making it better – in the relevant sense – than some items that it was not formerly better

than.

23 Those semi-Humeans who remain uncomfortable with the claim that five years of anxiety is

worse than the pain and discomfort involved in getting a filling, but who are willing to hold that

Mozart is more artistically creative that Britney Spears or that Citizen Kane is a better movie than

Plan Nine from Outer Space should feel free to modify the current example by replacing

discomforts with artists or films. All essential points will remain the same.

24 It may be worth noting that Chang will have to tell a similar story to avoid similar problems, no

matter what account of parity she ends up favoring: she cannot hold that it is always rationally

permissible to trade items that are on a par, even when the only relevant value is the value,

relative to which, they are on a par. For given the structure of the cases that she takes to show

parity (those involved in the small-improvement argument), such trades can easily result in loss

25

of overall value. She avoids these problems in the Ethics paper by giving no indication regarding

the rationality of choice when faced with two items that are on a par.

25 In fact, it may seem that I am assuming a dichotomy thesis, since the rule, as stated, has no

provision for equality of value. For if the intervals for two items, A and B, merely shared the

same upper and lower bounds, it would still be rationally permissible to choose A over a slightly

improved B, as long as the improvement in B didn’t raise its lower bound higher than A’s upper

bound. But we can easily modify the rule to allow equality in the following circumstances: when

two items each have the same unique rationally required strength of preference.

26 If we deny that the values used in these ordered pairs admit of exact equality then there will be

five ways, and ‘parity’ will conflate three of them.

27 Chang, Incommensurability, pp. 4-5.


29 Elsewhere I have argued against the idea that the value of comparable items is what determines

the rational status of choices between them. Rather, it is comparisons of the wholesale rational

status of various options that allows us to interpolate the respective values of the items involved

in those options. See Brute Rationality, chapter four.

30 Chang, “The Possibility of Parity,” pp. 663-4.

31 If one objects to this possibility then one must object to the possibility of parity also, for these

relations between three items are virtually definitive of instances of parity: consider

Michelangelo, Mozart, and a composer just a bit worse than Mozart.


33 See Paul Weirich, “Risk’s Place in Decisions Rules,” Synthese 126 (2001): 427-441 and I.J.

Good, “Rational Decisions,” Journal of the Royal Statistical Society, Ser. B. 14 (1952): 107-114.

Value and Parity

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