## 1. Value Incommensurability



Incommensurability between values must be distinguished from the kind
of incommensurability associated with Paul Feyerabend (1978, 1981,
1993) and Thomas Kuhn (1977, 1983, 1996) in epistemology and the
philosophy of science. Feyerabend and Kuhn were concerned with
incommensurability between rival theories or paradigms -- that
is, the inability to express or comprehend one conceptual scheme, such
as Aristotelian physics, in terms of another, such as Newtonian
physics.



In contrast, contemporary inquiry into value incommensurability
concerns comparisons among abstract values (such as liberty or
equality) or particular bearers of value (such as a certain
institution or its effects on liberty or equality). The term
"bearer of value" is to be understood broadly. Bearers of
value can be objects of potential choice (such as a career) or states
of affairs that cannot be chosen (such as a beautiful sunset). Such
bearers of value are valuable in virtue of the abstract value or
values they instantiate or display (so, for example, an institution
might be valuable in virtue of the liberty or equality that it
engenders or embodies).


### 1.1 Measurement and Comparison



The term "incommensurable" suggests the lack of a common
measure. This idea has its historical roots in mathematics. For the
ancient Greeks, who had not recognized irrational numbers, the
dimensions of certain mathematical objects were found to lack a common
unit of measurement. Consider the side and the diagonal of a unit
square. These can be compared or ranked ordinally, since the diagonal
is longer. However, without the use of irrational numbers, there is no
way to specify with cardinal numbers exactly how much longer the
diagonal is than the side of a unit square. The significance of this
kind of incommensurability, especially for the Pythagoreans, is a
matter of some debate (Burkert 1972, 455-465). Hippasus of Metapontum,
who was thought by many to have demonstrated this kind of
incommensurability, is held by legend to have been drowned by the gods
for revealing his discovery (Heath 1921, 154; von Fritz 1970,
407).



Given these historical roots, some authors reserve the term
"incommensurable" for comparisons that can be made, but
not cardinally (Stocker 1980, 176; Stocker 1997, 203; Chang 1997b, 2).
Others interpret the idea of a common measure more broadly. On this
broader interpretation, for there to be a common measure, all that is
required is that ordinal comparisons or rankings are possible. Values
or bearers of value are then incommensurable only when not even an
ordinal comparison or ranking is possible (e.g., Raz 1986; Rabinowicz
2021a). On this interpretation, incommensurability is defined as the
relation that holds between two items when neither is better than the
other nor are they equally as good.



Others
have not given an exact
definition of the term, but use it as an inclusive umbrella term for
comparability problems in general. This inclusive interpretation has
the advantage of encompassing a field of diverse philosophical
discussions which engages in problems concerning value comparisons.
This entry encourages the use of "incommensurable" in the
etymologically correct way i.e., to refer to the lack of a cardinal
scale.


### 1.2 Incommensurable or Incomparable?



Because the idea of comparison is closely tied to the topic of value
incommensurability, this has led to use of the term
"incomparable" alongside "incommensurable" in
the literature. Some authors use the terms interchangeably (e.g., Raz
1986). Others use them to refer to distinct concepts (e.g., Chang
1997b). This entry will use the term "incomparable" to
refer to the possibility that no positive value relation holds between
two value bearers (Chang 1997b). Positive value relations specify how
two items compare (e.g., "better than") rather than how
two items do not compare (e.g., "not better than").



Incomparability is often taken to be a three-place relation: *A* is
incomparable with *B* with respect to *V*. "*V*" is here some
specific consideration for which the items are being compared. One
career may be incomparable to another with respect to the sense of
purpose it will bring to your life, yet they may be comparable with
respect to financial stability since one is clearly better than the
other in this regard. Some argue that without specifying this
"covering consideration" the comparative claim makes no
sense (Chang 1997; Thomson 1997; Andersson 2016b). Often, however, the
covering consideration is not explicitly expressed, but implicitly
assumed by the context of utterance.



Specifying the covering consideration also allows us to identify
"noncomparability". If no single covering consideration is
applicable to the things we are comparing, then the things are
noncomparable. For example, the number four is noncomparable with the
color blue with respect to their tastiness. This form of comparative
failure is considered to be of no interest from the perspective of
practical reasoning and is consequently not given much consideration
in the literature.



From the fact that two things are incommensurable i.e., lack a common
unit of measurement, it does not follow that they are incomparable. It
is possible to correctly judge that one thing is better than the other
while it being impossible to measure how much better it is. However,
when there is incomparability there is also incommensurability. If no
positive value relation holds between two things, then they cannot be
placed on the same cardinal scale.



While both incommensurability and incomparability are important
concepts, much of the recent research has focused on the more specific
possibility of incomparable value bearers. Different competing
accounts have been given for examples that seem to point to the
possibility of things being incomparable. These examples often take
the form similar to that of Joseph Raz's example in which a
person faces the choice between two successful careers: one as a
lawyer and one as a clarinetist. Neither career seems better than the
other, and they also do not appear to be equally good. If they were of
equal value, then a slightly improved version of the legal career
would be better than the musical career, but this judgment appears
incorrect (Raz 1986, 332).



The focus on incomparability can be motived by its possible
significance for rational choice. Comparing alternatives are central
for rational choice, we want to know what alternative is the best, and
thus examples of incomparability are taken to be a threat to rational
decision-making. Incommensurability on the other hand is mostly of
theoretical interest. The possibility of incommensurable values
introduces restrictions for normative theories, in the sense that they
should not assume that all values can be represented on the same
cardinal scale. The focus on incomparability can thus be justified by
referring to its relation to practical reason and rational choice.



The remainder of section 1 considers proposed ways in which to
conceive of value incommensurability.


### 1.3 Conceptions of Value Incommensurability



This section outlines three conceptions of value incommensurability,
each one capturing some sense in which incommensurability is due to
the lack of a common measure.



The first conception characterizes value incommensurability in terms
of restrictions on how the further realization of one value outranks
realization of another value. James Griffin has proposed forms of
value incommensurability of this sort. One form involves what he calls
"trumping." In a conflict between values *A* and
*B*, *A* is said to trump *B* if
"*any* amount of *A*, no matter how small, is more
valuable than *any* amount of *B*, no matter how
large" (Griffin 1986, 83). A weaker form of value
incommensurability involves what Griffin calls
"discontinuity." Two values, *A* and *B*,
are incommensurable in this sense if "so long as we have enough
of *B* any amount of *A* outranks any further amount of
*B*; or that enough of *A* outranks any amount of
*B*" (Griffin 1986, 85).



If values are incommensurable in this first sense, there is no
ambiguity whether the realization of one value outranks realization of
the other. Ambiguity as to whether the realization of one value
outranks realization of the other, however, is thought by many
theorists to be a central feature of incommensurable values. The
second and third conceptions of value incommensurability aim to
capture this feature.



According to the second conception, values are incommensurable if and
only if there is no true general overall ranking of the realization of
one value against the realization of the other value. David Wiggins,
for example, puts this forward as one conception of value
incommensurability. He writes that two values are incommensurable if
"there is no general way in which A and B trade off in the whole
range of situations of choice and comparison in which they
figure" (1997, 59).



This second conception of value incommensurability denies what Henry
Richardson calls "strong commensurability" (1994,
104-105). Strong commensurability is the thesis that there is a true
ranking of the realization of one value against the realization of the
other value in terms of one common value across all conflicts of
value. A denial of such a singular common value, however, does not
rule out what Richardson calls "weak commensurability"
(1994, 105). Weak commensurability is the thesis that in any given
conflict of values, there is a true ranking of the realization of one
value against the realization of the other value in terms of some
value. This value may be one of the values in question or some
independent value. This value also may differ across value conflicts.
The denial of strong commensurability does not entail a denial of weak
commensurability. Even if there is no systematic or general way to
resolve any given conflict of values, there may be some value in
virtue of which the realization of one value ranks against realization
of the other. Donald Regan defends the thesis of strong
commensurability (Regan 1997).



The third conception of value incommensurability denies both strong
and weak commensurability (Richardson 1994, Wiggins 1997, Williams
1981). This conception claims that in some conflicts of values, there
is no true ranking of values.



This third conception of value incommensurability is sometimes said to
be necessary to explain why, in conflicts of value, a gain in one
value does not always cancel the loss in another value. This view
assumes that, whenever there is a true ranking between the realization
of one value and the realization of another value, the gain in one of
the values cancels the loss in the other. Many commentators question
that assumption. This entry leaves open the possibility that when
there is a true ranking between the realization of one value and the
realization of another value, the gain in one of the two values need
not cancel the loss in the other.



If we accept this possibility, a number of questions arise. One
question is what a ranking of realizations of values means if a gain
in one value does not cancel the loss in the other. A second question
is whether the first and second conceptions of value
incommensurability each admit of two versions: one version in which
the gain in one value cancels the loss of the other and one version in
which it does not. A third question concerns the relation between
value incommensurability and tragedy. It may be thought that what
makes a choice tragic is that, no matter which alternative is chosen,
the gain in value cannot cancel the loss in the other value. Not all
authors, however, regard all value conflicts involving incommensurable
values as tragic (Richardson 1994, 117). Wiggins, for example,
reserves the second conception of value incommensurability for what he
calls "common or garden variety incommensurable" choices
and the third conception for what he calls "circumstantially cum
tragically incommensurable" choices (1997, 64).


## 2. Incomparability



Rather than focus on commensurability between abstract values, recent
research focuses on the incomparability between concrete bearers of
value, often in the context of choice (Broome 1997, 2000; Chang 1997,
2002; Griffin 1986; Raz 1986). Bearers of value sometimes appear
incomparable in cases like Joseph Raz's example of the choice
between careers (described above in subsection 1.2).



The case for incomparability in such examples relies in part on what
Ruth Chang calls the "Small Improvement Argument" (Chang
2002b, 667). As noted in the initial discussion of the example, if the
legal and musical careers were of equal value, then a slightly
improved version of the legal career would be better than the musical
career, but this judgment appears incorrect. The Small Improvement
Argument takes the following general form: "if (1) *A* is
neither better nor worse than *B* (with respect to *V*),
(2) *A*+ is better than *A* (with respect to
*V*), (3) *A*+ is not better than *B* (with
respect to *V*), then (4) *A* and *B* are not
related by any of the standard trichotomy of relations (relativized to
*V*)" where *V* represents the relevant set of
considerations for purposes of the comparison (Chang 2002b,
667-668). In addition to Raz, Derek Parfit and Walter
Sinnott-Armstrong are among those who have advanced the Small
Improvement Argument (Parfit 1984; Sinnott-Armstrong 1985). A similar
argument, but for preference relations has, however, a longer
history. Leonard J. Savage hints towards this possibility already
1954, in 1958 R. Duncan Luce presents a version of the argument that
he attributes to Howard Raiffa, and it is also discussed by Ronald de
Sousa in 1974 (Savage 1954; Luce 1958; de Sousa 1974).



Focusing on the incomparability of bearers of value has given rise to
two lines of inquiry in the literature. The first concerns the
relation between incomparability and vagueness; some argue that
alleged examples of incomparability are better understood in terms of
vagueness. The second concerns the range of comparative relations that
can hold between two items; some argue that the Small Improvement
Argument does not establish incomparability but rather that there are
more value relations than previously believed. This section summarizes
debate within each line of inquiry.


### 2.1 Vagueness



Raz distinguishes incomparability from what he calls the
"indeterminacy" of value. Recall that Raz defines two
bearers of value as incomparable if and only if it is not true that
"either one is better than the other or they are of equal
value." The indeterminacy of value is a case of vagueness: it is
neither true nor false of two items that "either one is better
than the other or they are of equal value." Raz regards the
indeterminacy of value to result from the "general indeterminacy
of language" (1986, 324).



In contrast, other philosophers argue for interpreting alleged
examples of incomparability as vagueness (Griffin 1986, 96; Broome
1997, 2000; Andersson 2017; Elson 2017; Dos Santos 2019). Some have
argued that the Small Improvement Argument fails to rule out the
possibility that it is indeterminate how the value bearers relate;
they may be related by one of the standard trichotomous relations, but
it could be indeterminate which (Wasserman 2004; Klockseim 2010;
Gustafsson 2013).



There are also more positive arguments in favor of the vagueness
interpretation. For example, Broome introduces what he calls a
"standard configuration" (1997, 96; 2000, 23). Imagine the
musical and legal careers from Raz's example. Fix the musical
career as the "standard." Now imagine variations in the
legal career arranged in a line such that in one direction, the
variations are increasingly better than the standard and in the other
direction, the standard is increasingly better than the variations.
There is an intermediate zone of legal careers that are not better
than the standard and such that the standard is not better than the
legal careers. If this zone contains one item, Broome defines this
legal career to be equally good with the standard. If this zone
contains more than one item, the zone is either one of "hard
indeterminacy" or one of "soft indeterminacy." A
zone cannot be both one of hard indeterminacy and one of soft
indeterminacy. In a zone of hard indeterminacy, it is false that the
legal careers are better than the standard and false that the standard
is better than the legal careers (1997, 73, 76). In a zone of soft
indeterminacy, it is neither true nor false that the legal careers are
better than the standard and neither true nor false that the standard
is better than the legal careers (1997, 76). The latter is a zone of
vagueness. Broome argues that indeterminate comparatives, including
"better than" are softly indeterminate, thus there is no
hard indeterminacy and no room for the possibility suggested by the
Small Improvement Argument.



By understanding incomparability to entail vagueness, Broome disagrees
with Raz (Broome 2000, 30). Raz defines incomparability so that it is
compatible with vagueness, but not so that it entails vagueness.
Griffin also argues that incomparability entails vagueness (1986, 96).
Where Broome disagrees with Griffin is with regard to the width and
significance of the zone of soft indeterminacy. Broome takes Griffin
to suggest that if there is a zone of soft indeterminacy, it is narrow
and unimportant. Broome argues that vagueness need not imply either
narrowness or lack of importance (2000, 30-31). 



Central to Broome's argument is his controversial
"collapsing principle" for comparatives: For any *x*
and *y*, if it is false that *y* is *F*er than *x*
and not false that *x* is *F*er than *y*, then it is
true that *x* is *F*er than *y* (1997, 74). Many
counterexamples have been presented to show the implausibility of the
principle (Carlson 2004, 2013; Elson 2014b; Gustafsson 2018). While
there are attempts to defend the collapsing principle, or versions of
it, (Constantinescu 2012; Andersson & Herlitz 2018) the
counterexamples make Broome's argument less convincing. Another
line of argument has consequently been developed in defense of the
vagueness interpretation. It is argued that the vagueness
interpretation is theoretically parsimonious since it is natural to
accept the existence of evaluative vagueness and if it can
effortlessly account for alleged examples of incomparability then
there is no reason to accept the more mysterious notion of
incomparability or to introduce more value relations beyond the
standard trichotomous relations (Andersson 2017; Elson 2017).


### 2.2 "Roughly Equal" and "On a Par"



The second line of inquiry concerns the set of possible comparative
relations that can obtain between two items. The small improvement
argument for the incomparability of the musical career and the legal
career in Raz's example assumes what Chang calls the
"trichotomy thesis." The trichotomy thesis holds that if
two items can be compared in terms of some value or set of values,
then the two items are related by one of the standard trichotomy of
comparative relations, "better than," "worse
than," or "equally good" (2002b, 660). A number of
authors have argued that these three comparative relations do not
exhaust the space of comparative relations. If they are correct, the
musical career and the legal career may, in fact, be comparable.



James Griffin and Derek Parfit argue that items may in fact be
"roughly equal" and hence comparable (Griffin 1986, 80-81,
96-98, and 104; 1997, 38-39; 2000, 285-289; Parfit 1987, 431). As an
illustration, Parfit imagines comparing two poets and a novelist for a
literary prize (1987, 431). Neither the First Poet nor the Novelist is
worse than the other and the Second Poet is slightly better than the
First Poet. If the First Poet and the Novelist were equally good, it
would follow that the Second Poet is better than the Novelist. This
judgment, according to Parfit, need not follow. Instead, the First
Poet and the Novelist may be roughly equal. The intuition is that even
though three items display the respects in virtue of which the
comparisons are made, some comparisons are inherently rough so that
even though two alternatives are not worse than one other, they are
not equally good. In turn, the musical and legal careers in
Raz's example may be roughly equal. Parfit later referred to
this possibility as there being "evaluative imprecision"
(Parfit 2016, 113).



"Roughly equal," as used here, is to be distinguished from
two other ways in which the term has been used: (1) to refer to a
small difference in value between two items and (2) to refer to a
choice of little significance (Raz 1986, 333). As used here, two items
A and B are said to be roughly equal if neither is worse than the
other and C's being better than B does not imply that C is
better than A when the comparisons are all in virtue of the same set
of respects.



There is some debate as to whether "roughly equal" is in
fact a fourth comparative relation to be considered in addition to the
three standard relations, "better than," "worse
than," and "equally good." One way to conceive of
"roughly equal" is as a "roughed up" version
of "equally good." On this interpretation, the trichotomy
thesis basically holds; there are simply precise and rough versions
(Chang 2002b, 661, fn. 5). Furthermore, "roughly equal" is
a relation that can be defined only in virtue of three items, and as
such, appears to be something distinct from a standard comparative
relation. The standard comparative relations are binary; transitivity
with respect to them is a separate condition (Hsieh 2005, 195).



A separate proposal for a genuine fourth relationship is Ruth
Chang's argument for "on a par" (Chang 1997; Chang
2002b). Two items are said to be on a par if neither is better than
the other, their differences preclude their being equally good, and
yet they are comparable. Whereas "roughly equal" is
invoked to allow for comparability among alternatives that display the
same respects (e.g., literary merit), "on a par" is
invoked to allow for comparability between alternatives that are
different in the respects that they display. Imagine comparing Mozart
and Michelangelo in terms of creativity. According to Chang, neither
Mozart nor Michelangelo is less creative than the other. Because the
two artists display creativity in such different fields, however, it
would be mistaken to judge them to be equally creative. Nevertheless,
according to Chang, they are comparable with respect to creativity.
Something can be said about their relative merits with respect to the
same consideration. According to Chang, they are on a par.



Chang's argument relies on invoking a continuum that resembles
Broome's standard configuration. Chang asks us to imagine a
sequence of sculptors who are successively worse than Michelangelo
until we arrive at a sculptor who is clearly worse than Mozart in
terms of creativity. Chang then brings to bear the intuition that
"between two evaluatively very different items, a small
unidimensional difference cannot trigger incomparability where before
there was comparability" (2002b, 673). In the light of this
intuition, because Mozart is comparable to this bad sculptor, Mozart
is also comparable to each of the sculptors in the sequence, including
Michelangelo. The soundness of this so-called Chaining Argument has,
however, been questioned (Boot 2009; Elson 2014a; Andersson
2016a).



Whether "roughly equal" or "on a par" imply
comparability is a matter of some debate. "Roughly equal"
and "on a par," for example, are intransitive, so to
recognize them as distinct comparative relations would require us to
reconsider the transitivity of comparative relations (Hsieh 2007).
Some authors suggest that one of the three standard comparative
relations obtains between all items that are claimed to be
incomparable, roughly equal, or on a par (Regan 1997). In the case of
"on a par," Joshua Gert and Erik Carlson have argued that
it can be defined in terms of the three standard comparative relations
(Gert 2004; 2015; Carlson 2010). Gert's suggestion is developed
further by Wlodek Rabinowicz who provides a Fitting Attitudes account
of value relations (Rabinowicz 2008; 2012). The Fitting Attitudes
account typically analyzes goodness in terms of a normative component
and an attitudinal component. By acknowledging that there can be two
levels of normativity, requirement and permissibility, the account
leaves room for both parity and standard value relations. *X* is
better than *Y* if and only if it is rationally required to
prefer *X* to *Y*, and *X* and *Y* are on a par if
and only if it is rationally permissible to prefer *X* to
*Y* and also rationally permissible to prefer *Y* to
*X*. Interestingly, preferences and the lack of preferences
together with the two levels of normativity can be combined in 15
different ways. This means that the fitting attitudes analysis
provides the conceptual space for 15 possible value relations.



Another view is that values can be "clumpy," meaning that
the values sort items into clumps. According to this view, once we
recognize the way in which the relation "equally good"
functions in the context of clumpy values, items that appear to
require "roughly equal" or "on a par" can be
judged equally good (Hsieh 2005).


## 3. Arguments for Value Incommensurability and Incomparability



While recent research has focused on value incomparability and how to
interpret examples that have the structure described by the Small
Improvement Argument, earlier research had less focus on the structure
of value but focused more on substantial consideration that talks in
favor of incomparability. In this section, such considerations will be
discussed.



First, a note on terminology. Most of the arguments discuss something
that is similar to the phenomenon of incomparability but refer to the
phenomenon in terms of "incommensurability". In this
section, the terminology of the discussed authors will be respected,
and thus "incommensurability" will sometimes be used, even
though, the authors possibly refer to the phenomenon of
incomparability.



It should be noted that value pluralism seems central for the
possibility of incomparability. After all, the most direct argument
against the possibility that values are incommensurable or
incomparable is based on value monism (e.g., Mill 1861 [1979] and Sidgwick
1874 [1981]). Donald Regan, for example, argues that "given any two
items (objects, experiences, states of affairs, whatever) sufficiently
well specified so that it is apposite to inquire into their
(intrinsic) value in the Moorean sense, then either one is better than
the other, or the two are precisely equal in value" (Regan 1997,
129).



This argument has been questioned. As Ruth Chang points out, by
referring to John Stuart Mill, that values may have both qualitative
and quantitative aspects could in principle allow for value bearers to
be incomparable due to a difference in their qualitative features.
(Chang 1997b, 16-17).



For purposes of this entry, it will not be assumed that value monism
rules out incomparability. In any case, many philosophers argue for
some form of value pluralism (Berlin 1969, Finnis 1981, Nagel 1979,
Raz 1986, Stocker 1990, Taylor 1982, Williams 1981). Although this
entry will not assume value pluralism, most philosophers who argue for
incommensurability or incomparability are value pluralists, so it will
be simpler to present their views by talking of separate values.


### 3.1 Constitutive Incommensurability



It has been argued that value incomparability is constitutive of
certain goods and values and consequently we should assume its
existence. Two versions of this second argument will be discussed
here.



One version of this argument comes from Joseph Raz. Consider being
offered a significant amount of money to leave one's spouse for
a month. The indignation that is typically experienced in response to
such an offer, according to Raz, is grounded in part in the symbolic
significance of certain actions (1986, 349). In this case, "what
has symbolic significance is the very judgment that companionship is
incommensurable with money" (1986, 350). Although this form of
value incommensurability looks like trumping, Raz does not see this as
a case of trumping. He rejects the view that companionship is more
valuable than money. If such a view were correct, then those who forgo
companionship for money would be acting against reason (1986, 352).
Instead, Raz takes the view that a "belief in incommensurability
is itself a qualification for having certain relations" (1986,
351). Someone who does not regard companionship and money as
incommensurable simply has chosen a kind of life that may be
fulfilling in many ways, but being capable of having companionship is
not one of them.



In Raz's account, the symbolic significance of judging money to
be incommensurable with companionship involves the existence of a
social convention that determines participation in that convention
(e.g., marriage) that requires a belief in value incommensurability.
This conventional nature of belief in value incommensurability in
Raz's account raises a question for some authors about its
robustness as an account of value incommensurability. For example,
Chang objects that incommensurability appears to become relative to
one's participation in social conventions (2001, 48). It remains
an open question how much of a problem this point raises. Raz's
account appears to illustrate a basic sense in which the values of
money and companionship can be incommensurable. Insofar as it is not
against reason to choose money over companionship, there is no general
way to resolve a conflict of values between money and companionship.
In Raz's account, the resolution depends upon which social
convention one has chosen to pursue.



Elizabeth Anderson advances a second argument for constitutive
incommensurability. Her account is grounded in a pragmatic account of
value. Anderson reduces "'x is good' roughly to
'it is rational to value x,' where to value something is
to adopt toward it a favorable attitude susceptible to rational
reflection" (1997, 95). She argues that in virtue of these
attitudes there may be no good reason to compare the overall values of
two goods. Pragmatism holds that if such a comparison serves no
practical function, then the comparative value judgment has no truth
value, meaning that the goods are incommensurable (1997, 99). Because
the favorable attitudes one adopts toward goods help to make them
good, Anderson's account can be seen as an argument for
constitutive incommensurability (Chang 2001, 49).



Anderson advances three ways in which there may be no good reason to
compare the overall values of goods. First, it may be boring or
pointless to engage in comparison. To illustrate, "the project
of comprehensively ranking all works of art in terms of their
intrinsic aesthetic value is foolish, boring, and stultifying"
(1997, 100). Second, Anderson points to instances in which "it
makes sense to leave room for the free play of nonrational motivations
like whims and moods" as in the choice of what to do on a
leisurely Sunday afternoon (1997, 91). Third, Anderson argues that the
roles that goods play in deliberation can be so different that
"attempts to compare them head to head are incoherent"
(1997, 91). Imagine that the only way to save one's dying mother
is to give up a friendship. Rather than compare their overall values,
argues Anderson, ordinary moral thinking focuses on what one owes to
one's mother and one's friends (1997, 102). This focus on
obligation recognizes mother and friend each to be intrinsically
valuable and yet valuable in different ways (1997, 103). There is no
good reason, according to Anderson, to compare their overall values
with regard to some common measure.



Chang argues against each of the three points raised by Anderson
(Chang 2001). In response to the first point, Chang notes there are
occasions in which comparisons do need to be made between goods for
which Anderson argues there is no good reason to make comparisons. In
response to the second point, Chang argues that the range of instances
for which the second argument applies is small. In response to the
third point, Chang contends that Anderson's argument assumes
that if goods are comparable then they have some value or evaluative
property in common. Chang points out that this need not be the
case.


### 3.2 Moral Dilemmas



Both value incommensurability and incomparability have been invoked to
make sense of a central feature of supposed moral
dilemmas--namely, that no matter which alternative the agent
chooses, she fails to do something she ought to do. The apparent value
conflicts involved in these choices have led some philosophers to
relate moral dilemmas to the incomparability or incommensurability of
values. Henry Richardson, for example, takes the situation confronting
Sophie in the novel *Sophie's Choice*--that one of
her two children will be spared death, but only if she chooses which
one to save--to point to the incommensurability of values (1994,
115-117).



It has been argued that the mere fact of a moral dilemma does not
imply incomparability. James Griffin, for example, argues that the
feature of "irreplaceability" in moral dilemmas often may
be mistaken as evidence for incomparability (1997, 37).
Irreplaceability is the feature that what is lost in choosing one
alternative over another cannot be replaced by what is gained in
choosing another alternative. Although a conflict of values displays
this feature, not all instances of irreplaceability need involve
plural values. Some moral dilemmas, for example, may involve not a
conflict of values, but a conflict of obligations that arises from the
same consideration. Consider forced choices in saving lives. If there
is a dilemma, it need not involve conflicting values, but rather
conflicting obligations that arise from the same consideration. Walter
Sinnott-Armstrong calls such dilemmas "symmetrical" (1988,
54-58). The dilemma encountering Sophie, it may be said, does not
point to the incommensurability of values.



Richardson acknowledges that the moral considerations underlying
Sophie's dilemma are not incommensurable. Nonetheless, he takes
value incommensurability to be essential to understanding the tragedy
of the dilemma that Sophie encounters. "It is a distinguishing
feature of love, including parental love," he writes,
"that it cherishes the particular and unique features of the
beloved" (115). He concludes, "the fact that she cannot
adequately represent each child's value on a single scale is
what makes the choosing tragic" (116). By locating the
incommensurability of values at the level of what is valuable about
each of her children, Richardson argues that the tragedy of the
dilemma points to incomparability.



Another common approach to argue for value incommensurability is with
reference to "non-symmetrical" dilemmas. As the name
suggests, in non-symmetrical dilemmas, the alternatives are favored by
different values (Sinnott-Armstrong 1988). If these values are
incommensurable in the third sense as discussed in subsection 1.3,
there is no systematic resolution of the value conflict. Consider
Jean-Paul Sartre's well-known example of his pupil who faced the
choice between going to England to join the Free French Forces and
staying at home to help his mother live (Sartre 1975, 295-296). No
matter which alternative he chooses, certain values will remain
unrealized. An idea along these lines is considered, for example, by
Walter Sinnott-Armstrong (1988, 69-71) and Bernard Williams (1981,
74-78) in their discussions of moral dilemmas.


### 3.3 *Akrasia*



Value incommensurability also features in debates about
*akrasia* (Nussbaum 2001, 113-117). David Wiggins, for example,
invokes the idea of value incommensurability to suggest "the
heterogeneity of the psychic sources of desire satisfaction and of
evaluation" (1998, 266). This heterogeneity, according to
Wiggins, allows for a coherent account of the agent's attraction
to what is not best. It allows for a divergence between desire and
value such that the akratic individual can be attracted to a value
that should not be sought at that point in time. Wiggins invokes value
incommensurability to capture the idea that a gain in the value that
should not be sought does not reduce the loss in choosing what is not
best.



In contrast, Michael Stocker denies that value incommensurability is
required for a coherent account of *akrasia* (1990, 214-240).
For Stocker, coherent *akrasia* is possible with a single value
in just the way that it is possible to be attracted to two objects
that differ with respect to the same value (e.g., "a languorous
lesser pleasure and a piquant better pleasure" (1990, 230)).
Recall the discussion of quantitative and qualitative aspects of a
single value at the outset of section 3.


## 4. Deliberation and Choice



As suggested above much of the inquiry into value incomparability is
motivated more generally by theories of practical reason and rational
choice. Even if a conception of justified choice can accommodate value
incomparability, questions remain about how to justify choice on the
basis of incomparability and how to reason about incomparability. This
section considers these issues as they have been discussed in the
contemporary philosophical literature.



It is worth noting the potential for drawing connections between the
philosophical literature and the literature in psychology and the
social sciences on decision-making. One area for such potential is the
psychological literature on the difficulty of making decisions (Yates,
Veinott, and Patalano 2003). Jane Beattie and Sema Barlas (2001), for
example, advance the thesis that the observed variation in the
difficulty of making trade-offs between alternatives can be explained
in part by the category to which the alternatives belong. The authors
consider three categories: commodities ("objects that are
appropriately bought and sold in markets"), currencies
("objects that act as stand-ins for commodities"), and
noncommodities ("objects that either cannot be transferred
(e.g., pain) or that lose some of their value by being traded in
markets (e.g., friendship)") (Beattie and Barlas 2001, 30). The
authors' experimental findings are consistent with participants
holding normative commitments about exchanging currencies and
noncommodities similar to those considered in the discussion of
constitutive incommensurability in subsection 3.2. For example,
Beattie and Barlas report that participants "had a significant
tendency to choose noncommodities over commodities and
currencies" and that choices between noncommodities and
currencies were the easiest for participants (2001, 50-51). The
authors interpret these results to support the view that people choose
noncommodities over currencies on the basis of a rule without engaging
in a calculation of trade-offs (2001, 51-53). In the context of
empirical research, it should also be noted that philosophers have
contributed with empirical research on the characterization of hard
choices (Messerli and Reuter 2017a, 2017b).


### 4.1 Optimization and Maximization



At a minimum, for the choice of an alternative to qualify as
justified, there must not be an overriding reason against choosing it.
Beyond that, conceptions of justified choice differ in what is
required for the choice of an alternative to qualify as justified.



Ruth Chang defines "comparativism" as the view that
"comparative facts are what make a choice objectively correct;
they are that in virtue of which a choice is objectively rational or
what one has most or sufficient normative reason to do. So, whether you
are a consequentialist, deontologist, virtue theorist, perfectionist,
contractualist, etc., about the grounds of rational choice, you should
be, first and foremost, I suggest, a comparativist" (2016, 213).
If alternatives are incomparable, then the lack of a comparative fact
precludes the possibility of justified choice.



One response has been to argue that apparently incomparable
alternatives are, in fact, comparable. As discussed in subsection 2.2,
judgments of incomparability frequently involve comparisons that are
difficult and it may be that judgments of incomparability are mistaken
(Regan 1997) or that, due to vagueness, it is indeterminate which
value relation holds. In addition, as discussed, alternatives that
appear incomparable by way of "better than," "worse
than," or "equally good" may be comparable by way of
some fourth comparative relation, such as "roughly equal"
or "on a par." This means that there is a comparative fact
that makes a choice objectively correct in cases of apparent
incomparability. It does not, however, help us identify the
objectively correct alternative.



A common form of comparativism is *optimization*.
According to optimization, the fact that an alternative is at least as
good as the other alternatives is what justifies its choice.
Consequently, if two alternatives are incomparable no justified choice
can be made between them. Another line of response, one from within
the economics literature, has been to distinguish between
"optimization" and "maximization" as theories
of justified choice (Sen 1997, 746; Sen 2000, 486). The theory of
maximization as justified choice only requires the choice of an
alternative that is not worse than other alternatives. Because
incomparable alternatives are not worse than one another, the choice
of either is justified according to the theory of maximization as
justified choice. Maximization is thus a rejection of comparativism.
However, Hsieh (2007) argues that proponents of comparativism have no
reason to reject maximization as an account of justified choice and
consequently incomparability need not pose a problem for the
possibility of justified choice.


### 4.2 Cyclical Choice



One objection voiced against accounts that permit justified choice
between alternatives that are roughly equal or on a par or between
incomparable alternatives is that such accounts may justify a series
of choices that leaves a person worse off. Consider Raz's
example of career choice. Suppose the person chooses the musical
career over the legal career. At a future time, she has the
opportunity to pursue a legal career that is slightly worse than the
initial legal career. Suppose this slightly worse legal career and the
musical career are judged roughly equal or on a par. If justified
choice permits her to choose either of two alternatives when they are
roughly equal or on a par, then she would be justified in choosing the
slightly worse legal career. Similarly, if justified choice does not
require the comparability of alternatives, she could be justified in
choosing the slightly worse legal career. Through a series of such
apparently justified choices, she would be left significantly worse
off in a manner analogous to a "money pump" (Chang 1997,
11).



One response is to question whether the problem posed by choices of
this sort is serious. John Broome, for example, notes that after
having chosen one kind of career, a person may change her mind and
choose the kind of career she previously rejected. According to
Broome, there would be a puzzle only if she did not repudiate her
previous choice (2000, 34).



Another line of response is that the considerations that make some
alternatives worthy of choice count against the constant switching
among alternatives envisioned in this objection. First, the constant
switching among alternatives is akin to not choosing an alternative.
If the alternatives are such that choosing either is better than
choosing neither, then the considerations that make the alternatives
worthy of choice count against constantly switching among them.
Second, to switch constantly among careers appears to misunderstand
what makes the alternatives worthy of choice. Not only is pursuing a
career the kind of activity that depends upon continued engagement for
its success, but it is also the kind of activity that is unlikely to
be judged truly successful unless one demonstrates some commitment to
it. Third, for a career to be considered successful, it may require
the chooser to adopt a favorable attitude toward the considerations
that favor it over other careers. In turn, when subsequently presented
with the choice of a legal career, the considerations favoring it may
no longer apply to her in the same way as they did before (Hsieh
2007).



Ruth Chang advances a hybrid view on rational choice to meet the
challenge of cyclical choice. She distinguishes "given
reasons" from "will-based" reasons. Roughly put,
given reasons could here be understood as those that are grounded in
normative facts while will-based reasons are "reasons in virtue
of some act of the will; they are a matter of our creation. They are
voluntarist in their normative source. In short, we create will-based
reasons and receive given ones." (Chang 2013, 177). Will-based
reasons come into play when the given reasons no longer can guide our
actions. When two alternatives are on a par, given reasons fail to
guide us and at this stage, will-based reasons can provide guidance
and guarantee that the agent commits to her choice. Anders Herlitz
(2019) argues that Chang's approach and other "two-step
models" violate an intuitively plausible constraint on rational
choice called Basic Contraction Consistency. By violating this
constraint two-step models also allow for money pumps. This could,
however, possibly be avoided by introducing additional formal
conditions for the second step in the model (Herlitz 2019,
299-307).


### 4.3 Rational Eligibility



The idea expressed in the distinction between optimization and
maximization in subsection 4.1 can be expressed more generally in
terms of the idea of rational eligibility. To say that an alternative
is rationally eligible is to mean that choosing it would not be an
unjustified choice. Which alternatives are judged rationally eligible
may vary with the theory of justified choice. According to
maximization as a theory of justified choice, an alternative is
rationally eligible if and only if there is no better alternative.



Isaac Levi (1986; 2004) argues for
"*v*-admissibility" as a criterion of justified
choice. For *v*-admissibility, value incomparability does not
pose a problem for the possibility of justified choice. An alternative
is *v*-admissible if and only if it is optimal according to at
least one of the relevant considerations at hand. In some conflicts of
value, maximization and *v*-admissibility specify the same
alternatives as rationally eligible. Suppose that alternative
*X* is better than alternative *Y* with respect to
consideration *A* and alternative *Y* is better than
alternative *X* with respect to consideration *B*.
According to maximization as a theory of justified choice, both
*X* and *Y* are rationally eligible; neither alternative
is better than the other with respect to *A* and *B*
taken together. Both alternatives are also rationally eligible
according to *v*-admissibility; *X* is optimal with
respect to *A* and *Y* is optimal with respect to
*B*.



In some conflicts of value, maximization and *v*-admissibility
specify different sets of alternatives as rationally eligible.
*V*-admissibility is more restrictive than maximization (Levi
2004). Add to the above example alternative *Z*. Suppose that
*X* is better than *Z*, which is better than *Y*,
all with respect to *A*. Suppose also that *Y* is better
than *Z*, which is better than *X*, all with respect to
*B*. According to maximization as a theory of justified choice,
*X*, *Y*, and *Z* are rationally eligible; no
alternative is better than the other with respect to *A* and
*B* taken together. However, *Z* is not rationally
eligible according to *v*-admissibility. *Z* is not
optimal with respect to *A*. Nor is it optimal with respect to
*B*. Only *X* and *Y* are rationally eligible
according to *v*-admissibility. According to Levi,
*v*-admissibility captures what he takes to be a plausible
judgment--namely, that it would be unjustified to choose the
alternative that is second worse on all relevant respects (Levi 2004).
The plausibility of this judgment might be questioned. Suppose that
*Z* is only slightly worse than *X* with respect to
*A* and *Z* is only slightly worse than *Y* with
respect to *B*. Does the judgment still hold?



For Joseph Raz, incomparability also does not pose a problem for the
possibility of justified choice (1997). If incomparable options give
us reasons to choose both alternatives, they are both rationally
eligible from the perspective of justified choice. As such, the choice
of either alternative is justified on the basis of reason.



One question that arises is this. If an agent has reason to choose
either alternative and they are not equally good, what makes her
choice of one alternative over another intelligible to her? For Raz,
what explains the choice of one alternative over the other is the
exercise of the will. By the will, Raz has in mind "the ability
to choose and perform intentional actions" and "the most
typical exercise or manifestation of the will is in choosing among
options that reason merely renders eligible" (1997, 111).



John Finnis advances a similar view in response to the question of
intelligibility. Finnis writes, "in free choice, one has reasons
for each of the alternative options, but these reasons are not
causally determinative.... No factor but the choosing itself
*settles* which alternative is chosen" (1997, 220). In a
choice between alternatives each favored by different, incomparable
values, even though there are reasons to choose both alternatives,
because reasons are not causally determinative, the lack of a reason
to choose one alternative over another need not render the choice
unintelligible.



Donald Regan challenges this view. According to Regan, unless grounded
in an adequate reason, "a decision to go one way rather than
another will be something that happened to the agent rather than
something she did" and hence be unintelligible to the agent
herself (1997, 144). Suppose the agent has no more reason to choose
one alternative over another and the choice, as suggested above, is
settled by her wants. On Regan's view, if the agent's
choice is to be intelligible to her, her wants must be grounded in
reasons. Because she has no more reason to choose one alternative over
another initially, the reasons grounding her wants must be available
to her only after the initially relevant reasons are exhausted. This
strikes Regan as implausible (1997, 150). Regan concludes that no
choice between incomparable bearers of value is intelligible in the
ways suggested by Raz or Finnis.


### 4.4 External Resources



A number of authors have argued that practical reason has available to
it the resources to accommodate incomparability in ways that would
appear to address the concern raised by Regan.



Charles Taylor outlines two such sets of resources. First, we are able
to appeal to "constitutive goods that lie behind the life
goods" our sense of which is "fleshed out, and passed on,
in a whole range of media: stories, legends, portraits of exemplary
figures and their actions and passions, as well as in artistic works,
music, dance, ritual, modes of worship, and so on" (1997, 179).
Second, we cannot escape the need to live an integrated life or to
have this, at a minimum, as an aspiration (1997, 180). Given that a
life is finite, leading a life involves an articulation of how
different goods fit into it relative to one another. More generally,
our lives take on a certain "shape" and this shape
provides guidance in making choices in the face of incomparability
(1997, 183). Michael Stocker similarly points out that alternatives
are rarely considered in the abstract (1997). Instead, they are
usually considered in concrete ways in which they are
valuable--for example, as part of one's life. Once
considered in such concrete contexts, there are considerations
according to which alternatives can be evaluated for purposes of
justified choice. In his analysis of incommensurability, Fred
D'Agostino discusses the role of social institutions in
resolving value conflicts (2003).



Another resource that has been invoked is morality. Recall Elizabeth
Anderson's discussion of the example of the choice between
saving the life of one's mother and maintaining a close
friendship. Anderson regards the attempt to invoke a comparison of
values as incoherent from the perspective of practical reason.
Instead, ordinary moral thinking focuses on the obligations one has to
one's mother and one's friends. In turn, Anderson suggests
that the obligations themselves will provide guidance (1997, 106). The
availability of such resources to reason is independent of her
theories of value and rationality. John Finnis also points to
principles of morality as guiding reason which avoids comparability
problems (1997). It remains an open question as to how wide a range of
cases it is in which morality can provide such guidance.



One worry that may arise in appealing to such external resources is
that they address the problem of incomparability by simply denying it.
The shape of one's life or the "constitutive goods that
lie behind the life goods," for example, would appear to be
sources of value. Insofar as they provide a value against which to
resolve the initial value conflict, it might be said that there was no
problem of incomparability in the first place.



Two responses to this worry can be given. First, even if these
external resources can ground comparisons, it does not follow that
they provide a systematic resolution to value conflicts. Insofar as
the shapes of people's lives differ, the way in which two
individuals resolve the same value conflict may be different. The fact
that it may be consistent with reason to resolve the same value
conflict in different ways points to the possibility of
incomparability.



Second, in the case of moral considerations, there may not be any
denial of incomparability. Moral considerations may provide guidance
without comparing alternative courses of action (Finnis 1997,
225-226). Furthermore, some philosophers argue that the moral
wrongness of certain actions is intelligible only in virtue of
incomparability. For example, Alan Strudler argues that to deliberate
about the permissibility of lying in terms of comparable options is to
misunderstand the wrong in lying (1998, 1561-1564).


### 4.5 Non-Maximizing Choice



It would appear that conceptions of justified choice that do not rely
on comparisons avoid the problems posed by incomparability. Stocker
aims to provide one such account of justified choice (1990; 1997). Two
features help to distinguish his account. First, he argues for
evaluating alternatives as "the best" in an absolute,
rather than a relative, sense. Optimization and maximization rely on
choosing "the best" in a relative sense: given the
relevant comparison class, there is no better alternative. To be
"the best" in an absolute sense, an alternative
"must be, of its kind, excellent--satisfying, or coming
close to, ideals and standards" (1997, 206). This is the sense,
for example, in which a person can be the best of friends even if we
may have even better friends. More generally, an alternative can be
absolutely best even if there are better alternatives, and even if an
alternative is relatively best, it may not be absolutely best. The
second distinctive feature of Stocker's account is his appeal to
a good life, for example, or part of a good life or project. This
appeal does not require the alternative to be the best for that life
or project. Instead, the alternative need only be good enough for that
life or project to qualify as a justified choice.



Stocker's account of justified choice differs from the concept
of "satisficing" as used in the economics and rational
choice literature. Introduced into the economics literature by Herbert
Simon (1955), satisficing is the process of choosing in which it is
rational to stop seeking alternatives when the agent finds one that is
"good enough" (Byron 2004). Where satisficing differs from
Stocker's account is that satisficing is instrumentally rational
in virtue of a more general maximizing account of choice. In
situations in which finding the best alternative is prohibitively
costly or impossible, for example, satisficing becomes rational. In
contrast, on Stocker's account, choosing the alternative that is
"good enough" is non-instrumentally rational (Stocker
2004).



Objections discussed in previous sections may be raised with respect
to Stocker's account. Suppose two alternatives are both good in
an absolute sense and incomparable. According to Stocker's
account, insofar as both alternatives are good enough for an
agent's life, the choice of either alternative appears
justified. As discussed in subsection 4.2, Regan and others may object
that the choice of either alternative is not intelligible to the
agent. Also, the appeal to a good life may raise the worry discussed
in subsection 4.4 that Stocker's account addresses the problem
of incomparability by simply denying it.


### 4.6 Deliberation about Ends



The topics of value incommensurability and incomparability also arise
in accounts that concern deliberation about ends. This section
discusses two accounts.



The first account is by Henry Richardson (1994). Richardson argues for
the possibility of rational deliberation about ends. According to
Richardson, if comparability is a prerequisite for rational choice,
choices involving conflicting values could be made rationally if each
of the values were expressed in terms of their contribution to
furthering some common end. This conception of choice treats this
common end as the one final end relevant for the choice. According to
Richardson, the idea that comparability is a prerequisite for rational
choice seems to rule out rational deliberation about ends (1994,
15).



Richardson defends an account of rational deliberation about ends that
does not depend upon comparability. In his account, rational
deliberation involves achieving coherence among one's ends.
Briefly, coherence is "a matter of finding or constructing
intelligible connections or links or mutual support among them and of
removing relations of opposition or conflict" (Richardson 1994,
144). For Richardson, coherence among ends need not result in their
being comparable (1994, 180).



The second account is by Elijah Millgram (1997). Like Richardson,
Millgram argues that comparability is not a prerequisite for
deliberation. However, in contrast to Richardson, Millgram argues that
practical deliberation results in the comparability of ends (1997,
151). By this he means that through deliberation, one develops a
coherent conception of what matters and a "background against
which one can judge not only that one consideration is more important
than another, but *how much* more important" (1997, 163).
For Millgram, comparing one's ends is a "central part of
attaining unified agency" (1997, 162).



Millgram proposes two ways in which deliberation results in the
comparability of ends. The first proposal is that one can learn what
is important and how it is important through experience (1997, 161).
The second proposal is that deliberation about ends is
"something like the construction by the agent of a conception of
what matters ... out of raw materials such as desires, ends,
preferences, and reflexes" (1997, 168). Millgram identifies an
objection to each proposal and briefly responds to each.



The objection to the first proposal is this. If the incomparability of
ends can be resolved by experience, this suggests that the judgment of
incomparability reflects incomplete knowledge about the values
expressed in these ends. In other words, experience seems to help only
if the values expressed in these ends are themselves comparable (1997,
168). Millgram responds as follows. The agent who uses her experience
to develop a coherent conception of what matters is like the painter
who uses her experience to paint a picture that is not a copy of an
existing image. Even if the ends are comparable in her conception of
what matters, the values they reflect need not be comparable just as
the painting need not be an exact copy of an existing image.



The objection to the second proposal is this. The second proposal
suggests that deliberation is not driven by experience, which places
it in tension with the first proposal. Millgram responds by continuing
the analogy with the painter. Imagine a painter who paints a picture
that is not a copy of an existing image. Just because the painting is
not a copy of an existing image does not mean there is no source of
correction and constraint on it. Similarly, deliberation may involve
the construction by the agent of a conception of what matters, but
this does not imply that it is not informed or constrained by
experience (1997, 168-169).


### 4.7 Risky Actions



Caspar Hare (2010) introduces and discusses a problem relating to how
rational choice theory can encompass risky actions involving outcomes
that are on a par. If we assume that two outcomes, *A* and
*B*, are on a par, it follows that a small improvement, or mild
sweetening as Hare phrases it, to one of the outcomes would not break
the parity relation. We can imagine two actions, *X* and
*Y*. If we opt for *X* then we will either end up with a
sweetened *A* in state 1 or a sweetened *B* in state 2, and
the outcomes are equiprobable. If we opt for *Y*, we will end up
with *B* in state 1 or *A* in state 2, and the outcomes are
equiprobable. On the one hand, it seems as if we ought to opt for
*X* since we will end up with a sweetened alternative, *A*+
or *B*+. On the other hand, it is difficult to say why *X*
is better than *Y*. The outcome in state 1 is not better if we do
*X* rather than *Y* since the outcomes, *A*+ and
*B*, are on a par, and the outcome in state 2 is not better if we
do *Y* rather than *X* since the outcomes, *B*+ and
*A*, are on a par. The problem can be construed as a lottery
where one lottery is deemed comparable with another, yet their outcomes
are incomparable (see Rabinowicz, 2021b, for this axiological
formulation of Hare's problem). Hare argues that we should
"take the sugar", i.e., we ought to opt for X (see also
Bader 2019). Inspired by a Fitting-Attitudes Analysis of value Wlodek
Rabinowicz argues that even though outcomes may be on a par, it is
possible for an action to be better than another (2021b). Others such
as Schoenfield (2014), Bales, Cohen & Handfield (2014), and Doody
(2019) reach the opposite conclusion.


## 5. Social Choices and Institutions



As discussed above, social practices and institutions play a role in
the inquiry into value incommensurability and incomparability. They
are claimed by some philosophers to ground the possibility of these
phenomena as in the case of constitutive incommensurability
(subsection 3.2), and to help resolve value conflicts, as in the case
of providing external resources for practical reason (subsection 4.4).
This section discusses additional areas in which considerations about
social institutions intersect with the inquiry at hand.



To begin, some philosophers have pointed to a structural similarity
between a single individual trying to choose in the face of
incomparability and the process of incorporating the varied interests
and preferences of the members of society into a single decision. The
preferences of different individuals, for example, may be taken to
reflect differing evaluative judgments about alternatives so that
combining these different preferences into a single decision becomes
analogous to resolving value conflicts in the individual case. Given
this analogy, Fred D'Agostino has applied methods of
decision-making at the social level from social choice theory and
political theory to consider the resolution of value conflicts at the
individual level (2003).



At the same time, Richard Pildes and Elizabeth Anderson caution
against wholeheartedly adopting this analogy. The analogy, according
to them, assumes that individuals already have rationally ordered
preferences. Given incomparability, however, there is no reason to
make such an assumption. In turn, Pildes and Anderson argue that
"individuals need to participate actively in democratic
institutions to enable them to achieve a rational ordering of their
preferences for collective choices" (1990, 2177).



Value incommensurability and incomparability also have been considered
with respect to the law. Matthew Adler discusses the variety of ways
in which legal scholars have engaged the topic of value
incommensurability (1998). One question is whether the possibility of
value incommensurability poses a problem for evaluating government
policy options and laws, more generally. Some authors respond that it
does not. Cass Sunstein, for example, argues that recognition of value
incommensurability helps "to reveal what is at stake in many
areas of the law" (1994, 780). According to Sunstein, important
commitments of a well-functioning legal system are reflected in
recognizing value incommensurability.



More generally, a number of scholars have focused on the relation
between incomparability and the structure of social and political
institutions. John Finnis, for example, takes the open-endedness of
social life to render it impossible to treat legal or policy choices
as involving comparable alternatives (1997, 221-222). Michael
Walzer's account of distributive justice also relates
incomparability to the structure of social and political institutions.
According to Walzer (1983), different social goods occupy different
"spheres," each one governed by a distinct set of
distributive norms. What is unjust is to convert the accumulation of
goods in one sphere into the accumulation of goods in another sphere
without regard for that second sphere's distributive norms.
Underlying Walzer's account, it seems, is a commitment to a kind
of constitutive incommensurability. Given its connection to the
possibility of plural and incompatible ways of life, the concepts of
value incommensurability and incomparability also play a role in many
accounts of political liberalism, including Joseph Raz's account
(1986) and Isaiah Berlin's account (1969). The latter's
inquiry into the relation between incommensurable values and political
institutions motivated much of the further inquiry into the topic.