Things are sometimes said to be incommensurable. The meaning of theterm can take many different interpretations. Central to allinterpretations, however, is the difficulty of making comparisons,often raising profound questions about practical reason and rationalchoice. This entry explores these interpretations, examines commontheories on what it means for two things to be incommensurable withrespect to value, and considers the implications of valueincommensurability

• 1. Measurement and Comparison
  • 1.1 The Many Meanings of “Incommensurable”
• 2. The Possibility of Incommensurability
  • 2.1 Incommensurability is Vagueness
  • 2.2 “Roughly Equal” and “On a Par”
• 3. Arguments for Value Incommensurability
  • 3.1 Constitutive Incommensurability
  • 3.2 Moral Dilemmas
• 4. Deliberation and Choice
  • 4.1 Optimization, Maximization, and Comparativism
  • 4.2 Cyclical Choice
  • 4.3 Risky Actions
• 5. The Repugnant Conclusion and Spectrum Arguments
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Measurement and Comparison

Much of life involves making comparisons as we weigh the merits of theoptions available to us. These choices can seem trivial, like decidingbetween cereal or oatmeal for breakfast, or they can be moresignificant, like choosing whether to study law or philosophy. Often,we can identify the best option for us. But sometimes, making acomparison feels impossible, as neither option seems to be better,worse or equally good as the other. This difficulty of determining howthe options relate can be due to the fact that the options areincommensurable.

In this case, it is the options that are incommensurable. Thephenomenon can more generally be said to hold between particularbearers of value where “bearer of value” is to beunderstood broadly and can include things such as objects of potentialchoice (such as a career) or states of affairs that cannot be chosen(such as a beautiful sunset). Such bearers of value are valuable invirtue of the abstract value or values they instantiate ordisplay.

While it’s clear that value incommensurability can complicateeveryday decision-making, it also presents a theoretical challenge fornormative theories that assume options and values can be readilycompared and ranked. What remains less clear, however, is how weshould understand incommensurability. The term has been used todescribe different phenomena, each with various explanations. Thisfirst section will provide an overview of how “valueincommensurability” has been interpreted.

1.1 The Many Meanings of “Incommensurable”

The term “incommensurable” suggests a lack of commonmeasure. In philosophical discussions, it more specifically refers tothe absence of either a cardinal scale or an ordinal scale by which wecan compare the values of two value bearers. Some authors reserve theterm “incommensurable” for comparisons that can be madeordinally, but not cardinally (Stocker 1980, 176; Stocker 1997, 203;Chang 1997, 2). That is, to some, oatmeal may be clearly better thancereal for breakfast, but it is impossible to say how much better.

Others offer a more demanding definition of the term. They do notconsider the absence of a cardinal scale sufficient; forincommensurability to hold, even an ordinal comparison or ranking mustbe impossible (e.g., Raz 1986; Rabinowicz 2021a). On thisinterpretation, incommensurability refers to the relationship betweentwo items when neither is better than the other, nor are they equallygood.

Some prefer a definition of incommensurability in which two valuebearers are considered incommensurable if their relationship can onlybe described in negative terms—that is, no positive valuerelation holds between them. This definition depends on the notion“positive value relation” which lacks a clear definitionbut is believed to be intuitively understandable. Traditionally, it isassumed that there are three such relations: betterness, worseness,and equality. If this traditional view is correct, this definitionaligns extensionally with the interpretation mentioned above. However,if additional positive value relations are acknowledged, as some arguethey should be, the two interpretations diverge. This possibility willbe discussed in Section 2. Both definitions, however, explain why itis difficult, and even impossible, to determine whether cereal isbetter, worse, or equally as good as oatmeal for breakfast, giventheir incommensurability.

Others have not given an exact definition of the term, but use it asan inclusive umbrella term for comparability problems in general. Thisinclusive interpretation has the advantage of encompassing a field ofdiverse philosophical discussions that engage in problems concerningvalue comparisons. However, this inclusiveness comes at the cost ofprecision. James Griffin, for example, gives two examples of what helabels incommensurability. One involves what he calls“trumping.” In a conflict between valuesA andB,A is said to trumpB if“any amount ofA, no matter how small, is morevaluable thanany amount ofB, no matter howlarge” (Griffin 1986, 83). A weaker form of valueincommensurability involves what Griffin calls“discontinuity.” Two values,A andB,are incommensurable in this sense if “so long as we have enoughofB any amount ofA outranks any further amount ofB; or that enough ofA outranks any amount ofB” (Griffin 1986, 85). These suggested forms ofincommensurability are, however, compatible withA andB being cardinally measurable. For example, in the case of“discontinuity,” if some amount ofA is betterthan any amount ofB, this superiority might still bemeasurable with a precise cardinal value. The fact that additionalinstances ofB do not change the ordinal ranking ofA andB does not entail that the evaluativedifference between them cannot be expressed cardinally. This, andother forms of incommensurability compatible with cardinal rankings,will not be discussed further in this entry.

To complicate matters further, not only is the notion of valueincommensurability used differently by philosophers, but the termvalue incomparability is also common in the literature, withno clear consensus on its meaning. Some authors use the terms“incommensurability” and “incomparability”interchangeably (e.g., Raz 1986). Others use them to refer to distinctconcepts (e.g., Chang 1997).

In this entry, the term “incomparable” will refer to caseswhere no positive value relation exists between two value bearers(Chang 1997). The term “incommensurable” will refer to thecases where neither value bearer is better than the other nor are theyequally as good. As mentioned above, if the standard three valuerelations fully exhaust the space of possible value relations the twoterms will point to the same examples, but, as will be discussed inSection 2, we shall not assume that there are only three positivevalue relations. If there are additional positive value relations,incomparability is one, but not the only, subset ofincommensurability.

Of course, when two value bearers are incommensurable, cardinalcomparisons are impossible. Unfortunately, our terminology lacks adistinct term to describe cases where cardinality is absent, butordinality remains possible. While this is an interesting possibility,it has received less attention than the more radical notion of valueincommensurability. For this reason, ordinality without cardinalitywill not be addressed further in this entry.

Value comparisons are often taken to be a three-place relation:A is compared withB with respect toV.“V” is here some specific consideration for whichthe items are being compared. One career may be incommensurable toanother with respect to the sense of purpose it will bring to yourlife, yet they may be comparable with respect to financial stabilitysince one is clearly better than the other in this regard. Some arguethat without specifying this “covering consideration” thecomparative claim makes no sense (Chang 1997; Thomson 1997; Andersson2016b). Often, however, the covering consideration is not explicitlyexpressed but implicitly assumed by the context of utterance.

Specifying the covering consideration also allows us to identify“noncomparability”. If the covering considerationisn’t applicable to the items we are comparing, then they arenoncomparable. For example, the number four is noncomparable with thecolor blue with respect to their tastiness. This form of comparativefailure is considered to be of no interest from the perspective ofpractical reasoning and is consequently not given much considerationin the literature.

2. The Possibility of Incommensurability

The philosophical interest on incommensurability is often motivated byits possible significance for rational choice (Broome 1997, 2000;Chang 1997, 2002; Griffin 1986; Raz 1986). Comparing alternatives iscentral for rational choice, intuitively we want to know whatalternative is the best, and thus examples of incommensurability maypose a challenge to rational decision-making. As we will see, manyhave met this challenge by developing theories of rational choice thatallow for incommensurability or reject the possibility ofincommensurability. However, let us first consider the arguments infavor of incommensurability.

The possibility of incommensurability is often argued for byintroducing examples that seem to point to its possible instantiation.These examples often take a form similar to that of Joseph Raz’sexample in which a person faces the choice between two successfulcareers: one as a lawyer and one as a clarinettist. Neither careerseems better than the other, and they also do not appear to be equallygood. If they were of equal value, then a slightly improved version ofthe legal career would be better than the musical career, but thisjudgment appears incorrect (Raz 1986, 332).

Ruth Chang has called this the “Small ImprovementArgument” (Chang 2002, 667). The Small Improvement Argumenttakes the following general form: If (1)A is neither betternor worse thanB (with respect toV), (2)A+ is better thanA (with respect toV),(3)A+ is not better thanB (with respect toV), then (4)A andB are not better, worseor equally as good (with respect toV), whereVrepresents the relevant set of considerations for purposes of thecomparison (Chang 2002, 667–668). By providing examples in whicheach premise is true we have succeeded in showing that there isincommensurability.

In addition to Raz, Derek Parfit, and Walter Sinnott-Armstrong areamong those who have advanced the Small Improvement Argument (Parfit1984; Sinnott-Armstrong 1985). A similar argument, but for preferencerelations has, however, a longer history. Leonard J. Savage hints atthis possibility already 1954, in 1958 R. Duncan Luce presented aversion of the argument that he attributes to Howard Raiffa, and itwas also discussed by Ronald de Sousa in 1974 (Savage 1954; Luce 1958;de Sousa 1974).

Some, however, do not accept the Small Improvement Argument; theyreject the possibility of incommensurability and argue for completecomparability. For example, it could be that value bearers are, infact, comparable, but due to epistemic constraints, they appearincommensurable to us (Forrester 2022). With more knowledge about thevalue bearers, it might be possible to provide both an ordinal andcardinal ranking of them, but for some reason, acquiring all therelevant knowledge may be practically difficult or even impossible.Others argue that the relevant concepts or natural language do notallow for incommensurability (Regan 1997; Dorr, Nebel & Zuehl2023). One way to argue for this is to claim that it is a logical factthat all comparatives take the form “x is at least asF asy” or “y is at least asF asx”. From considerations such as these, itis established that there cannot be value incommensurability.

Another influential view is that the Small Improvement Argument merelyestablishes incommensurability and not incomparability; the argumentpoints to the existence of additional value relations beyond“better than”, “worse than”, and“equally as good”. It is argued that incommensurabilitydoes not imply incomparability but rather involves a positive valuerelation. This perspective is preferable from the perspective ofrational choice, as it is argued that the existence of a positivevalue relation between two options allows for a rational decision tobe made (more on this in 4.1). This view is often contrasted with aconservative view, which holds that alleged cases ofincommensurability can be accounted for within the framework of thethree standard value relations if we acknowledge the possibility ofvagueness.

The next two sections summarize the two latter views.

2.1 Incommensurability is Vagueness

It is plausible that it can be indeterminate of two items how theyrelate with respect to their value. That is, there can be valueindeterminacy, which is a separate notion from valueincommensurability and value incomparability. For example, Raz arguedthat both incomparability and indeterminacy of value are possible,with the latter resulting from the “general indeterminacy oflanguage” (1986, 324).

In contrast, some philosophers argue that there is noincommensurability and that indeterminacy can account for allegedcases of incommensurability (Griffin 1986, 96; Broome 1997, 2000,2022; Andersson 2017; Elson 2017; Dos Santos 2019). In essence, it isirrefutable that semantic vagueness exists. For example, consider thepredicate “is bald.” This predicate is vague because ithas borderline cases: some individuals are clearly bald, others areclearly not bald, and some fall into a borderline category where it isindeterminate whether they are bald. This indeterminacy does notdissolve by making a precise count of the number of hairs on theindividuals that fall into the borderline category; the indeterminacyarises from the vagueness of the predicate.

The same applies to value predicates such as “is at least asgood as.” For instance, while it may be obvious thatAis at least as good asB and thatB is at least asgood asC, the predicate may exhibit borderline cases. Itmight be indeterminate whetherD is at least as good asB or whetherB is at least as good asD.The vagueness of the predicate can thus lead to situations where it isindeterminate which value relation—such as “betterthan,” “worse than,” or “equally goodas”—holds between the items being compared. Thisindeterminacy, it is argued, can easily be mistaken forincommensurability. Remember, incommensurability arises when it isfalse that one value bearer is better, worse, or equally as good asanother. Indeterminacy, on the other hand, occurs when it is neithertrue nor false that any of these relations individually obtain.Furthermore, indeterminacy is often considered less worrisome thanincommensurability; after all, one of the standard value relationsdoes obtain, but it is indeterminate which one.

Adherents of the view have also argued that the Small ImprovementArgument fails to rule out the possibility that it is indeterminatehow the value bearers relate; they may be related by one of thestandard trichotomous relations, but it could be indeterminate whichone (Wasserman 2004; Klockseim 2010; Gustafsson 2013a).

There are also more positive arguments in favor of the vaguenessinterpretation. The most influential comes from John Broome, whoargues that vagueness is incompatible with incommensurability.Therefore, since vagueness cannot be denied, Broome suggests we shouldreject incommensurability. His argument is somewhat technical andrequires a detailed explanation that cannot be fully provided here.But it can be noted that central to his argument is his controversial“collapsing principle” for comparatives (1997, 74). Manycounterexamples have been presented to show the implausibility of theprinciple (Carlson 2004, 2013; Elson 2014b; Gustafsson 2018). Whilethere are attempts to defend the collapsing principle, or versions ofit (Constantinescu 2012; Andersson & Herlitz 2018), thecounterexamples weaken Broome’s argument. If the principlecentral to his reasoning is questionable, we should be cautious aboutaccepting his conclusion that incommensurability does not exist.

There are, however, additional arguments supporting the vaguenessinterpretation. For example, some argue that it is theoreticallyparsimonious: since it is natural to accept the existence ofevaluative vagueness, and if it can easily account for alleged casesof incommensurability, there is no need to accept the more mysteriousnotion of incommensurability or introduce additional value relationsbeyond the standard trichotomous ones (Andersson 2017; Elson2017).

2.2 “Roughly Equal” and “On a Par”

Others have argued that the Small Improvement Argument may supportvalue incommensurability but it need not necessarily support theexistence of incomparability. Instead, they propose that some or allcases of incommensurability represent a previously overlookedadditional way in which things can be positively related.

Central to their argument is the claim that the Small ImprovementArgument implicitly assumes that things can only be positively relatedin terms of one of the standard trichotomy of comparative relations,“better than,” “worse than,” or “equallygood” this is what Chang calls the “TrichotomyThesis” (2002b, 660). If these three comparative relations donot exhaust the space of comparative relations we cannot arrive at theconclusion that the items under consideration are not positivelyrelated; the musical career and the legal career may, in fact, becomparable with respect to a fourth value relation.

The first arguments along these lines were expressed by James Griffinand Derek Parfit who argue that items may in fact be “roughlyequal” and hence comparable (Griffin 1986, 80–81,96–98, and 104; 1997, 38–39; 2000, 285–289; Parfit1987, 431). As an illustration, Parfit presents an examplestructurally similar to Raz’s comparison of two careers. InParfit’s example, the comparison involves two poets and anovelist competing for a literary prize (1987, 431). Neither the FirstPoet nor the Novelist is worse than the other and the Second Poet isslightly better than the First Poet. If the First Poet and theNovelist were equally good, it would follow that the Second Poet isbetter than the Novelist. This judgment, according to Parfit, need notfollow. Instead, the First Poet and the Novelist may be roughly equal.The intuition is that even though three items display the respects invirtue of which the comparisons are made, some comparisons areinherently rough so that even though two alternatives are not worsethan one other, they are not precisely equally good. In turn, themusical and legal careers in Raz’s example may be roughly equal.Parfit later referred to this possibility as there being“evaluative imprecision” allowing for the relation“imprecisely equally as good” (Parfit 2016, 113).

“Roughly equal,” as used here, is to be distinguished fromtwo other ways in which the term has been used: (1) to refer to asmall difference in value between two items and (2) to refer to achoice of little significance (Raz 1986, 333). As used here, two itemsA and B are said to be roughly equal if neither is worse than theother and C’s being better than B does not imply that C isbetter than A when the comparisons are all in virtue of the same setof respects.

One way to conceive of “roughly equal” is as a“roughed up” version of “equally good.” Onthis interpretation, the trichotomy thesis holds; there are only threepositive value relations, but these can be precise or rough (Chang2002, 661, fn. 5). This account may appear very similar to thevagueness interpretation; however, it is important to note that Parfitexplicitly distinguishes it from semantic vagueness (Parfit 2016).When introducing the notion of “evaluative imprecision,”he explicitly states: “Such imprecision is not the result ofvagueness in our concepts, or our lack of knowledge, but is part ofwhat we would know if we knew the full facts” (2016, 113). Thismight suggest that imprecision is akin to metaphysicalvagueness—i.e., vagueness inherent in the fabric of the worldrather than our concepts. However, Parfit rejects this interpretationas well. According to him, evaluative imprecision and rough equalityshould not be equated with vagueness.

A similar but separate and more developed proposal is RuthChang’s argument for the concept of “on a par”(Chang 1997; Chang 2002). Two items are said to be on a par if neitheris better than the other, their differences preclude their beingequally good, and yet they are not incomparable. Imagine comparingMozart 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 not incomparable but infact comparable with respect to creativity. Something positive can besaid about their relative merits with respect to the sameconsideration. According to Chang, they are on a par.

To argue for the comparability of the two artists, Chang presents the“Chaining Argument”. She asks us to imagine a sequence ofsculptors who are successively worse than Michelangelo until we arriveat a sculptor who is clearly worse than Mozart in terms of creativity.Chang then brings to bear the intuition that “between twoevaluatively very different items, a small unidimensional differencecannot trigger incomparability where before there wascomparability” (2002b, 673). In light of this intuition, becauseMozart is comparable to this bad sculptor, Mozart is also comparableto each of the sculptors in the sequence, including Michelangelo. (Forobjections to the argument see Boot 2009; Elson 2014a; Andersson2016a).

Chang argues that her account differs from Parfit’s, assertingthat parity constitutes a distinct fourth value relation rather than a“roughened” version of equality. On her interpretation,rough equality corresponds to betterness or worseness withoutcardinality. That is, stating that the First Poet is roughly equal tothe Novelist is equivalent to asserting that one is better than theother, though it is impossible to specify by how much. On thisinterpretation of “rough equality,” there is a starkdifference between the notions. Unfortunately, the elusiveness ofParfit’s “rough equality” and “impreciseequality” makes it difficult to determinately ascertain howthese notions ought to be understood and, consequently, how theydiffer from Chang’s concept of parity.

Interestingly, some have argued that we can accept parity and acceptthe trichotomy thesis. For example, Erik Carlson (2010) has arguedthat parity can be defined in terms of the three standard comparativerelations and provides a formal definition of the relation.

Inspired by Joshua Gert (2004), Wlodek Rabinowicz (2008; 2012) hasargued that while the trichotomy thesis may be false, the existence ofparity does not threaten the traditional trichotomy of preferencerelations: prefer, equiprefer, and disprefer. He demonstrates this byproviding a Fitting Attitudes account of value. The Fitting Attitudesaccount typically analyzes goodness in terms of a normative componentand an attitudinal component. By acknowledging that there can be twolevels of normativity— requirement, and permissibility—theaccount accommodates both parity and standard value relations.

On the account,X is better thanY if and only if itis rationally required to preferX toY, andX andY are on a par if and only if it is rationallypermissible to preferX toY and also rationallypermissible to preferY toX. Interestingly,preferences and the lack of preferences, combined with the two levelsof normativity, yield 15 possible combinations. This means that theFitting Attitudes analysis provides conceptual space for 15 possiblevalue relations. Rabinowicz thus provides an account that allows forseveral value relations beyond parity, betterness, worseness, andequality, making Chang’s claim about a fourth possible valuerelation seem modest. However, he acknowledges that these are merelylogical possibilities and that other factors may limit which of thesecan be instantiated. While there is room for plenty of relations, hedefines imprecise equality in the same way as parity.

Johan Gustafsson (2013b) has, however, questioned Rabinowicz’sapproach. He aims to show that the axiological argument for parity canalso apply to preference relations. Thus, if Chang’s argument iscorrect, we should also accept the possibility of a fourth preferencerelation.

3. Arguments for Value Incommensurability

While recent research has focused on interpreting examples with thestructure described by the Small Improvement Argument, earlierresearch placed less emphasis on the structure of value and insteadconcentrated on substantive considerations that supportedincommensurability, which at the time was understood to imply valueincomparability.

The most obvious argument for value incommensurability comes fromvalue pluralism (e.g., Berlin 1969). If one value bearer instantiatesone value and another value bearer instantiates a completely differentvalue, then it is possible that these two value bearers areincommensurable with respect to their value. One can of course resistthis claim and object that the two value bearers may be comparabledespite the fact that they instantiate values that differ greatly incharacter. Here the notion of “covering consideration”becomes relevant. When comparing value bearers with respect to theiroverall value, they may seem incommensurable. However, there can beother covering considerations to which they are comparable. To give anexample: an act that instantiates equality may seem incommensurablewith an act that instantiates liberty when considering their overallvalue. However, if the focus shifts to the criterion of increasingliberty, the latter act is clearly better.

Pluralism alone does not necessarily entail incommensurability.However, many of the arguments in favor of value incommensurabilityprovide examples of cases where we face choices involving alternativesthat instantiate different values, and which we intuitively deem to beincommensurable. Thus, pluralism is often accepted, either implicitlyor explicitly.

One need, of course, not refer to a plethora of values in order toargue for the possibility of incommensurability. Two values that arenormatively irreducible are sufficient. Consider e.g., the Dualism ofPractical Reason as discussed by Henry Sidgwick. Roughly, Sidgwick(1874 p. 507–509) argued that what is morally right cansometimes conflict with what is prudential right. Our duty and ourself-interest are derived from different basic principles and are thusnormatively irreducible. This results in a dualism of practical reasonthat can, on some occasions, lead to conflicting requirements. In thesame sense, it is possible to argue that there are personal andimpersonal values that are normatively irreducible and hence give riseto incommensurability.

We should also note that value monism may be compatible withincommensurability. As Ruth Chang points out, by referring to JohnStuart Mill, that value may have both qualitative and quantitativeaspects could in principle allow for value bearers to be incomparabledue to a difference in their qualitative features. (Chang 1997,16–17). To this, one can of course question if Mill is to becharacterized as a monist.

In this section, some specific, substantial considerations in favor ofincommensurability will be discussed.

3.1 Constitutive Incommensurability

It has been argued that value incommensurability is constitutive ofcertain goods and values and consequently, we should assume itsexistence.

One version of this argument comes from Joseph Raz. Consider beingoffered a significant amount of money to leave one’s spouse fora month. The indignation that is typically experienced in response tosuch an offer, according to Raz, is grounded in part in the symbolicsignificance of certain actions (1986, 349). In this case, “whathas symbolic significance is the very judgment that companionship isincommensurable with money” (1986, 350). Although this form ofvalue incommensurability looks like trumping, Raz does not see this asa case of trumping. He rejects the view that companionship is morevaluable than money. If such a view were correct, then those who forgocompanionship for money would be acting against reason (1986, 352).Instead, Raz takes the view that a “belief in incommensurabilityis itself a qualification for having certain relations” (1986,351). Someone who does not regard companionship and money asincommensurable simply has chosen a kind of life that may befulfilling in many ways, but being capable of having companionship isnot one of them.

In Raz’s account, the symbolic significance of judging money tobe incommensurable with companionship involves the existence of asocial 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 inRaz’s account raises a question for some authors about itsrobustness as an account of value incommensurability. For example,Chang objects that incommensurability appears to become relative toone’s participation in social conventions (2001, 48). It remainsan open question how much of a problem this point raises. Raz’saccount appears to illustrate a basic sense in which the values ofmoney and companionship can be incommensurable. Insofar as it is notagainst reason to choose money over companionship, there is no generalway to resolve a conflict of values between money and companionship.In Raz’s account, the resolution depends upon which socialconvention one has chosen to pursue.

Elizabeth Anderson advances a second argument for constitutiveincommensurability. Her account is grounded in a pragmatic account ofvalue. Similar to a Fitting Attitudes account of value Andersonreduces “‘x is good’ roughly to ‘it isrational to value x,’ where to value something is to adopttoward it a favorable attitude susceptible to rationalreflection” (1997, 95). She argues that in virtue of theseattitudes, there may be no good reason to compare the overall valuesof two goods. Pragmatism holds that if such a comparison serves nopractical function, then the comparative value judgment has no truthvalue, meaning that the goods are incommensurable (1997, 99). Becausethe favorable attitudes one adopts toward goods help to make themgood, Anderson’s account has been seen as an argument forconstitutive incommensurability (Chang 2001, 49). However, it would bemore correct to label it constitutive indeterminacy since on her viewit is not false that the standard value relations obtain, it is ratherneither true nor false that they obtain.

Anderson advances three ways in which there may be no good reason tocompare the overall values of goods. First, it may be boring orpointless to engage in comparison. To illustrate, “the projectof comprehensively ranking all works of art in terms of theirintrinsic aesthetic value is foolish, boring, and stultifying”(1997, 100). Second, Anderson points to instances in which “itmakes sense to leave room for the free play of nonrational motivationslike whims and moods” as in the choice of what to do on aleisurely Sunday afternoon (1997, 91). Third, Anderson argues that theroles 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 motheris to give up a friendship. Rather than compare their overall values,argues Anderson, ordinary moral thinking focuses on what one owes toone’s mother and one’s friends (1997, 102). This focus onobligation recognizes mother and friend each to be intrinsicallyvaluable and yet valuable in different ways (1997, 103). There is nogood reason, according to Anderson, to compare their overall valueswith 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 areoccasions in which comparisons do need to be made between goods forwhich Anderson argues there is no good reason to make comparisons. Inresponse to the second point, Chang argues that the range of instancesfor which the second argument applies is small. In response to thethird point, Chang contends that Anderson’s argument assumesthat if goods are comparable then they have some value or evaluativeproperty in common. Chang points out that this need not be the case.As previously mentioned, we cannot assume that two value bearers areincommensurable simply because they instantiate different values.

3.2 Moral Dilemmas

Value incommensurability has been invoked to make sense of a centralfeature of supposed moral dilemmas—namely, that no matter whichalternative the agent chooses, she fails to do something she ought todo. The apparent value conflicts involved in these choices have ledsome philosophers to relate moral dilemmas to the incommensurabilityof values. A harrowing example of a moral dilemma is the situationSophie faces in Sophie’s Choice, where, at a Nazi concentrationcamp, she is forced by a guard to choose which of her two childrenwill live while the other is condemned to die. If she refuses todecide, both children will be killed. Examples like this may suggestthat the incommensurability of her children’s lives is whatmakes this situation a moral dilemma.

However, this may be a hasty conclusion, as it has been argued thatthe mere existence of a moral dilemma does not necessarily implyincommensurability. James Griffin, for example, argues that thefeature of “irreplaceability” in moral dilemmas often maybe mistaken as evidence for incommensurability (1997, 37).Irreplaceability is the feature that what is lost in choosing onealternative over another cannot be replaced by what is gained inchoosing another alternative. Choosing two scoops of vanilla ice creamover one scoop of vanilla ice cream should not cause a feeling ofirreplaceability, however, choosing two scoops of vanilla ice creamover one scoop of chocolate ice cream may cause a feeling ofirreplaceability, even if you clearly prefer vanilla over chocolate.This feeling of irreplaceability or even regret can thus arise incases of comparability, it may even be rational (see Hurka 1996). Ifwe experience irreplaceability in moral dilemmas, we should not takethis as evidence for incommensurability.

Furthermore, some moral dilemmas may involve not a conflict of values,but a conflict of obligations that arises from the same consideration.The dilemma encountering Sophie, it may be said, does not point to theincommensurability of values as the options may be equally bad, butrather a conflict of obligations that are equally strong. WalterSinnott-Armstrong calls such dilemmas “symmetrical” (1988,54–58).

Another common approach to argue for value incommensurability is withreference to “non-symmetrical” dilemmas. As the namesuggests, in non-symmetrical dilemmas, the alternatives are favored bydifferent values (Sinnott-Armstrong 1988). If these values areincommensurable there is no systematic resolution of the valueconflict. Consider Jean-Paul Sartre’s well-known example of hispupil who faced the choice between going to England to join the FreeFrench Forces and staying at home to help his mother live (Sartre1975, 295–296). Thus, if value pluralism is correct, it allowsfor the possibility of non-symmetrical dilemmas. If the phenomenologyof these dilemmas cannot be explained by irreplaceability, thisprovides some support for the possibility of incommensurability.

4. Deliberation and Choice

As suggested above much of the inquiry into value incommensurabilityis motivated more generally by theories of practical reason andrational choice. This section considers these issues as they have beendiscussed in contemporary philosophical literature.

4.1 Optimization, Maximization, and Comparativism

The connection between value relations and choice is captured byoptimization. According to optimization, the fact that an alternativeis better or equally as good as the other alternatives is whatjustifies its choice. Consequently, if two alternatives areincommensurable no justified choice can be made between them. Thisunderscores the normative significance of value incommensurability: ifincommensurability is sufficiently pervasive, the scope for justifiedchoice becomes constrained.

However, optimization can be contrasted with“maximization” as a theory of justified choice (Sen 1997,746; Sen 2000, 486). According to this theory, justified choice onlyrequires the choice of an alternative that is not worse than otheralternatives. Because incommensurable alternatives are not worse thanone another, the choice of either is justified according to the theoryof maximization as justified choice. After all, as Raz argues (1997),if incommensurable options give us reasons to choose bothalternatives, then the choice of either alternative is justified onthe basis of reason. Thus, if maximization is correct the possibilityof incommensurable alternatives is less worrying. However, as we willsee in the next subsection, it may have some unwantedconsequences.

Ruth Chang has argued for a view somewhat similar to optimizationcalled “comparativism”. According to this view:“comparative facts are what make a choice objectively correct;they are that in virtue of which a choice is objectively rational orwhat one has most or sufficient normative reason to do. So, whetheryou are a consequentialist, deontologist, virtue theorist,perfectionist, contractualist, etc., about the grounds of rationalchoice, you should be, first and foremost, I suggest, acomparativist” (2016, 213). By “comparative fact”,Chang refers to a positive value relation, such as one of thetraditional three or an additional relation, like parity. Ifalternatives are incomparable rather than positively related, thepossibility of making an objectively rational choice is ruled out.This perspective thus rejects maximization. While her view is similarto optimization in that both require a positive value relation for ajustified choice, optimization restricts justification to thetraditional three relations, whereas comparativism allows any positivevalue relation to justify a choice.

Just as optimization, comparativism also entails that ifincomparability is pervasive, the scope for justified choice becomesconstrained. Those who find this to be a worrying conclusion canrespond that seemingly incomparable alternatives are, in fact,comparable. As discussed in Section 2, judgments of incomparabilitycan be mistaken, and it is possible that, despite appearances, apositive value relation obtains between two seemingly incomparablealternatives. This means that there is a comparative fact that makes achoice objectively correct in cases of apparent incomparability. Thereremains the issue of determining which alternative we are justified inchoosing. This depends on the nature of the apparent incomparabilityand our preferred theory of justified choice. Some suggestions comenaturally: If the alternatives are on a par, we may be justified inchoosing either. If it is indeterminate how the alternatives relate,it may likewise be indeterminate which alternative we are justified inchoosing. Finally, if we lack sufficient knowledge of the alternativesto determine how they relate, we may also lack sufficient knowledge tomake a justified choice.

One can object to optimization and maximization by arguing that, attimes, we are justified in choosing what is “good enough”;we can be satisficers. Optimizers and maximizers might argue that wesometimes have instrumental reasons to settle for what is good enough,aiming to achieve an overall maximal or optimal outcome later.Satisficers, however, contend that we can have non-instrumentalreasons for choosing what is good enough (Slote 1989; Byron 2004). Forexample, a person who does not always seek to maximize but insteadsettles for a moderate amount of a good expresses, according to some,a virtuous trait, and it is clear they are justified in acting in thismanner. If this view is correct, we must reject optimization andmaximization, and incommensurability may no longer be incompatiblewith justified choice.

The relation between comparativism and satisficing is less clear. Ascomparativism is formulated above it does not express whichcomparative facts that grounds a justified choice. It is thus intheory possible to claim that the fact that an alternative is goodenough compared to the alternatives justifies the choice. This doesnot, however, seem to be what Chang has in mind. To her, it is onlyjustified to choose an alternative that is better than, equally asgood, or on a par with the alternatives. For more on this see Stocker(1990; 1997) and Chang (2016, 228).

4.2 Cyclical Choice

One objection voiced against accounts that permit justified choicebetween alternatives that are roughly equal or on a par or betweenincomparable alternatives is that such accounts may justify a seriesof choices that leave a person worse off. Consider Raz’s exampleof career choice. Suppose a person chooses a musical career over alegal career. At a later time, she has the opportunity to pursue alegal career that is slightly worse than the initial legal career.Suppose this slightly worse legal career and the musical career arejudged to be roughly equal, on a par, or incomparable. If justifiedchoice permits her to choose between two alternatives when they areincommensurable, then she would be justified in choosing the slightlyworse legal career. Later, she may have the opportunity to pursue amusical career that is slightly worse than her initial musical career.This new musical career may also be roughly equal, on a par, orincomparable with the legal career, justifying her choice of theslightly worse musical career. Through a series of such justifiedchoices, she could end up significantly worse off. To complicatematters further, assume she is now offered the option to pay a smallmonetary cost to swap from the worse musical career back to theinitial musical career. Since the initial musical career is better, itseems justified for her to pay a small amount to obtain it. However,she has now returned to the same choice situation she faced initially,but through a series of justified choices, she has lost money. Thisappears to be an undesirable feature of a theory of justifiedchoice.

One line of response is that the considerations that make somealternatives worthy of choice count against the constant switchingamong alternatives envisioned in this objection. First, the constantswitching among alternatives is akin to not choosing an alternative.If the alternatives are such that choosing either is better thanchoosing neither, then the considerations that make the alternativesworthy of choice count against constantly switching among them.Second, switching constantly among careers appears to misunderstandwhat makes the alternatives worthy of choice. Not only is pursuing acareer the kind of activity that depends upon continued engagement forits success, but it is also the kind of activity that is unlikely tobe judged truly successful unless one demonstrates some commitment toit. Third, for a career to be considered successful, it may requirethe chooser to adopt a favorable attitude toward the considerationsthat favor it over other careers. In turn, when subsequently presentedwith the choice of a legal career, the considerations favoring it mayno longer apply to her in the same way as they did before (Hsieh2007). When a choice is made, some of our preferences may genuinelyshift to align with and deepen our appreciation of the chosenalternative, making it the better option of the two.

John Broome (2000) acknowledges that decision-making can sometimescreate value, as described above, but he doubts that this is alwaysthe case. Instead, he suggests that choosing a career in law over onein music is also, inherently, a decision to choose a career in lawover less favorable options in music. Thus, if you choose a career inlaw over one in music and are later presented with the opportunity toswitch to a less successful career in music, the decision has alreadybeen made; you should stick to the career in law. Of course, one isfree to change their mind and pursue a career that was previouslyrejected. Such behavior is not problematic, according to Broome,provided one repudiates their previous choice (2000, 38). While it istrue that such a change may leave you worse off than you could havebeen, as long as you disown your prior choice, your action is notirrational or puzzling according to Broome. By this, he rejects theview that it is inherently irrational to end up worse off than youcould have been. The problem, he argues, arises “[i]f at onesingle time you are willing to endorse both decisions, then you arecertainly in a puzzling condition” (2000, 34).

Ruth Chang advances a hybrid view on rational choice to meet thechallenge of cyclical choice. She distinguishes “givenreasons” from “will-based” reasons. Roughly put,given reasons could here be understood as those that are grounded innormative facts while will-based reasons are “reasons in virtueof some act of the will; they are a matter of our creation. They arevoluntarist in their normative source. In short, we create will-basedreasons and receive given ones.” (Chang 2013, 177). Will-basedreasons come into play when the given reasons no longer can guide ouractions. When two alternatives are on a par, given reasons fail toguide us and at this stage, will-based reasons can provide guidanceand guarantee that the agent commits to her choice. Once a choice hasbeen made between two alternatives that are on a par, we can commit toone option and thereby will reasons into existence that ensure we willstick to that choice if we face the same decision again.

This latter view captures a general idea that incommensurabilityprovides us with an opportunity to express our will. Instances ofincommensurability allow us to not merely act as automatons thatmerely respond to our given reasons but a possibility to exercise ourwill (e.g., Raz 1997).

4.3 Risky Actions

Caspar Hare (2010) introduces and discusses a problem relating to howrational choice theory can encompass risky actions involving outcomesthat are on a par. If we assume that two outcomes,A andB, are on a par, it follows that a small improvement, or mildsweetening as Hare phrases it, to one of the outcomes would not breakthe parity relation. We can then imagine two actions,X andY. If we opt forX then we will either end up with asweetenedA in state 1 or a sweetenedB in state 2,and the outcomes are equiprobable. If we opt forY, we willend up withB in state 1 orA in state 2, and theoutcomes are equiprobable.

Now should we doX orY? On the one hand, it seemsas if we ought to opt forX since we are sure that will endup with a sweetened alternative,A+ orB+ which ispreferable to merelyA orB. On the other hand, itis difficult to say whyX is better thanY. Theoutcome in state 1 is not better if we doX rather thanY since the outcomes,A+ andB, are on apar, and the outcome in state 2 is not better if we doYrather thanX since the outcomes,B+ andA,are on a par.

Hare argues that we should “take the sugar”, i.e., weought to opt forX. There is, however, an ongoing debate withlittle consensus on whether there are reasons to take sugar or not(see e.g., Schoenfield 2014; Bales, Cohen & Handfield 2014; Bader2018; Doody 2019; Rabinowicz 2021b).

5. The Repugnant Conclusion and Spectrum Arguments

We often come across the notion of value incommensurability in thefield of population axiology. It was, after all, a puzzle withinpopulation axiology that led Parfit to introduce the notion of“rough equality” and later the notion of“imprecision”. He suggested that by acknowledging thepossibility of “rough equality” we may be able to escapethe so-called Repugnant Conclusion (Parfit 1987, 430) which statesthat: “For any possible population of at least ten billionpeople, all with a very high quality of life, there must be some muchlarger imaginable population whose existence, if other things areequal, would be better even though its members have lives that arebarely worth living” (Parfit, 388). The conclusion finds supportin what Parfit calls the Continuum Argument (Parfit 2016). We areasked to imagine a spectrum of possible populations, starting with apopulation consisting of excellent lives. At each step in thespectrum, there is a small drop in the quality of life for eachindividual, but this is compensated for by a much larger population,making the latter population overall better than the former. As weprogress along the spectrum, the quality of life continues to decreasewhile the population size increases. Eventually, we arrive at a verylarge population whose members have lives that are barely worthliving. By the transitivity of betterness, we can infer that thispopulation is better than the one at the top of the spectrum.

If we assume that the standard three value relations fully exhaust theway populations can relate with respect to value then the transitivityof these relations seems, indeed, to imply the Repugnant Conclusion.However, if we allow for the possibility of e.g., parity, it ispossible to claim that some adjacent populations in the spectrum arerelated by such a relation and thus we have found a way to block theargument. If there are instances of parity along the spectrum thesequence of betterness relations is broken and we can no longer referto the transitivity of betterness to reach the conclusion (Chang2016).

We need of course not refer to parity, incomparability, or some otherform of incommensurability to argue that there is a break along thesequence of betterness relations. It is also possible to claim thatfor some adjacent populations in the spectrum, the larger populationis worse than the smaller population. This may, however, be moredifficult to accept as it clashes with our intuitions concerning thegoodness of the populations; it is easier to accept that the largerpopulation is not better than the smaller one than to accept that itis worse.

It should also be noted that the relation invoked must be persistentin the sense that it will obtain between two populations despitequantitative increases to the larger population. That is, if we canpoint to a break in the spectrum where two populations are related bye.g., parity, the relation must persist despite making the largerpopulation even larger (Handfield & Rabinowicz 2018; Chang 2022).If the relation did not persist there would be a sufficiently largepopulation that was better than its adjacent smaller population and wehave failed to block the sequence of betterness relations.

It may seem surprising that parity can be persistent in this sense, asit appears to contradict the intuitions underlying the ChainingArgument. According to this argument, a sufficient number ofdiminutions can break the parity relation between e.g., two differentcareers. In cases of persistent parity, however, quantitativeimprovements cannot break the relation. Chang admits that persistentparity is generally implausible: “it is not the case for any twoitems on a par that differ by one being a slight diminution in qualityand a large enhancement in quantity, that no matter how much weincrease the quantity, the items will remain on a par—twocareers may be on a par, but if we increase the salary of one of themenough, it can be better” (Chang 2022, 421). However, in aspectrum like the one discussed above, Chang suggests that persistentparity might be plausible.

Invoking non-standard value relations to address the RepugnantConclusion is not limited to parity. The broader notion of“incommensurability” is often invoked (e.g., Hájek& Rabinowicz (2022)), and Parfit (2016) introduced the concept of“imprecise equality” to address the Repugnant Conclusion.Nor is this approach limited to discussions of the RepugnantConclusion; similar reasoning applies to other arguments that use aspectrum to reach counterintuitive results.

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fitting attitude theories of value |incommensurability: of scientific theories |moral dilemmas |practical reason |value: pluralism |value theory

Acknowledgments

For helpful discussions and comments, Nien-hê Hsieh would liketo thank Rahul Kumar, Martin Sandbu, Alan Strudler, Kok-Chor Tan, andSara Toomey. A special debt of gratitude is given to WalterSinnott-Armstrong for his support and for his extremely detailedcomments and suggestions. Hsieh also would like to thank Jennifer Woofor research assistance.