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CHAPTER 1
Incommensurability and Incomplete Comparability
SUMMARY
A central characteristic of two incommensurable values is the absence of any equivalence relation: no amount of one value is equivalent – not even roughly equivalent – to any amount of the other value. Many philosophers deny a relation between incommensurability and incomparability. This is not correct. Incommensurability of values is an important, although not sufficient, cause of what might be called 'incomplete comparability' of alternatives for choice. Two options A and B are incompletely comparable, if it is simultaneously (1) not true that A is better than B, (2) not true that A is worse than B and (3) not true that A is (roughly) equally good as B. I refer to this value relation as '3NT' ('triply not true'). This 3NT value relation may be the cause of significant problems of incommensurability for rational decision making and complete justification of the choice – problems that are discussed in chapter 4.
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Incommensurability literally means 'inability to be compared by a common standard'. There are different versions of incommensurability, such as semantic, mathematical and value-incommensurability. When I use the notion 'incommensurability' without further specification, I mean 'incommensurability of values', which is the topic of this book. Incommensurability and commensurability of values can be defined as follows.
Incommensurability
Two values are incommensurable if they have different dimensions that cannot be reduced to each other or to a common dimension so that their amounts cannot be measured and compared on a common cardinal scale of units of value.
Commensurability
Two values are commensurable if they can be reduced to each other or to a one-dimensional 'super-value' (e.g., pleasure or monetary value), so that their amounts can be measured and compared on a common cardinal scale of units of value.
These definitions need further explanation. A key notion is 'dimension'. Dimension means a measurable extent. Disparate values differ in dimensions. For instance, a dimension of freedom differs from a dimension of equality, and dimensions of quality of a work of art differ from dimensions of quality of food. The amounts of a value may differ. For instance, the amounts of a particular freedom, say freedom of speech or freedom of movement, may vary from small to large. If we compare two alternatives for choice, for instance, two restaurants, we compare them with respect to the relevant values, for instance, quality of food and quality of decor. These values have different dimensions. This means that the extent of quality of food is expressed in another dimension (unit of value) than the extent of quality of decor, just as the extent of unlike physical measures, such as length and weight, is expressed in disparate dimensions. Just as length cannot be measured in units of weight, and vice versa, so can amounts of unlike human values not be measured on one and the same scale of units of a particular dimension, unless they can be reduced to each other or to a common one-dimensional value (e.g., pleasure or monetary value). In the latter case, the values are commensurable. Otherwise they are incommensurable. Another phrase in the previous definitions is 'cardinal scale'. A cardinal scale measures amounts of values, expressed in quantities of units of value. It should be distinguished from an ordinal scale – a list of rankings in terms of 'more/less value' or 'more/less importance' – terms that do not indicate how much the amounts of value differ in quantities of units of value. As we will see, incommensurability excludes measurements and comparisons on a common cardinal scale, but not necessarily on a common ordinal scale.
Some theorists identify incommensurability with incomparability. Many others deny a relation between these notions. This chapter, and chapters 2 and 3, will show why the latter view is not correct. Also the former view is not entirely correct because many options that bear incommensurable values are comparable. Take, for example, two restaurants: restaurant A, which has excellent food, and restaurant B, which has inferior food but a slightly nicer decor. Although quality of food and quality of decor are incommensurable values, comparison of the options is not difficult: other things being equal, restaurant A is overall better than restaurant B. To give another example, take two societies: A and B. The citizens of society A have basic liberties (e.g., freedom of movement, speech and religion) and amply sufficient economic welfare to live a decent life. The citizens of society B have somewhat more economic welfare but lack basic liberties. Incommensurability of the values 'economic welfare' and 'basic liberties' does not prevent the comparability of the two societies: society A can be ranked higher than society B, assuming that basic liberties are more important than somewhat increased welfare above a level that is already amply sufficient. Because of the many cases in which incommensurable values do not cause any problem for the comparability of options, several theorists tend to trivialize the relation between incommensurability and incomparability. For instance, Michael Stocker points at the omnipresence of unproblematic incommensurability as an indirect argument against difficulties for rational decision making and rational justification of choices. Similarly, Amartya Sen finds it regrettable that in the literature so much attention is paid to something that is so 'omnipresent' and has so 'little discriminating relevance' as incommensurability. He argues:
Noncommensurability can hardly be a remarkable discovery in the world in which we live. And it need not, by itself, make it very hard to choose sensibly. For example, a fine mango may give us nutrition as well as some palatal or olfactory pleasure, whereas buying the record of a good song may offer a very different reward (not immediately reducible into the dimensions of the other) ... and yet we may have no great difficulty in opting for the mango when immensely hungry or starved, and going for the song, when well endowed with tasty food but short of melodious entertainment. The choice need not be hard to make in many situations, despite the non-commensurability involved. The distinct dimensions of values may not be reducible into one another, and yet there may be no problem whatsoever in deciding what one should sensibly do when our priorities or weights over these values are clear enough.
Sen's and Stocker's arguments against the significance of incommensurability for practical reasoning and justified choice are based on the misunderstanding that if A is omnipresent and often does not cause B, A cannot be an important cause of B. This fails to recognize that a cause may be important without being sufficient. Many people smoke, but many smokers do not get lung cancer. The explanation is that smoking is an insufficient, instead of unimportant, cause of lung cancer. We shall see that incommensurability is the central, although not sufficient, cause of what I call 'incomplete comparability'. In addition to incommensurability, the satisfaction of additional conditions is required for incomplete comparability. Presently we will discuss these conditions. Ruth Chang gives several examples in support of the view that incommensurability does not pose problems for the comparability of options. However, these examples lack at least one of the two additional conditions of 'incomplete comparability'. In the previous quotation Sen argues that incommensurability can 'hardly be a remarkable discovery' because – although 'the distinct dimensions of values may not be reducible into one another' – 'there may be no problem whatsoever in deciding what one should sensibly do when our priorities or weights over these values are clear enough'. However, assignment of the right priorities and weights is precisely the central problem of incommensurability if the additional conditions are satisfied.
INCOMPLETE COMPARABILITY
If A and B are incomparable, A is neither better than, nor worse than, nor equally good as, B: otherwise A and B would not be incomparable. Conversely, if A is neither better than, nor worse than, nor equally good as, B, it may be a sign – although it does not logically demonstrate – that A and B are incomparable (for reasons that I will mention later, I prefer the notion 'incomplete comparability' to 'incomparability'). In line with this thought, which I will further substantiate, I define 'incomplete comparability' as follows.
Incomplete comparability
Two options A and B are incompletely comparable if – all things considered and in an impartial and objective perspective – it is simultaneously
1. not true that? (i) A is (definitely) better than B,
2. not true that? (ii) A is (definitely) worse than B,
3. not true that?(iii) A and B are (roughly) equally good.
Call this threefold denial '3NT' (triply not true).
Some terms in the definition need an explanation. Option A is '(definitely) better' than option B if reason shows that it is better to choose A instead of B (so that it is irrational or less rational to choose B rather than A), and A is 'definitely worse' than B if reason shows that it is better to choose B instead of A (so that it is irrational or less rational to choose A rather than B). 'Impartial and objective' means 'detached from a specific personal belief, intuition or subjective preference'. The three 'not true' statements must be explained in this light: reason as such – that is, reason detached from a specific personal belief, intuition or subjective preference – neither shows that it is better to choose one option rather than the other nor shows that it does not matter which option is chosen. In other words, reason as such 'under-determines the choice' (see also the explanation given in chapter 4).
At first sight 3NT is puzzling and is difficult to understand. Indeed, if A is not better than B and B is not better than A, it seems to follow that A and B are equally good; and if A is not equally good as B, then it seems to follow that A is better than B or B is better than A. The puzzle is due to the tacit assumption that A and B are (completely) comparable. The puzzle disappears if 3NT is caused by incomparability (or incomplete comparability).
Many theorists recognize the possibility of '3NT' but explain it differently. Raz and Adam Morton interpret 3NT as 'incomparability'. Derek Parfit explains 3NT as 'imprecise equality', John Broome as 'vagueness' and T. K. Seung and Daniel Bonevac as 'indeterminacy'. As indicated earlier, I regard 3NT as a sign of 'incomplete comparability'. The designation '3NT' remains neutral between the different interpretations, but I think the only correct explanation is 'incomplete comparability', as I hope to make plausible in this chapter and the three following ones. In chapter 4 I will show that 3NT as such – that is, irrespective of how it is explained – has important problematic consequences for practical reason, rational decision making and complete justification of the choice. Chang emphatically denies that 3NT means incomparability. She interprets it as a fourth value relation within the domain of (complete) comparability. She calls this fourth value relation 'parity' and explains it as 'imprecise cardinal equality'. In chapter 3 I will show that this interpretation is mistaken and that it conceals important implications of 3NT for practical reasoning. There I will also give reasons why 'incomplete comparability' is an adequate explanation of 3NT. I use the terms '3NT' and 'incomplete comparability' interchangeably.
CONDITIONS OF INCOMPLETE COMPARABILITY (3NT)
We shall see that in addition to incommensurability of the relevant values, two other conditions must be satisfied before 3NT applies and can be spoken of incomplete comparability of the options. One of the reasons why there is much confusion about the possible relation between incommensurability of values and incomplete comparability of options is that many thinkers do not realize that the additional conditions must also be fulfilled.
If we compare two valuable options, we compare them with respect to a particular value. Ruth Chang calls this the 'covering value'. For instance, if we want to compare two persons with respect to their philosophical talent, then 'philosophical talent' is the covering value. Most covering values have multiple 'contributory values' – values that contribute to the content of the covering value. For example, the covering value 'philosophical talent' has, among others, 'originality' and 'analytical skill' as contributory values. Suppose we want to evaluate two options with respect to a covering value that consists of two contributory values. The options are incompletely comparable (in the sense of 3NT), if and only if the contributory values are not only incommensurable but also satisfy the two additional conditions. If one or more of the three conditions are not fulfilled, the options are completely comparable.
Conditions of incomplete comparability (3NT):
1. Incommensurability: The contributory values have unlike dimensions that cannot be reduced to each other or to a common dimension so that their amounts cannot be measured and compared on a common cardinal scale of units of value.
2. Significant bidirectionality: One option contains a significantly larger amount of one contributory value, while the other option contains a significantly larger amount of another contributory value.
3. Symmetry: The contributory values are 'in the same league'; that is, neither contributory value is significantly more important than the other.
Here follows a further explanation of each condition.
INCOMMENSURABILITY
If the covering value has only one dimension (i.e., if the covering value does not contain disparate contributory values), the options are completely comparable. This is the case, for instance, if we compare careers with respect to their salaries, or if we compare different kinds of food with respect to their vitamin C content or if we evaluate a slimming diet and physical exercise with respect to their weight-reducing effect. These examples lack the 'incommensurability condition' because the relevant covering value concerns a one-dimensional common measure: respectively, salary, vitamin C content and weight reduction. Let us consider the example of weight reduction mainly by means of calorie-intake reduction (lifestyle C) versus weight reduction mainly by means of increased physical exercise (lifestyle E) (see table 1.1).
Compared to lifestyle E, lifestyle C means a significantly larger reduction of calorie intake, while, conversely, lifestyle E means a significantly larger increase of physical exercise. So there is significant bidirectionality – one of the additional conditions of incomplete comparability. Besides, there is multidimensionality: the unit of increased physical exercise (minute) differs from the unit of reduced food intake (calorie). Still the two lifestyles are completely comparable, because the 'incommensurability condition' is not satisfied. The two lifestyles can be reduced to the one-dimensional covering value 'weight reduction'. This shows that 'multidimensionality' is no problem if we can reduce the different dimensions to a single one. Therefore, we can answer the question which lifestyle is overall better with respect to weight reduction. Obviously it would not be correct to add up the reduced calories and increased exercise minutes and to conclude that – given the fact that the total scores of both lifestyles are equal (150) – they are equally good. This would be correct only if the unit of reduced food intake (calorie) is equivalent to the unit of increased exercise (minute), which is not the case. We have to determine the relative importance or comparative effectiveness of the two dimensions with respect to weight reduction in order to be capable of answering the question which lifestyle is better with respect to weight reduction. In other words, we have to determine how many calories of reduced food intake are equivalent to how many minutes of increased physical exercise.
(Continues…)
Excerpted from "Incommensurability and Its Implications for Practical Reasoning, Ethics and Justice"
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Copyright © 2017 Martijn Boot.
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