It is natural to assume that every value bearer must be good, bad, or neutral. This paper argues that this assumption is false if value incomparability is possible. More precisely, if value incommensurability is possible, then there is a fourth category of absolute value, in addition to the good, the bad, and the neutral.
The Absolute Trichotomy Thesis If x is a value bearer, then x is good, bad, or neutral.Footnote 1
While this thesis is compelling, I will argue that it’s false if there is value incommensurability. I will argue that, if there can be value incommensurability, then value bearers can belong to a fourth category of absolute value, in addition to the good, the bad, and the neutral. To get a grip on this fourth category of absolute value, it may help to first consider the comparative counterpart of the Absolute Trichotomy Thesis:
The Comparative Trichotomy Thesis If x and y are value bearers, then (i) x is better than y, (ii) x is worse than y, or (iii) x and y are equally good.Footnote 2
The Comparative Trichotomy Thesis is false in case there is value incomparability, which is typically defined negatively in terms of the absence of other comparative value relations:Footnote 3
An item x is incomparable with an item y if and only if (i) x and y are value bearers, (ii) x is not better than y, (iii) x is not worse than y, and (iv) x is not equally good as y.
Following this negative model, we can define a fourth category of absolute value as follows:Footnote 4
An item x is undistinguished if and only if (i) x is a value bearer, (ii) x is not good, (iii) x is not bad, and (iv) x is not neutral.
This kind of absolute counterpart of incomparability has been suggested from time to time.Footnote 5 In the following, I will present a new argument for its possibility.Footnote 6
Suppose that there are two specific evaluative dimensions and that these dimensions are incommensurable and apply to the same domain of value bearers. In addition to these specific evaluative dimensions, suppose that there is also value simpliciter, that is, overall value that takes all the specific dimensions into account. Finally, suppose, as seems plausible, that there is an overall neutral item. (If, for example, an item is neutral with respect to each specific evaluative dimension, it should be overall neutral.) Let a be the value for this neutral item along the first specific evaluative dimension, and let b be the item’s value along the other. We will represent items by ordered pairs of their value along the two specific evaluative dimensions. Accordingly, we will represent this (overall) neutral item by the tuple \(\langle a, b\rangle \), so we have
\(\langle a, b\rangle \) is neutral.
Compare \(\langle a, b\rangle \) with items that are better along one dimension but worse along the other. Since these dimensions are incommensurable, there should be some improvement along one dimension and some detriment along the other dimension that results in an item that is incomparable with \(\langle a, b\rangle \). Let \(\delta \) be the size of the improvement, and let \(\varepsilon \) be the size of the detriment. Hence
\(\langle a, b\rangle \) is incomparable with \(\langle a + \delta , b - \varepsilon \rangle \).
Note that we do not claim that all improvements in one dimension combined with any detriment in the other dimension results in an item that is incomparable to the original item. The claim is just that there is some improvement and some detriment in the two dimensions that makes the resulting item incomparable to the original.
Now, consider the following principles of the logic of value:Footnote 7
If x is neutral and y is good, then y is better than x.
If x is neutral and y is bad, then y is worse than x.
If x is neutral and y is neutral, then x and y are equally good.
The main intuitive idea behind these principles is that the neutral represents the zero-point of the evaluative scale (or the origin of the evaluative space). To be good is, intuitively, to have positive value.Footnote 8 Something positive on the evaluative scale must be above (on that scale) anything that is at the zero-point on the evaluative scale, that is, a good item must be better than anything that is neutral. So we should accept (3). Similarly, to be bad is, intuitively, to have negative value.Footnote 9 Something negative on the evaluative scale must be below (on that scale) anything that is at the zero-point on the evaluative scale, so a bad item must be worse than anything that is neutral. So we should accept (4). Finally, if two items are both neutral, they are both at the zero-point of the evaluative scale. Hence they are both at the same point on the evaluative scale, that is, they are equally good. So we should accept (5).
Analogously, think about contributory value. Items that are good in contributory value make the world better. Items that are bad in contributory value make the world worse. And items that are neutral in contributory value leave the value of the world as it is. So all items that are neutral in contributory value have the same effect on the value of the world. Hence all items that are neutral in contributory value are equal in contributory value.
Next—from (1), (2), (3), (4), and (5)—we have
\(\langle a + \delta , b - \varepsilon \rangle \) is not good, not bad, and not neutral.
Since \(\langle a + \delta , b - \varepsilon \rangle \) can be evaluated along all of the specific evaluative dimensions, it seems to be a value bearer. Furthermore, since \(\langle a + \delta , b - \varepsilon \rangle \) dominates some items in all specific evaluative dimensions, it should plausibly be (overall) better than those items. For instance, \(\langle a + \delta , b - \varepsilon \rangle \) should be better than \(\langle a, b - 2\varepsilon \rangle \). Since \(\langle a + \delta , b - \varepsilon \rangle \) is comparable in value to some other items, we have
\(\langle a + \delta , b - \varepsilon \rangle \) is a value bearer.
Finally, from (6) and (7), we have
\(\langle a + \delta , b - \varepsilon \rangle \) is undistinguished.
Hence, if value incommensurability is possible, undistinguishedness must be so too.
It may be objected that we have assumed that, in addition to the specific evaluative dimensions, there is an overall, all-things-considered, value simpliciter dimension. Hence one could reject the above argument if one rejects the possibility of value simpliciter.
But the assumption of a value simpliciter dimension is unessential. As long as some evaluative dimensions depend on other evaluative dimensions, we can restate the argument so that it does not assume the possibility of value simpliciter.
It’s easy to find examples of undistinguishedness. We all have good days and bad days. But consider a day that’s neither good nor bad—a day whose value is in between. Would that day have been a good day if it had been slightly better or a bad day if it had been slightly worse? Plausibly, it wouldn’t. But, if so, that day can’t be a neutral day. Hence it must be an undistinguished day. The idea is that, in between the good days and the bad days, there’s a range of undistinguished days. And, among the days in this range, some days are better than others.
Or consider movies. Some movies are good; some movies are bad. But a lot of movies are neither good nor bad. The movies in this latter category aren’t all equally good, however—some are slightly better than others. But, if so, they can’t all be neutral. Hence some movies are undistinguished.Footnote 10
von Neumann and Morgenstern (1947, p. 630) and Quinn (1977, p. 77). Following Chang (1997, pp. 27–28), we distinguish incomparability, which holds between value bearers, from non-comparability, which is the failure of comparability when one of the relata is not a value bearer. As we have defined incomparability, Chang’s suggestion of a fourth positive value relation she calls ‘parity’—which can hold between two value bearers such that neither is better or worse than the other and they are not equally good—would be a form of incomparability. Given that ‘parity’ normally means ‘the state of condition of being equal’ (OED3), it isn’t entirely well-suited as a term for a relation that rules out equality. See Gustafsson (2013, pp. 444–445).
While ‘undistinguished’ is better than earlier terms for this value category (see Gustafsson 2020, p. 88n12), it’s a bit of a mouthful. Helen Yetter-Chappell suggests, the three syllables shorter, ‘meh’.
Carlson (1997, p. 101), Espinoza (2009, p. 35), and Gustafsson (2016, p. 855, 2020, p. 88). The Stoics had a similar category of items that are neither good nor bad but which differ in value within the category. See Sextus Empiricus (Pyr. 3.191; 2000, p. 194; Math. 11.62; 1997, p. 13), Diogenes Laertius (7.104–105; 2018, p. 349), and Gustafsson (2020, p. 91n18).
Carlson puts forward a similar argument—which is structurally a variation of a case by Espinoza (2009, pp. 35–36). Carlson (2011, p. 58) writes
Suppose that beautiful objects and pleasant experiences are among the bearers of goodness, and that ugly objects and unpleasant experiences are among the bearers of badness. Suppose also that some beautiful objects are incomparable in value to some pleasant experiences. Then it appears highly likely that there are [undistinguished] objects. Consider the question whether there is, for a given beautiful object a, some ugly object b, whose ugliness exactly counterbalances the beauty of a, so that [the mereological sum of a and b] is neutral. If there is such a b, let c be a pleasant experience, whose value is incomparable to that of a. Barring holistic effects, it seems that [the mereological sum of b and c] must be [undistinguished].
A potential problem with this argument is that it’s unclear whether the mereological sum with an ugly part and a pleasant part would be overall ugly and pleasant. Since this sum has one part that is a bearer of (negative) aesthetic value and one part that is a bearer hedonic value yet no part that is a bearer of both kinds of value, it’s unclear whether the sum would be a bearer of either kind of value. And, if so, it’s unclear whether the sum would be a value bearer. Moreover, as Carlson notes, the last inference in the argument might be blocked by holistic effects. The new argument does not rely on the replacement of parts in mereological sums. So it sidesteps these problems. Andreou (2021, p. 313) assumes that there are two items such that one is better than the other yet they are both neither good nor bad. From this assumption, she derives that there is an undistinguished item. But, without further argument, it’s unclear why we should grant her assumption, which isn’t needed for the new argument.
Halldén (1957, p. 104) assumes these principles as axioms. Chisholm and Sosa (1966, p. 248) derive these principles as theorems. Chisholm and Sosa’s axioms, however, rule out incomparability; so we cannot rely on their proofs of these principles here. But these principles are intuitively plausible in themselves.
In Chisholm and Sosa’s (1966, p. 245) words, something good is something that ‘rates the world a plus’.
Again, in Chisholm and Sosa’s (1966, p. 245) words, something bad is something that ‘rates the world a minus’.
‘Good’ and ‘bad’ seem to be related in the same way as other contraries like ‘tall’ and ‘short’, which clearly admit a range of intermediate (‘medium height’) levels. That is, there is a range of lengths at which someone is neither tall nor short. In the same way, there seems to be a range of value levels at which items are neither good nor bad. See Gustafsson (2020, p. 89n14).
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I wish to thank Erik Carlson, Erik Malmqvist, Daniel Ramöller, and Christian Tarsney for distinguished comments. Financial support from the Swedish Foundation for Humanities and Social Sciences is gratefully acknowledged.
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Gustafsson, J.E. The possibility of undistinguishedness. Philos Stud 180, 609–613 (2023). https://doi.org/10.1007/s11098-022-01889-0
- The trichotomy thesis
- The absolute trichotomy thesis
- Absolute value
- Logic of value