Consider

• The Absolute Trichotomy ThesisÂ Â Â If x is a value bearer, then x is good, bad, or neutral.Footnote 1

While this thesis is compelling, I will argue that itâ€™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 ThesisÂ Â Â If x and y are value bearers, then (i) x is better thanÂ y, (ii) x is worse thanÂ 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 itemÂ x is incomparable with an itemÂ y if and only if (i) x and y are value bearers, (ii) x is not better thanÂ y, (iii) x is not worse thanÂ y, and (iv) x is not equally good asÂ y.

Following this negative model, we can define a fourth category of absolute value as follows:Footnote 4

• An itemÂ 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 itemâ€™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

1. (1)

$$\langle a, b\rangle$$ 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

1. (2)

$$\langle a, b\rangle$$ 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

1. (3)

If x is neutral and y is good, then y is better thanÂ x.

2. (4)

If x is neutral and y is bad, then y is worse thanÂ x.

3. (5)

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 acceptÂ (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 acceptÂ (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 acceptÂ (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.

Nextâ€”from (1), (2), (3), (4), andÂ (5)â€”we have

1. (6)

$$\langle a + \delta , b - \varepsilon \rangle$$ 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

1. (7)

$$\langle a + \delta , b - \varepsilon \rangle$$ is a value bearer.

Finally, from (6) andÂ (7), we have

1. (8)

$$\langle a + \delta , b - \varepsilon \rangle$$ 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.

Itâ€™s easy to find examples of undistinguishedness. We all have good days and bad days. But consider a day thatâ€™s neither good nor badâ€”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 wouldnâ€™t. But, if so, that day canâ€™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, thereâ€™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 arenâ€™t all equally good, howeverâ€”some are slightly better than others. But, if so, they canâ€™t all be neutral. Hence some movies are undistinguished.Footnote 10