1 Indeterminate Critical-Level Utilitarianism

One way to amend Critical-Level Utilitarianism so that it avoids each of these counter-intuitive conclusions is to also claim that it is indeterminate which well-being level is the critical level:

This makes some assumptions about the logic of indeterminacy. We have a determinately true disjunction where no disjunct is determinately true – that is, the disjunction of the claims, for each well-being level in the critical range, that that level is the critical level.Footnote ⁷

John Broome’s account of Indeterminate Critical-Level Utilitarianism relies on supervaluationism.Footnote ⁸ According to supervaluationism, the evaluation of a statement involving vague or indeterminate terms depends on its sharpenings – that is, the admissible ways it can be made precise. On Broome’s version of supervaluationism, we may assert a statement ‘ $ S$ ’ if and only if ‘ $ S$ ’ is true under each one of its sharpenings.Footnote ⁹ To apply supervaluationism to Indeterminate Critical-Level Utilitarianism, we let the well-being levels in the range of indeterminacy be the extensions of the sharpenings of the term ‘critical level’, and we assume for simplicity that the indeterminacy of ‘critical level’ is the only source of indeterminacy. We can then assert the statement that ‘some well-being level in the range of indeterminacy is the critical level’, since this will be true given each sharpening of ‘critical level’. But, for every well-being level $ l$ in the range of indeterminacy, we may not assert the statement ‘ $ l$ is the critical level’, since this will be false given some sharpening of ‘critical level’ (assuming that there is more than one level in the range).

Indeterminate Critical-Level Utilitarianism could also be coupled with an epistemic view of indeterminacy, where indeterminacy is merely a kind of ignorance. On the epistemic view, there are sharp boundaries to the extensions of vague or indeterminate terms but we do not know and perhaps cannot know where those boundaries lie.Footnote ¹⁰ Applying the epistemic view to Indeterminate Critical-Level Utilitarianism, we let the well-being levels in the range of indeterminacy be a set of well-being levels such that we know that one of them is the extension of ‘critical level’ and, if there is more than one level in the range, we are ignorant, for each level in the range, as to whether that level is the extension of ‘critical level’. So we know that one of the well-being levels in the range of indeterminacy is the critical level. But, for every well-being level in the range of indeterminacy, we don’t know whether that level is the critical level (assuming again that there is more than one level in the range).

Let $ I$ be the set of well-being levels in the range of indeterminacy. Then, on either supervaluationism or the epistemic view of indeterminacy, Indeterminate Critical-Level Utilitarianism entails that

Indeterminate Critical-Level Utilitarianism avoids each one of the Repugnant Conclusion, the Mirrored Repugnant Conclusion, and the Sadistic Conclusion. Given a range of indeterminacy with an upper bound sufficiently higher than the neutral level and a lower bound sufficiently lower than the neutral level, none of these conclusions is determinately true on Indeterminate Critical-Level Utilitarianism. Yet, while these conclusions are not determinately true on Indeterminate Critical-Level Utilitarianism, they are not determinately false either. Following Broome, however, we may feel that the indeterminacy of these conclusions is enough to mitigate their repugnance.Footnote ¹¹

2 Undistinguished Critical-Range Utilitarianism

We have seen how we can avoid both the Repugnant Conclusion and the Sadistic Conclusion if we add indeterminacy to Critical-Level Utilitarianism. But, in much the same way, we can also avoid these conclusions if we add incomparability to the theory. There is a structurally analogous variation of Critical-Level Utilitarianism, where, instead of a range of indeterminacy, there is a range of undistinguishedness. This is a range of well-being levels such that adding a person whose well-being falls in this range renders (other things being equal) the resulting outcome incomparable to the original. Consider

If $ U$ and $ I$ contain the same well-being levels, then Critical-Range Utilitarianism will entail that an outcome $ X$ is at least as good as an outcome $ Y$ if and only if Indeterminate Critical-Level Utilitarianism entails that $ X$ is determinately at least as good as $ Y$ . The theories still differ, however, in that, when Indeterminate Critical-Level Utilitarianism entails that $ X$ is indeterminately at least as good as $ Y$ , Critical-Range Utilitarianism entails that $ X$ is incomparable with $ Y$ .

Suppose we further accept that lives at the well-being levels in $ U$ are undistinguished – that is, that they are value bearers but they are not good, not bad, and not neutral.Footnote ¹³ Then we can accept

Note that, since undistinguished lives are still value bearers, this view is consistent with the claim that a first life is at least as good as a second life if and only if the first life is at a well-being level at least as high as the second life. That is, we can compare lives at well-being levels in the range of undistinguishedness.

Let Undistinguished Critical-Range Utilitarianism be the combination of Critical-Range Utilitarianism and the Personal Critical-Range View.Footnote ¹⁵ Given Undistinguished Critical-Range Utilitarianism, we avoid both the Repugnant Conclusion and the Sadistic Conclusion (and the Mirrored Repugnant Conclusion). So it seems that Indeterminate Critical-Level Utilitarianism and the combination of Critical-Range Utilitarianism and the Personal Critical-Range View both avoid repugnance and sadism.Footnote ¹⁶

There are, of course, other worries. For instance, Critical-Range Utilitarianism is open to the Greediness Objection – that is, if we improve the lives in an outcome and add some people with lives at a well-being level in the critical range (other things being equal), the resulting outcome may be incomparable to the original.

One motivation for having a critical range is to capture the Intuition of Neutrality – that is, to capture the intuition that, while we are in favour of making people happy, we are neutral about creating happy people.Footnote ¹⁷ But, if improving people’s lives is an improvement and adding a life is neutral, then the combination of improving and adding should result in an outcome that is better, rather than an outcome that is incomparable with the original.Footnote ¹⁸ Nevertheless, Indeterminate Critical-Level Utilitarianism faces much the same problem, because, if we improve the lives in an outcome and add some people with lives at a well-being level in the critical range (other things being equal), the resulting outcome may be indeterminate in comparison to the original according to Indeterminate Critical-Level Utilitarianism – rather than determinately better.Footnote ¹⁹

3 The Disjunctive Repugnant Conclusion

So we have two approaches for amending Critical-Level Utilitarianism with essentially the same formal structure. And they both avoid entailing the various problematic conclusions we have considered. But they differ in whether this is done by introducing indeterminacy or incomparability. As Broome notes, indeterminacy and incomparability lead to much the same practical problems.Footnote ²⁰ And the views agree about all comparisons of outcomes that do not involve indeterminacy or incomparability. That is, they will do so if the range of indeterminacy, $ I$ , includes the same well-being levels as the range of undistinguishedness, $ U$ . The two theories agree, for any two outcomes $ X$ and $ Y$ , about whether $ X$ is determinately at least as good as $ Y$ .Footnote ²¹ (And the outcomes are incomparable according to Critical-Range Utilitarianism if and only if their comparison is indeterminate on Indeterminate Critical-Level Utilitarianism.) So one may wonder if we have any reason to favour one of these approaches over the other.

I shall argue, however, that these approaches differ in their ability to avoid repugnance. Even if we merely wish to avoid entailing that something repugnant is determinately true, Indeterminate Critical-Level Utilitarianism still fails in this regard. While the two theories agree, for any two outcomes $ X$ and $ Y$ , whether $ X$ is determinately at least as good as $ Y$ , the theories can still disagree about general claims about comparisons of outcomes. To see this, we shall consider two conclusions which are disjunctions of the previous ones. According to

And, similarly, according to

These two disjunctive conclusions seem on a par in repugnance with the Repugnant Conclusion.

Moreover, there is a straightforward argument that the Disjunctive Repugnant Conclusion should be repugnant. For each disjunct in these conclusions, any value ordering of outcomes that satisfies the disjunct is repugnant. So each of these disjuncts entails that the value ordering of outcomes is repugnant. By argument by cases, we then find that each of these disjunctions entails that the value ordering of outcomes is repugnant. So these disjunctive conclusions should be repugnant too. Formally, the argument can be put as follows. Let $ \mathrm{R}\mathrm{C}$ be the Repugnant Conclusion, let $ \mathrm{S}\mathrm{C}$ be the Sadistic Conclusion, and let $ \mathrm{R}$ be that the value ordering of outcomes is repugnant. Since any value ordering of outcomes satisfying at least one of $ \mathrm{R}\mathrm{C}$ and $ \mathrm{S}\mathrm{C}$ is repugnant, we have $ \mathrm{R}\mathrm{C}\supset \mathrm{R}$ and $ \mathrm{S}\mathrm{C}\supset \mathrm{R}$ . Then – from $ \mathrm{R}\mathrm{C}\supset \mathrm{R}$ , $ \mathrm{S}\mathrm{C}\supset \mathrm{R}$ , and $ \mathrm{R}\mathrm{C}\vee \mathrm{S}\mathrm{C}$ – we have $ \mathrm{R}$ by argument by cases.Footnote ²³

There is a further argument that these disjunctive conclusions should be repugnant if ‘repugnant’ is used in an evaluative sense. This is how it is used by, for example, J. M. E. McTaggart, who was the first to call conclusions like the Repugnant Conclusion ‘repugnant’. He writes:

A standard view in the logic of value is the principle of disjunctive interpolation, that is, the principle that disjunctions fall between their disjuncts in terms of intrinsic value.Footnote ²⁵ If, for example, $ p$ is intrinsically bad and $ q$ is intrinsically bad, then the disjunction $ p\vee q$ is also intrinsically bad. Analogously, the repugnance of a disjunction should fall between its disjuncts in terms of repugnance. So, if both the Repugnant Conclusion and the Mirrored Repugnant Conclusion are repugnant, the Disjunctive Repugnant Conclusion should be repugnant too. Likewise, if both the Repugnant Conclusion and the Sadistic Conclusion are repugnant, the Either-Repugnant-or-Sadistic Conclusion should be so too.

The problem is that, regardless of which well-being levels are in the range of indeterminacy, Indeterminate Critical-Level Utilitarianism entails both of these disjunctive conclusions. Or, at least, it does so given either of the two standard views of indeterminacy – namely, supervaluationism and the epistemic view.Footnote ²⁶ Let a precise version of Critical-Level Utilitarianism be Critical-Level Utilitarianism with a certain well-being level as the precise critical level. So, for each well-being level, we have a unique precise version of Critical-Level Utilitarianism where that level is the critical level. Every precise version of Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion. This is because, whichever well-being level is the critical level, Critical-Level Utilitarianism entails at least one of the disjuncts in the Disjunctive Repugnant Conclusion. Moving on, the rest of the argument proceeds differently depending on whether we adopt supervaluationism or the epistemic view of indeterminacy.

On supervaluationism, we may assert the statement ‘Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion’ if it is true on each one of its sharpenings. Having assumed for simplicity that the only source of indeterminacy is the indeterminacy of ‘critical level’, each sharpening of the statement will state that a certain precise version of Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion. And, since each precise version of Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion, we have that each sharpening of the statement is true. Hence we may assert that Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion, even if the critical level is indeterminate.

On the epistemic view, we know that one well-being level in the range of indeterminacy is the critical level. So, if we know that Indeterminate Critical-Level Utilitarianism is true, we know that some precise version of Critical-Level Utilitarianism is true, even though we don’t know which version it is. But, since every precise version of Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion, we then know that the Disjunctive Repugnant Conclusion is true. Hence we know that Indeterminate Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion.

So, on both of these views, we find that Indeterminate Critical-Level Utilitarianism entails the Disjunctive Repugnant Conclusion. And, changing what needs to be changed, we find that Indeterminate Critical-Level Utilitarianism entails the Either-Repugnant-or-Sadistic Conclusion. Accordingly, Indeterminate Critical-Level Utilitarianism does not avoid these repugnant disjunctive conclusions.

Undistinguished Critical-Range Utilitarianism, however, entails neither the Disjunctive Repugnant Conclusion nor the Either-Repugnant-or-Sadistic Conclusion. It entails that both of these conclusions are false, since it entails that each of their disjuncts is false. Hence we have an argument for favouring Undistinguished Critical-Range Utilitarianism over the formally very similar view, Indeterminate Critical-Level Utilitarianism.