Suppose you can create a person whose life would be worthwhile, in a way that would affect no one else. Many of us believe that, though it would be morally permissible to create such a person, it would not be morally required. If, on the other hand, the person’s life would be miserable, then it would clearly be wrong for you to create her. This is one version of the widely discussed

Procreation Asymmetry At least when other things are equal, it is morally permissible but not required to create people with good lives, though it is wrong to create people with bad lives.1

Of course, other things are never really equal. Procreation involves significant costs, transforms our lives and relationships, and gives us new values and responsibilities. It is no wonder that we should have a moral prerogative to decide whether or not to have children because of what procreation entails for us. The Asymmetry is supposed to go deeper than that. Those of us who accept it believe we would not be required to create happy people even by, say, pressing a button to populate a distant planet with wonderful lives. And if some public policy would not be morally required on the basis of its effects on independently existing people, we do not think it could be required by virtue of causing more happy people to exist.

The second half of the Asymmetry—that it is wrong to create people with bad lives—is uncontroversial. My focus is on the first half—that it is permissible but not required (for short, optional) to create people with good lives. This optionality claim is a deontic analogue of (one version of) what John Broome calls the intuition of neutrality—that expansions to the population are, very often, neither good nor bad.2 A particularly strong version of neutrality says that creating happy people never, by itself, makes things better or worse. Broome argues that the intuition of neutrality should be rejected, and I agree.3 But I do not think the strong version of the intuition is very widely shared.4 It would seem to me a good thing if the world contained more wonderful lives. What I find hard to believe is that we could be morally required to create such lives. Broome explicitly leaves open the possibility that a deontic version of neutrality could be acceptable.5 That is what I want to investigate here.

Some might take the Asymmetry to be a non-starter without the axiological intuition of neutrality. After all, if it is good to create happy people, then we must have some moral reason to do so. And, at least in idealized cases where their lives would contain no suffering and have no negative effects on others, we have no reason not to create them. But if we have some reason to do something, and no reason not to do it, then surely we ought to do it. Therefore, we ought to create happy people, at least in such cases. So, we might think, the Asymmetry must be false.6

In my view, this argument is compelling up to the final inference. We do have moral reason to create happy people. And, in cases where other things are equal, we ought to create them. This seems to me the intuitively correct result: I believe that pressing the planet-populating button would be a good thing to do, that you have some reason to press it, that you have more reason to press it than not to press it, and indeed that you should press it. But it does not follow that you are morally required to press the button.

There is a difference between saying that we should or ought to do something and saying that we must or have to do it, in the sense that failing to do it would be wrong.7 “Should” and “ought” are weak necessity modals, in contrast to strong necessity modals such as “must,” “have to,” “required,” and “obligatory.”8 The comparative weakness of the former class can be illustrated by sentences like “You ought to do the dishes but you don’t have to” or “You ought to wash your hands—in fact, you have to,” in contrast to apparent contradictions like “You have to do the dishes but it’s not as if you ought to” or apparent redundancies like “You have to wash your hands—in fact, you ought to.”9

There are various accounts of the precise semantic difference between weak and strong necessity modals. But many agree that weak necessity modals are related to maximization: we ought to choose our best option, in some sense.10 If one of your options is better than all of the others—which need not be the same as its having the best outcome, from anything like an agent-neutral, welfarist perspective—then that is what you ought to choose. Or, as some philosophers might prefer, if you have more reason to do something than you have to do anything else, then that is what you have most reason, and therefore ought, to do.11 By contrast, it does not seem to follow from the fact that one of your options is better than all of the others, or that you have more reason to choose it than any of the others, that you are morally required to choose that option. Thus, the optionality of creating happy people does not commit us to its neutrality. Creating happy people may be a good thing, and something we have reason to do, without being morally required.

Though I reject the intuition of neutrality, and I think we have some moral reason and sometimes ought to create happy people, I am strongly attracted to the Asymmetry.12 The problem is that even this thesis is inconsistent with other plausible, purely deontic principles. Thus, an argument can be mounted against the Asymmetry without appealing to the goodness of creating happy people as a premise.

My primary aim in this paper is to present and explore these puzzles. In my view, they are not fatal for the Asymmetry. They do, however, highlight important choice points for developing a theory that incorporates it. I will use the puzzles to motivate a kind of theory that is not just consistent with the goodness of creating happy people, but which appeals to that goodness in resolving the puzzles. Such a strategy, if successful, would provide reason for other proponents of the Asymmetry to reject the intuition of neutrality and to embrace the existence of reasons to create happy people.

The puzzles are variations on Derek Parfit’s Mere Addition Paradox in population axiology.13 But they differ from Parfit’s paradox, and most of the subsequent impossibility theorems it has inspired, in crucial ways. They do not involve any “repugnant conclusion” involving vast populations of lives that are “barely worth living.” They do not rely on any numerical representation of welfare,14 or claims about “slight differences” in welfare.15 Most importantly, they involve purely deontic principles about which acts are morally permissible, eschewing any claims about which outcomes are better or worse. As we shall see, this last difference is especially important, since it is dubious whether our deontic notions are subject to the kinds of structural constraints that apply to betterness (e.g., transitivity).16

I begin by laying out a formal framework for our investigation. I then formulate and explore some preliminary puzzles involving binary principles, each of which specifies an option as permissible or impermissible in a choice between it and one other option. These principles are shown to be incompatible with certain “consistency” conditions on permissible choice. However, we will see some reason to be skeptical of such conditions. I therefore show how to formulate global versions of the binary principles, which are shown to be inconsistent even in the absence of any general consistency conditions. The rest of the paper explores some possible ways of resolving the puzzles. Ultimately, I develop a solution that appeals to some claims about when and why people are wronged, and to the goodness of creating happy people. I suggest that, by reflecting on how wrongings work, we can reasonably reject global analogues of attractive binary principles in population ethics, choice consistency conditions that link the global to the binary principles, and arguments for those conditions involving principles of sequential choice.

The recent literature has seen a wide variety of attempts to capture the Asymmetry. The approach developed here falls under a broader category of views that appeal to individual complaints (also sometimes called “losses” or “harms”) against being worse off than one would or could have been otherwise, or against being avoidably created with a bad life.17 If a person is created with a bad life, when she might never have existed at all, then she has a complaint. If we merely fail to create a person with a good life, then she has no complaint (or, on some views, she does, but it has no moral significance). Theories differ widely as to when exactly complainants are wronged. The view developed here appeals to a moralized conception of complaints, on which the kinds of complaints that give rise to wrongings are not merely complaints against being worse off than one would or could have been otherwise, but rather complaints against (roughly) being worse off than one should have been otherwise. This approach is made possible by distinguishing what we should or ought to do from what we are required to do, and the moral optionality of bringing people into existence from its axiological neutrality.

This section lays out the framework in which our puzzles will be formulated.

A population is a (nonempty) set of people. I assume that, for any populations M and N, there is a population M ∪ N, which contains all the people in M and all the people in N.

A welfare level is a degree to which things could be good for a person. Some welfare levels are greater than others: where a and b are welfare levels, a > b if and only if it is better for a person to have a life at level a than to have a life at level b.

A welfare distribution w is a function that assigns, to each individual i in some population, a welfare level w_i. There is an operation ⊕ of combining distributions. If w and v are welfare distributions defined on disjoint populations, w ⊕ v is the combined distribution that maps each individual i in w’s population to w_i and each individual j in v’s population to v_j. For any welfare level c and population N, c_N denotes the constant distribution that assigns c to every individual i in N.

I think of the purely deontic part of our moral theory as telling us, in any situation, which of our options are permissible. Here the options will be individuated by the welfare distributions they bring about. Every finite, nonempty set of welfare distributions will constitute a menu. I assume that, on every menu, there is at least one permissible option.

In treating the objects of choice as being individuated by the welfare distributions they bring about, I am assuming a kind of welfarism: that the only morally relevant considerations in the choices at issue are their effects on people’s well-being.18 In my view, welfarism is not a plausible general assumption. But surely there are some principles that constrain some possible choices, including ones that bring new people into existence, on the basis of their effects on people’s well-being. I want to study those principles.

This section lays out our initial puzzles. These involve principles concerning purely binary choices between pairs of distributions, along with structural requirements of “consistency” in permissible choice from different menus. We will later consider worries about such requirements, and develop generalizations of these puzzles that do without them. But it will be helpful to have the binary puzzles on the table first.

Let us start with a very weak commitment of the Asymmetry. Suppose that we must choose between distributions like Small and Equal Big in the first and third rows of Table 1 (ignore the second row for now). In Small, only Ann exists, at welfare level 80; in Equal Big, she and some number n of Bobs exist, also at level 80. (The numbers are just for illustrative purposes; the reader might imagine that they represent years of happy life.) These distributions differ by constant addition—expanding the population at a constant level of well-being. According to the Asymmetry, we are not required to create happy people. So we should not be required to choose Equal Big; it is permissible to choose Small. More generally, in a binary choice, constant addition is not required—for short, it is omissible:

Binary Constant Omissibility For any welfare level b and disjoint populations M and N, we are not required to choose b_M∪N when the only alternative is b_M.

Our second principle concerns benign addition—adding people to a population in a way that benefits others.19 Consider a choice between Small and Unequal Big in the first two rows of Table 1. Unequal Big relates to Small by benign addition: it makes Ann better off and adds some happy Bobs. The claim is that, so long as the Bobs are sufficiently well off, we must choose Unequal Big when the only alternative is Small. In a binary choice, benign addition is morally required, at least when the additional lives are sufficiently good:

Binary Benign Addition There exists a welfare level c such that, for any levels a > b and disjoint populations M and N, we are required to choose a_M ⊕ c_N when the only alternative is b_M.

This principle can be motivated by the idea that we are required to “make people happy” even if not to “make happy people.”20 We have a duty of beneficence, which requires us to benefit others at least when the cost to ourselves is sufficiently low. The creation of additional worthwhile lives is not the kind of “cost” that can undermine—or, adapting a phrase from Broome, “swallow up”—the duty to make people better off.21 We cannot permissibly make Ann worse off in order to avoid creating sufficiently happy Bobs.

Some might reject Binary Benign Addition on the grounds that we are not morally required to benefit people, only to avoid and prevent harm, where “benefit” and “harm” are understood in terms of good or bad things in people’s lives.22 The welfarist framework assumed here ignores this sort of information: only people’s welfare levels matter, not the goods or bads that determine those welfare levels. It would be worthwhile to revisit the puzzles discussed here in a richer framework that accommodates such information. I suspect that similar puzzles would arise: we could just as well imagine cases of benign addition that relieve the original people’s suffering, rather than adding pure “benefits.” But I won’t try to substantiate that suspicion here.23

Consider next a choice between Unequal Big and Equal Big in the last two rows of Table 1. This is a fixed-population choice. In Unequal Big, Ann is better off than all the Bobs. In Equal Big, they are equally well off, at some intermediate welfare level. Our third principle says that, no matter how well off each Bob would be in Unequal Big, we can find some number of Bobs and assign some higher level to everyone in Equal Big, while assigning an even higher level to Ann in Unequal Big, such that it would be wrong to choose Unequal Big. More generally:

Binary Non-Elitism For any welfare level c, there exist levels a > b > c and disjoint populations M and N such that it is impermissible to choose a_M ⊕ c_N when the only alternative is b_M∪N.24

This is a weak requirement of distributive justice. If we are ever morally required to make tradeoffs between different people’s interests, it seems that some tradeoff of the kind specified by Binary Non-Elitism—e.g., an arbitrarily large benefit to arbitrarily many worse-off people at the arbitrarily small expense of arbitrarily few better-off people—should be required.

Our first puzzle is that these three conditions—Binary Constant Omissibility, Binary Benign Addition, and Binary Non-Elitism—are inconsistent, given two “consistency” conditions for permissible choice, both due to Amartya Sen.25 The first condition is a requirement of contraction consistency:

Alpha If it is permissible to choose x from menu T, then it is permissible to choose x from any subset S ⊆ T to which it belongs.

Equivalently, if an option is impermissible in a menu S, it must be impermissible in any expansion T of S. We cannot make a right wrong by removing options, or make a wrong right by adding options.

The second condition is a requirement of expansion consistency. It says that a merely permissible option cannot become obligatory merely by adding new options:

Delta If two options are both permissible in menu S, then neither of them is required—i.e., the only permissible option—in any expansion T of S.26

Equivalently, if an option is required in some menu, and it is permissible in some subset of that menu, then it must also be required in that smaller menu. To motivate this condition, suppose that two options x and y are both permissible in some menu, but that one of them—say, x—becomes required when we add some new option z to the menu. Why are we no longer permitted to choose y from the larger menu? Intuitively, it must be because of its relation to the new option z. But since we are supposedly required to choose x from the larger menu, it is (by hypothesis) impermissible to choose z. How can the addition of an impermissible option make it wrong to choose what was previously permissible, and hence turn a mere permission into an obligation?27

We can now state our first puzzle:

Observation 1 Binary Constant Omissibility, Binary Benign Addition, and Binary Non-Elitism are inconsistent, given Alpha and Delta.

We can illustrate the proof using the distributions in Table 1. Suppose that welfare level c = 70 satisfies Binary Benign Addition, so that benign addition is required (in a binary choice) when the additional lives would be at level 70. And suppose that our higher levels a = 85 and b = 80 and populations M = {Ann} and N = {Bob₁, . . ., Bob_n} satisfy Binary Non-Elitism, given our choice of c = 70. We can then reason as follows. In a choice between Small and Unequal Big, we are required to choose Unequal Big, by Binary Benign Addition. Thus, it cannot be permissible to choose Small when all three distributions are available, by contraposing Alpha. And in a choice between Unequal Big and Equal Big, we are required to choose Equal Big, by Binary Non-Elitism. So it cannot be permissible to choose Unequal Big when all three are available, again by contraposing Alpha. Therefore, Equal Big is the only permissible option in the three-option menu; it is required. Since Equal Big is permissible in the three-option menu, it must also be permissible in a binary choice with Small, by Alpha. And by Binary Constant Omissibility, Small must also be permissible in that binary choice. Since both Small and Equal Big are permissible in a binary choice, we cannot be required to choose Equal Big from the three-option menu, by Delta—contrary to what we just showed. (The proof does not depend on these particular welfare levels or populations; any distributions satisfying the relevant principles will do.)

The binary principles involved in this first puzzle resemble analogous claims in a version of Parfit’s Mere Addition Paradox—what he calls the Up–Down Argument, which involves “raising, adding, and redistributing.”28 It may therefore be tempting to address it by trying to adapt some existing response to Parfit’s paradox. Parfit himself suggests a view that, when translated to deontic terms, violates Binary Non-Elitism. He suggests that an outcome like Equal Big may not be better than one like Unequal Big—even though it is surely not worse—because “the best things in people’s lives would be worse,” however slightly.29 Though this claim “would not be in itself plausible,” Parfit finds it less implausible than the Repugnant Conclusion. Those who share Parfit’s assessment may similarly deny that we are required to choose Equal Big in a binary choice with Unequal Big, even though we are surely permitted to do so. Though not in itself plausible, some might find this claim less implausible than rejecting the Asymmetry.

However, it will not be enough to reject Binary Non-Elitism. For we can formulate another puzzle for the Asymmetry that involves no analogous “qualitative loss.” Consider the choice between distributions Small and Better for Many in the first and third rows of Table 2. Better for Many relates to Small by mere addition: it leaves Ann unaffected, and differs only by the addition of some Bobs—in this case, at level 90. Proponents of the Asymmetry should believe that, no matter how well off the Bobs are, we are not required to expand the population; it should be permissible to choose Small, when the only alternative is Better for Many:

Binary Mere Omissibility For any welfare levels a and b and disjoint populations M and N, we are not required to choose a_M ⊕ b_N when the only alternative is a_M.

Consider next a binary choice between Small and Better for One, in the second row of Table 2. The latter is better for Ann and otherwise differs only via the addition of Bobs who are just as happy as Ann would have been in Small. This is a case of what I will call very benign addition. Very benign addition ensures that every life in the resulting distribution is at least as good as every life in the original, and that some are better. Intuitively, very benign addition is morally required in a binary choice:

Binary Very Benign Addition There exists a welfare level b such that, for any level a > b and disjoint populations M and N, we are required to choose a_M ⊕ b_N when the only alternative is b_M.

For our third principle, consider a binary choice between Better for One and Better for Many. This is a fixed-population choice. It is a choice between making n Bobs better off, or making only Ann better off. Intuitively, we are morally required to choose the distribution that is better for the greater number—at least, for some welfare levels like these and some numbers of people:

Binary Number Sensitivity For any welfare level b, there exists a welfare level a > b and disjoint populations M and N such that it is impermissible to choose a_M ⊕b_N when the only alternative is b_M ⊕ a_N.

Unlike Binary Non-Elitism, this principle has nothing to do with equality, or with the relative importance of benefiting the worse off, or with the relative sizes of benefits. It simply appeals to the idea that it would be wrong to choose the distribution that is (sufficiently) worse for (sufficiently) more people. While of course some would deny this,30 it would be a surprising result if the best way to preserve the Asymmetry were to reject the moral significance of numbers in this way.

Here is our second puzzle:

Observation 2 Binary Mere Omissibility, Binary Very Benign Addition, and Binary Number Sensitivity are inconsistent, given Alpha and Delta.

The proof is similar to that of Observation 1. Consider a welfare level b that satisfies Binary Very Benign Addition—say, b = 80. Choose another level—say, a = 90—and populations—say, M = {Ann} and N = {Bob₁, . . ., Bob_n}—that satisfy Binary Number Sensitivity. In a binary choice between Small and Better for One, we are required to choose Better for One, by Binary Very Benign Addition. So it is impermissible to choose Small when all three distributions are available, by Alpha. In a binary choice between Better for One and Better for Many, we are required to choose Better for Many, by Binary Number Sensitivity. So it is impermissible to choose Better for One when all three distributions are available, again by Alpha. Therefore, we are required to choose Better for Many from the three-option menu, and thus also permitted to choose it in a binary choice with Small, by Alpha. But Small is also permissible in that binary choice, by Binary Mere Omissibility. So we cannot be required to choose Better for Many from the three-option menu, by Delta—a contradiction.

In my view, the binary principles involved in these puzzles are very hard to reject, insofar as we are attracted to the Asymmetry. I therefore want to take a closer look at our so-called consistency conditions.

The least familiar condition in the binary puzzles above is Delta. This condition is a weakening of the more widely known expansion consistency condition Beta:31

Beta If two options are permissible in a menu S, and one of them is permissible in an expansion T of S, then so is the other.

Proponents of the Asymmetry, however, should reject Beta. In a choice between creating some person with a good life and creating no one, we are permitted to do either; in a choice between creating that person with an even better life and creating no one, we are permitted to do either. But in a choice between creating the person with a good life, creating her with the better life, and creating no one, we are permitted to create her with a better life, but not to create her with the worse one. This pattern violates Beta.32

Beta is also at odds with tenets of common-sense morality having nothing to do with procreative choices, such as the necessity constraint on self-defense. Suppose that a reckless driver will hit a pedestrian, causing permanent quadriplegia, unless the pedestrian, using some sort of remote-control device, redirects the car into a pole, causing the driver to become quadriplegic instead. It seems permissible for the pedestrian either to harm the driver or to allow herself to be harmed. The same would be true if the pedestrian could instead redirect the car into a smaller pole, causing paraplegia instead of quadriplegia: it is permissible either to harm the driver in this less severe way or to allow herself to be harmed. But if the pedestrian had all three options—to harm the driver in the more severe way, to harm the driver in the less severe way, or to allow herself to be harmed—only the latter two options are permissible. This pattern violates Beta.33

Delta, however, is a significant and reasonable weakening of Beta. It does not give rise to the problems above. From the permissibility of either adding or not adding a person at a higher level (in a binary choice), and of either adding or not adding her at some lower level (in a binary choice), Delta implies that no one of these options is required when all three are available. This is consistent with the permissibility of either adding her at the higher level or not adding her at all, when all three options are available. Similarly, it is consistent with the necessity constraint on self-defense.

In the presence of Alpha, however, Delta is still quite strong. Together they imply that the binary requirement relation—must choose rather than—is transitive: if we are required to choose x when the only alternative is y, and required to choose y when the only alternative is z, then we are required to choose x when the only alternative is z.34 Thus, the binary puzzles of Section III are structurally just like axiological puzzles involving the transitivity of better than. But, while the transitivity of better than is widely accepted,35 the transitivity of binary requirement is more questionable.

Consider an example due to Leo Katz.36 Al and Chloe enter an emergency room after a car accident. Al is in danger of losing both his legs; Chloe is in danger of losing her index finger. We can help only one of them. Ordinarily we would be required to help Al. But Al and Chloe are married, and Chloe is a passionate amateur pianist. It is thus enormously important to Chloe—and, therefore, to Al—that her index finger be restored to full use. So Al prefers that we help Chloe, even though this would mean that he loses his legs. Arguably, in such a case, it would be permissible to save Chloe’s finger rather than Al’s legs.

Now suppose that another patient, Bea, is in danger of losing just one of her legs. In a choice between saving both of Al’s legs and saving just one of Bea’s, we would be required to save Al’s legs. And in a choice between saving Bea’s leg and Chloe’s finger, we would be required to save Bea’s leg. By the transitivity of binary requirement, we would be required to save Al’s legs rather than Chloe’s finger, contrary to what we supposed above.

It is unclear whether this violation of transitivity for binary requirement is due to a violation of Alpha or Delta. If we are required to save Chloe’s finger rather than Al’s legs, this violates Alpha, since any option that is permissible when all three are available would be impermissible in some binary choice. If we are merely permitted to save Chloe’s finger rather than Al’s legs, but required to save Al’s legs when all three options are available, it violates Delta. I lean towards the second possibility, so I am inclined to see this case as a violation of Delta.

There is a familiar way to reconcile these judgments with the structural principles, by individuating the alternatives more finely than by whom we help and how—for example, by treating saving Al’s legs when the only alternative is Chloe’s finger and saving Al’s legs when the only alternative is Bea’s leg as different options, distinguished by (among other things) Al’s preference that we save Chloe’s finger instead.37 I do not claim that this strategy is illegitimate. But, in our framework, the objects of choice are individuated coarsely, by their welfare distributions alone; our puzzles require Alpha and Delta to be understood accordingly. The intuitive judgments in the triage case at least suggest that those principles are not sacrosanct under sufficiently coarse-grained individuation of alternatives, even if they would be compatible with the principles given a more fine-grained criterion of individuation.

If we wish to preserve the Asymmetry, however, it will not be enough to simply reject Alpha or Delta. For, as we shall see in Section V, we can formulate versions of our puzzles in which those conditions play no role. These puzzles involve “global” variations on our earlier principles, which apply to arbitrary menus as opposed to merely binary ones. In order to preserve the Asymmetry, we will need to figure out which of these global principles fail, and why.38

Let’s begin with our omissibility conditions, whose binary versions are firm commitments of the Asymmetry. The binary conditions said that we would not be required to expand the population in a certain way, when our only alternative was simply not to expand the population in that way. Our global analogues of these conditions will say that we are not required to expand the population if we could also—perhaps among other options—simply not expand that population. For example, regarding the distributions in Table 1, we are not required to choose Equal Big from any menu that includes Small; regarding the distributions in Table 2, we are not required to choose Better for Many from any menu that includes Small. More generally:

Constant Omissibility For any welfare level b and disjoint populations M and N, we are not required to choose b_M∪N from any menu containing b_M.

Mere Omissibility For any welfare levels a and b and disjoint populations M and N, we are not required to choose a_M ⊕ b_N from any menu containing a_M.

Each of these global principles entails its binary analogue, which in turn entails it given Alpha and Delta.

The simplest reformulation of our benign addition principles would say that it is wrong to choose a distribution when there is an alternative that is related to it by (very) benign addition. However, we can make do with even weaker versions of these principles, which say that if it is permissible to choose some distribution, then it is permissible to choose any distribution that is related to it via (very) benign addition (where the conditional here is to be treated as material). For example, if it is permissible to choose Small in Table 1 (or Table 2), then it must also be permissible to choose Unequal Big (or Better for One). More generally:

Benign Addition There exists a welfare level c such that, for any levels a > b and disjoint populations M and N, if it is permissible to choose b_M from a menu S containing a_M ⊕ c_N, then it is permissible to choose a_M ⊕ c_N from S.

Very Benign Addition There exists a welfare level b such that, for any level a > b and disjoint populations M and N, if it is permissible to choose b_M from a menu S containing a_M ⊕ b_N, then it is permissible to choose a_M ⊕ b_N from S.

Unlike Constant Omissibility and Mere Omissibility, these principles do not entail their binary analogues, though the binary principles entail the global ones given Alpha. They can be motivated by appealing to a duty of beneficence together with the optionality of creating happy people. It seems wrong to make everyone worse off than they could have been otherwise, simply because making everyone better off would have also, unobjectionably, created new lives that would have been well worth living. If it is not wrong, in some circumstance, to do this, then it should be at least permissible to create the new lives.

Finally, our fixed-population principles can be reformulated to say that it is wrong to choose a distribution like Unequal Big (or Better for One) when one like Equal Big (or Better for Many) is available:

Non-Elitism For any welfare level c, there exist levels a > b > c and disjoint populations M and N such that it is impermissible to choose a_M ⊕ c_N from any menu containing b_M∪N.

Number Sensitivity For any welfare level b, there exists a welfare level a > b and disjoint populations M and N such that it is impermissible to choose a_M ⊕ b_N from any menu S containing b_M ⊕ a_N.

These principles entail their binary analogues and are entailed by the binary principles given Alpha.

We have the following analogues of Observations 1 and 2:

Observation 3 Constant Omissibility, Benign Addition, and Non-Elitism are inconsistent.

Observation 4 Mere Omissibility, Very Benign Addition, and Number Sensitivity are inconsistent.

To prove Observation 3, we first choose a welfare level c that satisfies Benign Addition, and then choose levels a and b and populations M and N that satisfy Non-Elitism. Consider the menu consisting of b_M, a_M ⊕ c_N, and b_M∪N. By Non-Elitism, it is wrong to choose a_M ⊕ c_N. So by Benign Addition, it is wrong to choose b_M as well. Thus, we are required to choose b_M∪N, which violates Constant Omissibility. The proof of Observation 4 is analogous.

The lesson of the global puzzles is that if we want to retain the Asymmetry, it’s not enough to reject Alpha or Delta. We also need to justify the failure of one or more of the global principles, which are (in my view) plausible independently of any general commitment to Alpha and Delta.

In the next two sections, I want to consider some responses to these puzzles that are based on recent discussions of the Asymmetry, and which are consistent with the binary principles of Section III. As we shall see, these responses lead to further puzzles of their own. This will help us to appreciate the full scope of the challenge for the Asymmetry, and thus to develop a more adequate solution to the puzzles.

I introduced Binary Constant Omissibility and Binary Mere Omissibility, in Section III, as firm commitments of the Asymmetry. It is much less obvious, however, that proponents of the Asymmetry must accept the global analogues of these conditions. And there is a plausible rationale for why they might be rejected.

Say that an option is maximal on some menu if it is permissible in a binary choice with each alternative on that menu. Teruji Thomas argues that the permissible options on any menu are all and only the maximal options on that menu.39 Since we are assuming there to be at least one permissible option on every menu, this requires there to be at least one maximal option on every menu. For example, in Table 1, the binary principles of Section III imply that, if any distribution is maximal, it must be Equal Big: Small is impermissible in a binary choice with Unequal Big, which is in turn impermissible in a binary choice with Equal Big. Similarly, in Table 2, the binary principles imply that, if any distribution is maximal, it must be Better for Many. (And it is independently plausible that these distributions are maximal.) So if all and only the maximal options are permissible, then we are required to choose Equal Big in Table 1 and Better for Many in Table 2—contrary to Constant Omissibility and Mere Omissibility. And since each of these distributions is merely permissible in a binary choice with Small, we have a violation of Delta.

This pattern of judgments can be illustrated by the following concrete view, which is stated (though not endorsed) by Thomas. To formulate this view, assume that welfare levels are represented by real numbers. Say that a person has a complaint against distribution u, relative to an alternative v, if she is worse off in u than in v (including having negative welfare in u while not existing in v), with the size of her complaint proportional to how much worse off she is. In a binary choice between u and v, we are required to choose u if and only if both (1) the sum of complaints against u relative to v is less than the sum of complaints against v relative to u, and (2) u contains greater total well-being than v. From an arbitrary menu S, we are permitted to choose u from S if and only if u is maximal in S. In short, the view says that it is permissible to choose an option if and only if there is no alternative to it that offers both a lesser sum of complaints (relative to it) and a greater sum of well-being.

This is a very well-behaved view. It satisfies all of the principles we have introduced so far, with the exceptions of Constant Omissibility, Mere Omissibility, and Delta (and hence Beta as well). And it is natural to identify permissible options with maximal ones.40 It also strikes at a weak point in our original binary puzzles, since, as we saw in Section IV, there is reason to be suspicious of Delta. So there is much to be said in favor of this solution to our puzzles.

However, it seems to me unattractive from a point of view that is committed to the Asymmetry. In particular, the sort of omissibility it offers with respect to procreation seems to me too fragile. Our intuition is that creating happy people is not morally required. On the view under consideration, that is true when the only alternative is simply not to create them. But as soon as we have the additional alternative to create those same people in a way that benefits others, we are required to create them, even though we are not required or even permitted to create them in that way; we are instead required to create them in a way that does not benefit others. This does not capture our intuition.

This kind of verdict seems especially implausible in cases of malign addition, when people are added in a way that makes others worse off. For example, in Table 3, Malign Big relates to Small by malign addition: Ann is made worse off, and some Bobs are added. If we find the Asymmetry attractive, then we should think that malign addition is not morally required. If we are not morally required to create new people, how could we be morally required to create people in a way that is harmful to others? The following principle says that we are not:

Malign Omissibility For any welfare levels a, b, and c (where b > c), and disjoint populations M and N, we are not required to choose c_M ⊕ a_N from any menu containing b_M.

The Delta-denying view we are considering violates Malign Omissibility. When all three of Table 3’s distributions are available, it is wrong to choose Small because Benign Big offers a lesser sum of complaints (relative to Small) and a greater sum of well-being. It is wrong to choose Benign Big (assuming n ≥ 2) because it offers less total well-being and has the same population as Malign Big (and therefore necessarily offers a greater sum of complaints relative to it). So we are required to choose Malign Big when all three are available, even though it relates to Small by malign addition.

More generally, we have the following variation on Observation 4, using an innocuous strengthening of Number Sensitivity (which simply adds the existence of a middle level in between the two used in the principle):

Number Sensitivity⁺ For any welfare level c, there exist welfare levels a > b > c and disjoint populations M and N such that it is impermissible to choose a_M ⊕ c_N from any menu S containing c_M ⊕ a_N.

Observation 5 Malign Omissibility, Benign Addition, and Number Sensitivity⁺ are inconsistent.

The proof is familiar. We first choose a welfare level c that satisfies Benign Addition, and then levels a and b and populations M and N that satisfy Number Sensitivity⁺, given our choice of c. We then consider the menu consisting of b_M, a_M ⊕ c_N, and c_M ⊕ a_N. It is wrong to choose a_M ⊕ c_N by Number Sensitivity⁺, and thus wrong to choose b_M by Benign Addition. So we are required to choose c_M ⊕ a_N, which violates Malign Omissibility. We can get a similar variation on Observation 3 using a weakening of Malign Omissibility and an innocuous strengthening of Non-Elitism in place of Number Sensitivity⁺.41

Perhaps the best option for proponents of the Asymmetry will, ultimately, embrace that malign addition is sometimes morally required. But this conclusion seems to me quite at odds with the spirit of the Asymmetry. I would therefore prefer, if there is one, a solution that avoids this result.

In the previous section, we considered a view that violates Delta, along with the global Constant Omissibility, Mere Omissibility, and Malign Omissibility conditions. I now want to consider the possibility of rejecting Alpha, along with the global Benign Addition conditions. The idea is that, even though benign addition is required in a binary choice, it can be permissible to choose a distribution in the presence of an alternative related to it by benign addition, when and because it would be wrong to choose the second alternative due to the presence of some third. For example, while it is wrong to choose Small in a binary choice with Unequal Big, Better for One, or Benign Big, it is permissible to choose Small—and wrong to choose Unequal Big, Better for One, or Benign Big—when Equal Big, Better for Many, or Malign Big is available.

I agree with these verdicts and that Alpha and the global Benign Addition conditions should be rejected. The question is what explains the verdicts, and why those conditions are false.

One possible explanation can be found in Johann Frick’s treatment of the Mere Addition Paradox.42 Frick suggests that benign addition can be objectionable because of the inequality it brings about. This inequality is not unjust in a binary choice, when the only way to avoid it would be to prevent the existence of the worse off, whose lives are worth living. Objecting to their existence in such circumstances would seem to regard them as “a blot on the Universe.”43 But it is unjust when the inequality can be avoided by making the additional people better off. For this reason, we may find it permissible to choose a distribution even though it would be impermissible, on grounds of injustice, to choose an alternative that is related to it by benign addition—at least, in the presence of a third distribution that makes the second one unjust.44

I am sympathetic to the general structure of this view, and to its verdicts about our cases and principles. Frick’s view seems capable of explaining these judgments in a way that is independently plausible and tied to more familiar moral phenomena. However, I do not think an appeal to equality can resolve the puzzles in full generality. For we can generate a similar puzzle with a kind of benign addition that does not introduce inequality.

Consider the distributions Small and Equal Big⁺ in the first two rows of Table 4. Equal Big⁺ relates to Small by making Ann better off and adding some Bobs who would be just as well off as Ann. This is a case of benign addition that produces no inequality, which we can call egalitarian addition. Intuitively, we cannot permissibly choose a distribution that would be worse for everyone in its population merely because making them better off would bring new people into existence who would be just as well off as them (at least, supposing they would be sufficiently well off):

Egalitarian Addition There exists a welfare level c such that, for any welfare level b > c and disjoint populations M and N, if it is permissible to choose c_M from a menu S containing b_M∪N, then it is permissible to choose b_M∪N from S.

There can be no egalitarian objection to Egalitarian Addition, since both distributions are perfectly equal.45

According to Egalitarian Addition, it is either impermissible to choose Small from the three-option menu in Table 4, or it is permissible to choose Equal Big⁺ (assuming the lives are sufficiently good). The latter possibility can be ruled out by a fixed-population principle that limits our concern for equality. It says that it can sometimes be wrong to make everyone equally well off if we can make sufficiently many people sufficiently better off and sufficiently few not too much worse off:

Non-Extreme Priority For any welfare level c, there exist welfare levels a > b > c > d and disjoint populations M and N such that it is impermissible to choose b_M∪N from any menu containing d_M ⊕ a_N.

To reject this principle in a way that resolves our puzzles, one would have to think that inequality is so important that it is always permissible to choose an equal distribution (at least, at any welfare level above the threshold guaranteed by Egalitarian Addition) even if that means sacrificing arbitrarily large gains for arbitrarily many people at the arbitrarily small expense of a single person. This seems to me an extreme view.

But if it is impermissible to choose Equal Big⁺ from Table 4, then it is impermissible to choose Small, by Egalitarian Addition. So we are required to choose Malign Big⁺. More generally:

Observation 6 Malign Omissibility, Egalitarian Addition, and Non-Extreme Priority are inconsistent.

I omit the proof, which is by now familiar.

The lesson is that a concern for inequality only seems to save the Asymmetry if we give it so much weight as to reject Non-Extreme Priority, for example by giving absolute priority to the worse off. Perhaps that will ultimately prove the best strategy for proponents of the Asymmetry. But it seems to me too extreme. More importantly, the intuitions that favor the Asymmetry have nothing to do with equality. So it seems especially surprising that maintaining the Asymmetry should require such an extreme attitude towards inequality. It seems to me that if we are going to reject Benign Addition, we ought to reject Egalitarian Addition as well. We therefore need some other explanation for rejecting these principles.

Let’s take a step back. It seems to me that, in order to solve our puzzles, we need to ask why the Asymmetry is supposed to be true in the first place. We can then appeal to that explanation in order to help us solve the puzzles.

I will work with a particularly simple explanation of the Asymmetry, which appeals to the idea that

Wrongs Require Victims An act is wrong only if it wrongs someone.46

More exactly, an act is wrong by virtue of its effects on people’s well-being only if it wrongs someone by virtue of its effects on her well-being. (If there are wrongs of “cosmic impertinence,”47 or other kinds of victimless wrongdoing, these fall outside the realm of beneficence.) I will assume, moreover, that wrongings are wrongdoings: it is wrong to wrong someone. If you create a person with a bad life, there is someone whom you have wronged, and so you have done something wrong. By contrast, if you fail to create a person, or you create a person with a sufficiently good life, you wrong no one, and so you have done nothing wrong. This explanation has the virtue of not immediately overgeneralizing to support the axiological intuition of neutrality: it is much less plausible that what is better must be better for someone.

This explanation is, of course, controversial. Some take Wrongs Require Victims to be refuted by Parfit’s nonidentity problem: they think it wrong to create a person, even with a very good life, when one could instead create a different person with a better life.48 I am not so sure. I agree that we ought to create the better life in nonidentity cases. But if there is nothing bad about the other life—suppose it contains no suffering and is otherwise wonderful—it is not at all obvious to me that it would be wrong to create it.49 In any case, there are various responses to the nonidentity problem which are consistent with Wrongs Require Victims, though some of these would require departures from the welfarist framework we have been assuming.50 I find the idea at least plausible enough to be worth exploring as a possible foundation for the Asymmetry, which may help us choose between possible solutions to our puzzles.

When is a person wronged by virtue of the effects of our choices on her well-being? I want to suggest a way of thinking about how wrongings work that sheds light on the choice between Alpha- and Delta-denying responses to our puzzles; I think it favors the Alpha-denying route.

The problem has to do with sequences of choices made over time. Consider the decision tree in Figure 1, in which we can bring about any of the distributions in Table 3.

At node 1, we can either bring about Malign Big or go up to node 2, where we face a choice between Small and Benign Big. On an Alpha-denying solution to our puzzles, it is permissible to choose Small in a nonsequential choice between all three distributions. Intuitively, it should therefore be permissible to make the sequence of choices that bring about Small in this case; it would be strange to think that we can choose Small in one step but not in two. So it must be permissible to go up at node 1 and go up at node 2. But if a sequence of choices is permissible, then every choice in the sequence must be permissible. So it must be permissible, at node 2, to go up and choose Small. But, once we are at node 2, we face a binary choice between Small and Benign Big. On an Alpha-denying solution to our puzzles, it is wrong to choose Small when the only alternative is Benign Big. It should therefore be wrong to choose Small at node 2. As Thomas puts it, “a permissible choice cannot be permissibly implemented.”61 This seems bizarre.

This is a serious challenge, which must, I think, be answered if any Alpha-violating view is to be accepted. In response, I want to say that it remains permissible, at node 2, to choose Small, even though it would not be permissible to choose Small in a nonsequential, binary choice with Benign Big. The permissibility of a choice, I want to say, can depend on the sequence of which it is a part. This dependence, I think, can go in both directions: the permissibility of a choice can depend on what we did or could have done earlier, as well as on what we will do later. These claims can be motivated by considering sequential choice problems that arise from violations of the expansion consistency conditions Delta and Beta—problems which appeal to premises that are very similar to those marshalled against the Alpha violation above.

Let’s start with a Delta violation. Consider a sequential version of Katz’s triage case from Section IV, depicted in Figure 2. We can save both of Al’s legs, one of Bea’s legs, or Chloe’s finger. However, in order to help Al or Chloe, we first have to dismiss Bea, and then choose between the remaining two.

The Delta-violating judgments about the nonsequential case are that we are morally required to save Al’s legs when all three options are available, but that we are permitted to save either Al’s legs or Chloe’s finger when saving Bea’s leg is not an option. Suppose these judgments are correct. Since we are required to save Al’s legs in a nonsequential choice between all three options, we are presumably required to choose the sequence that terminates in saving Al’s legs in this case; it would be strange to think that we must save his legs in one step but not in two. So we must be required to go up at node 1 and then up at node 2. But if a sequence of choices is required, then presumably every choice in the sequence must be required. So we must be required, at node 2, to go up and help Al. But, once we are at node 2, we face a binary choice between saving Al’s legs and saving Chloe’s finger. And we are supposedly not required to save Al’s legs in such a binary choice; we can permissibly save Chloe’s finger instead. We should therefore not be required, at node 2, to go up and help Al after all. (An exactly parallel argument can be devised against a Delta-denying treatment of the Asymmetry, such as Thomas’s view considered in Section VI; simply replace saving Al’s legs with choosing Malign Big, saving Chloe’s finger with choosing Small, and saving Bea’s leg with choosing Benign Big.)

This challenge for Delta violations relies on very similar premises to the challenge for Alpha violations. The sequential choice problem for Alpha violations involved a “disappearing permission”: the permission to choose Small supposedly dissolves once we eliminate Malign Big. The case against Delta violations involves instead a “disappearing requirement”: the requirement to save Al’s legs supposedly dissolves once we dismiss Bea. Instead of a permissible choice that we are somehow not permitted to implement, we have an obligatory choice that we are somehow not obligated to implement. These patterns seem to me equally bizarre. But any proponent of the Asymmetry who accepts our binary judgments must reject either Alpha or Delta. So there is at least some pressure to regard Alpha and Delta violations as companions in guilt with respect to this problem.62

There is some daylight between the two arguments. One could in principle maintain, with the argument for Alpha, that every choice in a permissible sequence must be permissible, while denying the analogous premise in the argument for Delta, that every choice in an obligatory sequence must be obligatory. On such a view, we are required to save Al’s legs in two steps even though, once we have made the first step, we are no longer required to make the second. But that seems to me just as bizarre as saying that we are permitted to choose Small in two steps even though, once we have made the first step, we are no longer permitted to make the second. I find it hard to see what rationale might allow for the former possibility but not the latter.63

While proponents of the sequential choice argument for Alpha can perhaps, in principle, refrain from endorsing the analogous argument for Delta (thus allowing them to retain the binary principles involved in our puzzles), I think the most plausible responses to the latter can also help us answer the former. One is to deny the permissibility of saving Chloe’s finger at node 2, even though it would be permissible if we had never had the option to save Bea’s leg. On this view, we are indeed required to turn Bea away at node 1, because the threat to Al is more severe (“We’re very sorry, but we cannot save your leg, because Al is in danger of losing both of his”). But we cannot, after doing this, help Chloe instead (“Now that pesky Bea is gone . . .”). Saving Chloe’s finger would wrong Bea, even though we can no longer help her at the time of choice, and even though it would have been permissible to save Chloe’s finger if we had never had the option to save Bea’s leg. On this view, the past availability of an option can make a difference to the normative status of remaining options, because it can make a difference to who is wronged.64

Proponents of “resolute choice” in decision theory appeal to our past choices in order to justify seemingly counterpreferential choices at future choice nodes.65 While the rationality of resolute choice is controversial,66 I find it hard to deny that our past choices can make a difference to what it is morally permissible to do now. It can be wrong to do something that would be permissible but for the fact that we promised not to do it. It can be wrong to harm a person in self-defense if we are responsible for the threat they pose. It can be wrong to blame someone for doing something that we ourselves have recently done, even if their behavior is blameworthy. We need not take a stance here on the rational status of resolute choice. Perhaps a fully rational agent is required to have well-behaved preferences and to act in accordance with those preferences. This is consistent with the idea that our past choices can make a difference to what it is morally permissible to do now.67

My response to the sequential choice problem for Alpha violations will appeal not only to the idea that our past actions and options can affect the permissibility of what we do now, but also to the related possibility that our future actions can affect the permissibility of what we do now. This possibility is best illustrated by a different kind of sequential choice problem, arising from violations of the stronger expansion consistency property Beta. This condition says that if two options are both permissible in some menu, and one of them is permissible in some expansion of that menu, then the other is also permissible in that expanded menu. We saw in Section IV that Beta is almost immediately inconsistent with the Asymmetry, as well as other principles of common-sense morality. These Beta violations, however, lead to sequential choice problems, such as that depicted in Figure 3 based on our self-defense example.

In Figure 3, you are threatened by a reckless driver. You must first decide whether to redirect the driver into a smaller pole, causing her to become paraplegic. If you do not, you then face a choice, at node 2, between redirecting the driver into the bigger pole, causing her to become quadriplegic, and allowing yourself to be hit and become quadriplegic instead.68 Since it seems wrong to inflict quadriplegia when you could instead inflict paraplegia, it seems wrong to choose the sequence that goes up at node 1 and then up at node 2. But, at node 1, it seems permissible to go up: you are not required to redirect the driver into the smaller pole. And, once you are at node 2, you face a binary choice between two options that, in a nonsequential choice, would each be permissible. So, we might think, it must be permissible for you to go up at node 2, causing the driver to become quadriplegic. And, plausibly, a sequence of permissible choices must itself be permissible: if it is permissible to go up at node 1 and permissible to go up at node 2, it must be permissible to go up at node 1 and up at node 2. But, supposedly, it is not. (An exactly parallel argument can be devised against the Beta-violating pattern of judgments supported by the Asymmetry: simply replace the driver’s becoming paraplegic with creating some person with a better life, the driver’s becoming quadriplegic with creating the same person with a less good life, and allowing oneself to become quadriplegic with not creating the person at all.)

It would be hasty to treat this as a sound argument for Beta and against the common-sense morality of self-defense. But where does it go wrong? We could say, along the lines of our response to the sequential triage case, that it is wrong at node 2 to impose the greater harm in order to save yourself, because you previously had the option to save yourself in a less harmful way. But I find this hard to believe. I do not think you are in general required to allow yourself to be severely harmed simply because you previously passed up an opportunity to defend yourself in a slightly less harmful way. Similarly, I do not think you are morally prohibited from having a child simply because you previously passed up an opportunity to create that child with a better life. In these cases, it seems more plausible to say that your later choice makes the earlier choice wrong. It is wrong to pass up the opportunity to avert a threat in a less harmful way if you will simply go on to avert it in a more harmful way. It is wrong not to create a child with a better life if you will simply go on to create her with a worse life. It makes sense for us to regret our past choices, and for others to blame us for those choices, given what we later do, even if those past choices could have been part of a perfectly permissible sequence, if our future behavior had been different. The permissibility of a choice depends on the sequence of which it is a part.69

I have suggested that the permissibility of a choice can depend both on what we did in the past and on what we will do in the future. With both ideas in hand, we can return to the sequential choice problem for Alpha violations.

Suppose, in Figure 1, that we go up at node 1 and find ourselves at node 2. Why is it permissible to go up at node 2, bringing about Small, when our only alternative would be better for Ann and otherwise differ only by the addition of happy Bobs? Ann seems to have a legitimate complaint against our choosing Small, and no one seems to have a legitimate complaint, at this point, against our choosing Benign Big.

But even if the Bobs would not be wronged by our choice at node 2—since we could not have made them better off at the time of our decision—we will have wronged them nonetheless. Just as the quadriplegic reckless driver would be wronged by our earlier choice not to avert her threat in a less harmful way, I think the Bobs would be wronged by our earlier choice, at node 1, to forgo Malign Big. They can reasonably object that, given our future choice to create them anyway, we wronged them by not having made them better off. On this view, the permissibility of going up at node 1 does not follow from its being part of some permissible sequence; it depends also on what we later do.

Once we see how the Bobs are wronged by the sequence that terminates in Benign Big, we can explain why it is permissible to go up at node 2, choosing Small. Ann’s complaint against this choice is answered by the fact that it can only be satisfied by making it the case that we have wronged someone else. It therefore seems to me permissible at node 2 to choose Small, even though we would be required to choose Benign Big in a nonsequential choice between the two. Thus, the permissible option to choose Small can be permissibly implemented; the permission does not disappear.

I do not insist on this particular story about Figure 1. There are other ways to resist the sequential choice argument for Alpha: for example, by locating the Bobs’ wronging at node 2 rather than node 1, by attributing their wronging to the sequence without locating it at either node,70 or, more radically, by denying that sequences of choices can be permissible or impermissible to begin with.71 One way or another, we can reject the sequential choice argument for Alpha. This is compatible with accepting analogous principles as requirements of rationality, where the rational status of an agent’s choice is thought to depend only on the agent’s preferences between options. The moral permissibility of a choice does not similarly depend on some single binary relation over options (e.g., betterness). It depends on who is wronged, which in turn depends on the full menu of alternatives. To paraphrase Rawls,72 moral principles need not be mere extensions of principles of rational choice for an individual.73

Let’s take stock. We started with the idea that the Procreation Asymmetry remains plausible even if, as I believe, the axiological intuition of neutrality is false. I believe that creating happy people makes the world better, and that we therefore have some moral reason, and sometimes ought, to create them. It does not follow from this that we are morally required to create happy people.

But if we want to preserve the Asymmetry, it is not enough to simply deny that we are morally required to do what is best. For, as we have seen, the Asymmetry gives rise to purely deontic puzzles that do not appeal directly to any axiological claims. And it’s not enough to resolve those puzzles by rejecting choice consistency conditions such as Alpha or Delta. For we can formulate global versions of the puzzles in which those conditions play no role. We need to justify the rejection of one or more of those global principles.

I have suggested that we reject the global benign addition conditions. Benign addition is required in binary choices because it makes people better off without wronging anyone. But in the presence of other options, benign addition may wrong those who are created, when and because we ought to have made them even better off. That is why it can be permissible not to create them at all: those who stand to benefit from their existence are not wronged if the only way to satisfy their complaint would have wronged others. The structure of wronging thus explains why the global benign addition principles fail, and why Alpha—and the sequential choice principles which have been thought to support it—fail along with them.