MORALITY, UNCERTAINTY Chad Lee-Stronach Forthcoming in The Philosophical Quarterly Abstract Non-Consequentialist moral theories posit the existence of moral constraints: prohibitions on performing particular kinds of wrongful acts, regardless of the good those acts could produce. Many have argued that such theories cannot give satisfactory verdicts about what we morally ought to do when there is some probability that we will violate a moral constraint. In this article, I defend Non-Consequentialist theories from this critique. Using a general choice-theoretic framework, I identify various types of Non-Consequentialism that have otherwise been conflated in the debate. I then prove a number of formal possibility and impossibility results establishing which types of Non-Consequentialism can – and which cannot – give us adequate guidance through through a risky world. Keywords: Non-Consequentialism; Moral Absolutism; Moral Constraints; Decision Theory; Risk; Uncertainty; I INTRODUCTION Morally speaking, the world is a risky place. Everyday acts like driving, making a promise, or purchasing a product can – for all we know – cause harm, be insincere, or sustain others' wrongful practices. In light of this fact, it is surprising that few moral theories provide us any systematic guidance about which of our risky acts are permissible and which are not. Indeed, they fail to do so even if we idealise our everyday epistemic situation to grant us clear knowledge of what acts we can perform in any given choice context, what their 1 outcomes are likely to be, and precisely how to morally evaluate those outcomes. For those who hope that our theories might help navigate us through this risky world, it seems that our theories only provide us a map of a world far more certain than our own. In recent years, many have attempted to extend our existing moral theories to cases involving uncertainty. However, they have found that NonConsequentialist moral theories – those which hold that what is morally right is in some sense prior what is good – give unacceptable guidance in such cases.1 In particular, it seems that one of the hallmarks of Non-Consequentialism, moral constraints – prohibitions on particular types of acts, regardless of the good it might produce – systematically lead us to make unacceptable verdicts about the permissibility of acts that have some probability of violating a constraint. Let Moral Absolutism be the class of theories that posit moral constraints. This article investigates whether the following proposition is true: The Problem of Risk: No Moral Absolutist theory can give adequate verdicts about the permissibility of risky acts. Despite the vigorous, decades-long debate between Moral Absolutists and their critics, it still appears to be an open question whether the Problem of Risk is true. To answer it, I reformulate the debate using a formal choice-theoretic framework.2 First, I distinguish types of Moral Absolutism that have been conflated by critics and defenders alike. Second, I clarify the terms of the debate by precisely defining the adequacy conditions against which Moral Absolutism is being judged. I then prove that while it is true that some types of Moral Absolutism cannot jointly satisfy these adequacy conditions, it is also true that others can do so by adopting unorthodox formal approaches to decision-making under risk. The challenge then becomes to explain why these successful approaches are not 'gimmicky' (or ad hoc) formal solutions, but rather are firmly grounded in independently plausible substantive moral theory.3 I identify substantive Non-Consequentialist moral theory that justifies these unorthodox decision-theoretic approaches and moral constraints, more generally. On this basis, I conclude that the Problem of Risk is false. 2 Part II gives an overview of the existing debate. Part III formalises the debate, showing that while some versions of Moral Absolutism cannot give adequate verdicts in risky situations, others can do so. Part IV presents an overlooked substantive justification for those versions of Moral Absolutism that avoid the Problem of Risk. Part V concludes that, contrary to what critics allege, Moral Absolutism can make both a formal and substantive case for providing adequate moral guidance through a risky world. II THE PROBLEM OF RISK The world is also, of course, a complex place. To provide adequate 'guidance', a theory would have to not only determine what is right, but also provide a user-friendly set of instructions that would allow us to reliably determine what the theory considers right. The former task requires that a theory have a moral decision rule. The latter task requires a decision procedure, which is designed to track – and, therefore, assumes the existence of – a decision rule.4 As it stands, moral philosophers are still trying to ascertain what these moral decision rules could be and whether they are acceptable. That is the task of this article. It will be a further project to provide a workable decision procedure that not only gives us guidance in principle, but also in practice.5 To make the complex tractable, and the debate more concrete, we will consider the following simplified case: Sacrifice: To best ensure society's future happiness, we can bring about the ongoing torture of an innocent child living in isolation and squalor. Should we do so? Some will respond that to answer this question, they need more information. How much torture, exactly? How many people will benefit? How happy will they be? Others will feel that these questions are repugnant, the calculus irrelevant. This type of reaction captures the idea that particular acts – like torturing a child for the happiness of others – are always impermissible, regardless of how many would benefit. However, even if this reaction is understandable, it is unclear how it extends to cases like the following: 3 Risk of Sacrifice: To best ensure society's future happiness, we can run a risk of our causing an innocent child to live in torture. Should we do so? Suppose that you subscribe to the Moral Absolutist's position in Sacrifice. What do you say about Risk of Sacrifice? Strictly speaking, your position towards acts taken under conditions of certainty entails nothing about those taken under conditions of uncertainty. As such, we need to extend Moral Absolutism to cover cases involving risks of violating a moral constraint. To this end, it will be helpful to generalise from particular permissibility verdicts for a particular set of morally-relevant features (number of people, degree of risk, and so on) to what I shall call a moral decision rule, which determines what we are morally permitted to do, given our options and our best understanding of our situation. So, what moral decision rule should Moral Absolutists adopt? Just as it was tempting to eschew calculations of others' benefits in Sacrifice, it might be tempting to ignore the probabilities in Risk of Sacrifice. This could be done in two ways. According to a moral decision rule I shall call Positive Probability, any risk of violating a moral constraint is itself impermissible. However, this leads to what is known as the Paralysis Problem: given that all of our acts have some positive probability of violating a moral constraint.6 Ignoring the probabilities in the other direction leads to the opposite problem. Accepting a moral decision rule that prohibits only certainties of violating a constraint (call this rule: Certainty) leads Moral Absolutists to be self-effacing in real-world cases, since we can never be truly certain whether any act will violate a constraint. Noting that these extremes are unacceptable for Moral Absolutism, its critics have suggested an intermediate approach, called Moral Certainty, which holds that acts are impermissible if they are sufficiently certain to violate a moral constraint, where this can be specified as a fixed probability threshold, t. However, they then point out that Moral Certainty is also problematic, since it seems to generate inconsistent verdicts in cases like the following: Multiple Risks of Sacrifice: To best ensure society's future happiness, every week we can run a permissible risk of a child living in torture. For each week, the probability is below the threshold t. However, over time, 4 the cumulative probability will become greater than t. What should we do? So long as a permissible degree of risk exists, whatever that threshold happens to be, a theory that accepts Moral Certainty may nevertheless permit each individual risk while at the same time prohibiting all of the risks being run. To critics, this advice seems inconsistent, if not outright paradoxical: how could it be that we do something impermissible via a series of acts that are permissible? Another way to put the problem is that, implausibly, Moral Certainty seems to change its verdicts depending on whether we describe the very same risky acts individually or collectively.7 Thus, having considered these moral decision rules and found each to be wanting, critics make the following claim: The Problem of Risk: There exists no Absolutist moral decision rule that can give adequate verdicts about the permissibility of risky acts. III MODELLING THE PROBLEM OF RISK As it stands, the Problem of Risk is simply a conjecture. Critics of Moral Absolutism have considered only a few moral decision rules, which for all we know are not exhaustive. Defenders of Moral Absolutism have offered other moral decision rules, including more sophisticated versions of Moral Certainty.8 Unfortunately for Moral Absolutists, these new rules encounter difficulties of their own.9 Thus, the state of the debate is that some theorists conjecture that the Problem of Risk is true, whereas others argue that it is false. Who is correct? III.A A CHOICE-THEORETIC APPROACH To make progress on this question, I will now recast the debate over the Problem of Risk using a highly general choice-theoretic framework defined by Dietrich and List (2017).10 5 This choice-theoretic framework is distinctive in that it encodes what a moral theory says about the permissibility of a particular act in a given choice context, based on the moral properties of that act in that context. Different moral theories will give different lists of what moral properties exist and which ones are relevant to a given choice context. They will also rank moral properties differently, holding that some moral properties outweigh or defeat other moral properties. Given a set of available acts to choose from, and a ranking of the moral properties possessed by those acts, a moral decision rule will determine which (if any) of your available acts are permissible. Some aspects of this framework can be immediately applied to the Problem of Risk to sharpen the existing debate. For example, consider the following distinction the framework makes about different types of moral properties: • An option property is possessed by an act itself, irrespective of its context. • A context property is possessed by an act solely on the basis of its context. • A relational property is possessed by an act because of both the act itself and the context. As we will see in the following section, these property types allow us to distinguish otherwise conflated types of Moral Absolutism. Other aspects of the framework must be elaborated slightly to best shed light on the Problem of Risk. For example, to accommodate our target cases involving risk, we will take the relevant moral properties of acts to be epistemic modal properties, based on your best understanding of the possible outcomes an act, and how probable those outcomes are to occur, given that you perform the act. That is, the moral properties will relate to an act's prospect. The question for Moral Absolutists will be whether they can give acceptable verdicts about the permissibility of various prospects of violating a moral constraint. A further helpful elaboration will be to introduce the following two notions of moral equivalence: • Morally equivalent acts are equally permissible across contexts. 6 • Morally equivalent contexts agree on the permissibility of acts. These notions of moral equivalence will help us track whether permissibility verdicts are consistent by allowing us to substitute equivalent acts between equivalent contexts.11 I will also introduce a substantive distinction between two classes of moral properties: those pertaining to what is right, and those pertaining to what is good. As a first approximation, rightness properties denote whether an act expresses respect for others as persons. An act is wrongful to the extent that it expresses disrespect. Let a goodness property be associated with the states of affairs those acts produce, typically defined in terms of aggregate wellbeing. Understood in this extended framework, Substantive Consequentialism holds that the set of good-making properties is identical to the set of rightmaking properties. For instance, one might hold that respecting others as persons simply is acting in a way that maximises aggregate wellbeing. By contrast, Substantive Non-Consequentialism will hold that these sets of properties are distinct, arguing that it is possible to wrongfully maximise aggregate wellbeing or rightfully fail to do so. Moreover, they hold that right-making properties have some degree of priority over good-making properties. Moral Absolutist theories are Non-Consequentialist theories that posit a particularly strong priority of the right over the good: in Sacrifice, the rightness of not torturing a child defeats the goodness of any amount of happiness for others. With this extended framework in hand, we will now revisit the debate over the Problem of Risk. III.B TYPES OF MORAL ABSOLUTISM Understood in this framework, Moral Absolutism holds that there are some properties that always render an act morally impermissible. More precisely: Moral Absolutism: Some kinds of acts have a particular wrong-making property P , such that they are always impermissible. Although this definition helps to clarify the structure of Moral Absolutism, 7 it needs to be further refined. This is because, as Jackson and Smith (2006) note, there is a trivial sense in which almost all moral theories are absolutist: Here we need to understand P as a property of an action as opposed to a relation between an action and available alternatives to that action. Classical utilitarianism absolutely prohibits doing actions that fail to maximize utility. But an action's failing to maximize utility is a relation the action has to available alternatives. The distinctive feature of the kind of absolutism that we find, for example, in Kant and the Catholic tradition is that the absolutely prohibited kind is independent of the nature of any available alternatives.12 Following the earlier distinction between types of properties, we can capture the distinction between these kinds of Moral Absolutism within the choicetheoretic framework as follows: Option Absolutism: Whether an act possesses the absolutely prohibited property P depends only on the act, not on the context. Recall that in contexts of uncertainty, acts are evaluated in terms of their prospect (that is, the possible outcomes of the act, coupled with their probability). This means that if there is any act that is absolutely prohibited in such contexts, then it is prohibited by virtue of its prospect, irrespective of how that prospect compares to those of other available acts. Contrast Option Absolutism with: Relational Absolutism: Whether an act possesses the absolutely prohibited property P depends on both the act and the other available acts in the choice context. Relational Absolutism can include comparative considerations in the definition of P . For instance, whether or not an act possesses P may depend on it having, say, maximal rightness. As we shall see, however, Relational Absolutism does not precisely capture the moral commitments of those typically targeted by this critique, such as views that prioritise an individual's right to life over any amount of trivial pleasure for others. These views are better understood as being committed to the following version of Absolutism: 8 Property Absolutism: Whether an act possesses the absolutely prohibited property P depends whether that act possesses a particular privileged set of properties, regardless of what other morally relevant properties it possesses. Property Absolutism is very plausibly the true dialectical target of the critique of Absolutism. To see this, consider Sacrifice, whereby the privileged properties are those rightness properties concerning the importance of respecting the child's life, which are undefeated by any number of goodness properties that pertain to the population's contentment. This suggests that moral constraints can be understood as a type of Property Absolutist theory: Moral Constraint: Whether an act possesses the absolutely prohibited property P depends solely on its rightness properties, irrespective of its goodness properties. More generally, Property Absolutism aims to capture any moral theory that prohibits trade-offs between particular kinds of moral considerations.13 It is important to note that Property Absolutism, as defined, is compatible with Relational Absolutism. It can hold that the absolutely prohibited acts are those that, for example, fail to minimise a privileged set of wrongfulness properties. This point will be important later when we discuss the limits of the Problem of Risk. For now, we will apply this extended choice-theoretic framework beyond definitions of Moral Absolutism to a precise specification of what it means for a moral decision rule to be 'adequate'. III.C ADEQUACY CONDITIONS Using the extended choice-theoretic framework sketched above, I present formalisations of the adequacy conditions commonly accepted in the debate. To begin, it is generally assumed that Moral Absolutism cannot avoid the Problem of Risk by simply remaining silent about the permissibility of risky acts. This suggests the following condition: Action Guidance: For all choice contexts and all acts, if an act has a moral property, then it is either permissible or impermissible. 9 Clearly, a moral theory must do more than just satisfy Action Guidance. After all, moral decision rules like Certainty and Positive Probability satisfy it: the former consistently regards almost all acts to be permissible, while the latter is consistent in prohibiting practically everything. These decision rules are inadequate because they conflict with other conditions: Impermissible Risk: There exist acts that are absolutely impermissible even if they are not certain to violate a moral constraint. Permissible Risk: There exist acts that are permissible even if they have some positive probability of violating a moral constraint. These conditions ensure that Moral Absolutism is neither self-effacing (by violating Impermissible Risk) nor unduly prohibitive (by violating Permissible Risk). The following further adequacy condition is also implicitly at play in the debate over Moral Absolutism: Moral Equivalence: Morally equivalent acts in morally equivalent choice contexts are equally permissible. This condition articulates why Moral Certainty is an inadequate decision rule: it seems to evaluate morally equivalent risky acts differently. For example, in Multiple Risks of Sacrifice, it appears that you are permitted to run each risk when described individually but not as a sequence, even though they have morally equivalent sets of properties. A final adequacy condition is: Moral Dominance: All else equal, if one act is less wrongful but otherwise equally as good as another, then in a forced choice between the two acts, it alone is permissible. Moral Dominance is akin to a necessity constraint for risky situations. It exhorts us to avoid choosing an act that is unnecessarily wrongful. As mentioned, these adequacy conditions seem to be at least implicitly accepted in the existing debate over the Problem of Risk. Moreover, they appear to be highly plausible in their own right. In the next section, we will determine which types of Moral Absolutism are compatible with a moral decision rule that satisfies these conditions. 10 III.D OPTION ABSOLUTISM Recall that Option Absolutism determines the permissibility of an act solely on the basis of the properties of the act itself, irrespective of how it compares to available acts. In the case of risky acts, these properties are found in the act's prospect: that is, its possible outcomes and their probabilities of obtaining. Thus, whether or not an act is morally prohibited is solely a function of the features of its prospect. I will call this a: Prohibited Prospect: A prospect whose riskiness (measured in terms of expectation value or some higher-order statistical moment) exceeds some fixed threshold value that renders it always impermissible This can be understood as a generalisation of the fixed probability threshold that is standardly assumed in discussions of Moral Certainty. This lemma helps us establish the following: Lemma 1. Any Option Absolutist moral decision rule that satisfies Action Guidance, Permissible Risk, and Impermissible Risk must posit the existence of Prohibited Prospects. This result confirms that the critics of Moral Absolutism were correct with respect to Option Absolutism: such theories must posit some threshold-based rule like Moral Certainty. However, the class of possible thresholds is wider than previously noted. It may be based on the probability, expectation, variance, skew, or other statistical moments of the act. Importantly, in general, statistical moments are multiply realisable: within a sufficiently rich domain of choice contexts (that is, in a sufficiently risky and varied world), a single act or a sequence of acts can have a prospect that is equivalent to a prohibited prospect. These observations help reveal the first problematic result for Option Absolutism: Proposition 1. No Option Absolutist theory satisfies Action Guidance, Impermissible Risk, Permissible Risk, and Moral Equivalence.14 11 This result arises from the fact that so long as there exist permissibly risky acts, those acts can be accumulated to collectively possess a prohibited prospect. Thus, described individually, the acts are permissible, but, described collectively, they are impermissible. This result clarifies why the cases raised against Moral Certainty are so problematic: regardless of their level of description, morally equivalent sets of acts should be equally permissible. Option Absolutists must therefore either deny one of the above adequacy conditions or, since the result does not prove the existence of such cases, they may seek to deny that they are possible. One approach would be to posit a privileged level of act-description, precluding the possibility of intelligible comparisons between higherand lower-level descriptions of acts. Another approach might hold that moving between levels of description always involves changing the moral properties at play, such that there is a morally relevant difference between considering acts individually and considering them as a sequence. In this way, no sequence would ever be morally equivalent to a single act, since there are non-equivalent, sui generis moral properties that apply to each. Finally, Option Absolutists may hold that the set of impermissible risks is context-variant in a way that carefully avoids equivalencies between any permissible risks one might perform and any prohibited prospect they might, together, become equivalent to. The challenge for these approaches is to avoid inconsistent verdicts without invoking relational properties and, also, without being objectionably ad hoc in how they determine the privileged level of actdescription, the existence of emergent moral properties, or the context-variant threshold. Whatever the outcome of these theoretical manoeuvres, Option Absolutism faces another challenge: it violates Moral Dominance. Proposition 2. No Option Absolutist theory satisfies Action Guidance, Permissible Risk, Impermissible Risk, and Moral Dominance. This simple result exploits the fact that Option Absolutism, by definition, excludes comparative information about acts. Thus, it is apt to treat dominating acts and dominated acts alike once both pass the threshold of being a prohibited prospect. This is problematic because there is something to be 12 said in favour of dominating acts (namely, they are less wrongful), but nothing to be said in favour of dominated acts. Thus, if we are faced with a forced choice situation, Option Absolutism treats more and less wrongful acts alike, insisting that we face a moral dilemma. Again, Option Absolutists may instead seek to deny the possibility of such cases. One example would be to adopt a context-variant threshold for what counts as a prohibited prospect, whereby the relevant threshold is set to avoid violating Moral Dominance.15 However, this amounts to treating Option Absolutism as a covert form of Relational Absolutism, whereby the absolutely prohibited property is determined by reference to the prospects of the other available acts. Overall, in the face of these incompatibilities, it is difficult to see a plausible path forward for Option Absolutism. As we shall see, however, there are other avenues by which moral constraints can avoid the Problem of Risk. III.E RELATIONAL ABSOLUTISM Given the above results, it is tempting for Moral Absolutists to adopt Relational Absolutism, allowing for comparative considerations among acts. In particular, the following moral decision rule would seem appropriate: Expected Moral Value: An act is permissible if and only if it maximises expected ('probability-weighted') moral value. As we shall see, however, without further constraints on the moral theory, this way of avoiding the Problem of Risk amounts to a Faustian Gamble for Moral Absolutists: they give adequate verdicts about risky acts, but at the cost of surrendering their commitment to moral constraints. To illustrate, suppose that Moral Absolutists follow the suggestion of holding that the moral value of not violating a constraint is much greater than the value of violating a constraint for the sake of some good.16 Suppose also that they accept the following background assumption: Moral Separability: The contribution of a moral property to the moral 13 value of an act is always unaffected by whether that act possesses or lacks other moral properties. This simply holds that the moral value of any moral property – say, that of giving some amount of happiness to some individual – is unaffected by what other properties are relevant to the act or its context. With this often overlooked background assumption now made salient, we can now observe the following result: Proposition 3. No Relational Absolutist theory satisfies Moral Separability, Expected Moral Value, and Moral Constraint.17 This result arises from the fact that Moral Separability will allow for the aggregation of moral value of doing good to such a point that it will equal or outweigh the value of doing what is right. This shows that Moral Absolutists cannot avoid the Problem of Risk by simply adopting expected value theory. Rather, as we shall see, to make use of these decision-theoretic resources, Moral Absolutists must further clarify what it means for the right to be prior to the good. III.F PROPERTY ABSOLUTISM Having found both Option Absolutism and an unrestricted version of Relational Absolutism to be unsatisfactory solutions to the Problem of Risk, we will now see that Property Absolutism has a promising path forward. Indeed: Proposition 4. There exist Property Absolutist moral decision rules that satisfy Moral Constraint, Action Guidance, Permissible Risk, Impermissible Risk, Moral Dominance, and Moral Equivalence.18 The first moral decision rule we will consider is compatible with Moral Separability, but it drops Expected Moral Value in favour of a set of value functions representing multiple dimensions of value and a strict hierarchy between them. This is known as a lexicographic value function.19 This function allows us to define the following moral decision rule: 14 Lexicographic Moral Value: Given a ranked set of moral value functions, an act is permissible if it uniquely maximises expected value with respect to the highest-ranked value function; or, if there is a tie, then it is the tied act that uniquely maximises the next-highest-ranked value function; and so on. If there is no further value function, then all remaining tied acts are permissible. If we understand moral value as consisting of two dimensions – the right and the good – then this moral decision rule can straightforwardly uphold Moral Constraint. It exhorts us to maximise with respect to rightness, and to resort to maximising goodness only if our acts are equally right.20 Crucially, it also satisfies the adequacy conditions of the debate.21 Thus, it shows that the Problem of Risk is false with respect to Property Absolutism. Of course, this moral decision rule raises a number of questions of its own. In particular, within a general expected value framework, it implies that any prospect of doing what is right, no matter how slight, defeats any prospect of doing good, no matter how certain. What could justify this extremely strict hierarchy between the right and the good? We will revisit this question in the following section. An alternative approach to the lexicographic model is based on a denial of Moral Separability. A Property Absolutist theory that does so can adopt: Bounded Moral Value: The moral value of particular goodness properties, when they compete with rightness properties, diminishes such that their cumulative value asymptotically converges to a limit below the value of the rightness properties. This approach allows for less strict hierarchies between competing prospects concerning the right and the good, while nevertheless preserving Moral Constraint in cases of certainty. By positing Bounded Moral Value, Property Absolutists can adopt Expected Moral Value and avoid the Problem of Risk.22 Like the lexicographic approach, this model raises questions. In this case, the challenge is not so much justifying a maximally strict priority of the right over the good; the challenge is in justifying the bounded moral value of nonprivileged moral properties. After all, why should the moral value of someone's 15 benefit be diminished by the fact that others also benefit, or by the fact that it came at the cost of someone else?23 Without a satisfactory answer to these questions, the above solutions to the Problem of Risk appear unprincipled. However, I shall argue that these solutions are underwritten a well-developed but overlooked body of substantive Non-Consequentialist theorising. Not only does this theorising make sense of these formal possibility results, it also reveals an important but under-explored difference between how Moral Absolutists and their critics understand the structure and substance of morality. IV JUSTIFYING MORAL ABSOLUTISM We have arrived via various formal results to the conclusion that Moral Absolutism must make unorthodox structural commitments in order to give adequate verdicts about the permissibility of risky acts. I shall argue that these commitments are best understood as being entailed by Non-Consequentialist moral theorising that accepts the following: Moral Inseparability: The contribution of a moral property to the moral value of an act is sometimes affected by whether that act possesses or lacks other moral properties. Recall that, in the framework we are using, a moral theory determines the permissibility of acts according to its moral properties. Moral Separability obtains when a moral theory treats each property's moral value as being independent, unaffected by the other properties it is bundled with. By contrast, Moral Inseparability obtains when a moral theory treats at least some moral properties as being inseparable from the presence or absence of others, leading to evaluations of acts that cannot always be expressed as the linear sum of the individual value of its properties. Simply put, on this view, the moral value of acts depends on the combinations and interactions of the moral properties they possess. With the idea of Moral Inseparability now clearly in view, we can now more easily see a justification of moral constraints that has so far been overlooked 16 in the debate over the Problem of Risk. In Sacrifice, why should it be that there is not some number of people we could benefit to justify the torture of another? Assuming Moral Separability has led critics and proponents alike to posit infinite moral value to upholding constraints, which has led to the problematic assertion that life is of infinite value.24 Assuming Moral Inseparability makes possible the following, far more plausible, assertion: the moral value of your doing good fundamentally depends on your not performing particular kinds of wrongs. So, in cases like Sacrifice, there is limited to no moral value to your social beneficence, given that you tortured a child to do so. Moral Inseparability thus gives a distinctive understanding of the nature of the priority of the right over the good: it is priority in the sense of preconditionality : the moral worth of our acts depends on particular requirements being met. Without meeting these preconditions, you cannot justify doing wrong by finding a suitable amount of good that could flow from it. This rationale represents a deep point of difference between how Consequentialists and Non-Consequentialists understand morality. Indeed, although we reached the idea of Moral Inseparability by a formal route, Non-Consequentialists long-identified this point of difference by way of more substantive argumentation. For example, Immanuel Kant – Moral Absolutist par excellence – argues that the moral worth of acts is conditional on a 'good will', which has unconditional value. Kant holds that "it need not ... be the sole and complete good, but it must be the highest good and the condition of every other, even of all demands for happiness."25 Indeed, it is very plausible that Moral Inseparability allows us to best make sense of Non-Consequentialist moral concepts like 'right reason' accounts of practical reasoning, the doing/allowing distinction.26 Furthermore, the idea is invoked in discussions of distributive justice, such as by Larry Temkin (1993; 2012), who appeals to Moral Inseparability in his explorations of the measures and moral value of distributive equality.27 And perhaps the most extensive exploration and defence of Moral Inseparability is found in the work of Frances Kamm (1993; 1996; 2007) whose casuistic arguments give rise to a variety of 'contextual interaction' principles explaining how the moral contribution of 17 some moral properties of our acts may depend on the presence or absence of others.28 Critics of Moral Absolutism have ignored this rich vein of moral theorising. In doing so, they have overlooked a promising rationale for moral constraints, as well as the moral decision rules that allow Moral Absolutists to solve the Problem of Risk. To see this, we need to make precise what these theorists mean when they say that morality is "complex" or "intricate". As a first approximation, let us hold that the moral value of at least some goodness properties to some degree depends on an act having some rightness properties. These goodness properties are conditionally valuable. A plausible reading of these theorists is that this conditionality is generally one-directional: for example, the value of doing right is not affected by whether or not good is done. Thus, some properties (such as goodness) are conditionally valuable, whereas others (such as rightness) are unconditionally valuable. Evaluating an act will be complex because it may possess a combination of conditionally and unconditionally valuable properties. This means that evaluating an action requires more than merely listing its properties; we need to also acknowledge the structure (or "intricacy") of the particular combination of properties at hand.29 Both of the solutions to the Problem of Risk can be explained by combining Moral Inseparability with an agent-focused understanding of morality.30 With respect to Lexicographic Moral Value, the claim the Moral Absolutist is making is that the value of your beneficence is entirely conditional on you respecting others (in particular, by not torturing them). At best, these goodness considerations are relevant only for breaking ties between otherwise equally rightful acts. Similarly, when Moral Absolutists invoke Moral Inseparability, a commitment to Bounded Moral Value amounts to the claim that the value of your doing good is only partially cancelled when it runs counter to doing what is right. Both solutions are therefore entailed by more or less strict stances about how doing what is right constrains the moral value of doing good. Thus, by recalling their commitment to the priority of the right over the good, Moral Absolutism can refute the Problem of Risk. 18 V CONCLUSION Many believe that accepting moral constraints would lead us to make mistaken verdicts about the permissibility of risky actions. This article has shown that this belief is mistaken: using a general choice-theoretic model of Moral Absolutist theories, we have seen that there do exist moral decision rules that uphold moral constraints while offering adequate verdicts about the permissibility of risky acts. Justifying these decision rules, however, required re-examining the substantive underpinnings of moral constraints. I have proposed that moral constraints are most plausible when they are grounded in the idea that the moral properties of our acts are not always separable from one other. In particular, the moral value of doing good at least sometimes depends on whether that act is wrongful. Viewed in this lens, the fanaticism commonly attributed to Moral Absolutism fades; we are Absolutists only so long as we hold that the moral value of our acts crucially depends on our respecting that which matters most.31 Stanford University Northeastern University VI APPENDIX VI.A THE CHOICE-THEORETIC FRAMEWORK Acts: Let an act x be something that you are certain you would perform, if you were to intend to perform it. The set of all possible acts is denoted X . Acts are mutually exclusive relative to a choice context, such that when you choose to perform one act, you are thereby choosing not to perform any other act in that particular choice context. Choice Contexts: A choice context k minimally consists of a set of acts, denoted [k]. It can be enriched to include information about, among other things, the identity of the actor, time, and other features relevant to the choice situation. The set of all possible contexts is K. 19 Properties: A property P is a primitive that refers to a set of act-context pairs 〈x, k〉. The extension of P is denoted [P ]. The set of all possible properties is P . Act-Context Property: When an act-context pair 〈x, k〉 possesses a particular property P we write: 〈x, k〉 ∈ [P ]. The set of properties of an act-context pair is P (x, k). Option Property: For all x ∈ X and all k1, k2 ∈ K, 〈x, k1〉 ∈ [P ] if and only if 〈x, k2〉 ∈ [P ]. Context Property: For all k ∈ K and all x1, x2 ∈ X , 〈x1, k〉 ∈ [P ] if and only if 〈x2, k〉 ∈ [P ]. Relational Property: The set of P /∈ POption ⋃ PContext. Normative Relevance Function: N denotes a normative relevance function, which assigns to each context k ∈ K a set N(k) of morally relevant properties in that context. The set of morally relevant properties of an act in a particular context is denoted by N(x, k).32 Defeat Relation: denoted ., is a binary relation whose relata are subsets of the universal set of properties, P . When one set of properties P1 stands in this relation to another set P2, formally P1 . P2, then P1 defeats P2. If neither set of properties defeats the other, then P1 ∼ P2.33 Moral Decision Rule: Where R is a function from k to R(k) and R(k) is a subset of [k], a defeat relation is defined as: R(k) = {x ∈ [k] : it is not the case that the morally relevant properties of any other act in context k defeat the properties of x in k}.34 The following are structural features of the defeat relation that are normally hidden in standard treatments of moral decision-making under risk, but which are clearly and precisely expressible in this framework: Moral Separability: The defeat relation is separable if and only if for any comparable disjoint subsets P1, P2 and P3 of the universal set of properties P , P1 D P2 ⇐⇒ P1 ⋃ P3 D P2 ⋃ P3. 20 Moral Inseparability: The ranking relation is inseparable if and only if for some comparable disjoint subsets P1, P2 and P3 of the universal set of properties P , P1 D P2 but P1 ⋃ P3 4 P2 ⋃ P3. To recap, this choice-theoretic framework allows us to ranks acts according to their respective bundles of moral properties. Using a ranking that is based on a separable or inseparable defeat relation, a moral decision rule will hold that an act is permissible if and only if its set of properties is undefeated; an act is impermissible if and only if its set of properties is defeated by the set of properties of some other act. VI.B EXTENSIONS OF THE FRAMEWORK To formalise the Problem of Risk, I will make the following elaborations and extensions to Dietrich & List's framework. VI.B.1 MORAL DECISION-MAKING UNDER RISK As foregrounded by Dietrich & List (2017: Appendix D) the above framework can be elaborated to apply to situations of moral decision-making under risk. As a general approach, I will describe acts in situations of uncertainty in terms of their prospects (denoted λ): that is, the set of an act's possible outcomes, coupled with their probability of obtaining given that the act is performed. My use of the framework is neutral with respect to the various decision theories one might adopt.35 VI.B.2 THE RIGHT AND THE GOOD Dietrich and List (2017: 435-436) provide structural definitions of Consequentialism and Non-Consequentialism. To better track the dialectic between Absolutists and their critics, I will instead define these theories as follows: Substantive Consequentialism: The morally relevant properties are the goodness properties, which are identical to the rightness properties, such that ∀x ∈ X and ∀k ∈ K, N(x, k) = PGood(= PRight). 21 Substantive Non-Consequentialism: The morally relevant properties are the rightness properties as well as goodness properties, where PRight 6= PGood. With this distinction in hand, we can articulate how these theories rank bundles of these properties. Substantive Consequentialist defeat relations will rank singleton sets of properties. Their Non-Consequentialist counterparts will rank non-singleton sets that include bundles of rightness and goodness properties. Absolutist theories will have Non-Consequentialist defeat relations that have the following constraint: Moral Constraint: If an act x possesses a particular subset of wrong-making properties PWrongful (a subset of the rightness properties), then it is impermissible regardless of the good-making properties it possesses. These definitions isolate the substance of the views that are targeted by the Problem of Risk. As we shall see, however, the Problem of Risk targets views by virtue of their structure. As a first approximation, this Absolutist structure is as follows: Moral Absolutism: If 〈x, k〉 ∈ [P ], then 〈x, k〉 /∈ R(k).36 Where P is an absolutely prohibited moral property. Drawing on the structural distinctions between types of properties, we can define the following versions of Absolutism: Option Absolutism: The absolutely prohibited acts possess P solely by virtue of their option properties. Relational Absolutism: The absolutely prohibited acts possess P by virtue of their relational properties. Property Absolutism: There exist privileged properties P ∗ (for example, PWrongful) such that if 〈x, k〉 ∈ [P ∗] then 〈x, k〉 ∈ [P ], such that 〈x, k〉 /∈ R(k), regardless of what other properties 〈x, k〉 possesses. 22 To underwrite the moral decision rules that let Moral Absolutism avoid the Problem of Risk, I will briefly expand on the idea of Moral Inseparability.37 Property Possession: Recall that an act-context pair 〈x, k〉 possesses a set of moral properties. If a property P is present in that set, it is denoted {P}. If a property is absent, we denote it as {¬P}. Moral Dependence: A relation between sets of properties P1, P2, whereby (P1 | P2) means "P1 given P2". Conditional Value: A set of properties P1 is conditionally valuable if for some disjoint set of properties P2, (P1 | P2) (P1 | ¬P2). Unconditional Value: A set of properties P1 is unconditionally valuable if for any disjoint set of properties P2, (P1 | P2) ∼ (P1 | ¬P2). Using this sketch of a framework, Moral Inseparability theories will evaluate an act based on its structured set of properties, consisting of both its moral properties and the moral dependencies (if any) that exist between them. For example, P (x, k) ∈ {(PGood|PRight), PRight} represents that act x in context k possesses both a goodness property that morally depends on a rightness property and a rightness property that is unconditionally valuable. VI.B.3 MORAL EQUIVALENCIES We will next define various moral equivalence principles, formally defined as equivalence classes on the set of possible outcomes, acts, and contexts, where '≡' stands for the relation 'is morally equivalent to'. Morally Equivalent Acts: ∀x1, x2 ∈ X , x1 ≡ x2 ⇐⇒ ∀k ∈ K, x1 ∈ R(k)⇔ x2 ∈ R(k). This formulation makes precise the idea of 'equal permissibility' by defining morally equivalent acts as those that can be substituted between any context. Morally Equivalent Contexts: ∀k1, k2 ∈ K, k1 ≡ k2 ⇐⇒ ∀x ∈ X , x ∈ R(k1)⇔ x ∈ R(k2). 23 This formulation holds that contexts are morally equivalent when they always agree on the permissibility of acts. A corollary of Morally Equivalent Acts and Morally Equivalent Contexts is: Morally Equivalent Act-Context Pairs: 〈x1, k1〉 ≡ 〈x2, k2〉 ⇐⇒ x1 ≡ x2 and k1 ≡ k2. This shows that the above notions of moral equivalence can bridge different acts in different contexts. However, in various discussions of Moral Absolutism, there has been significant disagreement about putative cases of moral equivalency.38 In an attempt to avoid this, I will compare the same acts and choice contexts to themselves, albeit under different levels of description.39 Intuitively, a higher-level description of an act refers to a 'plan', 'policy', or 'course of action', one that will often correspond to a set or sequence of more specifically described (lower-level) acts. Similarly, a higher-level description of a context can often be understood as a planning context consisting of a number of discrete choices. I will hold that higher-level descriptions of act-context pairs are not only necessitated by lower-level descriptions but are also reducible to them in the sense that the moral properties of higher-level acts are always instantiated by, and explainable in terms of the moral properties of the lower-level acts on which they are based. In this way, higher-level descriptions of act-context pairs (denoted 〈X,K〉) are morally equivalent to their lower-level descriptions (denoted 〈x, k〉), because they pick out the very same sets of moral properties.40 In the following section, I will present formulations of the Adequacy Conditions that any moral decision rule should satisfy. These conditions are intended to hold for all levels of act-context description. VI.C ADEQUACY CONDITIONS Action Guidance: For all k in K and for all x in [k], if N(x, k) 6= ∅, then x ∈ R(k) or x /∈ R(k). Permissible Risk: There exist k ∈ K and x in [k] such that P (x, k) : 'probability of producing an outcome in which a moral constraint is violated 24 is greater than zero' and 〈x, k〉 /∈ [P ]. Impermissible Risk: There exist k ∈ K and x ∈ [k] such that P (x, k) : 'probability of producing an outcome in which a moral constraint is violated is less than one' and 〈x, k〉 ∈ [P ]. Moral Equivalence: If 〈x1, k1〉 ≡ 〈x2, k2〉, then 〈x1, k1〉 ∈ R(k1) ⇐⇒ 〈x2, k2〉 ∈ R(k2). Moral Dominance: For arbitrary subsets PR, PR+ ∈ PRight and PG ∈ PGood, where PR+ . PR, if P (x1, k) = {PR+ , PG} and P (x2, k) = {PR, PG}, then x1 ∈ R(k) and x2 /∈ R(k). VI.D PROOFS VI.D.1 OPTION ABSOLUTISM Prohibited Prospect: a prospect (denoted λ) whose expectation value or higher-order statistical moment exceeds some fixed threshold value that renders it always impermissible. Lemma 1. If an Option Absolutist theory satisfies Action Guidance, Permissible Risk, and Impermissible Risk, then it must posit the existence of Prohibited Prospects. Proof. Option Absolutism holds that within the universal set of possible acts there exists a subset of acts that are absolutely prohibited by virtue of the moral properties of the acts themselves. In moral decision-making under risk, an act is represented by its prospect: its set of probability-outcome pairs. We will assume that the set of possible, risky acts is ordered according to some measure of risk of violating a moral constraint (e.g. expected value or some higher-order statistical moment), such that acts that have more risk are defeated by those that have less. By Impermissible Risk, a subset of these risky acts are absolutely prohibited. By Permissible Risk, however, not all risky acts are absolutely prohibited. Hence, the set of Impermissible Risks is bounded by the set of Permissible Risks. If there is a least risky Impermissible 25 Risk, then that constitutes the threshold. If there is no such act, then the 'gap' between the sets is the unique threshold. In either case, there is a unique threshold value of risk delineating those acts that Option Absolutists consider absolutely prohibited from those that may be permissible. Lemma 2. If an Option Absolutist theory satisfies Permissible Risk, Moral Separability, and Moral Equivalence, then it satisfies the following Agglomeration Principle: for any arbitrary subset of permissible acts, {〈x1, k1〉, 〈x2, k2〉, ..., 〈 xn, kn〉}, its higher-level description, 〈X,K〉, is also permissible. Proof. Let {〈x1, k1〉, 〈x2, k2〉, ..., 〈xn, kn〉} be a set of permissible acts that have some non-zero probability of producing an outcome in which a moral constraint is violated. Note that, given Moral Separability, the moral properties (and, hence, permissibility) of the acts in each choice context are unaffected by the presence or absence of other acts' moral properties. Let K be a higher-level description of the above set of contexts {k1, ..., kn}. Being a reducible, higherlevel description, K is a morally equivalent context to {k1, ..., kn}. It follows that the set of acts {x1, ..., xn} is permissible in K. Let X be a higher-level description of these permissible risks. Given that X is morally equivalent to these permissible risks, X ∈ R(K). Proposition 1. No Option Absolutist theory satisfies Action Guidance, Impermissible Risk, Permissible Risk, Moral Separability and Moral Equivalence. Proof. By Permissible Risk, there exist a set of permissible acts, {〈x1, k1〉, 〈x2, k2〉, ..., 〈xn, kn〉}, that each have some positive probability of producing an outcome in which a constraint is violated. By Lemma 2, a higher-level description of such act-context pairs is also permissible. That is, 〈X,K〉 ∈ R(K). By Lemma 1, Option Absolutism posits the existence of Prohibited Prospects, λ. For a suitably rich domain of choice contexts, there exists some number n of permissible risks such that their higher-level description X is morally equivalent to some λ, and therefore absolutely prohibited. Thus, 〈X,K〉 ∈ R(K) but also 〈X,K〉 /∈ R(K), violating Action Guidance. Proposition 2. No Option Absolutist theory satisfies Action Guidance, Permissible Risk, Impermissible Risk, and Moral Dominance. 26 Proof. By Lemma 1, there exist prohibited prospects, λ. Let x1 be an act with a prohibited prospect. Let x2 be an act with a prohibited prospect that is more wrongful but equally as good as x1, such that x1 morally dominates x2. By Moral Dominance, in a restricted choice context involving only these two acts, x1 is permissible. Hence, x1 is both permissible and impermissible, violating Action Guidance. VI.D.2 RELATIONAL ABSOLUTISM Proposition 3. No Relational Absolutist theory satisfies Expected Moral Value, Moral Constraint, and Moral Separability. Proof. Suppose that a Relational Absolutist theory admits an expected value representation such that for any arbitrary act-context pairs 〈x1, k〉 and 〈x2, k〉, v(x1, k) > v(x2, k) just in case P (x1, k) . P (x2, k). Given Moral Separability, the defeat relation ranks property sets of the form PGood=n in increasing linear order with n, such that the value of acts with this property increases in proportion with the amount of good done. By Moral Constraint, there exists some subset of wrongful properties PWrongful, such that any act that possesses them is impermissible, regardless of its goodness properties. However, for any real-valued expected value assignment of these wrongful properties and some arbitrary rightness property PRight, there exists some number n such that if P (x1, k) = {PGood=n, PWrongful} and P (x2, k) = {PRight}, then v(x1, k) > v(x2, k). Given a choice between these two acts, x1 ∈ R(k) and x2 /∈ R(k), violating Moral Constraint. VI.D.3 PROPERTY ABSOLUTISM Proposition 4. There exist Property Absolutist moral decision rules that satisfy Moral Constraint, Action Guidance, Permissible Risk, Impermissible Risk, Moral Dominance, and Moral Equivalence. Proof. Lexicographic Moral Value: Assume a Property Absolutist theory whose defeat relation over prospects entails the moral decision rule Lexicographic Moral Value. To illustrate this rule, suppose there are two dimensions 27 of moral value (e.g. one based on the rightness properties and the other based on goodness properties), where these dimensions are ordered such that an act is morally permissible just in case it either: it uniquely maximises moral value with respect to the higher-ranked dimension; or, if it ties with some other act, it maximises the next ranked dimension (e.g. goodness). This decision rule satisfies Action Guidance, since for all acts, an act will either be permissible or impermissible depending on whether it has the same, more, or lesser lexicographic moral value than its alternatives. This rule satisfies Moral Dominance, since dominating acts will have higher lexicographic value than their alternatives. This rule satisfies Permissible Risk because there exist contexts in which an act that maximises lexicographic value nevertheless possesses some risk of bringing about an outcome in which a constraint is violated. Similarly for Impermissible Risk, where the impermissible act is one that has lower expected rightness (or, where there is a tie, lower expected goodness). It satisfies Moral Constraint if minimising the privileged wrongfulness properties has lexicographic priority over the goodness properties. Lastly, Moral Equivalence is satisfied because morally equivalent sets of properties have the same lexicographic moral value, such that they are equally permissible. Expected Moral Value: When coupled with Bounded Moral Value, this moral decision rule satisfies Action Guidance, Permissible Risk, Impermissible Risk, and Moral Dominance in a closely similar fashion to Lexicographic Moral Value, except it adopts a one-dimensional value function rather than a multi-dimensional one. This approach satisfies Moral Equivalence because if two acts' respective structured sets of properties are equally ranked across morally equivalent contexts, they are therefore equally permissible. It satisfies Moral Constraint if the value of doing good, versus that of doing what is right, is bounded such that for any arbitrary act-context pair and for some subset of rightness properties PWrongful (i.e. the particularly wrongful ones), some arbitrary rightness property PRight, and goodness property PGood=n, there exists no amount of good n such that {PGood=n, PWrongful} D {PRight}. 28 NOTES 1On characterisations of Non-Consequentialism, see Shelly Kagan, Normative Ethics (Boulder: Westview Press, 1998), 71-75. 2Franz Dietrich and Christian List, "What Matters and How it Matters: A ChoiceTheoretic Representation of Moral Theories," The Philosophical Review 126, no. 4 (2017): 421–79. 3Robert Nozick, "Moral Complications and Moral Structures," Natural Law Forum 13 (1968): p. 3. 4R Eugene Bales, "Act-Utilitarianism: Account of Right-Making Characteristics or DecisionMaking Procedure?," American Philosophical Quarterly 8, no. 3 (1971): 257–65. 5See Holly M. Smith, Making Morality Work (Oxford University Press, 2018). 6Sven Ove Hansson, The Ethics of Risk: Ethical Analysis in an Uncertain World (Palgrave Macmillan, 2013), ch. 2; Madeleine Hayenhjelm and Jonathan Wolff, "The Moral Problem of Risk Impositions: A Survey of the Literature," European Journal of Philosophy 20, no. 51 (2011): E26–E51. 7Frank Jackson and Michael Smith, "Absolutist Moral Theories and Uncertainty," The Journal of Philosophy 103, no. 6 (2006): 267–83. 8For example Ron Aboodi, Adi Borer, and David Enoch, "Deontology, Individualism, and Uncertainty: A Reply to Jackson and Smith," Journal of Philosophy 105, no. 2 (2008): 259–72. 9See Frank Jackson and Michael Smith, "The Implementation Problem for Deontology," chap. 14 in Weighing Reasons, ed. Errol Lord and Barry Maguire (Oxford: Oxford University Press, 2016), 338–54. 10Dietrich and List, "What Matters and How it Matters: A Choice-Theoretic Representation of Moral Theories." 11For a more precise formulation of these equivalencies, see Appendix. 12For notational consistency with Dietrich and List's framework, here I have replaced Jackson and Smith's 'K' for P . Jackson and Smith, "Absolutist Moral Theories," pp. 26768. See also: Alan Gewirth, "Are There Any Absolute Rights?," The Philosophical Quarterly 31, no. 122 (1981): p. 4. 13Relatedly, see Gustaf Arrhenius and Wlodek Rabinowicz, "Value Superiority," in The Oxford Handbook of Value Theory (Oxford University Press, 2015), 225–43. 14Here I am suppressing a further condition, Moral Separability, for expository purposes (see III.E and Appendix). Examples of Option Absolutism that seek to avoid this result by denying Moral Separability include: Seth Lazar, "Anton's Game: Deontological Decision Theory for an Iterated Decision," Utilitas 29, no. 1 (2017): 88–109; Sergio Tenenbaum, "Action, Deontology, and Risk: Against the Multiplicative Model," Ethics 127 (2017): 1–36. 29 15An example of this approach is Christian Tarsney, "Moral Uncertainty for Deontologists," Ethical Theory and Moral Practice 21, no. 3 (2018): 505–20. 16As suggested in Mark Colyvan, Damian Cox, and Katie Steele, "Modelling the Moral Dimension of Decisions," Noûs 44, no. 3 (2010): 503–29. 17For proof, see Appendix. 18For proof, see Appendix. 19Melvin Hausner, "Multidimensional Utilities," chap. 12 in Decision Processes, ed. R. M. Thrall, C. H. Coombs, and R. L. Davis (New York: John Wiley & Sons, Inc., 1954). 20See Chad Lee-Stronach, "Moral Priorities Under Risk," Canadian Journal of Philosophy 48, no. 6 (2018). 21For proof, see Appendix. 22For an exploration of this approach, see Seth Lazar and Chad Lee-Stronach, "Axiological Absolutism and Risk," Noûs 53, no. 1 (2019): 97–113. 23Alastair Norcross, "Two Dogmas of Deontology: Aggregation, Rights, and the Separateness of Persons," Social Philosophy and Policy 26, no. 01 (2009): 86. 24Michael Huemer, "Lexical Priority and the Problem of Risk," Pacific Philosophical Quarterly 91 (2010): 347. 25For discussion, see R. Langton, "Objective and Unconditioned Value," Philosophical Review 116, no. 2 (2007): Sec. 3. 26Shelly Kagan, "The Additive Fallacy," Ethics 99, no. 1 (1988); Shelly Kagan, The Limits of Morality (Oxford: Clarendon Press, 1991). 27See, for example Larry S. Temkin, Inequality, New York; Oxford, 1993, 154; Larry S. Temkin, Rethinking the Good (Oxford; New York: Oxford University Press, 2012), 430. 28Frances M. Kamm, Morality, Mortality: Death and Whom to Save from It (New York: Oxford University Press, 1993); Frances M. Kamm, Morality, Mortality: Rights, Duties, and Status (New York: Oxford University Press, 1996); Frances M. Kamm, Intricate Ethics: Rights, Responsibilities, and Permissible Harm (New York: Oxford University Press, 2007). 29For a brief specification of this account, see Appendix. 30Kamm, Morality, Mortality: Rights, Duties, and Status, ch. 9. 31For especially helpful discussions or comments on this paper (or its ancestors), I wish to thank Matthew Adams, Juliana Bidadanure, Yuna Blajer de la Garza, Renée Bolinger, John Cusbert, David Enoch, Abby Everett Jacques, Toby Handfield, Rebecca Hasdell, Josef Holden, Frank Jackson, Todd Karhu, Ten-Herng Lai, Carina Lee-Stronach, Kirsten Mann, Anne Newman, Philip Pettit, Oliver Rawle, Rob Reich, Sufyan Saleem, Andrew Sepielli, Mike Titelbaum, Kate Vredenburgh, Shang Long Yeo, anonmymous referees at The Philosophical Quarterly, audiences at the Moral, Social, and Political Theory Graduate Workshop at the Australian National University, and at the Center of Ethics in Society and the Political Theory Workshop, Stanford University. I owe extra special thanks to Chris Bottomley, Alan Hájek, Seth Lazar, Jeremy Strasser, and Sergio Tenenbaum. 30 32In what follows, I assume that the normative relevance function and defeat relation are context-invariant. For an exploration of context-variant approaches, see Dietrich and List, "What Matters and How it Matters: A Choice-Theoretic Representation of Moral Theories," p. 439. 33ibid., p. 432. 34In Dietrich and List's terminology, a 'Moral Decision Rule' corresponds to what they call a 'Rightness Function'. 35In particular, I wish to remain neutral between causal versus evidential decision theories. For an overview of these and other varieties of decision theory, see Edward Elliott, "Normative Decision Theory," Analysis 79, no. 4 (2019): 755–72. 36Also, to capture idea that such acts are always impermissible, the defeat relation must be non-reflexive, such that it does not rank P at least as highly as itself in cases where all of your available acts contain P . Dietrich and List, "What Matters and How it Matters: A Choice-Theoretic Representation of Moral Theories," p. 458. 37Here I only provide a brief, largely notational, sketch of the idea of the inseparability of some moral properties. For an account of the kind of non-monotonic deontic logic that might undergird this approach, see: John Horty, Reasons as Defaults (Oxford University Press, 2012). 38For example: Aboodi, Borer, and Enoch, "Deontology, Individualism." 39Based on the formal framework given in Christian List, "Levels: Descriptive, Explanatory, and Ontological," Noûs 4 (2019): 852–83. 40From this setup, it follows that one way to reject a putative moral equivalency will be to reject the above reducibility assumption, and hold that moral properties can emerge at different levels of act-context description. For example, see Tenenbaum, "Action, Deontology, and Risk: Against the Multiplicative Model." REFERENCES Aboodi, Ron, Adi Borer, and David Enoch. 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