1 Introduction

Adherents of the counterfactual comparative account of harm (CCA) often acknowledge that this account has problematic implications in cases of overdetermination and preemption. Some have tried to modify CCA in order to better handle such cases (Bradley 2009: 52–60; Hanna 2016; Immerman 2022; McMahan 2002: 128; Norcross 2005). Drawing on a suggestion made by Parfit (1984: 70–72), others have argued that CCA is correct in its standard form, and that the overdetermination and preemption problems can be solved by generalizing the account, so as to cover pluralities of events in addition to singular events. The most well-known such CCA-friendly account of “plural harm” is that of Neil Feit (2015; see also Feit 2022).Footnote 1 Recently, Magnus Jedenheim Edling (2022) has put forward a variant of Feit’s account.Footnote 2 In this paper, we shall argue that both Feit’s and Jedenheim Edling’s accounts are fatally flawed. We shall also present some general reasons for doubting that the overdetermination and preemption problems for CCA can be satisfactorily solved by appealing to plural harm.

2 CCA and the plural harm approach

As usually formulated, CCA applies only to singular events:

CCA

An event e harms a person S if and only if S would have been better off had e not occurred.Footnote 3

Problematically, CCA cannot account for the harm that apparently occurs in cases like the following:

Two Shooters

X and Y simultaneously, and independently of each other, shoot and kill Z. Either shot, by itself, would have been fatal. (Cf. Feit 2015: 362; Parfit 1984: 70)

CCA implies that neither shooting harms Z. A more intuitive judgment is that each shooting does. According to advocates of the plural harm approach, however, we can at least say something similar to this while still accepting CCA—namely, that Z is harmed by the plurality of X’s and Y’s shootings.

Proponents of the plural harm approach emphasize (e.g., Feit 2015: 370) that in this context, speaking of a “plurality” of two or more events is just a way of speaking about them; the plurality is neither a composite object with those events as parts, nor a set with those events as members. Moreover, to say that a plurality of events “harms” a person S is not to say that each of those events harms S—it is to say that those events harm S together. (In the standard jargon, ‘harms’ should be given a “collective” rather than a “distributive” reading.) This is analogous to how some pearls may together form a circle even though no individual pearl forms a circle. As Feit puts it, the idea is that “some basic facts about harm are irreducibly plural” (2015: 370).

We shall follow Feit and Jedenheim Edling in speaking of “subpluralities” of other pluralities. It should be borne in mind that every way of “partitioning” a plurality into subpluralities yields the very same plurality. Thus, using ‘[…]’ to denote a plurality, there is no distinction between the pluralities [e, e*, e**], [[e, e*], [e**]], and [[e], [e*, e**]]. They are all just the three events e, e*, and e**, referred to collectively. Further, every singular event is a plurality of itself, and every plurality is a subplurality of itself (although not a “proper” one).

Returning to Two Shooters, a natural suggestion, at least for proponents of CCA, is that the plurality of X’s shooting and Y’s shooting harms Z because Z would have been better off if neither event had occurred. As is often pointed out, however, a plurality of events being such that S would have been better off had none of the events in it occurred does not seem sufficient for the plurality’s harming S. Such a plurality may include events that are intuitively irrelevant to the harm done. It would be implausible to claim, for example, that Z is harmed by the plurality consisting of X’s shooting, Y’s shooting, and the entirely unrelated event of a certain blackbird’s singing (see, e.g., Parfit 1984: 71). The following account of plural harm incorporates the obvious solution to this problem:

The Minimal Plurality Account (MPA)

A plurality of events E harms S if and only if (i) S would have been better off had none of the events in E occurred, and (ii) there is no proper subplurality of E such that S would have been better off had none of the events in it occurred.

MPA implies that the plurality [X’s shooting, Y’s shooting, the blackbird’s singing] does not harm Z, since it has a proper subplurality, viz., [X’s shooting, Y’s shooting], which is such that Z would have been better off had neither event in it occurred. Since the one-event plurality [e] is the same thing as the event e, and [e] is harmful according to MPA just in case e is harmful according to CCA, MPA entails CCA. (In particular, note that any one-event plurality trivially satisfies MPA’s condition (ii).) Of course, since CCA, unlike MPA, is silent on when pluralities of more than one event are harmful, the reverse entailment does not hold. MPA is thus an extension of CCA.

3 Feit’s GPH and why it fails

Feit would, we think, consider MPA to be on the right track, but not quite accurate. He discusses an account, labeled ‘PH’ (Feit 2015: 371), which resembles MPA, and finds it wanting in certain respects. One of his objections to PH pertains also to MPA. Consider the following case:

Three Shooters

X, Y, and U simultaneously, and independently of each other, shoot and kill Z. Each pair of shots would have been fatal, but no single shot would, by itself, have killed (or even injured) Z.

In this case, MPA implies that there are three harmful pluralities, viz., [X’s shooting, Y’s shooting], [X’s shooting, U’s shooting], and [Y’s shooting, U’s shooting]. The plurality of all three shootings, on the other hand, does not satisfy clause (ii), and hence it does not harm Z according to MPA. Feit would reject this result, and claim that also the latter plurality harms Z.Footnote 4 This is the result yielded by Feit’s account General Plural Harm, or GPH (2015: 376). Let an ‘MPA-harm’ for S be a plurality that harms S according to MPA. (Occasionally, we shall also use ‘MPA-harm’ as a verb, with the corresponding meaning.) GPH can then be stated as follows:

General Plural Harm (GPH)

A plurality of events E harms S if and only if E is an MPA-harm, or a plurality of MPA-harms, for S.Footnote 5

GPH, just like MPA, entails CCA. (As we shall see in the next section, Feit goes on to slightly revise GPH.)

An immediate implication of GPH is that any plurality of harmful pluralities is itself harmful. In other words, GPH (unlike MPA) entails

Agglomeration

If each of two pluralities E and E* harms S, the plurality [E, E*] also harms S.

This allows for the possibility that a plurality harms a person, according to GPH, although she would have been worse off if no event in the plurality had occurred. The following is a case in point:

Painkillers

Z has a terrible headache and hence takes two painkillers, A and B. The pills fully relieve his headache but cause a somewhat unpleasant heartburn. A single pill would have fully relieved his headache without causing a heartburn. Z would have taken pill A even if he had not taken pill B, and he would have taken pill B even if he had not taken pill A.

The events Z’s taking pill A and Z’s taking pill B are both CCA-harms, and hence MPA-harms, for Z. GPH thus implies that the plurality of the two events also harms him. Whether this result is problematic is somewhat unclear. On the one hand, it seems to conflict with the core idea behind MPA and GPH, since the plurality leaves Z better off overall than he would have been had neither event occurred. On the other hand, the result may nonetheless be defensible, in view of the fact that taking only one pill would have left Z even better off.Footnote 6

Whatever one thinks about the harmfulness of this plurality, Painkillers also illustrates a much more serious problem for GPH. Although Feit does not explicitly formulate any account of plural benefit, it is clear that he accepts the widespread and attractive idea that benefit is, so to speak, the converse of harm (see, e.g., Feit 2015: 370, 380–381; 2016: 139; 2022).Footnote 7 According to this idea, MPA is easily supplemented so as to give an account also of plural benefit:

MPA

A plurality of events E harms (benefits) S if and only if (i) S would have been better (worse) off had none of the events in E occurred, and (ii) there is no proper subplurality of E such that S would have been better (worse) off had none of the events in it occurred.

Supplemented accordingly, GPH says that a plurality E benefits S just in case E is an MPA-benefit, or a plurality of MPA-benefits, for S.

GPH then implies that [Z’s taking pill A, Z’s taking pill B] benefits Z. He would have been worse off had neither event in this plurality occurred, and its only proper subpluralities are the singular events Z’s taking pill A and Z’s taking pill B. Each of those events is such that Z would have been better off had it not occurred.

The conclusion that [Z’s taking pill A, Z’s taking pill B] both harms and benefits Z is disastrous for GPH, since this account is intended to be an account of overall harm and benefit (see Feit 2015: 361; see also footnote 3 above). We take it to be an undisputable conceptual truth that if an event or a plurality of events is overall harmful for a person, then it is not also overall beneficial for this person. Hence, any plausible account of harm and benefit must satisfy the following adequacy condition:

Exclusion

No event or plurality of events is both overall harmful and overall beneficial for one and the same person.

By violating Exclusion, GPH is fatally flawed.

4 Feit’s QPH and why it fails

There is a twist, however. As we indicated above, it is not entirely correct that Feit accepts GPH. He argues that a certain “quantified” version of GPH, labeled ‘QPH’, is in fact more accurate (Feit 2015: 376–377). Let us say that a plurality E “MPA-harms S to degree n” (n > 0) just in case S would have been better off to degree n had none of the events in E occurred, and there is no proper subplurality of E such that S would have been better off to degree n had none of the events in it occurred. QPH can then be stated as follows:

Quantified plural harm (QPH)

A plurality of events E harms S to degree n if and only if E MPA-harms S to degree n, or is a plurality of MPA-harms, each of which MPA-harms S to degree n. Further, E harms S simpliciter if and only if there is some n such that E harms S to degree n.Footnote 8

QPH does not entail Agglomeration—on the contrary, QPH and Agglomeration are incompatible. Suppose that S would have been better off to degree 5 had event e not occurred, better off to degree 10 had event e* not occurred, and not better off at all had neither e nor e* occurred. There is then no n, such that [e, e*] MPA-harms S to degree n, or is a plurality of MPA-harms, each MPA-harming S to degree n. QPH hence implies that [e, e*] does not harm S, although each of e and e* does so.

However, QPH entails this weaker version of Agglomeration:

Weak agglomeration

If two pluralities E and E* harm S to the same degree, the plurality [E, E*] also harms S.

If we assume, in Painkillers, that abstaining from taking pill A and abstaining from taking pill B would have made Z better off to the same degree, QPH thus implies that [Z’s taking pill A, Z’s taking pill B] harms him. Supplementing QPH with the corresponding account of plural benefit, it is easy to verify that the resulting account also implies that this plurality benefits Z. Hence QPH, too, violates Exclusion.Footnote 9 In fact, QPH seems on the whole to fare even worse than GPH. It appears completely arbitrary to claim that two equally harmful pluralities always jointly make up a harmful plurality, but deny that two unequally harmful pluralities always do so.

5 Jedenheim Edling’s account and why it fails

Magnus Jedenheim Edling argues that Feit’s GPH yields dubious verdicts in preemption cases where the intuitively harmful events counterfactually depend on each other (2022: 1863–1865), as well as in some related cases (2022: 1869–1871). As a remedy, he suggests a slightly different account, called ‘New Plural Harm’ or ‘NPH’ (2022: 1866). In the same way that GPH builds on MPA, NPH builds on the following account:

Revised MPA

A plurality of events E harms S if and only if (i) S would have been better off had none of the events in E occurred, and (ii) no subplurality E* of E contains an event e such that S would have been better off had e but no other event in E* occurred.

Thus:

New Plural Harm (NPH)

A plurality of events E harms S if and only if E is a Revised MPA-harm, or a plurality of Revised MPA-harms, for S.Footnote 10

Like Feit, Jedenheim Edling intends his account as an account of overall harm (2022: 1854, fn. 1), and sees benefit as the converse of harm (2022: 1862).

Clearly, NPH entails both CCA and (unlike Revised MPA) Agglomeration. (In particular, note that when E is a singular event, Revised MPA’s first condition is satisfied if and only if E is a CCA-harm for S, and its second condition is satisfied trivially.) Since both Z’s taking pill A and Z’s taking pill B are CCA-harms for Z, NPH thus entails that the plurality [Z’s taking pill A, Z’s taking pill B] harms Z in Painkillers. But NPH, supplemented with the converse account of plural benefit, also implies that this plurality benefits Z. This is because this plurality is a Revised MPA-benefit for him. He would have been worse off if neither event in the plurality had occurred, and each event is such that if it had occurred without the other one, then he would not have been worse (but better) off. Hence, NPH violates Exclusion, and should accordingly be rejected.

6 A possible reply: denying that benefit is the converse of harm

A theoretical possibility would be for Feit and Jedenheim Edling to abandon their claim that harm and benefit should be given a parallel treatment. They could thus stick to their respective accounts of plural harm, and avoid violations of Exclusion by denying the claim—let us call it ‘Converse’—that benefit is the converse of harm.Footnote 11 Such a move would be problematic, however. Converse is widely accepted as well as intuitively plausible, and it provides a neat explanation of why Exclusion looks like an obvious conceptual truth. (See also Sect. 8.) Moreover, defenders of CCA about harm have at least two additional reasons to accept Converse. The first reason is that CCA about benefit has exactly the same degree of intuitive plausibility as CCA about harm. The claim that an event benefits a person just in case she would have been worse off in its absence seems neither more nor less plausible than the claim that an event harms her just in case she would have been better off in its absence. Rejecting CCA about benefit in order to avoid violations of Exclusion therefore appears arbitrary and ad hoc.

The second reason for adherents of CCA about harm to accept Converse is that CCA about harm and Exclusion together imply that an event benefits a person only if she would not have been better off had the event not occurred. This means that the correct account of benefit must be rather similar to CCA. Of course, the implication does not rule out that a person is benefitted by an event that leaves her equally well off as she would otherwise have been, or that she is neither harmed nor benefitted by an event that leaves her better off than she would otherwise have been. But if one or both of these possibilities are real, the defender of CCA about harm faces the task of explaining why a person cannot be harmed by an event that leaves her equally well off as she would otherwise have been, or why she cannot remain neither harmed nor benefitted by an event that leaves her worse off than she would otherwise have been. It is hard to think of plausible arguments for these asymmetries.Footnote 12

In addition, it is questionable whether denying Converse would get to the root of the problem. Letting ‘anti-harm’ denote the converse of harm, Feit’s and Jedenheim Edling’s accounts still imply that a plurality of events can be both harmful and anti-harmful for a person. This is implausible in itself, even if anti-harm does not exactly coincide with benefit. And things get worse, since these accounts also imply that it is impossible for a singular event to be both harmful and anti-harmful for a person. (We take it to be impossible for an event to leave a person both worse off and better off, overall, than she would otherwise have been.) It appears very strange that harmfulness and anti-harmfulness should be incompatible as regards singular events but compatible concerning pluralities of more than one event.

7 Capturing intuitions about plural and singular harm

We shall conclude this paper by providing, in this section and the next, some general reasons for thinking that CCA-friendly accounts of plural harm are unlikely to succeed. In the present section, we shall suggest that such accounts fail to accommodate certain central intuitions about plural and singular harm.

It may be thought that the lesson to learn from the failure of Feit’s and Jedenheim Edling’s accounts is that Agglomeration (or some weaker version thereof) is the culprit, and that proponents of the plural harm solution should stick to MPA or, perhaps, Revised MPA. We do not believe that this is the right conclusion, even though we find Feit’s and Jedenheim Edling’s reasons for preferring their respective accounts over MPA to be rather weak. In particular, it is far from obvious to us that the plurality of all three shootings harms Z in Three Shooters—after all, two shots would have been enough to kill Z, and MPA does have the plausible result that each two shot-plurality harms him. This is also the result yielded by Revised MPA. However, MPA and Revised MPA face more serious problems. One is that they classify what seem to be paradigmatic cases of harmful pluralities as harmless.Footnote 13 Consider:

Deadly Mixture

X and Y simultaneously, and independently of each other, use a syringe to inject a substance into Z’s body. X injects one substance, and Y injects another. Neither substance is toxic by itself, but their mixture is highly toxic. As a result, Z dies from poisoning.

In this case, [X’s injecting, Y’s injecting] seems clearly to qualify as a harmful plurality. Intuitively, Z is harmed by being injected with both substances—especially since neither injection would have affected Z’s well-being in the absence of the other one. Indeed, this is arguably more of a paradigm case of plural harm than are overdetermination and preemption cases. In Two Shooters, for example, each shooting would have negatively affected Z’s well-being (even) in the absence of the other one. In Deadly Mixture, however, [X’s injecting, Y’s injecting] does not harm Z according to MPA and Revised MPA. In the case of MPA, this is because each event in [X’s injecting, Y’s injecting] is a proper subplurality such that Z would have been better off had it not occurred. As regards Revised MPA, [X’s injecting, Y’s injecting] turns out harmless since it is a subplurality of itself, and contains an event such that Z would have been better off had this event but no other event in the subplurality occurred. Each of X’s injecting and Y’s injecting is such an event.

MPA and Revised MPA thus imply that whereas each of the two injections harms Z, their plurality does not. While it is plausible that each injection harms Z (in view of the occurrence of the other one), denying that they together harm Z seems contrary to the very idea of plural harm.

Of course, since MPA and Revised MPA imply that X’s injecting harms Z, and that Y’s injecting harms Z, MPA and Revised MPA imply that the two injections harm Z in a distributive sense of ‘harm’ (see Sect. 2). In other words, MPA and Revised MPA imply that the plurality [X’s injecting, Y’s injecting] is harmful in the sense that each singular event included in it is harmful. Clearly, however, this observation in no way accommodates the intuition that Deadly Mixture is a case of plural harm. Indeed, any two harms for a given person, even if entirely unrelated, make up a plurality that harms the person in the distributive sense. For instance, if Z is harmed by a mosquito bite as well as by an insulting remark, then the plurality of these events harms Z in the distributive sense, even assuming that the events have nothing whatsoever to do with each other. Such a case is very different from Deadly Mixture—again, it seems clear that the two injections (unlike the mosquito bite and the insulting remark) harm Z together. Thus, what needs to be accommodated is the claim that [X’s injecting, Y’s injecting] harms Z in the collective sense of ‘harms’—and the fact remains that MPA and Revised MPA are incompatible with that claim.

A further reason for pessimism about CCA with plural harm has to do with CCA’s implications about singular events in overdetermination and preemption cases—for example, X’s shooting in Two Shooters. As indicated in Sect. 2, while CCA problematically implies that X’s shooting does not harm Z, belonging to a plurality that harms Z might seem to be sufficiently close to itself harming Z to accommodate our intuitions about the case. On all CCA-friendly accounts of plural harm discussed here, however, an event can belong to a plurality that harms someone even if it is, intuitively, not at all involved in making trouble for her. Consider this case:

Late Shooter

X shoots and thereby kills Z. When Z is already dead, Y fires a shot, hitting Z’s body. If X had not shot Z, Y would still have shot, and would thereby have killed Z.

Intuitively, not only is Y’s action itself harmless to Z (although of course it would have harmed Z if X had not shot Z), it is not even involved in affecting Z’s well-being negatively. By the time of Y’s action and its effects, all work involved in harming Z is already completed and impossible to continue.Footnote 14 On all CCA-friendly accounts of plural harm discussed here, however, the plurality [X’s shooting, Y’s shooting] harms Z. Whether or not that implication is acceptable in isolation, it illustrates how far away, on these views, belonging to a plurality that harms someone is from itself harming her.Footnote 15 It is seriously doubtful, then, that placing Y’s act in a harmful plurality in cases like Two Shooters captures what needs to be captured. The same can be said about overdetermination and preemption cases more generally.

8 Counterfactuals and negatively affecting well-being

The points just made lead naturally to what we take to be the fundamental problem with both CCA and the various CCA-friendly accounts of plural harm that we have discussed. In our view, a very plausible idea about harm—and one that CCA and its main rivals can plausibly be seen as attempts to elucidate further—is that harming someone is negatively affecting her well-being.Footnote 16 Many well-known problems for CCA, including (but not limited to) those that concern preemption and overdetermination, illustrate that the view fails to do justice to this thought. A plausible diagnosis of this failure is that the notion of negatively affecting something cannot be captured in purely counterfactual terms. The following much-discussed preemption case provides a particularly clear illustration of this:

Dark Knight

Bobby Knight gets mad at a philosopher, Phil, in response to a perceived slight. So he chokes Phil. Luckily for Phil, Knight is in anger management. It’s taught him to better control his behavior. He choked Phil because he applied anger management techniques. If he hadn’t, he would have dismembered Phil. (Hanna 2016: 263; original version in Norcross 2005: 165–166)

It seems clear that Knight’s action harms Phil, contrary to what CCA yields. And it seems equally clear that Knight’s action also negatively affects Phil’s well-being. If harming is negatively affecting someone’s well-being, and if negatively affecting well-being cannot be analyzed counterfactually, it is unsurprising that these problems for CCA (which analyzes harming counterfactually) arise.

This diagnosis suggests that what CCA-friendly accounts of plural harm say about pluralities consisting of more than one event is bound to be implausible as well. For if harm is to be understood as negatively affecting someone’s well-being, then for some events to harm a person together is plausibly for them to negatively affect her well-being together. This idea about plural harm is intuitive in its own right and also helps explain why problems arise for CCA-friendly views of plural harm. For example, a plausible reason why the blackbird’s singing should not count as a member of a harmful plurality in Two Shooters is that it plays no role in negatively affecting the victim’s well-being level—it does so neither by itself nor together with any other events. In Deadly Mixture, by contrast, the two injections do seem to negatively impact the victim’s well-being level together—and this also appears to be a strong reason to think that they together harm him.

With respect to the problem that Painkillers poses for GPH and NPH, the idea that harming someone is connected to negatively affecting her well-being further supports the view that benefit is the converse of harm, since it is equally plausible that benefitting someone is positively affecting her well-being. This, in turn, explains why Exclusion seems obviously true, since an event or plurality of events cannot overall both negatively and positively influence someone’s well-being. In particular, we have a simple explanation of why the result that the plurality [Z’s taking pill A, Z’s taking pill B] both harms and benefits Z overall is unacceptable—it requires that the plurality both positively and negatively influences Z’s well-being overall, which cannot be the case.

Thus, if CCA’s problematic results are largely due to the fact that the notion of negatively affecting someone’s well-being cannot be captured in counterfactual terms, it is to be expected that all CCA-friendly accounts of plural harm—which likewise appeal solely to counterfactuals—will yield implausible results about when some events together harm a person.