1. Introduction
We quite naturally talk and think as if there is causation by absence. We might speak of a drought causing a forest fire, or a person’s failure to water a plant resulting in the plant’s death. Such talk is hardly restricted to the ‘folk’: for example, some medical pathologies are usually thought of as caused by absences, such as the congenital heart condition Fallot’s Tetralogy, where hypoxia is caused by the absence of heart muscle between left and right sides of the heart.Footnote 1 One of the most pressing difficulties facing absence causation is the problem of profligacy.Footnote 2 While we often talk as though some absences cause, in such situations there will also be many absences we would not consider to be causes. For example, Flora’s failure to water her own plant might be judged a cause of its death, whereas my failure to water Flora’s plant would likely not.Footnote 3 Similarly, the absence of heart wall tissue is identified by cardiologists as a cause of hypoxia in Fallot’s patients, but not the absence of a Gore-Tex graft patch commonly used for surgical correction. The problem of profligacy arises because many of these other absences seem credible as causes, though we might not be immediately inclined to think of them as such. Mumford puts the point like this: ‘So how is it specifically my failure to water the plants that caused their deaths rather than my neighbour’s failure?’ (Mumford, Reference Mumford2021, p. 72) This paper offers a novel response to this problem.
Profligacy about causation by absence is only a problem if the pattern of our judgments about absence causation is roughly correct in what it implies about the amount of absence causation. For someone prepared to accept much more absence causation than we normally acknowledge, profligacy is not a problem: ubiquitous causation by absence is simply a feature of the world. However, such a view will owe an explanation of why we acknowledge some causes, but not others. Lewis took this more permissive approach, offering a pragmatic explanation:
There are ever so many reasons why it might be inappropriate to say something true. It might be irrelevant to the conversation, it might convey a false hint, it might be known already to all concerned …. (Lewis, Reference Lewis2000, p. 196)
One complaint with this approach, however, is that it fails to capture our common-sense practice of explicitly denying many absences are causes, such as the Dalai Lama’s failure to water: we don’t only not say it is a cause of Flora’s death; typically, we explicitly deny it is.Footnote 4 The response to the problem of profligacy offered here avoids this problem to the extent that it does not endorse such permissiveness about absence causation in the first place. But this carries with it the burden of articulating the underlying difference between absences that cause and those that do not: an articulation of the theoretical criterion for absence causation.
This more conservative approach need not slavishly attempt to preserve all common-sense assertions about absence causation, but it should provide a principled account of significant groups of them. Common-sense thinking about absence causation takes in a wide range of absent phenomena belonging to diverse ontological categories, including actions, events, particulars, and kinds. The solution to the problem of profligacy given here focuses on two significant cases of absence causation: causation by holes, and causation by what I will call surface absences. I propose that these absences cause in virtue of being dependent on some material object. This criterion for absence causation is developed from metaphysical commitments implicit in our common-sense thinking about them. Moreover, the proposal remains roughly in line with the amount of absence causation acknowledged in our common-sense judgments, at least with respect to holes and surface absences. I also defend the proposal against objections and rivals, before concluding with an assessment of the prospects for extending the solution to a range of further cases.
2. The Problem of Profligacy, Norms, and Metaphysical Adequacy
A conservative response to the problem of profligacy requires a theoretical criterion of absence causation, but there are adequacy constraints. BeebeeFootnote 5 observes that we could account for the pattern of our common-sense judgments about absence causation by appeal to norms:
(II) The absence of an A-type event caused b if and only if
(i) b counterfactually depends on the absence ...; and
(ii) the absence of an A-type event is either abnormal or violates some moral, legal, epistemic, or other norm (Beebee, Reference Beebee, Collins, Hall and Paul2004, p. 296)
Beebee’s discussion takes place against the background assumption that causal relations should be analysed in terms of counterfactual claims, but the suggestion can be reformulated in terms more neutral to broader commitments about causation. Take the following schema for an analysis for absence causation:
Schema A: An absence a is counted as a cause of an event e iff (i) C-conditions obtain, and (ii) A-conditions obtain.
C-conditions are conditions specified by a general theory of causation, whereas A-conditions are those that must also obtain in cases of absence causation. The suggestion Beebee considers, then, is:
Norm: An absence a is counted as a cause of an event e iff (i) C-conditions obtain, and (ii) the absence violates some norm.
Why is norm violation relevant to absence causation? Analysing absence causation in terms of norm violation enables us to account for the wide range of cases of absence causation exhibited by our common-sense judgments. Flora, it seems fair to say, flouts some norm in not watering her plant, whereas the Dalai Lama doesn’t.Footnote 6 However, Beebee claims the proposed criterion is unacceptable as an account of absence causation.
Why is this? Principally, because it seems mistaken to make absence causation depend on norms. Beebee puts it this way: ‘nobody within the tradition of the metaphysics of causation that I’m concerned with here thinks that causal facts depend on human-dependent norms’ (Beebee, Reference Beebee, Collins, Hall and Paul2004, p. 296). Even if we move away from human-dependent norms to consider norms that are independent of human concerns, the approach is plausibly still open to the objection that the distinction between normal and abnormal cannot ground causation, as Mumford urges: ‘Very abnormal and highly improbable things happen all the time. Just consider the specific six lottery balls that the machine spews out in the weekly draw: each time a massively unlikely event occurs’ (Mumford, Reference Mumford2021, p. 74). There seem, then, to be non-trivial obstacles to the claim that whether an object or event is a cause has something to do with norm violation. In recent work on causation there have been serious attempts to defend the idea that the truth of some causal claims depends on norms.Footnote 7 Nonetheless, such accounts are playing defense precisely because of the intuitive implausibility of the idea that the causal determination of a later state of the world by an earlier state is dependent on human norms. Beebee and Mumford are right, at the very least, to prefer an account eschewing such a commitment. In what follows I take up the challenge of providing such a criterion.
3. An Instructive Case: Holes
There’s at least one specific category of absence for which a well-motivated criterion for absence causation can be given: holes. On some construals of the metaphysics of holes, holes are absences: what is not, rather than what is.Footnote 8 It’s natural enough before we start doing much philosophy to think of holes as part of the problematic ‘negative’ furniture of the world. Whether such an approach to holes is ultimately defensible is to be shown, in part, by offering a credible solution to the problem at hand. After all, it’s as much a part of common-sense thinking that holes can be causes, as that omissions, failures, wants, or lacks can. Holes feature in scientific causal stories: e.g. Fallot’s tetralogy is a congenital heart disease involving four heart defects. The relevant defect here being the existence of a hole in the septum between the left and right sides of the heart. This hole normally closes in the hours and days postpartum, but in Fallot’s patients it doesn’t, and is causally involved in the flow of deoxygenated blood from right to left sides of the heart, resulting in hypoxia. For a more prosaic example, consider the holes in the drum of a washing machine which seem to be causally involved in the outflow of dirty water, without which the machine would not function as desired.
Moreover, the problem of profligacy, at least at first glance, seems to be just as pressing for holes, construed as absences, as for other cases of absence causation. In the Fallot’s tetralogy example, common-sense and medical science judges that the hole in the septum is causally involved in bringing about certain pathologies. The hole, though, is not simply an absence of any kind of matter (that’s a void): it’s an absence of some specific sort of matter (for the purposes of the present example, call this heart wall tissue). Nonetheless, many other kinds of matter might plausibly enough be claimed to be absent exactly where the hole is located, in addition to the heart wall tissue that normally completes the septum. Gore-Tex, which is commonly used to surgically fill the hole, is also absent where the hole is; pericardium, similarly used in surgical correction, too. Moreover, absences of each of these have some claim to be a cause of the patient’s hypoxia: e.g., had there been Gore-Tex where the hole is, the patient would not have been hypoxic.
When one thinks about it, there seem to be very many kinds of stuff that are absent where the hole is, each of which has some fair claim to be a cause. Nonetheless, contrary to appearances, there is a principled, non-arbitrary reason for ruling out of court many of these absent kinds of matter. These relate to metaphysical features of holes, reflected in our pre-theoretical conception of holes.
Holes seem to be dependent entities: they depend rigidly for their existence on their material hosts: if the material host is destroyed, so too is the hole. Moreover, their existence and identity conditions seem intimately related to the kind of stuff the host is made of. Holes can be filled in many ways, but not all ways of filling destroy them. When Frodo fills the hole in the One Ring with his finger, he doesn’t destroy the hole, nor would he if he filled it with pitch. Only by filling a hole with the same sort of stuff its host is made of do we destroy it.Footnote 9 There is a distinction, therefore, between absences that count as holes, and those which don’t. If holes are absences, then only absences of the kind of stuff a host is made from can plausibly be identified with the hole in the host.
Consider again the threat of profligacy in the Fallot’s case: even if there is an absence of Gore-Tex exactly where there is an absence of heart-wall tissue, the Fallot’s patient’s hole is only identical to the absence of heart-wall tissue. My suggestion, then, and one clearly available to the friend of absence causation, is that only dependent absences cause. Using the schema outlined earlier, the proposal can be put as follows:
Holes: An absence a in a presently existing material host h is counted as a cause of an event e iff (i) C-conditions obtain, (ii) a is rigidly existentially dependent on h, and (iii) a is an absence of the kind of stuff the host is made of.
So, if Mary has a septal defect, the absence of Mary’s heart wall is a cause of her hypoxia, but not the absence of a Gore-Tex graft, because the former is an absence of the kind of stuff the material host (the heart) is made of. On this way of thinking about things, whatever other absences may be located exactly where the hole is, they will not count as causes. This offers a way to respond to the threatened proliferation of absences.
4. Common-Sense Preserved?
Objection 1: Some Puzzle Cases
The foregoing proposal offers the following elegant and intuitively attractive way of describing what happens in cases when holes are filled, but not destroyed, and subsequently voided again, such as when medical interventions are attempted but then fail. When a hole is filled, the filler prevents the hole from being a cause; when the filler is absent, the hole begins to play its causal role again, but we need not say that the absence of the filler is also a cause. Were the Fallot’s patient to have a Gore-Tex graft inserted, and which later failed to function properly, her pathology would still be caused by the absence of heart-wall tissue, rather than by the absence of a Gore-Tex graft. Having a Gore-Tex graft doesn’t change one’s medical pathology, even though subsequent removal of the graft may cause a return to hypoxia. The presence of Gore-Tex, it seems right to say, prevents the underlying pathology – the hole – from causing hypoxia. But what of the absence of Gore-Tex? Is this absence a cause of the subsequent hypoxia? On the view articulated here, we need not accept that the absence of Gore-Tex is a cause, at least not to the extent that we are offering an account of the causal role of absences that are exactly located where the hole is. Once the graft is removed, an absence of Gore-Tex may be located exactly where the absence of heart wall tissue is, but (absent special considerations) we need not accept that the absence of Gore-Tex as a cause of the returning hypoxia.
There are, however, some important distinctions to be drawn between different cases of graft failure, and related cases where a graft is absent. In these cases, the story will be more complex, and, in some cases, there will be reasons to acknowledge other absences as causes. However, these cases need not result in an unprincipled proliferation of causation by absence: the extension of absence causation can be limited and metaphysically principled. Moreover, these cases are compatible with the account of hole causation given here. Much will depend on the cases, though; here are five related cases to consider:
Case 1 (Ripped): a graft is inserted and subsequently fails because the Gore-Tex rips.
Case 2 (Dislodged): a graft is inserted and subsequently fails because the Gore-Tex becomes fully dislodged.
Case 3 (Partially-Dislodged): a graft is inserted and subsequently fails because the Gore-Tex becomes partially dislodged.
Case 4 (Removed):a graft is inserted and is subsequently fully removed surgically.
Case 5 (Missing Supplies):a graft is not inserted because the hospital’s supply of Gore-Tex grafts runs out.
In all these cases, the result is hypoxia in the patient. However, the causal history will be different in each case, with different absences seeming to be involved. How can the proposal account for these different causal histories?
Consider Dislodged and Removed. According to my proposal, the absence of heart-wall tissue causes the hypoxia, but not the absence of Gore-Tex: the underlying medical pathology is the cause we are after. The difference between Dislodged and Removed concerns simply whether the hole in the heart comes to do its causal work again by agential intervention or not. We should also say much the same thing about Partially-Dislodged, except that when the graft is partially dislodged, it opens only part of the persisting hole in the heart. Nonetheless, the hole in the heart, the absence of heart wall tissue, is a cause of hypoxia, but not the absence of Gore-Tex. None of these cases present a significant problem for the proposal.
What, then, should we say about Ripped, where hypoxia arises because of a tear in the Gore-Tex? Is the ensuing hypoxia caused by the absence of heart wall tissue, or the absence of Gore-Tex? The crucial question here is whether the proposal needs to deny that the absence of Gore-Tex is a cause in this case, as in Partially-Dislodged. I think there are reasons to treat this case differently. A tear is a hole, and the tear in the graft is a hole in something made of Gore-Tex. So, the absence of Gore-Tex in this case meets the conditions specified for causation by holes given at the end of section 3. By these lights, we are justified in treating the hole in the Gore-Tex as a cause, and so treating cases like Ripped differently from those like Partially-Dislodged, where, plausibly, no new hole is created. So, although Ripped will be a case where there might be two absences causing the hypoxia, there is no unjustified proliferation here.
Finally, what should we say about Missing Supplies, where the difference with Dislodged and Removed is that the graft is not inserted? The challenge raised by Missing Supplies is that, if you are prepared to accept absence causation, then it seems right to say that the ensuing hypoxia in Missing Supplies is caused by the hospital running out of grafts. However, the proposal need not deny this. What it will deny is that an absence of Gore-Tex located exactly where the absence of heart-wall tissue is located is a cause of the ensuing hypoxia. But must we think that the absence of Gore-Tex causally involved in this case is located exactly there, inside the heart? I will have more to say about the location of absences in the next section, but of Missing Supplies at least, it is tendentious to say that the absence of Gore-Tex is exactly located where the patient’s absence of heart-wall tissue is.
In Missing Supplies, the doctor cannot insert the graft into the heart, where it is needed to play its preferred causal role. This might tempt us to locate the absence of Gore-Tex causally contributing to the patient’s hypoxia inside their heart. But this claim about the location of the absence is, at best, in need of substantial defence. If we focus on another aspect of the case, the surgeon’s attempted intervention, this becomes clear. If we pay attention to the surgeon as she reaches for the graft to find it not to hand, orders a check to the stock levels on the computer, only to find none registered, and calls the logistics and supply department to find this confirmed, then it seems far less plausible to say that the absence of Gore-Tex is located exactly in the untreated patient’s heart. These features of the case suggest it is a mistake to locate the causally responsible absence in the heart at all; we should instead say something more like that the Gore-Tex is absent from the supply chain of the hospital (or more minimally, maybe just their storage cupboard), and not in the heart at all. Imagine the patient is transferred to another hospital, but on arrival it emerges that this hospital also has no grafts in supply: causal responsibility seems to shift to the supply cupboards of the new hospital (assuming they don’t share supply chains). The danger for the patient remains, but underlying this is the persisting absence of heart-wall tissue in their heart, not an absence of Gore-Tex in the heart. Construed in this way, Missing Supplies is compatible with the proposal.
An advantage of this way of thinking about Missing Supplies is that it affords a metaphysical explanation of the difference between this case and all the Fallot’s patients born before the invention of Gore-Tex. In the case of those patients, let alone early neolithic Fallot’s patients or their hominid ancestors (non-human primates can have septal defects tooFootnote 10), the inclination to judge their hypoxia to be a causal result of an absence of Gore-Tex is not strong. Such cases, were we to have to acknowledge them, would expose us again to the charge of profligacy. However, if the absence causing hypoxia in Missing Supplies is an absence in the hospital supply chain, not an absence in the patient’s heart, then this explains why no absence of Gore-Tex causes hypoxia in the patients born before the invention of Gore-Tex: at those times there was no relevant hospital supply chain for the Gore-Tex to either be present or absent in. Equally, there are medical materials humans will go on to develop that hospitals currently have no supply chain for, but these are not now cases of absence causation. The problem of profligacy, therefore, is kept at bay.
To summarise, there seems no reason to think that either Ripped or Missing Supplies is incompatible with the proposal developed here. In Ripped, the proposal can account for the causal action of the absence of Gore-Tex, because it is a hole. Missing Supplies can be accommodated to the extent that the proposal allows that other absences than holes can be causes. In the section 5 I show how the approach to avoiding proliferation taken here might be extended to other absences. Before doing so, however, there are two further objections to the basic proposal to consider.
Objection 2: Counterfactual Considerations Again
In response to the feature of the above proposal that, e.g., in the case of Fallot’s patients with surgical corrections, the presence of Gore-Tex prevents an effect, there may be residual temptation to draw the conclusion that, when the graft fails, the absence of Gore-Tex surely must be a cause. This temptation may be bolstered by the relevant counterfactuals concerning the absence of Gore-Tex: were there Gore-Tex there, the hypoxia would not have occurred. Indeed, in a range of similar situations it might be normal to speak like this; e.g., if a cork stopper in a glass bottle were removed and the bottle knocked over, we might be tempted to attribute the spillage to the absence of a cork, but not the absence of glass. To the extent, then, that such counterfactuals warrant common-sense claims about causation, the proposal will be partially revisionary with respect to some of our common-sense judgments about absence causation. This casts shade on the merits of the proposal as piece of descriptive metaphysics. One question, though, is how high a cost would these revisions be? It would be far less revisionary than the fully permissive response to the problem of profligacy mentioned at the outset. It would also be much less revisionary of common-sense judgments than denying absence causation outright: some articles of common-sense must be given up where the absences are not dependent entities, but no more than these. Nor should we expect our common-sense judgments about which absences are causes to be irrefragable: the challenge is to show that the broad sweep of our judgments is not fundamentally mistaken.
Note also that, unless committed to a counterfactual theory of causation, the counterfactual considerations that seem to lead us astray here count, at best, as defeasible evidence for our common-sense judgments. These considerations, however, don’t unproblematically support these common-sense judgments about absence causation, as the problem of profligacy itself highlights. Someone tempted to say the absence of cork in a bottle must be a cause, on counterfactual grounds, can easily be tempted to accept that the absence of pitch, gold, plastic, etc., are also causes, and on the same grounds. This way lies the permissive response to the problem of profligacy. So, it’s reasonable enough to contend that the advantages of the proposal make these revisions to common-sense judgements minimal enough to be acceptable.
Objection 3: Holes in Heterogeneously Composed Hosts
Thus far in discussing the cases, I’ve assumed the hole’s host to be homogenous in kind. In such cases there’s just one absent kind that is the causally relevant absence. What, though, should we say about cases where the host is heterogeneous in composition? Consider two cases: (i) a hole running through layers of different kinds of matter, e.g. a tooth cavity; and (ii) a hole surrounded on different sides by different kinds of matter, e.g. a disk formed of segments of differing kinds – e.g. platinum, gold, and silver - with a hole in the centre.
One way to deal with the first case is as follows: acknowledge three layers of absences of different kinds, corresponding to each layer of the tooth: enamel, dentin, and pulp. This would, of course, raise a question about whether we count each of these three absences as distinct holes, or whether we treat them as parts of a single hole. The latter answer aligns better with common-sense on the number of holes (there’s only one cavity), and so seems preferable.
However, this reply will not work straightforwardly in case (ii), the heterogeneous disk. Which of the three absences of kinds is causally relevant here? One answer is that each absence occupies just a sub-region of the space occupied by the hole, and so its causal relevance is limited to that region. The problem here is that any attempt to specify where each absence extends to will be arbitrary, particularly in cases where the host or the hole are not geometrically regular. An alternative solution is to say that each of the three absences fully occupies the space, and all are causally relevant. But this, too, faces significant problems. It would mean that the effect is causally overdetermined by the three absences. This is a cost that might be accepted, but there is a more serious objection: if holes are absences, and we accept there is only one hole there, we need to know which of the three absences is the hole. But there doesn’t seem to be any principled way to choose between them.
There is, however, a better response. In cases like (ii), the host has parts of differing specific kinds, but those parts also share a range of less specific kind properties standing in the relation of determinate to determinable. They instantiate, e.g., the kinds: material, metal, transition metal, and noble metal. So, we could say that, in these heterogenous cases, the hole is the absence of the most specific kind shared by each component part of the host. So, e.g., the hole in the case of the disk would be the absence of the kind noble metal.Footnote 11 Only this absence, and no other, is causally relevant. This solution avoids the problems facing the foregoing options: there is no arbitrariness arising from choosing between competing absences; no hint of causal overdetermination; and no problem specifying the spatial extent of each of the absences. The solution would also apply to the first case of a layered host, allowing a unified response to both cases.
5. Extending The Solution
The solution outlined above shows that the problem of profligacy can be answered, at least with respect to the causal contribution of holes. Can the proposal be extended to provide a unified account of absence causation? Recall that our judgements about absence causation take in a wide range of phenomena belonging to a range of different ontological categories: intentional objects (a wife’s grief caused by the absence of her dead husband), omissions (absences of action), holes (absences of matter), absences of kinds (she was born without any heart wall tissue between her ventricles, causing hypoxia), absences of particulars (this lump of heart wall tissue has been excised, and its absence is causing her hypoxia), localised absences (there are no Arctic penguins (in the Arctic)), brute absences (i.e. there are no unicorns (anywhere)). This diversity suggests we should at least be open to the possibility that there is no unified theory of absence causation taking in all this multiplicity. But this need not be a problem for the proposal – perhaps absence causation is a family of related phenomena, as might be true of causation more generally.
Irrespective, the proposal will be more credible to the extent that it can be extended to accommodate more categories of absence causation (or they can convincingly be explained away). The proposal must surely be able to accommodate the fact that very often we judge localised absences of material stuff to be causes, where those absences are not holes. Here is one such example, continuing the theme of congenital heart disease and similar to the Removed scenario discussed in the previous section: a patient, whose septal defect does not close shortly after birth, has a Gore-Tex graft fitted; subsequently, the graft causes inflammation of the heart wall tissue, leading their cardiologist to remove it. On my proposal, the graft first prevents the hypoxia caused by the hole, but the subsequent absence of the graft does not cause the ensuing hypoxia - instead, the absence of heart-wall tissue does. But what should we say about the subsidence of the inflammation? Prima facie, we should say that the cause is either the absence of the particular Gore-Tex graft, or the absence of Gore-Tex at the site of the graft.Footnote 12 More generally: non-hole absences of matter, either absences of particulars or absences of kinds, seem to be causes.
In this section I show how the proposal can be extended to examples of the kind just described. Call such kinds of absence surface absences to distinguish them both from holes and other absences (to be discussed later) that don’t act solely at the surface of an object (e.g., the removal of a supporting magnet from underneath a maglev train, or the absent Gore-Tex in the Missing Supplies case of section 4). The criterion given for holes is not geared to account for these cases, simply because surface absences are not holes. So, what criterion can be supplied for surface absences? And how is this related to the criterion for holes?
Firstly, it’s important to be clear about a range of theoretically significant differences between the holes and surface absences. Recall the two features of the metaphysics of holes central to the causal criterion for holes: (i) the rigid existential dependence of holes on their presently existing material hosts, and (ii) that the persistence conditions of holes involves a reference to kinds: holes cannot be destroyed by filling them with just any kind of matter, but must be filled with the kind of matter the host is made of. This led to the solution to the problem of profligate absences given on at the end of section 3, which construes these features as conditions on absence causation. In the present example, however, the absence of Gore-Tex is different in important ways to a hole. Principally, the former’s identity seems not to depend on the kind of material the heart wall is made of. As noted above, to make a hole one removes matter composing the host, and to destroy it by filling in, one must fill it with the kind of matter composing the host. To ‘make’ an absence of Gore-Tex in the present example, by contrast, the surgeon must remove matter of a quite different sort than composes the heart. The absence’s identity seems to depend, at least in part, on the kind of matter that was there earlier, and is now absent. Moreover, were it possible for the heart to undergo a complete replacement of all its parts, such that this resulted in a total change of the kind of matter the heart is composed of, this would not affect the continued existence of the absence of Gore-Tex at the surface of the heart. What would be required for that would be a change in what there is at the location of the surface of the heart.
The continued existence of the absence also seems not to depend on the presence of any particular kind of matter occupying the location where earlier there was Gore-Tex. E.g., while a patient is on a heart-lung bypass machine for a surgical procedure to have the Gore-Tex removed, air may flow over the heart’s interior surface where the detached Gore-Tex was, but later, when blood flow is restored to the heart, blood may be present where the air was. These changes seem irrelevant to the continued existence of the absence of Gore-Tex.
A final, important point of difference between holes and the present kind of absence concerns the spatial relations between the absence and the presence. A hole, intuitively, must have the following spatial feature: there must be at least one part of the hole not spatially connected with the host.Footnote 13 E.g., in a road tunnel through a mountain there will be parts of the hole unconnected with the mountain walls, such as the central portion through which one drives. A hole, intuitively, is not a mere two-dimensional surface: it occupies the space between its boundaries, which are connected with the host. This seems to be part of what is meant when we ordinarily speak of a hole being in a material object. By contrast, the absence of Gore-Tex that causes inflammation to subside doesn’t seem to have this spatial constraint, as we shall see shortly: all that is required is that the absence abuts the surface of the heart. What matters to the case is that the Gore-Tex ceases to abut the surface of the heart. Detachment of an object from a surface can create an absence at that surface. Such absences could, in principle, be merely two-dimensional (much as boundaries seem to be).
The upshot, then, is that there are a range of differences between holes and the kind of absence under discussion that must be taken into account. But are such absences nonetheless, like holes, dependent entities? If they are then, despite of the foregoing differences, there is a way to extend the account of absence causation to account for them. But what might these absences be dependent on? Two proposals seem obvious: the previously existing Gore-Tex graft, and the heart the surface absence abuts. There are reasons to think the absence is dependent on both, but in different ways. Specifically, I will argue that surface absences are non-rigidly dependent on the previously existing Gore-Tex, and rigidly dependent on the surface such absences abut.
The surface absence of Gore-Tex is not plausibly rigidly existentially dependent on the earlier Gore-Tex graft. Imagine that this particular Gore-Tex patch were instantaneously replaced with another perfect duplicate, which was itself later removed due to a suspicion about its structural integrity. Would it be plausible to say that there would then be an absence of Gore-Tex numerically distinct from the particular absence that would have been there, had only one graft been needed? Such a view is not incoherent, but faces the following problem: with respect to the double graft scenario, we would have to say that, after the removal of both grafts, there are two perfectly overlapping absences each of which has an equal claim to cause the subsequent subsidence of the inflammation. And, of course, the more surgical interventions after repeated graft failures, the more causally overdetermined is the subsidence of inflammation. Such causal overdetermination, though not incoherent, is best to be avoided. So, if such surface absences are dependent entities like holes, then their dependence on the prior existence of Gore-Tex grafts in those locations is more likely non-rigid.
Are there reasons to think that surface absences, like absence of Gore-Tex, are non-rigidly dependent on what was present earlier? The first reason relates to the point that the absence is crucially an absence at the surface of a material object. Imagine that, instead of surgical removal, the graft becomes detached from the heart wall, resulting in a subsidence of the inflammation, but the graft remains suspended, floating in the space within the hole. The causal upshot, with respect to the inflammation, would be the same as if the graft were completely excised. This reflects the fact that the absence causing the subsidence is a surface phenomenon of the heart. The absence of Gore-Tex at the heart wall is what causes the subsidence of inflammation of the heart wall. As the heart moves around in the chest cavity, what’s important to the patient’s on-going recovery (with respect to the inflammation) is the continued absence of Gore-Tex at the heart wall. Whatever causal credentials the absence has depends on what is happening at the surface of the heart, not what is happening with the persisting, suspended Gore-Tex graft.
Another reason to construe surface absences as dependent on what was present earlier is that it avoids ontological excess. Take the location (relative to the heart wall) where, after the removal of the Gore-Tex graft, there is supposed to be an absence of Gore-Tex. Is there also an absence of a bovine pericardium - an early technology used for the closure of septal defects but which, let us imagine, was not used in our patient’s case? Some defenders of absences who are motivated by a commitment to some form of truthmaker theory have been prepared to claim that there is. Consider the following colourful articulation of the idea from C. B. Martin:
I remember fixing a very formalistically inclined philosopher with the question, “Have you ever thought of how the non-being of a mosquito in a room takes up more space than the non-being of a hippopotamus?” He backed away, pupils enlarged, turned and, with a strangled cry, “No!”, fled. (Martin, Reference Martin1996, p. 62)
For my part, I am unconvinced that truthmaker theory compels a commitment to absences; but, quite independently of that debate, if we are permissive about which absences there are at any location, there is a problem of ontological excess waiting in the wings. If we acknowledge an absence of bovine pericardium at the location of the absence of Gore-Tex, then why not also an absence of porcine pericardium, or any surgically viable alternative to Gore-Tex, or indeed any other kind of matter whatever? Moreover, the causal problem of profligacy threatens to return: say one of these other kinds of matter, had it been present, would have caused inflammation; then isn’t that evidence that its absence is also causing the subsidence of inflammation? A theory more permissive about absences must offer some answer to these questions. Construing absences as dependent allows us to avoid ontological excess, as well as address our target problem of causal profligacy.
One part of the proposal, then, is as follows: the only absence at the site of the removed Gore-Tex graft is an absence of Gore-Tex; this is because surface absences at a location depend non-rigidly on the kinds of material objects that were there earlier. So, we can say that there is no absence of bovine pericardium where the absence of Gore-Tex is located because, throughout the heart’s history, there was no bovine pericardium located where the Gore-Tex was located. A fortiori, even though it’s true that bovine pericardium at that location would have caused inflammation, the subsidence of the inflammation is not caused by the absence of bovine pericardium. This result just fits with our common-sense judgments about these kinds of cases, and, moreover, parallels the cases discussed above in connection with holes.
Next, let’s consider the relationship between the surface absence and the material object it abuts. There’s reason to think that surface absences are rigidly existentially dependent on the particular material surfaces they are located at. So, e.g., the absence of Gore-Tex must also be rigidly dependent on the existence of the particular heart the graft has been removed from. Imagine that, after the patient’s various cardiac interventions, a heart transplant becomes necessary. So, the failing heart is excised and cremated, but the only heart available for transplantation is one with exactly the same kind of hole in it. Now, after this transplant what should we say about what there is inside the patient’s body, where previously there was a Gore-Tex patch and subsequently an absence of Gore-Tex? Should we say that there remains an absence of Gore-Tex in the body, now relative to the new heart wall? This seems a mistake. The absence of Gore-Tex surely tracks the trajectory of the old heart out of the body, much as it always did when the heart moved around in the patient’s chest while beating. When the heart is cremated, that, it seems, is the end of that absence. The alternative to rigid existential dependence raises awkward questions with no clear way to answer in a principled way: imagine that the surgeon now fits this new heart with a Gore-Tex graft which, in turn, requires later removal. Is the absence of Gore-Tex at the end of this process the same absence which was located there when the old heart was part of the body, or is it a numerically distinct absence? If it is the same absence as the original, then did that latter absence continue to exist in its same location within the body during the surgery when neither heart was attached to the rest of the body? Such questions seem to present no obvious way forward to answer them. Our grip on the existence and identity conditions of the absence seems to slip dramatically once we abandon rigid existential dependence: the neater solution is to say that the absence depends rigidly for its existence on a particular heart.
Drawing the foregoing discussion together, the proposal for dealing with the problem of profligacy for surface absences is as follows:
Surface Absences: A surface absence a is a cause of an event e at a surface s iff (i) C-conditions obtain, (ii) a is rigidly existentially dependent on the surface s of a material object, (iii) and a is an absence of the same kind as some earlier presence at that surface location.
We can now see how this causal criterion for surface absences and the earlier criterion for holes are related: both enshrine two central ideas: that absences (i) have patterns of dependency on material objects, and (ii) are absences of kinds of matter. Each category of absence differs in its specific patterns of dependence; but this is, I think, a quality of the proposal and not a flaw: every absence is what it is, and not another thing.
Moreover, we can see what would be required to account for cases involving neither holes nor surface absences, e.g. the maglev train example, or perhaps the absence of Gore-tex grafts in a supply chain: a plausible story according to which the absence is a dependent entity. The devil will be in the details, but here’s how such a story might go for the maglev train: when the magnetic track and the maglev train stand in certain relations, they temporarily compose an entity with complex causal interactions amongst its parts, maintaining a state of equilibrium (colloquially: the train hovers). The destruction of the magnetic track would result in an absence of magnetic material, where that absence depends on the previously existing system (and is thereby a cause of the train’s falling). The same outline of a story could be employed for a planet destroyed, Death Star-like, in a solar system, or Lactobacillus bacteria eradicated from a gastrointestinal tract.
6. Other Approaches – Role Functionalism
In this final section I offer some reasons for preferring the present proposal to one particularly interesting alternative: a functional role account of absence causation. According to this account, proposed by Tiehen, absences just are ‘exemplifications of second-order functional properties that are defined by their causal roles’ (Tiehen, Reference Tiehen2014, p. 505). Such an account is attractive insofar as it offers a neat way to locate absences in the realm of being: they are property exemplifications of a familiar sort. These functional property exemplifications are realised by more fundamental features of the arrangement of the physical world. So, to return to our guiding example, the heart wall in the patient with Fallot’s Tetralogy is a realiser for the property instance that causally results in blood flowing between left and right ventricles (and thereby her hypoxia). The functional role account therefore has the following commonality with the proposal defended here: in both cases the absences are construed as dependent entities. Moreover, in virtue of this similarity, both accounts have the resources to solve the problem of profligacy in the same way: by tying absence causation to existential dependence. Consider again the putative absences of heart wall tissue and of Gore-Tex in our patient (before any surgery): the functional role theorist can say that, for example, there is only one functional property realised by the heart, not two (or more).
Where the two proposals differ significantly, however, is over the question of multiple realisability of absences. Functional properties, defined by their causal roles, are multiply realisable by kinds: an organic heart with a septal defect and a synthetic heart made entirely of Gore-Tex, but with the same pathological morphology, would presumably both exemplify the same functional property. In contrast, the proposal developed in this paper makes absences dependent on material kinds, such that the organic and synthetic hearts must realise absences of different kinds: an absence of heart wall and an absence of Gore-Tex.
It might be thought that this difference speaks in favour of the functional role account of absences vis-à-vis the account offered here. The reasoning might be as follows: given that the organic and synthetic hearts share their morphology, they will allow blood to flow between the left and right chambers in much the same way, and so share a causal profile. Who could argue with this? The problem with this line of thought is that the functional role account involves a much stronger commitment than this: it involves the claim that absences just are the exemplification of those properties. The weaker commitment, that two objects made of different kinds of matter can share causal profiles, is perfectly compatible with the account of absence causation offered in this paper. So, what should we make of the stronger commitment? The difficulty for the functional role account is that it generates a problem distinguishing between cases of absence that should be kept distinct, or so I shall argue.
Consider three cases: (1) the heart of the Fallot’s patient before any surgical intervention – absent heart wall tissue between the ventricles; (2) the heart of the patient after the insertion of a Gore-Tex graft; and (3) a healthy, normal heart, whose heart muscle grew in the days postpartum to fill the hole that was in the heart in utero. (2) and (3) share the following feature: in both cases the causal upshot of the arrangement of matter in the heart is the same – no blood passes from one ventricle to another. Moreover, this causal upshot stands in contrast with the causal upshot of case (1), in which blood flows freely between the ventricles. However, cases (1) and (2) share the following similarity: there is an absence of heart wall between the ventricles, the hole. Moreover, in this respect cases (1) and (2) contrast with (3), in which there is no hole. The difficulty facing the functional role account of absences is that it cannot provide a principled account of this latter difference, whereas the account based on material kinds offered here can.
How so? Consider case (2), the patched heart. According to the functional role account, the absence is identical with an exemplification of a second-order functional property. The causal upshot of (2) is different from case (1) because the Gore-Tex graft is a causal preventer. So far, so good; but now consider (3), with the normal, healthy heart. The right thing to say in this case, barring ontological excess, is that there is no exemplification of the functional property: there is no absence in the normal, healthy heart. There is, as we would put it more naturally, no hole. Unlike case (2), it’s not that there’s one there, but it’s prevented from issuing in its normal causal upshot. But this is precisely what the functional role account cannot give a principled account of. From its perspective, the accretion of heart-wall tissue preventing blood flow across the ventricles is, with respect to the causal features of the cases, no different to the grafting of Gore-Tex to the heart to the same effect. In both cases, (2) and (3), then, they must say the same thing: either that in both cases there is the same kind of absence, or that the absence is to be found in neither case. Neither alternative is acceptable. In contrast, the account of absence causation offered here faces no difficulty explaining the difference between cases (2) and (3). In case (2) there is an absence of heart wall tissue – an absence that is dependent on the kind of material the host is made of; in case (3) there is none such.
7. Conclusion
I have presented and defended a way of solving the problem of profligacy for two important cases of absence causation – holes and surface absences – without excessive revision to common-sense or scientifically informed judgments. I also outlined more schematically how the solution may be extended to other absences, such as the collapsed maglev track and train, where there is some artefactual, material system constituted by objects of certain kinds. In a like manner to surface absences, when one of these kinds of object is absent, the causal credentials of the absence depend on the earlier presence constituting the system. This account, then, will plausibly apply also to organic systems, such as bodily organs, or the whole body, and to other non-living, but naturally occurring systems, like solar systems. Each of these is the object of study by some special science: biology, astrophysics, and thermodynamics. If these cases of absence causation comprise a uniform phenomenon, call them systemic absences, then the proposal might be extended to a very wide range of absences: a brain haemorrhage causing the destruction of a ‘language module’ in a cognitive system, causing aphasia; the absence of money in a bank account causing a credit warning when a mortgage payment cannot be transferred across the banking system. The prospects seem promising, then, for generalising the solution to a very wide range of cases of absence causation: any case for which there is good empirical reason for thinking some system is in play.
The prospects of the analysis are dimmer, however, with respect to omissions. Consider the case of Flora omitting to water her plants, causing their death. The analysis might apply if it were plausible that Flora, her actions, and her plants form a system, and that no one else forms such a system with those plants. This might explain why only Flora’s omission is a cause of their death, but not, e.g., the Dalai Lama’s omission. Perhaps Flora can, under certain conditions, form a system with her plants. Human societies, if they exist, seem to be systems in which the behaviour of the society depends on the actions of their members. So too might be families, or even communities of different kinds of animals coexisting in mutually dependent ways, such as humans and their domesticated hunting animals. Some prospects can be discerned for applying the solution to these cases, but properly evaluating them would require greater clarity in the currently murky area of social ontology. At this stage it might be better to remain agnostic.
Another reason for being cautious with respect to omissions is that the problem of profligacy arises slightly differently for omissions than it does for holes, surface absences, and systemic absences. For omissions, the problem of profligacy is first and foremost a problem in which the profligate absences are absent particulars: not just Flora’s omission, but also the Dalai Lama’s; the Queen of England’s, yours, mine, might be a cause of the plant’s death. Each of these candidate omissions is, intuitively, a different particular of the same kind. With respect to holes, for example, the problem arises in a different way. We might, after careful philosophical reflection, be tempted to think that the absence of different particulars of the same kind are equally good causes of hypoxia in the Fallot’s Tetralogy patient: the absence of some part of my heart wall, yours, the Queen’s. But it requires less philosophical sophistication to motivate the problem by pointing to absences of differing kinds: the absence of Gore-Tex, bovine pericardium, or porcine pericardium. This difference alone might lead to the suspicion that the present solution, which gives a central place to the kind that is absent, is not appropriate for ruling out profligate omissions. What should we say about omissions, which seem, intuitively, to be particulars? Clearly further work remains: though it’s worth recalling the possibility that absence causation may not be a unified phenomenon.
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