1. The causal exclusion problem

According to a common though not universal presentation, the causal exclusion problem is the conjunction of the following four individually plausible, but (seemingly) jointly inconsistent principles:

1. (1) The principle of mental causation: some physical effects have mental causes.Footnote ¹

2. (2) The principle of irreducibility: mental causes are distinct from physical causes.Footnote ²

3. (3) The principle of physical causal completeness: ‘if a physical event has a cause at t, it has a sufficient physical cause at t’ (Kim Reference Kim, McLaughlin, Beckermann and Walter2009, 38).

4. (4) The principle of causal exclusion: ‘no single event can have more than one sufficient cause occurring at any given time …’ (Kim Reference Kim2005, 42).Footnote ³

While each of these principles is individually plausible, they seem to form an inconsistent tetrad. In brief, how can behavioural effects have no more than a single sufficient physical cause, while they must simultaneously possess distinct mental causes as well?

There are those who resolve the causal exclusion problem by rejecting one of the principles constituting the causal exclusion problem. The reductionist argues that the evidence in favour of (1) mental causation; (3) physical causal completeness; and (4) causal exclusion is conclusive. So, (2), irreducibility must be rejected (Kim Reference Kim2005, 125; Ney Reference Ney2007). Notoriously, however, mental causes are multiply realizable and intuitively distinct from physical causes, so many find the principle of irreducibility ‘obviously true’ (Bogardus, Reference Bogardus2013, 446). The epiphenomenalist claims that the overwhelming evidence in favour of (2) irreducibility; (3) physical causal completeness; and (4) causal exclusion renders (2), mental causation, false (Robinson Reference Robinson2004, 158; Lyons Reference Lyons2006). But, mental causation is pre-theoretically intuitive, and serves as a foundation for moral responsibility and epistemic justification, so many think that abandoning mental causation amounts to ‘the end of the world’ (Fodor Reference Fodor1989, 77). The substance dualist contends that (1) mental causation; (2) irreducibility; and (4) causal exclusion are true, so (1), physical causal completeness, can be abandoned (Foster Reference Foster, Smythies and Beloff1989; Meixner Reference Meixner2008). However, due to twentieth-century scientific advances, most think the principle of physical causal completeness is ‘fully established’ (Papineau Reference Papineau, Gillett and Loewer2001, 33). There is also an expanding tribe of scholars, increasingly called the ‘compatibilists’, who embrace (1) mental causation; (2) irreducibility; and (3) physical causal completeness, thereby rejecting (4) causal exclusion in some way (Bennett Reference Bennett2003; Sider Reference Sider2003). Pre-theoretically though, presuming that behavioural effects, on a global scale, have more than a single sufficient cause is ‘a bit bizarre’ (cp. Schiffer Reference Schiffer1987, 148; Harbecke Reference Harbecke2008, 28; Kim Reference Kim, McLaughlin, Beckermann and Walter2009, 45) or even ‘absurd’ (Kim Reference Kim1993, 281).

2. Motivating the causal exclusion principle

While each of these positions deserve (and receives) its due attention, it is the latter compatibilist position that is of present concern. In order to properly evaluate the compatibilist position, it is helpful to first marshal together the arguments often provided in favour of the principle they reject, namely, the causal exclusion principle.

The literature contains at least five arguments in favour of the causal exclusion principle, though I will only expand upon the last one. First, there is an appeal to intuition: Jaegwon Kim claims that the causal exclusion principle is ‘virtually an analytic truth’ (Kim Reference Kim2005, 51), or, is prima facie obvious. This is less an argument than an assertion that the causal exclusion principle carries intuitive force, as some argue that the principles of mental causation and/or irreducibility are supported by brute intuitive strength. Second, the parsimony argument: as a general scientific value, we should ‘get by with the fewest possible entities’ (Kim Reference Kim1989, 98), so if one cause is sufficient, we should get by without positing additional causes (cp. Malcolm Reference Malcolm1968; Goldman Reference Goldman1969; Kim Reference Kim1989, 98), so we should exclude additional causes. Third, and most commonly, the coincidence argument: overdetermination is a rare coincidence—barns infrequently burn down by the simultaneous occurrence of a short circuit and a dropped match. Mental causation, however, is ubiquitous. Overdetermination, if true of mental causation, would be ubiquitous and these massive amounts of coincidence are unacceptable (cp. Schiffer Reference Schiffer1987, 148; Kim Reference Kim1998, 53; Kim Reference Kim2006, 558; Lim Reference Lim2013, 670–671; Roche Reference Roche2014, 817–818; Kroedel Reference Kroedel2015a, 367). Fourth, the additivity argument: if causation involves energy/momentum transfer, and one sufficient cause transfers all the requisite energy/momentum to the effect, then a second cause would either transfer surplus energy/momentum to the effect (pushing the effect twice as hard and/or far) or be incapable of transferring energy/momentum to an effect on account of the fact that it already possesses all its requisite energy/momentum (Kim Reference Kim1998, 53–55; Sider Reference Sider2003, 3–4; Carey Reference Carey2011, 253–254; Audi Reference Audi2013, 460; Paul and Hall Reference Paul and Hall2013, 147).

The fifth argument, the necessity argument, is perhaps the most problematic argument of all. The necessity argument is especially problematic because it, unlike other arguments, indicates that abandoning the causal exclusion principle ultimately leads to the failure of one or both of the principles of physical causal completeness or mental causation. Unfortunately, the necessity argument is underdeveloped in the literature, so I will presently attempt to shine some light on the necessity argument. Consider the following passage as an initial articulation of the necessity argument:

According to Kim, if the physical cause p is a sufficient cause, then the physical cause p suffices to, or is all that one needs to, ensure that p* will occur all by itself. So, the distinct event m is not necessary for p* to occur. Rather, m is ‘otiose’ (Kim Reference Kim2006, 558), or ‘superfluous’ (Corry Reference Corry2013, 33). Or, it suffers from ‘redundancy’ (Harbecke, Reference Harbecke2013, 65) and ‘dispensability’ (Lim Reference Lim2013, 670), and hence can be excluded.

The necessity argument presupposes that causal necessity and causal sufficiency stand in the following relations: if a alone is a sufficient cause for b, c is unnecessary as a cause for b; and, if a is necessary as a cause of b, c alone is an insufficient cause of b. This proposed relation between sufficient causes and necessary causes is controversial, so it will be defined, defended and nuanced below. But to begin, here is a classic expression of this intuition from Myles Brand:

According to Brand, if we say that b only needs conditions a, then we cannot simultaneously say that b also needs conditions c (i.e. that b does not only need conditions a). And, if we say that b needs conditions a, then we cannot also say that b only needs conditions c (i.e. that b does not need conditions a).

This inaugural articulation of the necessity argument requires the following clarifications and refinements. First, the proposed relationship that exists between a’s sufficiency for b and c’s unnecessity for b is not a relationship of logical necessity and logical sufficiency. It is possible for a to be logically sufficient for b, while c is necessary for b. To slightly modify an example from David Sanford, a is the poet looking at a bird in a prime number of ways that is more than 12 but less than 14. From this it is logically necessary that c, the poet looks at a bird in a prime number of ways that is more than 11 but less than 15. At the same time, a is logically sufficient for the fact that b, the poet looks at the bird in 13 ways and c is logically necessary for the fact that b (Sanford Reference Sanford1975, 109; cp. Engelhardt Reference Engelhardt2012, 237). Nor is the proposed relationship that exists between a’s sufficiency for b and c’s unnecessity for b a relationship of necessary conditions and sufficient conditions. Imagine that you shoot a gun, necessitating a ‘bang’ sound, but the gunshot is sufficient for some murder, while the sound is a necessary condition for the murder as well.

Rather, the problematic relationship that exists between a’s sufficiency for b and c’s unnecessity for b, is a relationship of causal necessity and causal sufficiency. It is not possible for a to be a sufficient cause of b, while at the same time maintaining that c is necessary as a cause (that is, as a partial cause, as a sufficient cause or as any other type of cause) of b. To return to the prior example, the gun blast is a sufficient cause of the murder, and though the sound coming from the gun blast is a necessary condition for the murder, it is not necessary that the sound be a cause of the murder. In fact, intuitively, it is not. Here is a perhaps unfortunate way of making the point: assume that a causes b, and that b requires 100 causal units in order for it to occur. If a delivers 100 causal units to b, then no causal unit contribution is needed from c. If a necessarily gives rise to another condition c, then c may be necessarily present for b, but this does not change the fact that b does not need any causal contribution from c. Further elaboration elsewhere clarifies that Brand has this in mind as well (cp. Brand and Swain Reference Brand and Swain1974).

Before noting the problems that the necessity argument poses to the mental causation debate, it is worth pointing out that the principle of physical causal completeness indicates that some physical event p is a sufficient cause of the behavioural effect p*. This follows from the fact that p* ‘Has a sufficient physical cause’ (Kim Reference Kim, McLaughlin, Beckermann and Walter2009, 38), and it captures the fact that the physical world is causally complete in itself. As Kim says, ‘there is no need to go outside the physical domain to find a cause … of a physical event’ (Kim Reference Kim2005, 16).

Not only does the principle of physical causal completeness indicate that some p is a sufficient cause of p*, but it also shows that some p is necessary as a cause of p*. This follows from the above definition of physical causal completeness as well. The fact that p* ‘has a sufficient physical cause’ entails that p* has a physical cause. Some even define the principle of physical causal completeness without reference to the causal sufficiency of the physical cause, to emphasize the necessity of some physical cause: ‘if a physical event has a cause at t, then it has a physical cause at t’ (Kim Reference Kim2005, 15; cp. Kroedel and Schultz Reference Kroedel and Schultz2016, 8). Imagine, for example, that Joe’s brain is connected to an exceptionally powerful fMRI machine that detects all brain activity. Joe snaps his finger. Might the fMRI machine detect that no brain activity occurred? Might some disembodied soul have inaugurated the finger snapping without any physical cause at all? It is common for those that endorse physical causal completeness to answer no to these types of possibilities (cp. Crisp and Warfield Reference Crisp and Warfield2001, 314; Kim Reference Kim2005, 46–50). Presumably, this is because physical causal completeness requires behavioural effects to have some physical cause.Footnote ⁴

The principle of mental causation indicates that some mental event m is necessary as a cause of p*. This follows from the fact that the principle of mental causation says some physical effect p* has a mental cause m. It is possible for physical effects to lack mental causes—the tree falling causes the dirt to scatter, the melting ice causes the river to flood, etc. But, mental causation clearly does not occur in these cases. It is also possible for physical effects to be preceded by necessarily occurring mental events—m as an epiphenomenal shadow accompanies some sufficient cause p of p*. But, mental causation clearly does not occur in these cases either. But, if the principle of mental causation is true on an occasion, some m is necessarily a cause of p*. If m is merely a necessarily present event prior to p*, or worse yet, does not occur at all, then mental causation fails in this instance. So, in order for mental causation to be true in this instance, some m is necessary as a cause of p*.

Some argue that, in the interests of parity, the principle of mental causation also indicates that m is a sufficient cause of p* as well (Crane Reference Crane1995, 231; Bennett Reference Bennett2003, 481). This does not follow from the definition of mental causation given above, and I do not endorse or require this stronger principle of mental causation—in fact, I argue against it. But some others do, so it will be discussed throughout the paper. These applications of the definitions of necessary causation and sufficient causation to the principles of physical causal completeness and mental causation are admittedly brief. Once the counterfactual model of causation is in place (§3), I shall bolster these definitions with their appropriate counterfactual tests.

Having set the stage, I now turn to four problems that the necessity argument raises in the mental causation debate. First: if p is a sufficient cause of p*, m is unnecessary as a cause for p*—if p is all the cause needed for p*, some m cannot also be needed as a cause of p*. But, by the principle of mental causation, some m is necessary as a cause for p*, or this is not a case of mental causation. So, if the principle of mental causation is true in this instance, some m is necessary as a cause of p*, but the necessity argument indicates that it is not, so the principle of mental causation is false. This first version of the necessity argument appears in the literature on several occasions (cp. Kim Reference Kim1989, 82; Kim Reference Kim1998, 44–45; Kim Reference Kim2005, 48–49; Moore Reference Moore2012, 323; Corry Reference Corry2013, 33).

The second problem merely inverts the first: according to the principle of mental causation, in cases of mental causation, some m is necessary as a cause of p*. If some m is necessary as a cause of p* in cases of mental causation, then p is not a sufficient cause of p* on those occasions where m is necessary as a cause as well, which violates the principle of physical causal completeness. For example, Sam steals a car, and, to secure the principle of mental causation, his decision is necessarily a cause of this effect. So, the physical cause is not all that is needed to cause this theft. This second problem makes several appearances in the literature (Bennett Reference Bennett2003, 481; Moore Reference Moore2012, 328). As noted, problems one and two serve as opposite sides of the same coin. Problem one indicates that the causal sufficiency of p for p* (from physical causal completeness) renders m unnecessary as a cause of p* (falsifying mental causation), while problem two indicates that the requirement that m be a cause of p* (from mental causation) renders it false that p is all the cause needed for p* (falsifying physical causal completeness).

Problem three: according to some, m is a sufficient cause of p*, so some p is unnecessary as a cause of p*. But, by the principle of physical causal completeness, some p is necessary as a cause of p*. So, in order for the principle of physical causal completeness to be true, some p is necessary as a cause of p*, but the necessity argument shows that it is not, so physical causal completeness is false. For example, Judy is a disembodied soul that decides to make turkey for supper, so she does. But, physical causal completeness indicates that some physical cause is necessary for this behaviour—she cannot make turkey without some accompanying neural stimulus. Yet, as it turns out, her disembodied decision is sufficient for her behaviour, so she could make turkey even without a neural cause—another result that is hard to swallow. This third problem is invoked on several occasions as well (Kim Reference Kim1998, 44–45; Kim Reference Kim2005, 48–49; Moore Reference Moore2012, 323; Roche Reference Roche2014).

Problem four merely inverts this issue: the principle of physical causal completeness indicates that some p is necessary as a cause of p*, which renders m an insufficient cause of p*. That is, since the principle of physical causal completeness indicates that some physical event must cause p*, it is not the case that m alone and by itself, as a disembodied soul, can cause p*. So, m is not a sufficient cause of p*. This conclusion poses problems for those, such as Karen Bennett, who maintain that the principle of mental causation requires m to be a sufficient cause of p*. Bennett gestures at, but ultimately rejects, this final version of the problem (Bennett Reference Bennett2003, 481). And, as noted, problems three and four serve as opposite sides of the same coin as well. Problem three indicates that the causal sufficiency of m for p* (possibly from mental causation) renders p unnecessary as a cause of p* (falsifying physical causal completeness), while problem four indicates that the requirement that some p be a cause of p* (from physical causal completeness) renders it false that m is all the cause needed for p* (possibly falsifying mental causation).

3. Counterfactualist compatibilism

Compatibilism, a doctrine coined by Terence Horgan (Reference Horgan1997, 166), and labelled a movement by Bennett (Reference Bennett2003, 473) suggests that physical effects have sufficient physical causes and distinct mental causes. To secure compatibilism, one must reject or substantially nuance the principle of causal exclusion. The principle of causal exclusion is, however, supported by, among other things, the necessity argument (§2). So, to secure compatibilism, one must reject or nuance the causal exclusion principle in a manner that responds to, among other things, the necessity argument.

Compatibilists typically overcome the necessity argument by positing an especially tight relation between the physical cause and mental cause of the effect (cp. Yablo Reference Yablo1992; Pereboom Reference Pereboom2002; Bennett Reference Bennett2003; Shoemaker Reference Shoemaker2007), where this tight relation ensures that the mental cause necessarily accompanies a physical cause of the effect, and vice versa. Therefore, contra the necessity argument, the mental cause and physical cause of the effect necessarily occur after all. In the next two sections, I discuss how this strategy plays out for one particular subset of compatibilists, namely, counterfactualist compatibilists.

Counterfactualist compatibilists (hereafter simply called ‘compatibilists’) endorse compatibilism via emphasis on a counterfactual model of causation (Loewer Reference Loewer2002, 658–660; Bennett Reference Bennett2003; Kallestrup Reference Kallestrup2006, 473; Marras and Yli-Vakuri Reference Marras, Yli-Vakuri, Gozzano and Orilia2008, 125; Walter Reference Walter2008, 678; Carey Reference Carey2011, 258–259; Arnadottir and Crane Reference Arnadottir, Crane, Gibb and Ingthorsson2013, 255; Roche Reference Roche2014; Kroedel Reference Kroedel2015b). Thus, to understand their position, it is important to highlight the relevant details of the counterfactual model of causation. The counterfactual analysis of causation, while rooted in a brief remark from David Hume, is popularized by David Lewis (Reference Lewis1986 and Reference Lewis1973a). For Lewis, for an event p to cause event p* there is (a chain of) causal dependence from p to p*, where the (chain of) causal dependence from p to p* obtains when there is (a chain of) counterfactual dependence from p to p* (Lewis Reference Lewis1986, 166–167; Lewis, Reference Lewis1973a, 563). Counterfactual dependence occurs when the following two statements are true:

1. (I) Had p occurred, p* would have occurred: p □→ p*.

2. (II) Had p not occurred, p* would not have occurred: ~p □→ ~p*.

For Lewis, (I) is automatically true, since p and p* are actual events. So, establishing the truth/falsity of (II) is paramount. The truth/falsity of counterfactuals is established by appealing to Lewis’ possible worlds semantics, according to which counterfactuals are nonvacuously true when the closest possible world where the antecedent and the consequent are both true is closer than any possible world where the antecedent is true but the consequent is false. Counterfactuals are false when the closest possible world where the antecedent and the consequent are both true is further from any possible world where the antecedent is true but the consequent is false. Counterfactuals are vacuously true when the antecedent is false in all possible worlds. For example, for the conditional ‘Had the square been round, then the Yankees would have won the world series’, the antecedent is metaphysically impossible, so it is false in all possible worlds, so it is impossible to locate the requisite worlds where the antecedent is true while the consequent is true or false. So, rather than being strictly true or strictly false, they are considered vacuously true. For ease of discussion, I shall refer to the former types of counterfactuals as true (rather than as non-vacuously true), the second types of counterfactuals as false and the latter types of counterfactuals as vacuous (rather than as vacuously true).

The truth/falsity of counterfactuals, then, requires a mechanism for discerning possible world proximity. Here it is: comparative closeness amongst possible worlds relies on the assumption that possible worlds are weakly ordered with respect to overall similarity of particular fact and natural law. According to Lewis, the furthest worlds are the worlds with large-scale violations of natural law. Closer worlds are worlds without large-scale violations of natural law, but worlds with significantly differing particular fact across time and space. Closer still are the worlds with a small-scale violation of law gives rise to minute distinctions of particular fact. The closest world is the actual world, which has no variation in particular fact or natural law (Lewis Reference Lewis1979, 472).

Within this counterfactual model of causation, the necessity argument reveals itself, among other places, in cases of overdetermination. In cases of overdetermination, more than a single sufficient cause brings about the same effect at the same time. Since either event is a sufficient cause of the effect, the other event is unnecessary as a cause of the effect. To use a classic example, two assassins shoot Smith at the same time, so Smith’s death is overdetermined by bullet a firing and bullet b firing. The following counterfactual test establishes this fact:

1. (III) Had bullet a fired without bullet b firing, the death c would have occurred: (a & ~b) □→ c.

2. (IV) Had bullet b fired without bullet a firing, the death c would have occurred: (b & ~a) □→ c.

If both of these counterfactuals are true, Smith’s death is overdetermined by two sufficient causes, indicating that each bullet firing is unnecessary as a cause of Smith’s death. That is, the bullet a firing suffices to cause Smith’s death because we can remove bullet b firing, leaving only bullet a firing, and Smith’s death still occurs. Similarly, the bullet b firing suffices to cause Smith’s death because we can remove the bullet a firing, leaving only the bullet b firing, and Smith’s death still occurs. Likewise, the bullet a firing is not needed to cause Smith’s death because we can remove the bullet a firing and Smith’s death still occurs. Nor is the bullet b firing needed as a cause of Smith’s death because we can remove the bullet b firing and Smith’s death still occurs.

Similarly, on the counterfactual account, the necessity argument, applied to the case of mental causation, takes the following form (cp. Mills Reference Mills1996, 107; Kim Reference Kim1998, 44–45; Bennett Reference Bennett2003, 480; Kim Reference Kim2005, 46–49; Carey Reference Carey2011, 257; Lim Reference Lim2013, 672; Kroedel Reference Kroedel2015a, 363):

1. (V) Had p without m occurred, p* would have occurred: (p & ~m) □→ p*.

2. (VI) Had m without p occurred, p* would have occurred (m & ~p) □→ p*.

If both of these counterfactuals are true, then the behavioural effect p* is overdetermined, since the individual sufficiency of each cause renders the other cause individually unnecessary.

The pieces are now in place to add counterfactual tests to the application of the concepts of necessary causation and sufficient causation to the principles of mental causation and physical causal completeness. As stated above, if mental causation is true in this instance, m is necessary as a cause of p*. The event m is necessary as a cause of p* if counterfactual (V) is false—if we take only m away and p* does not occur, then clearly m is needed for p* to occur. The event m is unnecessary as a cause of p* if counterfactual (V) is true—if we can wipe only m off the face of the universe and p* still occurs, then clearly m is not needed to bring about p*.Footnote ⁵ So, the principle of mental causation is false if counterfactual (V) is true.

Here is an objection: some compatibilists believe that counterfactual dependency is sufficient for causation. Counterfactual dependency is established via the truth of counterfactuals such as (II). So, if ~m □→ ~p* is true, then mental causation is established, regardless of whether counterfactual (V) is true as well (Kroedel Reference Kroedel2015a, 359–361; Kroedel Reference Kroedel2015b, 842–844). While counterfactual dependency may be a necessary condition for causation, it cannot be a sufficient condition for causation. After all, a long-standing criticism of the counterfactual account of causation is that it is possible to establish counterfactual dependency among causally unrelated events. For example, the counterfactual ‘Had the gunshot sound not occurred, the death would not have occurred’ is true, though the gunshot sound is not a cause of the death. Similarly, many worry that ~m □→ ~p* may be true, while it is also true that m is epiphenomal (Kim Reference Kim1998, 45; Esfeld Reference Esfeld2010, 101–102; Roche Reference Roche2014). The way to overcome this problem is to insist that the non-truth of counterfactual (V) is also a necessary condition for the truth of mental causation.Footnote ⁶

Similarly, as mentioned above, physical causal completeness requires that some p is necessary as a cause of p*. Some p is necessary as a cause of p* in this instance if counterfactual (VI) is false—if we wipe only any physical events away, and p* does not occur, then clearly some p is needed for p* to occur. Some p is unnecessary as a cause of p* if counterfactual (VI) is true—if we can wipe only the physical events off the face of the universe and p* still occurs, then clearly some p is not needed to bring about p*. So, physical causal completeness is false if counterfactual (VI) is true.

Physical causal completeness also required that p is a sufficient cause of p*. The event p is a sufficient cause of p* if, among other things, counterfactual (V) is true—if we keep only p, and p* still occurs, then clearly p is all that was need to cause p*. The event p is insufficient as a cause of p* if counterfactual (V) is false—if we keep only p, and p* does not occur anymore, then clearly p was not all that was needed to cause p*. So, physical causal completeness is false if counterfactual (V) is false. Likewise, some said the principle of mental causation requires that m is a sufficient cause of p*. The event m is a sufficient cause of p* if, among other things, counterfactual (VI) is true—if we keep only m, and p* still occurs, then clearly m is all that is needed to cause p*. The event m is insufficient as a cause of p* if counterfactual (VI) is false—if we keep only m, and p* does not occur anymore, then clearly m is not all that is needed to cause p*. So, mental causation may be false if counterfactual (VI) is false.

Here is an objection: this argumentation may rely upon a definition of sufficient causation that is questionable, and perhaps even unorthodox. To be sure, the definition of sufficient causation is variously articulated. As Elizabeth Anscombe indicates: ‘Now “sufficient condition” is a term of art whose users may therefore lay down its meaning as they please’ (Anscombe Reference Anscombe1971, 90). At least four definitions of sufficient causation are present in the relevant literature, though I shall only focus on two. First: p is a sufficient cause of p* if p is ‘enough’ (Anscombe Reference Anscombe1971, 91) for p*, so p ‘alone and by itself’ (Campbell Reference Campbell2004, 153) causes p*, which ‘implies that no other condition is necessary’ (Marras Reference Marras2007, 319) for p*. Call this individual sufficiency. According to the counterfactual analysis, p is individually sufficient for p* if counterfactual (V) is true. In the argumentation above, I assume that individual sufficiency is a necessary condition for sufficient causation.

But, perhaps individual sufficiency is not a necessary condition for sufficient causation because some other type of sufficient causation is a sufficient condition for sufficient causation. Here is a second definition of sufficient causation that may be preferable: p is a sufficient cause of p* if the material conditional p → p* is true. Call this nomological sufficiency. It is notoriously difficult to analyse nomological sufficiency in counterfactual terms. Most naturally, it seems that p is nomologically sufficient for p* when the counterfactual p □→ p* is true. But, as noted above, this test fails, since p and p* are stipulated as actual events, so the counterfactual is automatically true, even of unrelated events (Ruben Reference Ruben1981, 40). Here is another option: p is nomologically sufficient for p* when the logically equivalent counterfactual ~p* □→ ~p is true (Marc-Wogau Reference Marc-Wogau1962, 221–222; Tranøy Reference Tranøy1962, 241). This unfortunately renders the causal relation symmetric (Ruben Reference Ruben1981, 40). How about: p is nomologically sufficient for p* when the counterfactual ~p □→ (p □→ p*) is true (Ruben Reference Ruben1981, 240; Rasmussen Reference Rasmussen1982, 209; Mills Reference Mills1996, 106–107). This test solves both the ‘automatically true’ issue and the ‘causal symmetry’ issue, though it is not without its detractors (Kroedel Reference Kroedel2015a, 373). Thomas Kroedel argues that p is nomologically sufficient for p* if the material conditional p → p* is true in a suitable range of possible worlds (Kroedel Reference Kroedel2015a, 366). Relatedly, Jeff Engelhardt argues that p is nomologically sufficient for p* if p □→ p* is true in this world and relevant nearby possible worlds (Engelhardt Reference Engelhardt2012, 237). Either of these last two definitions can serve as a suitable definition of nomological sufficiency.

Perhaps this nomological sufficiency is a sufficient condition for sufficient causation. In other words, perhaps p is sufficient for p* if p □→ p* is true in a suitable range of possible worlds, and it is not necessary for counterfactual (V) to be true.Footnote ⁷ As Kroedel remarks, ‘Thus, the falsity of [VI] may well be compatible with m’s being a sufficient cause of [p*]’ (Kroedel Reference Kroedel2015a, 366). Or, Engelhardt seems to share a similar general view: ‘A does not need to suffice for K in isolation, however, in order to suffice for K. Rather, it need only be the case that A □→ K holds in actuality and relevant nearby possible worlds, as is the case’ (Engelhardt Reference Engelhardt2012, 237).

There are reasons to believe, however, that nomological sufficiency, while an important condition on sufficient causation, is not a sufficient condition for sufficient causation. First, nomological sufficiency is a relic of the regularity theory of causation, where the counterfactual account of causation is presently presumed, so it is unclear that nomological sufficiency can be the appropriated for use as sufficient causation in this context. But, perhaps it is possible to gerrymander nomological sufficiency into the counterfactual analysis? Perhaps. I tried to do so above, but the task is difficult. Second, nomological sufficiency is commonly rejected for a number of reasons. Most relevantly, nomological sufficiency fails to track causation, let alone causal sufficiency. Kim, for example, argues that a nomological sufficiency relation obtains between a series of shadows from a moving car, but these shadows are not causally efficacious (Kim, Reference Kim, McLaughlin and Cohen2007, 231–232). And, to return to previous examples, the gun’s sound is nomologically sufficient for the death, but the sound is not causally efficacious, let alone causally sufficient, for the death. Third, even granting this definition of sufficient causation, p is only nomologically sufficient for p* if the material conditional p → p* is true in a suitable range of possible worlds. But surely one of the worlds included in this suitable range of possible worlds is the one world that is actually most relevant to the causal exclusion problem, namely, the (p & ~m)-world. This must be the case because the principle of physical causal completeness states that in the circumstance where p and m both occur, p is nevertheless a sufficient cause for p*, which, in this context, must mean that p is able to do the work alone and by itself. For these reasons, while nomological sufficiency may be a necessary condition for sufficient causation, it is not a sufficient condition for sufficient causation. Hopefully this is uncontroversial, as even Kroedel grants that, while sufficient causation involves nomological sufficiency, nomological sufficiency ‘Had better not be a sufficient condition for causal sufficiency’ (Kroedel Reference Kroedel2015a, 373).Footnote ⁸

4. The compatibilist reply

Given these results, the compatibilist has a straightforward though daunting task. Namely, the compatibilist must secure the principles of mental causation and physical causal completeness, over and against the facts that mental causation is false if (V) is true but physical causal completeness is false if (V) is false, and mental causation may be false if (VI) is false but physical causal completeness is false if (VI) is true.

The compatibilist reply starts by highlighting a relevant disanalogy between the two assassins case and the mental causation case. The two assassins case involves independent sufficient causes, which yields the result that neither bullet is individually necessary as a cause for Smith’s death. The mental causation case, however, involves dependent causal processes, which yields the result that the two causal processes necessitate one another. As Barry Loewer explains: ‘In the two assassins case the two causes are metaphysically (and nomologically) independent. In the latter case m depends on N [i.e. p] since it is metaphysically (or physically) entailed by it’ (cp. Crisp and Warfield Reference Crisp and Warfield2001, 135; Loewer Reference Loewer2002, 658; Melnyk Reference Melnyk2003, 168; Bontly Reference Bontly2005; Walter Reference Walter2008, 678; Segal Reference Segal2009, 83; Carey Reference Carey2011, 261).

This dependency relation between m and p follows from the following plausible compatibilist assumptions. The compatibilist typically argues that mental events strongly supervene upon physical events, meaning that p determines that m occurs and m depends upon some p. Given this strong supervenience relation, it may be metaphysically impossible for p to occur without giving rise to m (Kallestrup Reference Kallestrup2006, 473; Marras and Yli-Vakuri Reference Marras, Yli-Vakuri, Gozzano and Orilia2008, 125; Walter Reference Walter2008, 678). Moreover, compatibilists typically endorse physicalism, according to which all events, physical and mental, are caused/determined by physical events, so m depends on some p. Since m depends upon some p, it is at least nomologically impossible for m to occur without some physical subvenience base. Note, however, that compatibilists also argue that mental events are multiply realizable, so m could occur without p, so long as another physical event p ₁ realizes m.

The compatibilist intuitions that some p necessitates m and that m implies that some p occurs, combined with the compatibilist acceptance of physical causal completeness, which states that p* implies that some p occurred, together entail that p cannot precede p* without m preceding p* as well (Kroedel Reference Kroedel2015a, 359; Lewis, 1973, 32). These assumptions also entail that m cannot precede p* without p preceding p* as well. Let the following expression of the argument stand for many:

This solution reveals itself in a counterfactual analysis as well. Namely, on compatibilism, it is not true that p without m occurs and p* still occurs, so counterfactual (V) is not true, so it is not established that m is unnecessary as a cause of p*, so it is not established that mental causation is false. Similarly, it is not true that m without some p occurs and p* still occurs, so counterfactual (VI) is not true, so it is not established that p is unnecessary as a cause of p*, so it is not established that physical causal completeness is false.

This is too quick, it requires the following details. The compatibilist has two ways to show that counterfactual (VI) is not true. Namely, the compatibilist can show that counterfactual (VI) is false or vacuous. The compatiblist has two strategies for establishing the falsity or vacuity of counterfactual (VI). First, the Replacement Strategy. The nearest possible world where m without p occurs, and p* still occurs is not the world of disembodied souls where no p occurs and m still causes p* alone. After all, that world is a distant world where both the principles of physical causal completeness and supervenience are false. Rather, the closest possible world where m without p occurs is the world where p is replaced by a slightly different realizer p ₁. This is a nearby possible world that only has a slight change in particular fact (cp. Crisp and Warfield Reference Crisp and Warfield2001, 314; Loewer Reference Loewer2002, 658–660; Block Reference Block2003, 136; Raatikainen Reference Raatikainen2010, 358; Lim Reference Lim2013, 673; Roche Reference Roche2014).

It is common to argue that the m and p ₁ world is nevertheless a p* world. My desire for a beer, realized by slightly different neurons, still causes me to reach for the beer. Indeed, some argue that this secures the principle of mental causation, as the m without p world is still a p* world, indicating that p* counterfactually depends on m (LePore and Loewer Reference LePore and Loewer1987, 639–640; Mills Reference Mills1996, 109; Loewer Reference Loewer2002, 658; Kallestrup Reference Kallestrup2006, 475–476; Zhong Reference Zhong2011, 134). This may be a mistake, however. While this move shows that p* counterfactually depends upon m, it also shows that p* does not counterfactually depend upon p. After all, if p does not occur and p* still occurs, p* is not counterfactually dependent upon p and hence p is not a cause of p* on the counterfactual analysis (Harbecke Reference Harbecke2014, 371; Kroedel Reference Kroedel2015a, 363–365).

The world where m is replaced by p ₁ may actually be the world where p* is replaced by as well. My desire for a beer, realized by slightly different neurons, causes a slightly different reaching for the beer. This view not only secures the counterfactual dependency of p* on p, but it is also a more consistently applied view on event fragility. That is, if one is prepared to say that a few different neural firings changes the neural event from p to p ₁, then one should also be prepared to say that the resulting few different muscle fibre activations changes the behavioural effect from p* to . The result is that the nearest possible world where m occurs without p is a world where m occurs, and p is replaced by p ₁, and p ₁ causes a slightly different behavioural effect . Thus, counterfactual (VI) is false. It is false that ‘Had m without p occurred, p* would have occurred’ since the nearest possible world is the world where m without p occurs and rather than p* occurs. Since counterfactual (VI) is false, it is false that p is unnecessary as a cause of p*, so it is false that physical causal completeness fails.

Notice, however, that this move renders it false that m is a sufficient cause of p*. After all, the counterfactual ‘Had m without p occurred, p* would have occurred’ is false, since the nearest possible world where m without p occurs is a world where p* does not occur, indicating that the presence of m alone does not guarantee that p* occurs (cp. Zhong Reference Zhongforthcoming, 10). This point is problematic for those who argue that the mental cause is a sufficient cause. Moreover, some, including some compatibilists, argue that the Replacement Strategy is problematic for other reasons as well. As Lewis himself acknowledges, the closest possible world may not be the most relevant possible world (Lewis Reference Lewis2000, 190; Paul and Hall Reference Paul and Hall2013, 161). Consider this counterfactual: had John not said all those mean things to Jenny, Jenny would not have left. The closest possible world is the world where John says very slightly fewer mean things, and Jenny still leaves, which fails to establish the counterfactual dependence of Jenny’s departure on John’s meanness. But, the most relevant possible world is the world where John says none of those mean things, and Jenny stays, which establishes counterfactual and causal dependence.

For these reasons, many compatibilists suggest the Excision Strategy is more appropriate (Harbecke Reference Harbecke2014, 366; Bennett Reference Bennett2003, 482; cp. Lewis Reference Lewis2000, 190; Collins et al., Reference Collins, Hall, Paul, Collins, Hall and Paul2004, 21; Paul and Hall Reference Paul and Hall2013, 161). According to the excision strategy, we do not replace the relevant event with a similar event, rather we completely delete the relevant event, replacing it with a vacuum. Thus, the nearest possible (m & ~p)-world is the world where p is excised, by a ‘metaphysical hole-puncher’ (Bennett Reference Bennett2003, 482), and replaced with empty space. In the nearest possible world where p is excised, the principle of physical causal completeness is still true, so p* would not occur, and supervenience is still true, so m would not occur either (Harbecke Reference Harbecke2014, 371). The former condition establishes that counterfactual (VI) is false. Had p not occurred, while m somehow still occurred, p* would still not have occurred, so counterfactual (VI) is false. The latter condition establishes that counterfactual (VI) may in fact be vacuous. Given that m can only exist if some p is present, but we have excised p without replacing it with another p ₁, m cannot occur either. So, there is no possible world where m occurs without p, rendering counterfactual (VI) vacuous. If the counterfactual is not vacuous in this way, then it is still false for the previously mentioned reason.

The results of the excision and replacement strategies are similar. In both cases, the counterfactual (VI) is false or vacuous. The truth of (VI), however, is required in order to establish that p is unnecessary as a cause, so the principle of physical causal completeness is not shown to be false. There is a general consensus that these arguments are persuasive. Even Kim, who was once critical of this type of compatibilist response, acknowledges that his original worries are ‘not quite right and at best incomplete’ (Kim Reference Kim2005, 46).

As for counterfactual (V), the compatibilist can show that this counterfactual is vacuous by appealing to the Vacuity Strategy. Here it goes: p metaphysically necessitates m (by Supervenience), so the counterfactual (p & ~m) □→ p* is vacuous. Or, there are no metaphysically possible worlds where p occurs without m, so it is impossible to evaluate whether p, without m, would cause p* (cp. Loewer Reference Loewer2002, 658; Bennett Reference Bennett2003, 479; Kallestrup Reference Kallestrup2006, 472; Walter Reference Walter2008, 678–679; Carey Reference Carey2011, 257; Shapiro Reference Shapiro2012, 522; Arnadottir and Crane Reference Arnadottir, Crane, Gibb and Ingthorsson2013, 255). Hence, it is impossible to establish that m is unnecessary as a cause of p*, so it is impossible to establish that the principle of mental causation is false.

In summary, the compatibilist loses mental causation if (V) is true, but loses physical causal completeness if (V) is false. So, the compatibilist argues that (V) is vacuous, thereby preserving both mental causation and physical causal completeness. And, the compatibilist may lose mental causation if (VI) is false, and loses physical causal completeness if (VI) is true. So, the compatibilist argues either that (VI) is vacuous, or will have to argue that mental causation is not lost if (VI) is false.

5. Problems with compatibilism

Unfortunately, these compatibilist victories come with heavy prices. Beginning with counterfactual (VI), the compatibilist shows that p is not unnecessary as a cause of p* by showing that (m & ~p) □→ p* is false or vacuous. For several reasons, it is unlikely that counterfactual (VI) is vacuous. First, all one needs to do in order to show that the antecedent is not metaphysically impossible is to adopt a replacement strategy. According to the replacement strategy, the nearest world where m occurs without p is the easily accessible world where m occurs with a slightly different realizer p ₁. If the compatibilist rejects this suggestion, and holds fast to the excision strategy, counterfactual (VI) is probably not vacuous either. Presumably, the disembodied soul world where m occurs without some p, though false, is nevertheless metaphysically possible. If so, counterfactual (VI) is not vacuous. To reject this possibility is to argue that physicalism is necessarily true. Some would find it question begging to rule out the possibility that disembodied souls are at least metaphysically possible.

For these reasons, the compatibilist may instead prefer to argue that counterfactual (VI) is false. The downside: it is the truth of this counterfactual that establishes what some take to be a central aspect of the principle of mental causation. For some, the principle of mental causation says that m is a sufficient cause of p*. The event m is a sufficient cause of p* if m alone, without p, can cause p*, or, if counterfactual (VI) is true. How can we say that m alone is all we need to cause p*, when it is not true that m all by itself causes p*? On compatibilism, (VI) is not true, so the causal sufficiency of the mental cause cannot be established.

This result serves as an objection to those compatibilists who maintain that m must be a sufficient cause of p*. This result is neither surprising, nor need it undermine compatibilism. It is not surprising because compatibilism is the view that m only exists if some p exists (by supervenience and physicalism), and that some p must cause p* (by physical causal completeness), so it is not surprising to learn that compatibilism does not state that m, without some p, is sufficient to cause p*. While the compatibilist probably cannot argue that m is a sufficient cause of p*, the compatibilist need not argue that m is a sufficient cause of p* anyway (Arnadottir and Crane Reference Arnadottir, Crane, Gibb and Ingthorsson2013, 259; Morris Reference Morris2015, 438). The principle of mental causation states that ‘some physical effects have mental causes’, it does not state that m is causally sufficient for p*. Moral responsibility is grounded if agents cause actions, not if agents, without physical influence qua disembodied souls, cause actions. Common sense indicates that mental events play some causal role, not that mental events, without physical influence as if in disembodied souls, cause behavioural effects.

As for counterfactual (V), the compatibilist shows that m is not unnecessary as a cause of p* by showing that (p & ~m) □→ p* is vacuous. However, it is the truth of this counterfactual that establishes that the principle of physical causal completeness is true. The principle of physical causal completeness says that p is a sufficient cause of p*. A necessary condition for p being a sufficient cause of p* is that p alone, without m, can cause p*, or, that counterfactual (V) is true. How can we say that p alone is all we need to cause p* when it is not true that p all by itself causes p*? On compatibilism, (V) is vacuous, so the principle of physical causal completeness cannot be established as true. This does not amount to the falsity of physical causal completeness, but it indicates there is no way to prove that physical causal completeness is true. As Kim complains, ‘we would not know what it could mean for both putative causes to be independently causally sufficient for the effect’ (Kim Reference Kim2005, 46). Or, as Daniel Lim frames it: ‘How … are we to verify that every physical event at time t has an independent, sufficient physical cause at t if the physical causes we are interested in can never occur without their non-physical counterparts’ (cp. Ritchie Reference Ritchie2005, 127; Lim Reference Lim2011, 3; Moore Reference Moore2012, 327; Harbecke Reference Harbecke2014, 370–371).

Not only does the vacuity strategy render it impossible to prove that physical causal completeness is true, but the vacuity strategy probably indicates that physical causal completeness is false. The principle of physical causal completeness says that p is a sufficient cause of p*, so p can cause p* without m, so counterfactual (V) is true. Yet according to the vacuity strategy, p causing p* without m cannot occur, so p is not a sufficient cause of p*, since (V) is vacuous. The physical cause p is only a sufficient cause of p* if p is all that is needed to cause p*. Yet it is not true that p* occurs when only p occurs, since p* only occurs when p and m occur. As Bennett indicates, ‘it certainly sounds as though p needs m’s help’ (Bennett Reference Bennett2003, 481; cp. Marras Reference Marras2007, 319). If p* also needs m to occur, how can p be all that is needed for p* to occur?

I take the former problem with the vacuity strategy to be unpleasant—philosophers generally, but not necessarily, avoid embracing doctrines that are metaphysically impossible to prove. I take the latter problem with the vacuity strategy to be deadly. If the principle of physical causal completeness fails, then compatibilism may fail (since physical causal completeness is one of the principles constituting the doctrine of compatibilism) and compatibilism loses attractiveness (since many philosophers want to hold on to the principle of physical causal completeness).

In summary, those attempting to motivate the causal exclusion problem argue that the sufficiency of the physical cause for the behavioural effect renders the mental cause unnecessary as a cause of the behavioural effect, and vice versa. Compatibilists respond that there obtains an especially tight relation between m and p, such that m and p are both necessary as causes for the behavioural effect. In so doing, however, the compatibilist also renders it impossible to establish that m and p are sufficient causes of the behavioural effect—the latter being a problem that is equal to or greater than the original difficulty. My conclusion is not that compatibilism is now a defunct position. Rather, viable avenues of response remain for the compatibilist, but more work needs to be done. Compatibilism, as currently construed and defended, has not fully disentangled itself from the grips of the causal exclusion problem.Footnote ¹⁰