The case for widespread simultaneous causation

The case for widespread simultaneous causation Abstract In this paper, I examine recent arguments for the widespread existence of simultaneous causation from Huemer & Kovitz and Mumford & Anjum, and conclude that they are mistaken. I argue that these arguments overlook two pictures of causation which are commonly assumed, which I call the Standard Modern Picture and the Contiguous Extended Picture. In this paper, I examine recent arguments for the widespread existence of simultaneous causation from Huemer & Kovitz and Mumford & Anjum and conclude that they are mistaken. It will be helpful to position this in the recent history of views on simultaneous causation. I think it is fair to say that the current mainstream philosophical view on simultaneous causation is that there is no simultaneous causation: it is ruled out either on physical or logical grounds. The view that simultaneous causation is logically impossible dates back at least to Hume.1 Many recent philosophers agree with Hume that simultaneous causation does not occur, but not with the claim that it is logically impossible. The guiding idea here seems to be that it is not the place of philosophy to dictate to current physics. For example, Lewis says that stipulating that a cause must always precede its effect ‘rejects a priori certain legitimate physical hypotheses that posit backward or simultaneous causation’ (1973: 170) On the other hand, Hall & Paul, both students of Lewis, are comfortable in following Hume in ruling out simultaneous causation by fiat accompanied with the advice that ‘simultaneous causation need not be taken too seriously’ (2013: 17). A contrary strand of thought on simultaneous causation dates back at least to Kant. This holds not just that simultaneous causation does in fact occur, but moreover that the majority of real-life cases of causation are simultaneous.2 Dummett (1978) and Brand (1980) defended versions of this view. But it has more recently come back into fashion, especially with defenders of the Powers Theory of Causation. In this paper, I focus on arguments from Huemer & Kovitz (2003) and Mumford & Anjum (2011) that make interesting new contributions to this line of thinking. I. HUEMER & KOVITZ’S ARGUMENT Huemer & Kovitz argue that all causes are simultaneous with their direct effects.3 Let us define the term direct cause as follows: event c is a direct cause of event e if and only if c is a cause of e and there are no events in the same causal process temporally located between c and e. Direct causation is ‘immediate’ in the sense of not being mediated by any intervening events, and the term immediate cause will be used interchangeably with the term direct cause. Huemer & Kovitz do not give a definition of the terms ‘direct cause’ and ‘immediate cause’ in their article, but I presume that they have the preceding sense in mind.4 Huemer & Kovitz begin by describing Hume's quantized view of time: there are smallest indivisible units of time (which we can call moments), and any moment has a next moment. Corresponding to these smallest moments, there are indivisible atomic events. On Hume's Sequential View of Causation, indirect causation is by way of a causal chain, and every causal chain is built out of direct causal links between atomic events that are contiguous to each other (i.e., spatially and temporally adjacent). As Hume points out, it cannot be that all causation is simultaneous on his view, for we cannot build up any extended causal chains using only links of zero length. ‘If one cause were co-temporary with its effect, and this effect with its effect, and so on, ‘tis plain there wou’d be no such thing as succession, and all objects must be co-existent.’5 Hume's view of time is outdated. Most philosophers now adopt the modern view that time has the mathematical structure of the continuum.6 This is incompatible with Hume's talk of the next instant of time, as the modern view implies that between any two points in time there is another point in time. Huemer & Kovitz propose to replace Hume's Sequential View of Causation with a view they call the Simultaneous Conception of Causation that is consistent with the modern view of time. On their view, causes and effects are temporally extended events, which can be divided indefinitely into further events.7 Then all direct causation is simultaneous: direct causation is always between a temporally extended cause and a simultaneous temporally extended effect. To illustrate this, consider Kant's example of a ball resting on a cushion. On Huemer & Kovitz's view, the event of the presence of a ball on a cushion extending over time interval Δt causes the event of the indentation in the cushion extending over the very same time interval Δt. Huemer & Kovitz do not merely present the Simultaneous Conception of Causation as one picture that is consistent with the Modern Conception of Time. They argue that their picture logically follows from the Modern Conception of Time in conjunction with another widely accepted and plausible principle about causation. They also do more than just claim that simultaneous causation is possible and occasionally occurs; they claim that simultaneous causation is common. The focus of this section is Huemer & Kovitz's argument that ‘in a world with a continuous temporal structure and no action at a temporal distance, then, a cause cannot precede its immediate effect: they must be simultaneous’.8 Crucial here is their application of Hume's restriction against action at a temporal distance. As Hume states it, the principle is that ‘nothing can operate in a time or place which is ever so little remov’d from those of its existence’.9 One way to understand this principle is as requiring intervening events in all causal processes. Empty waiting periods are never efficacious. As Le Poidevin puts it, ‘The egg is ready to be consumed 5 minutes after I started to boil it, not simply because 5 minutes have passed, but because of the changes going on inside the egg throughout that time. Again it is not time that heals all wounds, but rather the (psychological physical, political) changes that go on in time that do so.’10 Note that Hume's original restriction had two parts: (1) all direct causation is between events that are next to each other in time and (2) indirect causation is mediated by chains of direct causal links. Huemer & Kovitz mention only the first part in their formulation, and do not explain their own view of indirect causation. They state Hume's restriction as follows: ‘no occurrence can be directly causally relevant to an occurrence at a non-zero temporal distance from it.’11 Contrary to Huemer & Kovitz, there seem to be a number of alternative pictures of causation that are consistent with their restriction against action at a temporal distance, but do not involve simultaneous causation. The first picture one might think of is a picture allowing temporally extended events that are contiguous. For example, an event e1 extending over an open time interval [0, 1] might directly cause an event e2 that extends over a closed time interval [1, 2]. There is zero temporal distance between the end of e1 and the start of e2 but e1 is not simultaneous with e2, so this is direct causation at a zero temporal distance without simultaneous causation. Let's call this the Contiguous Extended Picture: all causes are temporally prior to effects, direct causation is only between temporally contiguous events, and furthermore this is not an empty requirement: there does exist direct causation between temporally extended events.12 Huemer & Kovitz do mention this first alternative picture and object that the Contiguous Extended Picture does in fact involve action at a temporal distance: e1 is at a non-zero temporal distance from the second half of e2. This reply needs to stretch their stated formulation of the principle of the impossibility of action at a temporal distance: as they state it says nothing about parts of occurrences. However, let's grant them this and move on. As we shall see, we do not need to suppose that causes are ever contiguous with their direct effects. Contrary to Huemer & Kovitz's claims, there are a number of alternative pictures that are consistent with their assumptions, and we will now focus on a second alternative picture. A gap in their argument is that Huemer & Kovitz haven’t argued for the existence of any direct causation. Without this, their argument doesn’t establish the existence of any simultaneous causation. So their argument leaves room for the possibility that all causes and effects are non-simultaneous and there is no direct causation—a picture where in the causal process between every cause and effect there are intermediary causes. I am not claiming that this picture is a new picture of causation. On the contrary, I think this is a commonly assumed modern picture of causation although it is seldom explicitly stated and sometimes overlooked. In what follows, I shall call it the Standard Modern Picture (not to be tendentious, but because this is a convenient label. I discuss later in this paper the question of how common this view is in the twentieth century). Note that adopting the Standard Modern Picture of causation does require a slightly different interpretation of the restriction against action at a temporal distance. We can no longer understand the restriction against action at a temporal distance as requiring every cause to be at zero temporal distance from its effects, or even connected to its effect by a chain of causes all at zero temporal distance from each other. Rather we should now understand the restriction against action at a temporal distance as requiring every cause to be connected to its effect by a chain of causes with infinitely many links. It can still be true that there are no temporal gaps within causal chains; however, the understanding of ‘no temporal gaps’ can no longer be understood as requiring chains of causes all at zero temporal distance from each other, but rather as requiring temporally dense causal chains: between any two events in the causal chain there is a third.13 Also note that it is not part of the Standard Modern Picture that all events are instantaneous. They can be of any length. But this picture places no restriction on how short an event can be, thus allowing for infinite chains of events between any two non-contiguous events. The Standard Modern Picture dispenses with direct causation. But do we have any good reasons for believing in direct causation? On Hume's Sequential View of Causation, indirect causation always requires direct causation: indirect causation requires a chain of direct causal links between atomic events. However, once we abandon Hume's quantized view of time in favour of a continuous view of time, there seems to be no reason to believe in atomic events, or to believe in direct causation at all.14 The Standard Modern Picture implies that there are infinitely many intermediate causes in every causal process, but again this seems to be a plausible view in a world with continuous temporal structure. With a few extra assumptions, it even follows from the standard regularity and counterfactual analyses of causation that all causal processes are dense in this sense. To put it briefly, causal theorists often assume determinism, and if instantaneous world states are permitted as causal relata, this would provide any given event with causes at every earlier time.15 So, in conclusion, although Huemer & Kovitz are right that given some assumptions the only direct causal links are cases of simultaneous causation, they give us no reason to believe in the existence of direct causation. I have not explored other alternative pictures here (for example, those involving overlap), but it has been enough to provide at least one plausible alternative picture which fits their assumptions but does not involve simultaneous causation. There may indeed be simultaneous causation, but Huemer & Kovitz's argument has not established this. II. CAUSAL CHAINS ON HUEMER & KOVITZ’S PICTURE Huemer & Kovitz's picture may even seem to imply the stronger conclusion: that all causation is simultaneous, and that there can be no indirect causation, in the sense of causal connections that are mediated by temporally intervening events. Huemer denies this in personal correspondence. He claims that not all causation is simultaneous on this picture. He says: ‘Clearly, we wouldn’t want to say “all causation is simultaneous,” since we would not want to deny, for example, that my setting the alarm clock at night causes it to go off the following morning. I would just say that some process must have been going on continuously in the clock during the interim.’ (personal correspondence) However, Huemer & Kovitz do not explain in their article how there can be non-simultaneous causation on their picture. They have said that all direct causation is simultaneous, so it follow that any non-simultaneous causation must be indirect. But they do not give any examples of indirect causation or explain how it works. How is indirect causation mediated by a causal process on Huemer & Kovitz's picture? They cannot say that it will be mediated by direct causal links on their picture, for they have said that all direct causation is simultaneous. Building up an indirect causal chain by linking together many direct simultaneous links in a Humean way will still only give a simultaneous link. Linking together causes at zero distance from each other will never reach a non-zero distance. This worry dates back to Hume: ‘[I]f one cause were co-temporary with its effect, and this effect with its effect, and so on, ‘tis plain there wou’d be no such thing as succession, and all objects must be co-existent.’). So Huemer & Kovitz owe us an explanation of what a causal process is, how causal processes avoids action at a temporal distance in Hume's sense, and how direct causal links relate to causal processes. In answer to the last question, perhaps an obvious answer is that simultaneous causal links join to a causal process by overlapping with it. For example: At time t0: event d (a force) simultaneously causes event b1 (the velocity of a particle), At times t: t0 ≤ t ≤ tn: causal process b1, …bn At time tn: bn (the velocity of a particle at time tn) simultaneously causes e (the velocity of a second particle). In Section IV, we will examine this picture further and compare it to Mumford & Anjum's picture. III. MUMFORD & ANJUM’S ARGUMENTS Mumford & Anjum (2011) also argue for the possibility of simultaneous causation. Indeed they go further and claim that causation is always simultaneous. This claim is part of their Powers Theory of Causation, a theory where causation involves the transfer of powers or dispositions. I will not be able to fully evaluate the Powers Theory in this paper. So, it is possible that they make an indirect case for the claim that all causation is simultaneous by way of arguing that the Powers Theory of Causation is more successful than any other theories of causation. Furthermore, there are some details in the Powers Theory that Mumford & Anjum say gives support to the simultaneity of causation that I cannot evaluate because I do not think they have presented them in enough detail. For example, they argue at various points that cause and effect are really one event rather than two, and that this supports the claim that all causation is simultaneous. (‘Maybe causation involves just one thing: a single event or process in which one thing gradually turns into another…’)16 I think this view needs further development before we can evaluate it. However, the arguments Mumford & Anjum do give are interesting and certainly worth examining. I begin by examining an argument I shall call the Billiard Ball Argument, and then proceed by examining arguments I have called the Arbitrary Temporal Gap Argument and the Regress Argument. III.1 The Billiard Ball Argument Mumford & Anjum argue that the standard paradigm examples of non-simultaneous causation are actually cases of simultaneous causation. They give the example of a billiard ball a hitting ball b which rolls off. They then argue that causation does not occur until the two billiard balls touch and it is over once they leave each other. What happens in the path and direction taken by ball a while it rolls is just the story of how it got to the point of impact. It is the impact that is causally efficacious, not how ball a got to the point of impact…Ball b does indeed roll away after the impact but isn’t this the story of what happened after the causation occurred? Doesn’t this case of causation complete itself with the impact?17 Their argument seems to be as follows: Anything that happens before the impact with ball b is not part of a cause of the impact (or anything that happens after the impact), but rather the story of what happened beforehand. Anything that happens after the impact is not part of the effect, but rather the story of what happened afterwards. Therefore, in this case causation is simultaneous. This is an interesting argument in that it seems to appeal to some intuitions we have that causation is simultaneous. In their eyes, the claim that all causation is simultaneous, far from being a wildly unpopular and counterintuitive claim as I have presented it does have some intuitive support. Indeed they do say at one point that it is ‘an attractive and intuitive view and we need some good arguments if they are to count against it…’.18 Another intuition that they may be relying on here is the view that causation is only occasional, or even fleeting (in this case, that it only occurs at the moment of impact). Again, this is unusual in the literature. Causation is often talked of as the cement of the universe, meaning the relation holding all events together.19 For Mumford & Anjum, causation seems to be the relation that holds some events together and one presumes that the other events are held together in some other way, or not held together at all. The Standard Modern Picture I outline in Section 1 assumes the opposite: that causation is dense in the sense that for any causal process, there are causes at every instant of that process. I do find something quite persuasive in Mumford & Anjum's claim that causation only happens at the moment of impact, but I suspect that they are tempting us to misinterpret our intuitions of the relative importance of causal factors as signs that causation is occasional. Although there are numerous causal interactions involved in a collision, it is the moment of collision that is most interesting and salient to the reader, so we are tempted to overlook other causal factors. Should we agree with Mumford & Anjum that ‘it is the impact that is causally efficacious, not how ball a got to the point of impact’? Surely this depends on what it is supposed to be causally efficacious of. To the extent that this argument is persuasive, I think it is because readers are allowed to equivocate on what is the relevant effect. I think that how ball a got to the point of impact is a cause of some events or event aspects and not others. For example, it may be a cause of the direction in which ball b rolls off. We are invited to focus only on the impact. But, as Mumford & Anjum acknowledge, the collision is actually extended over a short period of time. (‘Very slightly, when the balls collide, both a and b deform. They are not perfectly rigid. They squash ever so slightly against each other and then a pushes b away.’) On the Standard Modern Picture, any two events in this short causal process are connected by a continuous chain of intervening events. Suppose that this short causal process is part of a longer causal process that begins before the collision and ends after the collision. According to the Standard Modern Picture, any two events in this longer causal process are connected by an infinite chain of intervening events. It follows from this that some things that happen before the collision are part of a cause of (some events of) the collision. So we can reject premise (1). Similarly, we can reject premise (2) I expect that Mumford & Anjum will reject this reply because they hold that different processes are linked not by causation but by enabling each other. I return to this claim in Section IV. But I think it is fair to say that the billiard ball example cannot make a persuasive case alone (independently from the case they make for their whole theory of causation). Moving on, the next two arguments from Mumford & Anjum are both related to an earlier argument from Dummett and Russell which Mumford & Anjum reject.20 Mumford & Anjum present it as one argument but it seems to me that there are at least two separate lines of thought. They present it, not as a knockdown proof that all causation as simultaneous but merely as a problem for the standard account. They argue as follows: If we leave a temporal gap between cause and effect, we need to provide some story about what happens in that gap … How long is the gap and why is it of exactly that length? (Op. Cit.: 106) We may reconstruct the first argument as follows: III.2 The Arbitrary Temporal Gap Argument If there is non-simultaneous causation, then there will be a temporal gap between cause and effect. If there is a temporal gap between cause and effect, then we are lacking an explanation of the length of the gap. Therefore, all causation is simultaneous. However, this argument overlooks the possibility that there is no direct causation and between any two events there are further events explaining the time between the two. If the Standard Modern Picture is correct, then there is a temporal interval between any cause and effect but it is mediated by a continuous (i.e., non-gappy) chain of intermediaries determining the length of the interval between cause and effect, so we should reject premise (2). The length of the interval is explained by the length of the chain of intermediaries. The argument also overlooks the Contiguous Extended Picture presented above. Suppose the Contiguous Extended Picture is correct, and first consider the case of direct causation. There is no temporal gap between cause and effect, so we can reject premise (1). Next consider the case of indirect causation. Here the length of the interval between cause and effect is explained by the length of the chain of intermediaries, so we can reject premise (2). Note that I have argued elsewhere (together with …) that a version of the arbitrary temporal gap argument works. We used a version of this argument to argue that any creation of fictional characters must be simultaneous. The reason why the temporal gap argument it works in this limited case is that we used an additional premise: it is implausible that there any mechanisms that mediate between the concrete and abstract realms.21 Here is a related argument from Mumford & Anjum, appealing to the idea that there must be a cause in order to end a temporal gap. I have called it The Regress Argument. Suppose we have some assemblage of causes: then either their effect begins as soon as the causes are assembled, which [is] the position we will defend, or it doesn’t. Suppose it doesn’t and there is some gap between cause and effect. Then what, after such a gap, produces the effect? One might say that nothing makes the effect occur, after the gap, conceding that one cannot answer the question. Alternately, one might say that something more does occur that explains why the effect did eventually happen after a time interval. But then shouldn’t this further factor be considered one of the causes of the effect, among the others, and shouldn’t we then say that once it is in place, along with everything else, then the effect occurs immediately? If we deny this, and allow a gap between this assemblage of causes and its effect, we are left with exactly the same question again. (Op. Cit.: 111) Here is my reconstruction of the argument: III.3 The Regress Argument If there is non-simultaneous causation between the assemblage of causes and its effect, then there is a temporal gap between them. Suppose then that there is a temporal gap between {c} and e, where {c} is an assemblage of causes for effect e. Then there must exist another cause, f, in order to bring e about. But then f is part of the assemblage of causes for effect e. Suppose then that there is a temporal gap between {c, f} and e, where {c, f} is an assemblage of causes for effect e. But then there must exist another cause, g, in order to bring e about. This is an infinite regress. Therefore, all causation is simultaneous. A first problem with this argument is that premise (1) is false. On both the Standard Modern Picture and the Contiguous Extended Picture outlined above, we have no temporal gaps, and no simultaneous causation. Mumford & Anjum do acknowledge one way out of the argument, though they do not seem to anticipate models of causation where spacetime is dense will also avoid their argument. They say, ‘The cause and effect could be spatially adjacent without overlapping but with no temporal gap between them, presumably because they occupy adjacent spacetime points, which is possible if spacetime is discrete rather than dense…’22 Here they have anticipated a discrete version of the Contiguous Picture. The Contiguous Extended Picture I presented above is a model that assumes that spacetime is dense but still allows temporally contiguous (adjacent) events. The Standard Modern Picture is also a model that assumes that spacetime is dense. There seems to be another problem with this argument. How to explain it depends on how we interpret the phrase ‘assemblage of causes’ in this argument. One way to interpret the phrase ‘assemblage of causes’ is as a set of all causes that are sufficient for an effect. With this interpretation, steps (2) and (4) presuppose that once factors that are sufficient for a cause to occur are present then the effect will occur immediately, that is, with no time delay. The restriction against sufficient causes acting at a temporal distance is a restriction to what have been called ‘iron laws’.23 Armstrong distinguishes between laws that entail an effect come what may (iron laws) and laws that entail an effect only absent interfering conditions (oaken laws).24 We imagine laws of magic as reaching across time. Once a dose of delayed-action-mouse-maker is swallowed, the victim will be transformed into a mouse at 9 am the next morning (as in The Witches, Dahl 1983). This is irreversible; nothing can be done in the meantime to prevent the outcome. But is the actual world like this? Armstrong tentatively suggests otherwise. (‘It has been suggested… that the law of the disintegration of the radium atom, like other quantum laws, is a probabilistic but iron law. Under all physically possible circumstances, there is the same objective probability that, over a certain time-interval, the atom will disintegrate….’).25 Another way to interpret the phrase ‘assemblage of causes’ is just as the total set of causes that were present for a particular effect. This need not be a sufficient set but we are presupposing that the effect occurred. 26 It still seems to be an open question whether the assemblage of causes in this sense can act at a temporal distance. Mumford & Anjum are relying on the assumption that the actual laws of nature do not reach across time in this way. Again, a probabilistic iron law such as the one suggested above would violate this assumption. IV. CAUSAL CHAINS ON MUMFORD AND ANJUM’S PICTURE? In Section II, we saw that Huemer & Kovitz allow for extended causal chains by linking episodes of simultaneous causation with extended causal processes. Mumford & Anjum, on the other hand, insist that all causation is simultaneous. This amounts to a denial of the existence of causal chains. Instead they claim that causation involves overlapping temporally extended processes, which are not linked by causation, but rather by enabling each other.27 (‘[W]e can have any number of overlapping processes, some of which enable each other and contribute to each other but not in a way that should be understood by the dispositionalist as causal.’)28 So it seems that they have replaced the notion of a causal chain with the notion of an enabling chain. One example they give is of dissolving sugar in tea: ‘The sugar being dissolved did not cause the sweet tea to be drunk. It may have enabled the drinking of sweet tea… but it didn’t cause it.’29 The crucial role of this distinction between causation and enabling for Mumford & Anjum is one big difference between their view and other modern theories of causation. This distinction also helps us to understand their view that causation is fleeting or occasional. With the Standard Modern Picture, even in an uneventful period of time, with an object quietly persisting in an unchanging state, we have a causal process dense with causation. As I said above, Mumford & Anjum's view of causation as being only occasional or fleeting is at odds with the intuitive picture of causation as the cement of the universe holding all events together, but presumably the enabling relation is now playing part of this role. In my view, a thorough evaluation of the Powers Theory of Causation would depend on seeing a more detailed analysis of the enabling relation. V. CONCLUSION In this paper, I have considered several alternative general pictures of causation, some of which countenance simultaneous causation and some of which do not. I have not decided between these pictures, though I have rejected claims that pictures countenancing simultaneous causation are forced upon us. I do remain open minded that arguments proving the actual or possible existence of existence of simultaneous causation may come to light in future. Along the way, we have seen two modern pictures of causation where causation is non-simultaneous: the Standard Modern Picture and the Contiguous Extended Picture. I think one interesting question is which of these modern pictures has been assumed by those who have presented non-simultaneous analyses of causation in the past century. (Another interesting question is whether one is preferable to another.) The standard twentieth century analyses of causation, the counterfactual and modern regularity theories, usually have no requirements of temporal or spatial contiguity. Hume's requirement is not commonly mentioned either, though discomfort with the notion of action at a temporal distance is occasionally expressed. On the other hand, I have not seen any prohibitions against contiguity either, so it seems to me that the most popular modern picture of causation does not decide between the Standard Modern Picture and the Continuous Extended Picture or a combination of the two.30,31 Footnotes 1 ‘Some pretend that it is not absolutely necessary a cause should precede its effect; but that any object or action, in the very first moment of its existence, may exert its productive quality, and give rise to another object or action, perfectly co-temporary with itself. But beside that experience in most instances seems to contradict this opinion, we may establish the relation of priority by a kind of inference or reasoning…’ (Hume 1739: section ii). 2 ‘The great majority of efficient natural causes are simultaneous with their effects, and the sequence in time of the latter is due only to the fact that the cause cannot achieve its complete effect in one moment. But in the moment in which the effect first comes to be, it is invariably simultaneous with the causality of the cause. If the cause should have ceased to exist a moment before, the effect would never have come to be.’ (Kant 1781: A 203). 3 ‘[A] continuous temporal structure requires a simultaneous view of causation, given one plausible auxiliary assumption…. The impossibility of action at a temporal distance.’ ( Huemer and Kovitz 2003: 561). 4 Note that there are other senses of ‘direct cause’ in circulation: this phrase has been used to denote causes that are not mediated in specific technical senses. For example, Lewis’ counterfactual account of causation is sometimes stated in the following way: c is a direct cause of e iff if c hadn’t happened then e would not have happened, and c is an indirect cause of e iff c is connected to e by a chain of direct causes in the foregoing sense. (See for example, Bigelow and Pargetter 1991: 316. Lewis himself uses the term ‘causal dependence’ instead of ‘direct causation’.) But there may be events in the same causal process temporally located between c and e even when c is a direct cause of e in this sense. ‘Direct cause’ is also used in a technical sense in the causal modelling literature to denote a causal influence that is not mediated by other variables. (For example, see Hitchcock 2016.) 5 A Treatise of Human Nature, 1739, I iii, 2. 6 Current scientists are mostly in agreement that time and space have the structure of the continuum. Although there has been some talk about quantized time, there doesn’t seem to be experimental evidence for quantized time, or any well worked-out theories involving quantized time. For example, see 〈http://www.scientificamerican.com/article/is-time-quantized-in-othe/〉. 7 ‘[E]very event is already a temporally extended whole, which can be divided into indefinitely many parts, each of which is itself a temporally extended event.’ [Huemer and Kovitz 2003: 560). 8 Huemer & Kovitz (2003: 562). 9 Hume (1739: I. IV, ii). 10 Le Poidevin (2003: 27). 11 Huemer & Kovitz (2003: 561–2). 12 Note that the Contiguous Extended Picture requires the existence of events that extend over open intervals as well as over closed intervals, which may seem strange, but I find to be unobjectionable. After all, the open time interval [0, 1] has the same duration as the closed time interval [0, 1], and no experimental evidence could bear on the question of whether a particular event extends over an open time interval rather than over a closed time interval. (Josh Parsons has suggested to me that this picture involves a philosophically objectionable temporal asymmetry. Also see Parsons 2006: 151). I do not share this worry, though not much is hanging on it in this paper as I shall end up defending a different picture in this paper: the Standard Modern Picture. Edwin Mares has pointed out to me that this worry about open and closed intervals dates back to William Heytesbury in the fourteenth century.) Note also that the Contiguous Extended Picture is also compatible with infinitesimals, for there are still closed time intervals contiguous with open time intervals if we accept the existence of infinitesimals. 13 This requirement can be extended to require continuous causal chains, if the notion of no gaps needs to be proven in a more rigorous way. 14 Unless one has independent motivation for believing in simultaneous causation. 15 The following quote from Shoemaker (stating what he calls a ‘rather commonly supposed’ view) makes a similar point: ‘If time is dense or continuous, of course, we cannot in any case speak of a change as being caused by the state of the world at the immediately preceding instant, for in that case there is no immediately preceding instant. But I think that it is rather commonly supposed that if an event E occurs at time t and is caused, then, for any interval i, no matter how short, that begins at some time prior to t and includes all the instants between that time and t, the sequence of world states that exist during i contains a sufficient cause of E.’ (Shoemaker 1969: 376). 16 Mumford & Anjum (2011: 113). 17 Mumford & Anjum (2011: 108). 18 Mumford & Anjum (2011: 121). 19 Mackie, using Hume's phrase from the Abstract (1740), entitles his (1974) book on causation The Cement of the Universe. 20 The Russell/Dummett argument, sometimes called the bilking argument, claims that if there were a temporal gap between cause and effect then something could intervene in the gap and prevent the effect from occurring. I will not discuss the Russell/Dummett argument further, because it has already been thoroughly discussed and rejected in the literature. See, for example, Mumford & Anjum (2011: ch. 3), Ehring (1987) and Le Poidevin (2003: 226–7). 21 ‘Suppose that Tolstoy creates Anna Karenina at time t, by writing some sentences. When does the event of Anna's coming into existence occur? It would be implausible to postulate a time delay, say of exactly 3 minutes, or even of a split second, as it is implausible that there is a space-time mechanism mediating between the concrete and abstract realms. So the Creationist must surely claim that the events of Anna's coming into being and the event of Tolstoy's writing those sentences are simultaneous.’ (Brock, Maslen and Ngai 2013) 22 Mumford & Anjum (2011: 112). 23 We imagine laws of magic as reaching across time. Once a dose of delayed-action-mouse-maker is swallowed, the victim will be transformed into a mouse at 9 am the next morning (as in Dahl 1983). This is irreversible; nothing can be done in the meantime to prevent the outcome. But is the actual world like this? Armstrong distinguishes between laws that entail an effect come what may (iron laws) and laws that entail an effect only absent interfering conditions (oaken laws) (1983: 149). Ehring narrows this to ‘laws such that given the occurrence of c in the circumstance at a time t1, e will occur at t2 no matter how the circumstances change after t1’ (1987: 29). ‘It has been suggested… that the law of the disintegration of the radium atom, like other quantum laws, is a probabilistic but iron law. Under all physically possible circumstances, there is the same objective probability that, over a certain time-interval, the atom will disintegrate….’ (Armstrong:1983: 148). 24 Armstrong (1983: 149). Ehring narrows this to ‘laws such that given the occurrence of c in the circumstance at a time t1, e will occur at t2 no matter how the circumstances change after t1’ (1987: 29). 25 Armstrong (1983: 148). 26 Thank you to an anonymous referee for this journal for pointing out to me that Mumford & Anjum are not committed to sufficient causes in this Regress Argument. 27 ‘A key point to note in this model is that one causal process is not seen as the cause of another but only as an enabler; thus, we do not need to invoke causation between temporally distinct events’ (Mumford and Anjum 2011: 126). 28 Mumford & Anjum (2011: 127–8). 29 Mumford & Anjum (2011: 125). 30 The Standard Modern Picture involves a kind of density of causation within causal processes: on magnifying any part of a causal process, it predicts that there will always be further causal processes in shorter and shorter time frames. Regularity and counterfactual theorists do not normally provide a definition of causal process. I think that a simple notion of causal process is usually assumed however. We can call it the Humean notion of causal process. Let us say that events {e1, e2 e3 …en} are part of the same causal process iff e1 causes e2 which causes e3… which causes en. The Standard Modern Picture also seems to require another assumption: that whenever f is part of a causal process, then there are parts of f: {f1, f2 f3 …fn} , such that f1, f2 f3 …fn are also parts of that same causal process. 31 With particular thanks to Edwin Mares, Bradley Monton, Josh Parsons, Neil Sinhababu, and two anonymous referees for this journal for comments on earlier drafts of this paper. REFERENCES Armstrong D. ( 1983) What is a Law of Nature?  Cambridge: CUP. Bigelow J., Pargetter R. ( 1991) Science and Necessity . Cambridge: CUP. Google Scholar CrossRef Search ADS   Brand M. ( 1980) ‘ Simultaneous Causation’, in Van Inwagen P. (ed.), Time and Cause . Dordrecht: Reidel Publishing, 137– 53. Brock S., Maslen C., Ngai J. ( 2013) ‘ How to Create a Fictional Character’, in Barbero C., Ferraris M., Voltolini A. (eds) From Fictionalism to Realism – Fictional and Other Social Entities . 63– 86. Newcastle upon Tyne: Cambridge Scholars Publishing. Dahl R. ( 1983) The Witches . New York: Puffin, 2007 reprint. Dummett M. ( 1978) Truth and Other Enigmas . Duckworth. Ehring D. ( 1987) ‘ Non-simultaneous Causation’, Analysis , 47: 28– 32. Google Scholar CrossRef Search ADS   Hall N., Paul L.A. ( 2013) Causation: A Users Guide . Oxford: OUP. Google Scholar CrossRef Search ADS   Hitchcock C. ( 2016) ‘ Probabilistic Causation’, in Zalta E. N. (ed.), The Stanford Encyclopedia of Philosophy  (Winter 2016 Edition), 〈https://plato.stanford.edu/archives/win2016/entries/causation-probabilistic/〉 accessed June 2017. Huemer M., Kovitz B. ( 2003) ‘ Causation as Simultaneous and Continuous’, The Philosophical Quarterly , 53: 556– 65. Google Scholar CrossRef Search ADS   Hume D. [presumed], ( 1740) Abstract of a Book Lately Published Entitled A Treatise of Human Nature . London: Macmillan. Hume D. ( 1739) A Treatise of Human Nature . Brigge S. (ed.), 1888. Oxford: Clarendon Press. Le Poidevin R. ( 2003) Travels in Four Dimensions . Oxford: OUP. Lewis D. ( 1973) ‘ Causation’, The Journal of Philosophy , 70: 556– 67 and Postscripts, 1986. Google Scholar CrossRef Search ADS   Mackie J. L. ( 1974) The Cement of the Universe: A Study of Causation . Oxford: Clarendon Press. Mumford S., Anjum R. ( 2011) Getting Causes from Powers . Oxford: OUP. Google Scholar CrossRef Search ADS   Parsons J. ( 2006) ‘ Topological Drinking Problems’, Analysis , 66: 149– 54. Google Scholar CrossRef Search ADS   Shoemaker S. ( 1969) ‘ Time without Change’, The Journal of Philosophy , 66: 363– 81. Google Scholar CrossRef Search ADS   © The Author 2017. Published by Oxford University Press on behalf of The Scots Philosophical Association and the University of St Andrews. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Philosophical Quarterly Oxford University Press

The case for widespread simultaneous causation

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Abstract In this paper, I examine recent arguments for the widespread existence of simultaneous causation from Huemer & Kovitz and Mumford & Anjum, and conclude that they are mistaken. I argue that these arguments overlook two pictures of causation which are commonly assumed, which I call the Standard Modern Picture and the Contiguous Extended Picture. In this paper, I examine recent arguments for the widespread existence of simultaneous causation from Huemer & Kovitz and Mumford & Anjum and conclude that they are mistaken. It will be helpful to position this in the recent history of views on simultaneous causation. I think it is fair to say that the current mainstream philosophical view on simultaneous causation is that there is no simultaneous causation: it is ruled out either on physical or logical grounds. The view that simultaneous causation is logically impossible dates back at least to Hume.1 Many recent philosophers agree with Hume that simultaneous causation does not occur, but not with the claim that it is logically impossible. The guiding idea here seems to be that it is not the place of philosophy to dictate to current physics. For example, Lewis says that stipulating that a cause must always precede its effect ‘rejects a priori certain legitimate physical hypotheses that posit backward or simultaneous causation’ (1973: 170) On the other hand, Hall & Paul, both students of Lewis, are comfortable in following Hume in ruling out simultaneous causation by fiat accompanied with the advice that ‘simultaneous causation need not be taken too seriously’ (2013: 17). A contrary strand of thought on simultaneous causation dates back at least to Kant. This holds not just that simultaneous causation does in fact occur, but moreover that the majority of real-life cases of causation are simultaneous.2 Dummett (1978) and Brand (1980) defended versions of this view. But it has more recently come back into fashion, especially with defenders of the Powers Theory of Causation. In this paper, I focus on arguments from Huemer & Kovitz (2003) and Mumford & Anjum (2011) that make interesting new contributions to this line of thinking. I. HUEMER & KOVITZ’S ARGUMENT Huemer & Kovitz argue that all causes are simultaneous with their direct effects.3 Let us define the term direct cause as follows: event c is a direct cause of event e if and only if c is a cause of e and there are no events in the same causal process temporally located between c and e. Direct causation is ‘immediate’ in the sense of not being mediated by any intervening events, and the term immediate cause will be used interchangeably with the term direct cause. Huemer & Kovitz do not give a definition of the terms ‘direct cause’ and ‘immediate cause’ in their article, but I presume that they have the preceding sense in mind.4 Huemer & Kovitz begin by describing Hume's quantized view of time: there are smallest indivisible units of time (which we can call moments), and any moment has a next moment. Corresponding to these smallest moments, there are indivisible atomic events. On Hume's Sequential View of Causation, indirect causation is by way of a causal chain, and every causal chain is built out of direct causal links between atomic events that are contiguous to each other (i.e., spatially and temporally adjacent). As Hume points out, it cannot be that all causation is simultaneous on his view, for we cannot build up any extended causal chains using only links of zero length. ‘If one cause were co-temporary with its effect, and this effect with its effect, and so on, ‘tis plain there wou’d be no such thing as succession, and all objects must be co-existent.’5 Hume's view of time is outdated. Most philosophers now adopt the modern view that time has the mathematical structure of the continuum.6 This is incompatible with Hume's talk of the next instant of time, as the modern view implies that between any two points in time there is another point in time. Huemer & Kovitz propose to replace Hume's Sequential View of Causation with a view they call the Simultaneous Conception of Causation that is consistent with the modern view of time. On their view, causes and effects are temporally extended events, which can be divided indefinitely into further events.7 Then all direct causation is simultaneous: direct causation is always between a temporally extended cause and a simultaneous temporally extended effect. To illustrate this, consider Kant's example of a ball resting on a cushion. On Huemer & Kovitz's view, the event of the presence of a ball on a cushion extending over time interval Δt causes the event of the indentation in the cushion extending over the very same time interval Δt. Huemer & Kovitz do not merely present the Simultaneous Conception of Causation as one picture that is consistent with the Modern Conception of Time. They argue that their picture logically follows from the Modern Conception of Time in conjunction with another widely accepted and plausible principle about causation. They also do more than just claim that simultaneous causation is possible and occasionally occurs; they claim that simultaneous causation is common. The focus of this section is Huemer & Kovitz's argument that ‘in a world with a continuous temporal structure and no action at a temporal distance, then, a cause cannot precede its immediate effect: they must be simultaneous’.8 Crucial here is their application of Hume's restriction against action at a temporal distance. As Hume states it, the principle is that ‘nothing can operate in a time or place which is ever so little remov’d from those of its existence’.9 One way to understand this principle is as requiring intervening events in all causal processes. Empty waiting periods are never efficacious. As Le Poidevin puts it, ‘The egg is ready to be consumed 5 minutes after I started to boil it, not simply because 5 minutes have passed, but because of the changes going on inside the egg throughout that time. Again it is not time that heals all wounds, but rather the (psychological physical, political) changes that go on in time that do so.’10 Note that Hume's original restriction had two parts: (1) all direct causation is between events that are next to each other in time and (2) indirect causation is mediated by chains of direct causal links. Huemer & Kovitz mention only the first part in their formulation, and do not explain their own view of indirect causation. They state Hume's restriction as follows: ‘no occurrence can be directly causally relevant to an occurrence at a non-zero temporal distance from it.’11 Contrary to Huemer & Kovitz, there seem to be a number of alternative pictures of causation that are consistent with their restriction against action at a temporal distance, but do not involve simultaneous causation. The first picture one might think of is a picture allowing temporally extended events that are contiguous. For example, an event e1 extending over an open time interval [0, 1] might directly cause an event e2 that extends over a closed time interval [1, 2]. There is zero temporal distance between the end of e1 and the start of e2 but e1 is not simultaneous with e2, so this is direct causation at a zero temporal distance without simultaneous causation. Let's call this the Contiguous Extended Picture: all causes are temporally prior to effects, direct causation is only between temporally contiguous events, and furthermore this is not an empty requirement: there does exist direct causation between temporally extended events.12 Huemer & Kovitz do mention this first alternative picture and object that the Contiguous Extended Picture does in fact involve action at a temporal distance: e1 is at a non-zero temporal distance from the second half of e2. This reply needs to stretch their stated formulation of the principle of the impossibility of action at a temporal distance: as they state it says nothing about parts of occurrences. However, let's grant them this and move on. As we shall see, we do not need to suppose that causes are ever contiguous with their direct effects. Contrary to Huemer & Kovitz's claims, there are a number of alternative pictures that are consistent with their assumptions, and we will now focus on a second alternative picture. A gap in their argument is that Huemer & Kovitz haven’t argued for the existence of any direct causation. Without this, their argument doesn’t establish the existence of any simultaneous causation. So their argument leaves room for the possibility that all causes and effects are non-simultaneous and there is no direct causation—a picture where in the causal process between every cause and effect there are intermediary causes. I am not claiming that this picture is a new picture of causation. On the contrary, I think this is a commonly assumed modern picture of causation although it is seldom explicitly stated and sometimes overlooked. In what follows, I shall call it the Standard Modern Picture (not to be tendentious, but because this is a convenient label. I discuss later in this paper the question of how common this view is in the twentieth century). Note that adopting the Standard Modern Picture of causation does require a slightly different interpretation of the restriction against action at a temporal distance. We can no longer understand the restriction against action at a temporal distance as requiring every cause to be at zero temporal distance from its effects, or even connected to its effect by a chain of causes all at zero temporal distance from each other. Rather we should now understand the restriction against action at a temporal distance as requiring every cause to be connected to its effect by a chain of causes with infinitely many links. It can still be true that there are no temporal gaps within causal chains; however, the understanding of ‘no temporal gaps’ can no longer be understood as requiring chains of causes all at zero temporal distance from each other, but rather as requiring temporally dense causal chains: between any two events in the causal chain there is a third.13 Also note that it is not part of the Standard Modern Picture that all events are instantaneous. They can be of any length. But this picture places no restriction on how short an event can be, thus allowing for infinite chains of events between any two non-contiguous events. The Standard Modern Picture dispenses with direct causation. But do we have any good reasons for believing in direct causation? On Hume's Sequential View of Causation, indirect causation always requires direct causation: indirect causation requires a chain of direct causal links between atomic events. However, once we abandon Hume's quantized view of time in favour of a continuous view of time, there seems to be no reason to believe in atomic events, or to believe in direct causation at all.14 The Standard Modern Picture implies that there are infinitely many intermediate causes in every causal process, but again this seems to be a plausible view in a world with continuous temporal structure. With a few extra assumptions, it even follows from the standard regularity and counterfactual analyses of causation that all causal processes are dense in this sense. To put it briefly, causal theorists often assume determinism, and if instantaneous world states are permitted as causal relata, this would provide any given event with causes at every earlier time.15 So, in conclusion, although Huemer & Kovitz are right that given some assumptions the only direct causal links are cases of simultaneous causation, they give us no reason to believe in the existence of direct causation. I have not explored other alternative pictures here (for example, those involving overlap), but it has been enough to provide at least one plausible alternative picture which fits their assumptions but does not involve simultaneous causation. There may indeed be simultaneous causation, but Huemer & Kovitz's argument has not established this. II. CAUSAL CHAINS ON HUEMER & KOVITZ’S PICTURE Huemer & Kovitz's picture may even seem to imply the stronger conclusion: that all causation is simultaneous, and that there can be no indirect causation, in the sense of causal connections that are mediated by temporally intervening events. Huemer denies this in personal correspondence. He claims that not all causation is simultaneous on this picture. He says: ‘Clearly, we wouldn’t want to say “all causation is simultaneous,” since we would not want to deny, for example, that my setting the alarm clock at night causes it to go off the following morning. I would just say that some process must have been going on continuously in the clock during the interim.’ (personal correspondence) However, Huemer & Kovitz do not explain in their article how there can be non-simultaneous causation on their picture. They have said that all direct causation is simultaneous, so it follow that any non-simultaneous causation must be indirect. But they do not give any examples of indirect causation or explain how it works. How is indirect causation mediated by a causal process on Huemer & Kovitz's picture? They cannot say that it will be mediated by direct causal links on their picture, for they have said that all direct causation is simultaneous. Building up an indirect causal chain by linking together many direct simultaneous links in a Humean way will still only give a simultaneous link. Linking together causes at zero distance from each other will never reach a non-zero distance. This worry dates back to Hume: ‘[I]f one cause were co-temporary with its effect, and this effect with its effect, and so on, ‘tis plain there wou’d be no such thing as succession, and all objects must be co-existent.’). So Huemer & Kovitz owe us an explanation of what a causal process is, how causal processes avoids action at a temporal distance in Hume's sense, and how direct causal links relate to causal processes. In answer to the last question, perhaps an obvious answer is that simultaneous causal links join to a causal process by overlapping with it. For example: At time t0: event d (a force) simultaneously causes event b1 (the velocity of a particle), At times t: t0 ≤ t ≤ tn: causal process b1, …bn At time tn: bn (the velocity of a particle at time tn) simultaneously causes e (the velocity of a second particle). In Section IV, we will examine this picture further and compare it to Mumford & Anjum's picture. III. MUMFORD & ANJUM’S ARGUMENTS Mumford & Anjum (2011) also argue for the possibility of simultaneous causation. Indeed they go further and claim that causation is always simultaneous. This claim is part of their Powers Theory of Causation, a theory where causation involves the transfer of powers or dispositions. I will not be able to fully evaluate the Powers Theory in this paper. So, it is possible that they make an indirect case for the claim that all causation is simultaneous by way of arguing that the Powers Theory of Causation is more successful than any other theories of causation. Furthermore, there are some details in the Powers Theory that Mumford & Anjum say gives support to the simultaneity of causation that I cannot evaluate because I do not think they have presented them in enough detail. For example, they argue at various points that cause and effect are really one event rather than two, and that this supports the claim that all causation is simultaneous. (‘Maybe causation involves just one thing: a single event or process in which one thing gradually turns into another…’)16 I think this view needs further development before we can evaluate it. However, the arguments Mumford & Anjum do give are interesting and certainly worth examining. I begin by examining an argument I shall call the Billiard Ball Argument, and then proceed by examining arguments I have called the Arbitrary Temporal Gap Argument and the Regress Argument. III.1 The Billiard Ball Argument Mumford & Anjum argue that the standard paradigm examples of non-simultaneous causation are actually cases of simultaneous causation. They give the example of a billiard ball a hitting ball b which rolls off. They then argue that causation does not occur until the two billiard balls touch and it is over once they leave each other. What happens in the path and direction taken by ball a while it rolls is just the story of how it got to the point of impact. It is the impact that is causally efficacious, not how ball a got to the point of impact…Ball b does indeed roll away after the impact but isn’t this the story of what happened after the causation occurred? Doesn’t this case of causation complete itself with the impact?17 Their argument seems to be as follows: Anything that happens before the impact with ball b is not part of a cause of the impact (or anything that happens after the impact), but rather the story of what happened beforehand. Anything that happens after the impact is not part of the effect, but rather the story of what happened afterwards. Therefore, in this case causation is simultaneous. This is an interesting argument in that it seems to appeal to some intuitions we have that causation is simultaneous. In their eyes, the claim that all causation is simultaneous, far from being a wildly unpopular and counterintuitive claim as I have presented it does have some intuitive support. Indeed they do say at one point that it is ‘an attractive and intuitive view and we need some good arguments if they are to count against it…’.18 Another intuition that they may be relying on here is the view that causation is only occasional, or even fleeting (in this case, that it only occurs at the moment of impact). Again, this is unusual in the literature. Causation is often talked of as the cement of the universe, meaning the relation holding all events together.19 For Mumford & Anjum, causation seems to be the relation that holds some events together and one presumes that the other events are held together in some other way, or not held together at all. The Standard Modern Picture I outline in Section 1 assumes the opposite: that causation is dense in the sense that for any causal process, there are causes at every instant of that process. I do find something quite persuasive in Mumford & Anjum's claim that causation only happens at the moment of impact, but I suspect that they are tempting us to misinterpret our intuitions of the relative importance of causal factors as signs that causation is occasional. Although there are numerous causal interactions involved in a collision, it is the moment of collision that is most interesting and salient to the reader, so we are tempted to overlook other causal factors. Should we agree with Mumford & Anjum that ‘it is the impact that is causally efficacious, not how ball a got to the point of impact’? Surely this depends on what it is supposed to be causally efficacious of. To the extent that this argument is persuasive, I think it is because readers are allowed to equivocate on what is the relevant effect. I think that how ball a got to the point of impact is a cause of some events or event aspects and not others. For example, it may be a cause of the direction in which ball b rolls off. We are invited to focus only on the impact. But, as Mumford & Anjum acknowledge, the collision is actually extended over a short period of time. (‘Very slightly, when the balls collide, both a and b deform. They are not perfectly rigid. They squash ever so slightly against each other and then a pushes b away.’) On the Standard Modern Picture, any two events in this short causal process are connected by a continuous chain of intervening events. Suppose that this short causal process is part of a longer causal process that begins before the collision and ends after the collision. According to the Standard Modern Picture, any two events in this longer causal process are connected by an infinite chain of intervening events. It follows from this that some things that happen before the collision are part of a cause of (some events of) the collision. So we can reject premise (1). Similarly, we can reject premise (2) I expect that Mumford & Anjum will reject this reply because they hold that different processes are linked not by causation but by enabling each other. I return to this claim in Section IV. But I think it is fair to say that the billiard ball example cannot make a persuasive case alone (independently from the case they make for their whole theory of causation). Moving on, the next two arguments from Mumford & Anjum are both related to an earlier argument from Dummett and Russell which Mumford & Anjum reject.20 Mumford & Anjum present it as one argument but it seems to me that there are at least two separate lines of thought. They present it, not as a knockdown proof that all causation as simultaneous but merely as a problem for the standard account. They argue as follows: If we leave a temporal gap between cause and effect, we need to provide some story about what happens in that gap … How long is the gap and why is it of exactly that length? (Op. Cit.: 106) We may reconstruct the first argument as follows: III.2 The Arbitrary Temporal Gap Argument If there is non-simultaneous causation, then there will be a temporal gap between cause and effect. If there is a temporal gap between cause and effect, then we are lacking an explanation of the length of the gap. Therefore, all causation is simultaneous. However, this argument overlooks the possibility that there is no direct causation and between any two events there are further events explaining the time between the two. If the Standard Modern Picture is correct, then there is a temporal interval between any cause and effect but it is mediated by a continuous (i.e., non-gappy) chain of intermediaries determining the length of the interval between cause and effect, so we should reject premise (2). The length of the interval is explained by the length of the chain of intermediaries. The argument also overlooks the Contiguous Extended Picture presented above. Suppose the Contiguous Extended Picture is correct, and first consider the case of direct causation. There is no temporal gap between cause and effect, so we can reject premise (1). Next consider the case of indirect causation. Here the length of the interval between cause and effect is explained by the length of the chain of intermediaries, so we can reject premise (2). Note that I have argued elsewhere (together with …) that a version of the arbitrary temporal gap argument works. We used a version of this argument to argue that any creation of fictional characters must be simultaneous. The reason why the temporal gap argument it works in this limited case is that we used an additional premise: it is implausible that there any mechanisms that mediate between the concrete and abstract realms.21 Here is a related argument from Mumford & Anjum, appealing to the idea that there must be a cause in order to end a temporal gap. I have called it The Regress Argument. Suppose we have some assemblage of causes: then either their effect begins as soon as the causes are assembled, which [is] the position we will defend, or it doesn’t. Suppose it doesn’t and there is some gap between cause and effect. Then what, after such a gap, produces the effect? One might say that nothing makes the effect occur, after the gap, conceding that one cannot answer the question. Alternately, one might say that something more does occur that explains why the effect did eventually happen after a time interval. But then shouldn’t this further factor be considered one of the causes of the effect, among the others, and shouldn’t we then say that once it is in place, along with everything else, then the effect occurs immediately? If we deny this, and allow a gap between this assemblage of causes and its effect, we are left with exactly the same question again. (Op. Cit.: 111) Here is my reconstruction of the argument: III.3 The Regress Argument If there is non-simultaneous causation between the assemblage of causes and its effect, then there is a temporal gap between them. Suppose then that there is a temporal gap between {c} and e, where {c} is an assemblage of causes for effect e. Then there must exist another cause, f, in order to bring e about. But then f is part of the assemblage of causes for effect e. Suppose then that there is a temporal gap between {c, f} and e, where {c, f} is an assemblage of causes for effect e. But then there must exist another cause, g, in order to bring e about. This is an infinite regress. Therefore, all causation is simultaneous. A first problem with this argument is that premise (1) is false. On both the Standard Modern Picture and the Contiguous Extended Picture outlined above, we have no temporal gaps, and no simultaneous causation. Mumford & Anjum do acknowledge one way out of the argument, though they do not seem to anticipate models of causation where spacetime is dense will also avoid their argument. They say, ‘The cause and effect could be spatially adjacent without overlapping but with no temporal gap between them, presumably because they occupy adjacent spacetime points, which is possible if spacetime is discrete rather than dense…’22 Here they have anticipated a discrete version of the Contiguous Picture. The Contiguous Extended Picture I presented above is a model that assumes that spacetime is dense but still allows temporally contiguous (adjacent) events. The Standard Modern Picture is also a model that assumes that spacetime is dense. There seems to be another problem with this argument. How to explain it depends on how we interpret the phrase ‘assemblage of causes’ in this argument. One way to interpret the phrase ‘assemblage of causes’ is as a set of all causes that are sufficient for an effect. With this interpretation, steps (2) and (4) presuppose that once factors that are sufficient for a cause to occur are present then the effect will occur immediately, that is, with no time delay. The restriction against sufficient causes acting at a temporal distance is a restriction to what have been called ‘iron laws’.23 Armstrong distinguishes between laws that entail an effect come what may (iron laws) and laws that entail an effect only absent interfering conditions (oaken laws).24 We imagine laws of magic as reaching across time. Once a dose of delayed-action-mouse-maker is swallowed, the victim will be transformed into a mouse at 9 am the next morning (as in The Witches, Dahl 1983). This is irreversible; nothing can be done in the meantime to prevent the outcome. But is the actual world like this? Armstrong tentatively suggests otherwise. (‘It has been suggested… that the law of the disintegration of the radium atom, like other quantum laws, is a probabilistic but iron law. Under all physically possible circumstances, there is the same objective probability that, over a certain time-interval, the atom will disintegrate….’).25 Another way to interpret the phrase ‘assemblage of causes’ is just as the total set of causes that were present for a particular effect. This need not be a sufficient set but we are presupposing that the effect occurred. 26 It still seems to be an open question whether the assemblage of causes in this sense can act at a temporal distance. Mumford & Anjum are relying on the assumption that the actual laws of nature do not reach across time in this way. Again, a probabilistic iron law such as the one suggested above would violate this assumption. IV. CAUSAL CHAINS ON MUMFORD AND ANJUM’S PICTURE? In Section II, we saw that Huemer & Kovitz allow for extended causal chains by linking episodes of simultaneous causation with extended causal processes. Mumford & Anjum, on the other hand, insist that all causation is simultaneous. This amounts to a denial of the existence of causal chains. Instead they claim that causation involves overlapping temporally extended processes, which are not linked by causation, but rather by enabling each other.27 (‘[W]e can have any number of overlapping processes, some of which enable each other and contribute to each other but not in a way that should be understood by the dispositionalist as causal.’)28 So it seems that they have replaced the notion of a causal chain with the notion of an enabling chain. One example they give is of dissolving sugar in tea: ‘The sugar being dissolved did not cause the sweet tea to be drunk. It may have enabled the drinking of sweet tea… but it didn’t cause it.’29 The crucial role of this distinction between causation and enabling for Mumford & Anjum is one big difference between their view and other modern theories of causation. This distinction also helps us to understand their view that causation is fleeting or occasional. With the Standard Modern Picture, even in an uneventful period of time, with an object quietly persisting in an unchanging state, we have a causal process dense with causation. As I said above, Mumford & Anjum's view of causation as being only occasional or fleeting is at odds with the intuitive picture of causation as the cement of the universe holding all events together, but presumably the enabling relation is now playing part of this role. In my view, a thorough evaluation of the Powers Theory of Causation would depend on seeing a more detailed analysis of the enabling relation. V. CONCLUSION In this paper, I have considered several alternative general pictures of causation, some of which countenance simultaneous causation and some of which do not. I have not decided between these pictures, though I have rejected claims that pictures countenancing simultaneous causation are forced upon us. I do remain open minded that arguments proving the actual or possible existence of existence of simultaneous causation may come to light in future. Along the way, we have seen two modern pictures of causation where causation is non-simultaneous: the Standard Modern Picture and the Contiguous Extended Picture. I think one interesting question is which of these modern pictures has been assumed by those who have presented non-simultaneous analyses of causation in the past century. (Another interesting question is whether one is preferable to another.) The standard twentieth century analyses of causation, the counterfactual and modern regularity theories, usually have no requirements of temporal or spatial contiguity. Hume's requirement is not commonly mentioned either, though discomfort with the notion of action at a temporal distance is occasionally expressed. On the other hand, I have not seen any prohibitions against contiguity either, so it seems to me that the most popular modern picture of causation does not decide between the Standard Modern Picture and the Continuous Extended Picture or a combination of the two.30,31 Footnotes 1 ‘Some pretend that it is not absolutely necessary a cause should precede its effect; but that any object or action, in the very first moment of its existence, may exert its productive quality, and give rise to another object or action, perfectly co-temporary with itself. But beside that experience in most instances seems to contradict this opinion, we may establish the relation of priority by a kind of inference or reasoning…’ (Hume 1739: section ii). 2 ‘The great majority of efficient natural causes are simultaneous with their effects, and the sequence in time of the latter is due only to the fact that the cause cannot achieve its complete effect in one moment. But in the moment in which the effect first comes to be, it is invariably simultaneous with the causality of the cause. If the cause should have ceased to exist a moment before, the effect would never have come to be.’ (Kant 1781: A 203). 3 ‘[A] continuous temporal structure requires a simultaneous view of causation, given one plausible auxiliary assumption…. The impossibility of action at a temporal distance.’ ( Huemer and Kovitz 2003: 561). 4 Note that there are other senses of ‘direct cause’ in circulation: this phrase has been used to denote causes that are not mediated in specific technical senses. For example, Lewis’ counterfactual account of causation is sometimes stated in the following way: c is a direct cause of e iff if c hadn’t happened then e would not have happened, and c is an indirect cause of e iff c is connected to e by a chain of direct causes in the foregoing sense. (See for example, Bigelow and Pargetter 1991: 316. Lewis himself uses the term ‘causal dependence’ instead of ‘direct causation’.) But there may be events in the same causal process temporally located between c and e even when c is a direct cause of e in this sense. ‘Direct cause’ is also used in a technical sense in the causal modelling literature to denote a causal influence that is not mediated by other variables. (For example, see Hitchcock 2016.) 5 A Treatise of Human Nature, 1739, I iii, 2. 6 Current scientists are mostly in agreement that time and space have the structure of the continuum. Although there has been some talk about quantized time, there doesn’t seem to be experimental evidence for quantized time, or any well worked-out theories involving quantized time. For example, see 〈http://www.scientificamerican.com/article/is-time-quantized-in-othe/〉. 7 ‘[E]very event is already a temporally extended whole, which can be divided into indefinitely many parts, each of which is itself a temporally extended event.’ [Huemer and Kovitz 2003: 560). 8 Huemer & Kovitz (2003: 562). 9 Hume (1739: I. IV, ii). 10 Le Poidevin (2003: 27). 11 Huemer & Kovitz (2003: 561–2). 12 Note that the Contiguous Extended Picture requires the existence of events that extend over open intervals as well as over closed intervals, which may seem strange, but I find to be unobjectionable. After all, the open time interval [0, 1] has the same duration as the closed time interval [0, 1], and no experimental evidence could bear on the question of whether a particular event extends over an open time interval rather than over a closed time interval. (Josh Parsons has suggested to me that this picture involves a philosophically objectionable temporal asymmetry. Also see Parsons 2006: 151). I do not share this worry, though not much is hanging on it in this paper as I shall end up defending a different picture in this paper: the Standard Modern Picture. Edwin Mares has pointed out to me that this worry about open and closed intervals dates back to William Heytesbury in the fourteenth century.) Note also that the Contiguous Extended Picture is also compatible with infinitesimals, for there are still closed time intervals contiguous with open time intervals if we accept the existence of infinitesimals. 13 This requirement can be extended to require continuous causal chains, if the notion of no gaps needs to be proven in a more rigorous way. 14 Unless one has independent motivation for believing in simultaneous causation. 15 The following quote from Shoemaker (stating what he calls a ‘rather commonly supposed’ view) makes a similar point: ‘If time is dense or continuous, of course, we cannot in any case speak of a change as being caused by the state of the world at the immediately preceding instant, for in that case there is no immediately preceding instant. But I think that it is rather commonly supposed that if an event E occurs at time t and is caused, then, for any interval i, no matter how short, that begins at some time prior to t and includes all the instants between that time and t, the sequence of world states that exist during i contains a sufficient cause of E.’ (Shoemaker 1969: 376). 16 Mumford & Anjum (2011: 113). 17 Mumford & Anjum (2011: 108). 18 Mumford & Anjum (2011: 121). 19 Mackie, using Hume's phrase from the Abstract (1740), entitles his (1974) book on causation The Cement of the Universe. 20 The Russell/Dummett argument, sometimes called the bilking argument, claims that if there were a temporal gap between cause and effect then something could intervene in the gap and prevent the effect from occurring. I will not discuss the Russell/Dummett argument further, because it has already been thoroughly discussed and rejected in the literature. See, for example, Mumford & Anjum (2011: ch. 3), Ehring (1987) and Le Poidevin (2003: 226–7). 21 ‘Suppose that Tolstoy creates Anna Karenina at time t, by writing some sentences. When does the event of Anna's coming into existence occur? It would be implausible to postulate a time delay, say of exactly 3 minutes, or even of a split second, as it is implausible that there is a space-time mechanism mediating between the concrete and abstract realms. So the Creationist must surely claim that the events of Anna's coming into being and the event of Tolstoy's writing those sentences are simultaneous.’ (Brock, Maslen and Ngai 2013) 22 Mumford & Anjum (2011: 112). 23 We imagine laws of magic as reaching across time. Once a dose of delayed-action-mouse-maker is swallowed, the victim will be transformed into a mouse at 9 am the next morning (as in Dahl 1983). This is irreversible; nothing can be done in the meantime to prevent the outcome. But is the actual world like this? Armstrong distinguishes between laws that entail an effect come what may (iron laws) and laws that entail an effect only absent interfering conditions (oaken laws) (1983: 149). Ehring narrows this to ‘laws such that given the occurrence of c in the circumstance at a time t1, e will occur at t2 no matter how the circumstances change after t1’ (1987: 29). ‘It has been suggested… that the law of the disintegration of the radium atom, like other quantum laws, is a probabilistic but iron law. Under all physically possible circumstances, there is the same objective probability that, over a certain time-interval, the atom will disintegrate….’ (Armstrong:1983: 148). 24 Armstrong (1983: 149). Ehring narrows this to ‘laws such that given the occurrence of c in the circumstance at a time t1, e will occur at t2 no matter how the circumstances change after t1’ (1987: 29). 25 Armstrong (1983: 148). 26 Thank you to an anonymous referee for this journal for pointing out to me that Mumford & Anjum are not committed to sufficient causes in this Regress Argument. 27 ‘A key point to note in this model is that one causal process is not seen as the cause of another but only as an enabler; thus, we do not need to invoke causation between temporally distinct events’ (Mumford and Anjum 2011: 126). 28 Mumford & Anjum (2011: 127–8). 29 Mumford & Anjum (2011: 125). 30 The Standard Modern Picture involves a kind of density of causation within causal processes: on magnifying any part of a causal process, it predicts that there will always be further causal processes in shorter and shorter time frames. Regularity and counterfactual theorists do not normally provide a definition of causal process. I think that a simple notion of causal process is usually assumed however. We can call it the Humean notion of causal process. Let us say that events {e1, e2 e3 …en} are part of the same causal process iff e1 causes e2 which causes e3… which causes en. The Standard Modern Picture also seems to require another assumption: that whenever f is part of a causal process, then there are parts of f: {f1, f2 f3 …fn} , such that f1, f2 f3 …fn are also parts of that same causal process. 31 With particular thanks to Edwin Mares, Bradley Monton, Josh Parsons, Neil Sinhababu, and two anonymous referees for this journal for comments on earlier drafts of this paper. REFERENCES Armstrong D. ( 1983) What is a Law of Nature?  Cambridge: CUP. Bigelow J., Pargetter R. ( 1991) Science and Necessity . Cambridge: CUP. Google Scholar CrossRef Search ADS   Brand M. ( 1980) ‘ Simultaneous Causation’, in Van Inwagen P. (ed.), Time and Cause . Dordrecht: Reidel Publishing, 137– 53. Brock S., Maslen C., Ngai J. ( 2013) ‘ How to Create a Fictional Character’, in Barbero C., Ferraris M., Voltolini A. (eds) From Fictionalism to Realism – Fictional and Other Social Entities . 63– 86. Newcastle upon Tyne: Cambridge Scholars Publishing. Dahl R. ( 1983) The Witches . New York: Puffin, 2007 reprint. Dummett M. ( 1978) Truth and Other Enigmas . Duckworth. Ehring D. ( 1987) ‘ Non-simultaneous Causation’, Analysis , 47: 28– 32. Google Scholar CrossRef Search ADS   Hall N., Paul L.A. ( 2013) Causation: A Users Guide . Oxford: OUP. Google Scholar CrossRef Search ADS   Hitchcock C. ( 2016) ‘ Probabilistic Causation’, in Zalta E. N. (ed.), The Stanford Encyclopedia of Philosophy  (Winter 2016 Edition), 〈https://plato.stanford.edu/archives/win2016/entries/causation-probabilistic/〉 accessed June 2017. Huemer M., Kovitz B. ( 2003) ‘ Causation as Simultaneous and Continuous’, The Philosophical Quarterly , 53: 556– 65. Google Scholar CrossRef Search ADS   Hume D. [presumed], ( 1740) Abstract of a Book Lately Published Entitled A Treatise of Human Nature . London: Macmillan. Hume D. ( 1739) A Treatise of Human Nature . Brigge S. (ed.), 1888. Oxford: Clarendon Press. Le Poidevin R. ( 2003) Travels in Four Dimensions . Oxford: OUP. Lewis D. ( 1973) ‘ Causation’, The Journal of Philosophy , 70: 556– 67 and Postscripts, 1986. Google Scholar CrossRef Search ADS   Mackie J. L. ( 1974) The Cement of the Universe: A Study of Causation . Oxford: Clarendon Press. Mumford S., Anjum R. ( 2011) Getting Causes from Powers . Oxford: OUP. Google Scholar CrossRef Search ADS   Parsons J. ( 2006) ‘ Topological Drinking Problems’, Analysis , 66: 149– 54. Google Scholar CrossRef Search ADS   Shoemaker S. ( 1969) ‘ Time without Change’, The Journal of Philosophy , 66: 363– 81. Google Scholar CrossRef Search ADS   © The Author 2017. Published by Oxford University Press on behalf of The Scots Philosophical Association and the University of St Andrews. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

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