The final version of this paper appeared in Dialectica. Please quote only from the final version.

On the Supposed Temporal Asymmetry of Counterfactual Dependence; or: It Wouldn’t Have Taken a Miracle! Gabriele CONTESSA

The thesis that a temporal asymmetry of counterfactual dependence characterizes our world plays a central role in Lewis’s philosophy, as. among other things, it underpins one of Lewis most renowned theses—that causation can be analyzed in terms of counterfactual dependence. To maintain that a temporal asymmetry of counterfactual dependence characterizes our world, Lewis committed himself to two other theses. The first is that the closest possible worlds at which the antecedent of a counterfactual conditional is true is one in which a small miracle occurs—i.e. one whose laws differ from the actual laws in a small spatiotemporal region. The second is that our world is characterized by a temporal asymmetry of miracles. In this paper, I will argue, first, that the latter thesis is either false or incompatible with the picture of the relations among temporal asymmetries endorsed by Lewis and, second, that former thesis conflicts with some of the intuitions which seem to guide us when engaging in counterfactual reasoning. If there is any fact of the matter as to which possible worlds in which the antecedent of a counterfactual conditional is true are closest to the actual world, these are not worlds at which a small miracle occurs.

1. What is the Temporal Asymmetry of Counterfactual Dependence? In our world, there are apparently many asymmetries in time. For example, effects seem never to precede their causes; lower entropy states (almost?) never follow higher entropy states; human beings have memories of their past but not of their future. Some philosophers claim that some of these asymmetries can be explained in terms of other, more fundamental asymmetries. One of these philosophers was David Lewis.

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According to Lewis, ‘[…] the asymmetry of counterfactual dependence serves to explain […] more familiar asymmetries’ (Lewis 1979, p.459), including the temporal asymmetry of causation— the fact that causes always precede their effects—and what Lewis called the asymmetry of openness, ‘[…] the obscure contrast we draw between the “open future” and the “fixed past” […]’ (Lewis 1979, p.459). At the beginning of his paper “Counterfactual Dependence and Time’s Arrow”, Lewis characterizes the asymmetry of counterfactual dependence as follows:

The way the future is depends counterfactually on the way the present is. If the present were different, the future would be different; and there are counterfactual conditionals, many of them as unquestionably true as counterfactuals ever get, that tell us a good deal about how the future would be different if the present were different in various ways. [I]n general the way things are later depends on the way things were earlier. Not so in reverse. Seldom, if ever, we can find a clearly true counterfactual about how the past would be different if the present were different. Such a counterfactual, unless clearly false, normally is not clear one way or the other. It is at best doubtful […] whether the way things are earlier depends on the way things will be later (Lewis 1979, p.455).

A few pages later, Lewis provided a more precise description of the asymmetry of counterfactual dependence:

Consider those counterfactuals “if it were that A it would be that C” in which the supposition A is indeed false, and in which A and C are entirely about states of affairs at two times tA and tC respectively. Many such counterfactual are true in which C is also false and in which tC is later than tA. These are counterfactuals that say how the way things are later depends on the way things were earlier. But if tC is earlier than tA, then such counterfactuals are true if and only if C is true. These are the counterfactuals that tell us how the way things are earlier does not depend on the way things will be later. (Lewis 1979, p.458)

The thesis that an asymmetry of counterfactual dependence characterizes our world plays a crucial role in Lewis’s philosophy. Among other things, this thesis underpins one of Lewis’s most

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renowned theses—that causation can be analysed in terms of counterfactual dependence (Lewis 1973b). If counterfactual dependence was temporally symmetric in our world, then, an advocate of a Lewisian account of causation would have a hard time trying to explain why “backward” counterfactual dependence does not open the door to backward causation. Second, the thesis that an asymmetry of counterfactual dependence characterizes our world is in turn underpinned by other theses that commit the advocate of the Lewisian account to very specific views about, among other things, counterfactual reasoning and the closeness of possible worlds. In this paper, I argue that Lewis’s own strategy, which grounds the asymmetry of counterfactual dependence in an asymmetry of miracles, is either ineffective or incompatible with the picture of the relations among temporal asymmetries endorsed by Lewis. Second, I argue that the principle proposed by Lewis to order possible worlds with respect to their closeness to the actual world conflicts with some of the intuitions which seem to guide us when engaging in counterfactual reasoning. To maintain that a temporal asymmetry of counterfactual dependence characterizes our world, Lewis committed himself to two other important theses. The first is that the closest possible worlds at which the antecedent of a counterfactual conditional is true is one in which a small miracle occurs—i.e. one whose laws differ from the actual laws in a small spatiotemporal region. The second is that our world is characterized by a temporal asymmetry of miracles. In this paper, I will argue, first, that the latter thesis is either false or incompatible with the picture of the relations among temporal asymmetries endorsed by Lewis and, second, that former thesis conflicts with some of the intuitions which seem to guide us when engaging in counterfactual reasoning. If there is any fact of the matter as to which possible worlds in which the antecedent of 3

a counterfactual conditional is true are closest to the actual world, these are not worlds at which a small miracle occurs. 2. Counterfactuals, Determinism, and the Nomocentric Principle According to Lewis’s analysis of counterfactual conditionals, the proposition schema ‘If it were that A, then it would be that C’ is (non-vacuously) true if and only if some possible world at which both A and C are true is closer to the actual world than any possible world at which A is true and C is false, or, more concisely, if and only if the closest A-world (i.e. the closest possible world at which A is true) is a C-world (i.e. possible world at which C is true) (see, for example, (Lewis 1973a)). So, for example, the counterfactual conditional ‘If the pilot of Enola Gay decided not to press the button, the atomic bomb would not have been dropped on Hiroshima at 8:15 a.m. on August 6, 1945’ is true if in the closest possible world in which (a counterpart of) the pilot of Enola Gay decided not to press the button no atomic bomb was dropped on Hiroshima at 8:15 a.m. on August 6, 1945. The problem now is that of determining which of the possible worlds in which the pilot decided not to press the button is the closest to the actual world. For the sake of simplicity, Lewis assumed that the actual laws of nature (i.e. the ones which are true of the actual world) are (bi-directionally) deterministic. Lewis claimed that ‘[…] indeterminism is neither necessary nor sufficient for the asymmetries [he is] discussing’ (Lewis 1979, p.460). Moreover, as Lewis pointed out, the success of quantum mechanics, which is our best reason to believe in indeterminism, ‘[…] is reason to believe that the world is indeterministic in both directions, so that the actual future and present are nomically compossible with various alternative pasts’ (Lewis 1979, p.460). Following Montague, Lewis defined a deterministic system of laws as follows: 4

A deterministic system of laws is one such that, whenever two possible worlds both obey the laws perfectly, then they are exactly alike throughout all time, or else they are not exactly alike through any stretch of time. They are always alike or never. They do not diverge, matching perfectly in their initial segments but not thereafter; neither do they converge (Lewis 1979, pp.460-461).

Now, the problem is that, if the actual laws are deterministic and the closest possible world in which the pilot decides not to press the button is a nomically possible world (i.e. a world whose laws are the same as those of the actual world), then we would have to conclude that counterfactual dependence in our world is symmetric in time. If we represented the history of the actual world as a trajectory in a sufficiently large state-space, the trajectories of all nomically possible worlds would be parallel to it. So, the world at which the pilot decides not to press the button is a world whose entire history differs (to some degree) from the history of the actual world. I will call the nomocentric principle the principle according to which some nomically possible A-world are always closer to the actual world than any other A-worlds. If the nomocentric principle is correct, then there are as many true backward counterfactual conditionals as there are forward counterfactual conditionals and, therefore, the thesis that an asymmetry of counterfactual dependence characterizes our world would turn out to be false. One could pursue a number of strategies to avoid this conclusion. In this paper, I will focus on the strategy Lewis himself actually pursued. 3. Miracle and the Strong Historiocentric Principle In his article “Causation”, Lewis wrote:

The respects of similarity that enter into the overall similarity of worlds are many and varied. In particular, similarities in matters of fact trade off against similarities of law. The prevailing laws of nature are important to the character of a world; so similarities of law are weighty. Weighty, but

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not sacred. We should not take it for granted that a world that conforms perfectly to our actual laws is ipso facto closer to actuality than any world, where those laws are violated in any way at all. It depends on the nature and the extent of the violation, on the place of the violated laws in the total system of laws of nature, and on the countervailing similarities and differences in other respects (Lewis 1973b, p.197).

What Lewis seemed to have in mind in this passage is what he calls a small miracle. According to Lewis, a possible world in which a small miracle occurs is a world in which “[t]he deterministic laws of [the actual world] are violated […] in a simple, localized, inconspicuous way” (Lewis 1979, p.468). As a matter of fact, however, a possible world in which a small miracle occurs is simply a world whose laws differ from the laws of the actual world in a small spatio-temporal region. Consider, for example, the nomically impossible world W*. W* is exactly like the actual world in every detail until just before tA, which is the time at which the pilot decides to press the button in the actual world. According to the actual laws, that state would lead to the pilot deciding to press the button. In W*, however, the laws in the spatio-temporal region around the aircraft when the pilot takes the decision are slightly different from those of the actual world. According to the set of laws of W*, the very state of the world that in the actual world leads to the pilot deciding to press the button leads to the pilot deciding not to press it. The world trajectory of the actual world and that of W* lie on the same trajectory until just before tA but, when the miracle occurs, the point which represents the state of W* “jumps” on a parallel trajectory, the trajectory of a world at which the pilot has decided not to press the button. The question is now whether W* is closer to the actual world than any nomically possible world. The answer to this question partly hinges on the criteria one chooses to adopt to order Aworlds with respect to their closeness to the actual world. If we adopt the nomocentric principle

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as I have suggested above, then our answer must be negative. Since the laws of W* differ from the laws of the actual world, W* is a nomically impossible world and, according to the nomocentric principle, there is always some nomically possible A-world that is closer to the actual world than any nomically impossible one. However, according to Lewis, the question should be answered positively. This is because Lewis rejected what I have called the nomocentric principle initially in favour of what I will call the strong historiocentric principle, according to which some “miraculous” A-world (i.e. a world at which A is true as a result of a small miracle) is closer to the actual world than any other possible A-world. Lewis’s stated motivation for this move is that the histories of miraculous A-worlds match the history of the actual world perfectly up to a certain point while the history of nomically possible A-worlds do not match the history of the actual world for any extent of time and as Lewis put it, ‘[…] a lot of match of particular fact is worth a little miracle’ (Lewis 1979, p. 469). 4. The Weak Historiocentric Principle and the Asymmetry of Miracles As Jonathan Bennett (1974) and Kit Fine (1975) independently pointed out, however, the adoption of the strong historiocentric principle would have disastrous consequences for Lewis’s theory of counterfactuals. Consider the world W**. In W**, a small miracle occurs to the effect that the pilot decides not to press the button, but, then, another small miracle occurs, the pilot’s thumb contracts, the pilot involuntarily presses the button exactly at the same instant in which he presses it in the actual world and the atomic bomb is dropped. Except for the short interval between the two miracles, the history of W** would seem to match the history of the actual world perfectly and, according to the strong historiocentric principle, this perfect match would seem to be worth two small miracles. If “doubly miraculous” A-worlds such as W** actually were the

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closest A-worlds, then most counterfactual conditionals we ordinarily take to be true would be false. In order to avoid this disastrous consequence, Lewis (1979) appealed to what he calls an asymmetry of miracles. Lewis argued that “divergence” miracles are smaller than “convergence” miracles. In other words, whereas it takes one miracle to make the history of a possible world diverge from the history of the actual world, it takes many little miracles to bring back the possible world in which one miracle has occurred to a perfect match of fact with the actual world. To support his claim, Lewis argued that anything that happens at a certain time leaves a myriad of “traces” in the future. The erasure of each of these traces, according to Lewis, requires one little miracle. So, it takes one little miracle for the pilot to involuntarily press the button, another little miracle to replace the memories of the pilot, so that he falsely remembers that he has pressed the button, and so on for each of the traces of the pilot’s decision. In worlds like W**, Lewis argued, we either have only two little miracles and imperfect match or many little miracles and perfect match. According to Lewis, imperfect match of fact is not worth a little miracle. I will call this the weak historiocentric principle. According to it, some singly miraculous A-world (i.e. a world at which one and only one little miracle occurs) is closer to the actual world than any other A-world. In other words, according to the weak historiocentric principle a lot of match of fact is worth one little miracle but no more than one. But are there any reasons to prefer the weak historiocentric principle to the nomocentric principle independently from the fact that the adoption of the weak historiocentric principle provides the advocate of the Lewisian analysis with the desired sort of temporal asymmetry of counterfactual dependence? I will turn to this crucial question in Section 7 and give it a negative answer. Before that, in Sections 5 and 6, I will argue that that the strategy that Lewis followed in 8

order to maintain that the asymmetry of counterfactual dependence characterizes a world whose laws are temporally symmetric is either ineffective or incompatible with the picture of the relations among temporal asymmetries that Lewis sketched. 5. Debunking the Asymmetry of Overdetermination According to Lewis, the asymmetry of miracles is not a brute fact about our world. It is a consequence of a deeper temporal asymmetry: the asymmetry of overdetermination. Lewis defined the determinant(s) of a fact at a certain time as follows:

Any particular fact about a deterministic world is predetermined throughout the past and postdetermined throughout the future. At any time, past or future, it has at least one determinant: a minimal set of conditions jointly sufficient, given the laws of nature, for the fact in question. Members of such set may be causes of the fact, or traces of it, or neither). (Lewis 1979, p.474).

Lewis then went on to suggest that: ‘[…] what makes convergence take so much more of a miracle than divergence […] is an asymmetry of overdetermination […]’ (Lewis 1979, p.474). In other words, Lewis claimed that at the actual world and at the closest possible worlds, events, like the pilot’s decision to press the button, have more determinants at any time in the future than in the past. Lewis suggested that the asymmetry of overdetermination, which underpins the asymmetry of counterfactual dependence is a de facto asymmetry that contingently characterizes our world and the possible worlds closest to it. It cannot be reduced to any other asymmetries that are not de facto themselves. In this and the next sections, I will challenge this analysis. Consider again the pilot’s decision to press the button. The pilot’s decision undeniably had a great number of consequences. Once the pilot decided to press the button, the muscles in his thumb contracted, the thumb pressed the button, the mechanism released the bomb, and the bomb fell on Hiroshima with the tragic consequences we all know. Beside these consequences,

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there were also a number of less momentous ones, such as the fingerprint of the pilot being impressed on the button, the pilot’s memory of that moment, and so on. Lewis seemed to think that each of these consequences of the pilot’s decision is one of its determinants, but, I will argue, this is not the case. Consider the actual world in which the pilot has decided to press the button thus initiating the chain of events that will culminates in the explosion of the atomic bomb on Hiroshima and, in particular, focus on the exact instant at which the bomb explodes. Is the explosion of the bomb a determinant of the pilot’s previous decision at that time? A determinant of an event was defined by Lewis as a minimal set of conditions jointly sufficient, given the laws of nature, for the event in question to occur. But the explosion of the bomb, in and of itself, is not sufficient to (post)determine the pilot’s decision to press the button to drop the bomb. There are many ways in which the bomb could have exploded exactly as it did without the pilot having decided to press the button. The explosion of the bomb is, thus, compatible with alternative past histories in which the pilot decides not to drop the bomb, including the one in which the pilot decides not to press the button but there is a fault in the electric circuit of the plane and the bomb is released at exactly the same instant in which it was released in the actual world. In other words, the explosion of the bomb alone is not a determinant of the pilot’s previous decision. The determinant of the pilot’s decision at the moment at which the bomb explodes, thus, must contain more than just the explosion of the bomb if it is to (post)determine the pilot’s previous decision. For example, it must contain the pilot’s fingerprint on the button. But the set formed by the explosion of the bomb and the pilot’s fingerprint on the button is not a determinant of the pilot’s previous decision either. There are worlds in which the bomb exploded 10

and in which there is a thumbprint on the button exactly like in the actual world, but the pilot has not decided to drop the bomb. One of them is the world in which the pilot decides not to press the button, but his thumb involuntarily contracts and presses the button. The determinant of the pilot’s decision at the moment in which the bomb explodes, thus, must contain more than just the explosion of the bomb and the pilot’s fingerprint on the button. For example, it has to include the pilot’s memory of his decision to press the button. This might still not be sufficient however. It is likely that there are worlds at which the bomb explodes, the thumbprint is on the button and the pilot remembers to have decided to press the button without him actually having decided to do so. For example, worlds at which the pilot falsely remembers to have decided to press the button even if he has decided not to. These alternative scenarios may well be implausible but they show that it takes a very large set of consequences of the pilot’s decision to press the button to have a determinant of that decision in the future and, once we have one such set of consequences, it seems extremely unlikely that we will be able to find other determinants of the pilot’s decision that do not include any of the consequences that are already members of that first determinant.1 At close scrutiny, Lewis’s assumption that each of the consequences of an event (post)determines the event thus appears to be false. In our example, the only determinant of the pilot’s decision at each time in the future is likely to be either the whole set of consequences of the decision at that time or a very large subset of them. Therefore, there seems thus to be no reason to believe that events ordinarily have more determinants in their future than in their past.

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6. Two Asymmetries of Causation Even if the asymmetry of overdetermination is not a genuine asymmetry, however, Lewis seemed to be onto a genuine asymmetry when talking about the asymmetry of “traces”. The problem, I suspect, is that Lewis misrepresented the nature of that asymmetry. It seems hardly deniable that everything that happens in our world has a great number of consequences, or, to put it in Lewis’s terms, every event leaves a number of “traces” in the future. If the notion of ‘trace’ is properly construed, Lewis might have even been right in claiming that there are more “traces” of the occurrence of an event in the future than in the past. What Lewis disregarded, however, is that, if there is such an asymmetry, this is a consequence of a temporal asymmetry of causation. In discussing the asymmetry of overdetermination, Lewis talked of determinants and “traces” but could not completely avoid causal language. It is not a chance that, as an example of how rare overdetermination of the present from the past is in our world, Lewis employed a standard example of causal overdetermination—the case of the victim whose heart is contemporarily pierced by two bullets shot by two independent shooters. As Lewis noted (while at pains to avoid causal language), cases of (causal) overdetermination are relatively rare in our world. Most events have no more than one cause. On the other hand, events seem often to have many effects. Causal forks are all but rare in our world. The pilot’s decision to press the button, for example, is the initial link of a number of causal chains that propagate in the future, but it is likely to be the link of a single causal chain from the past. If a trace of an event is defined as one of the links of the causal chain of which the event itself is a link, then Lewis may well be right in claiming that a vast majority of the events in our world leave more traces in their future than in their past. He might be also right in claiming that it takes one 12

miracle to break each causal chain to and form the event in question. However, in a world in which events are likely to have as many causes as effects, there would be no asymmetry of miracles. The problem for Lewis was that he could not appeal to an asymmetry of causal forks to underpin the asymmetry of miracles without thereby undermining the overall project of explaining the temporal asymmetry of causation in terms of the temporal asymmetry of counterfactual dependence. The asymmetry of causal forks, in and of itself, is not a temporal asymmetry. It only tells us that events usually have more effects than causes. If the asymmetry of causal forks is to underpin a temporal asymmetry of miracles, however, we also have to assume that a temporal asymmetry of causation characterizes the actual world, to the effect that effects never precede their causes. If backward causation was as likely as forward causation, there would be as many traces of the present in the past as there are in the future. In which case there would be no reason to believe that it takes more miracles for reconvergence than for divergence. If either the asymmetry of causal forks or the temporal asymmetry of causation failed to obtain in our world, miracles and counterfactual dependence would be temporally symmetric, with all of the disastrous consequences this would have for Lewis’s views on counterfactuals and causation. However, if in the actual world the asymmetry of miracles obtains as a consequence of the asymmetry of causal forks and temporal asymmetry of causation, then the relations among the various asymmetries in time are different from what Lewis envisaged. It would be the temporal asymmetry of causation that explains the temporal asymmetry of counterfactual dependence, not the reverse. So, even if in the actual world counterfactual dependence is time asymmetric, this cannot explain why causation is time asymmetric, which undermines what seems to be Lewis’s fundamental motivation for claiming that counterfactual dependence is asymmetric in time. 13

7. Would It Really Have Taken a Miracle? So far, I have argued that the strategy that Lewis followed in order to maintain that the asymmetry of counterfactual dependence can characterize a world whose laws are temporally symmetric is either ineffective or incompatible with the picture of the relations among temporal asymmetries that Lewis sketched. The trouble with Lewis’s account of the temporal asymmetry of counterfactual dependence, however, runs even deeper. Whether or not our world is characterized by a temporal asymmetry of counterfactual dependence depends to a great extent on which A-worlds are closest to the actual world. Therefore, if the temporal asymmetry of counterfactual dependence is to be a genuine asymmetry of our world on par with the other more familiar asymmetries in time, there must be a fact of the matter as to which A-worlds are closest to the actual world. So, since the nomocentric principle and the weak historiocentric principle disagree about which A-worlds are closer to the actual world, they cannot be both correct. In the remainder of this section, I will argue that, if there is a fact of the matter as to which A-worlds are closer to the actual world (and I take this to be a “big ‘if’”), then the nomocentric principle is more likely to be correct than the weak historiocentric principle. To do so, I will first argue that Lewis’ reasons for preferring the weak historiocentric principle over the nomocentric one are unconvincing and, then, I will argue that there are positive reasons to favour the nomocentric principle over the weak historiocentric one. Lewis’s stated reason for preferring the weak historiocentric principle over the nomocentric one was that, according to the weak historiocentric principle, large portions of the history of the closest miraculous A-world match large portions of the history of the actual world in every detail, while no portion of the history of the closest nomologically possible A-worlds matches perfectly the history of the actual world. As Lewis suggested, a lot of match of particular fact may well be 14

weightier than a small discrepancy in the laws, however, the relation between match of history and match of laws is not necessarily a trade off, as Lewis seemed to suggest. If we abandon the assumption that the actual world is deterministic (which is at least dubious anyway), partial match of histories is compatible with perfect match of laws. If the actual world is to some extent indeterministic, as, according to Lewis himself, our best theories seem to suggest then there are nomically possible A-worlds portions of whose history matches perfectly with portions of the history of the actual world. If the actual world is indeterministic, it is plausible to assume that the closest A-world is a world that is governed by the same indeterministic laws that govern the actual world and whose history matches perfectly the history of the actual world until a certain time tD
counterfactual reasoning. ‘What would have happened if the pilot had decided not to press the button?’, a historian might ask. However, a psychologist might ask: ‘What would have had to happen for the pilot to decide not to press the button?’. The acceptance of the weak historiocentric principle would seem to make all backward counterfactual reasoning hopelessly sterile. If Lewis’s weak historiocentric principle is the one that orders possible worlds correctly with respect to their closeness to the actual world, then, as strange as it may seem, the correct answer to the psychologist’s question would be: ‘The laws of nature in a small spatio-temporal region around the aircraft would have had to differ from what they actually were’. Our intuitions though seem to tell us that a less outlandish difference would have been sufficient to make the antecedent of the counterfactual true. We seem to believe that there are alternative histories that are perfectly compatible with the laws of the actual world and would lead to the pilot’s decision not to press the button. When the psychologist engages in backward counterfactual reasoning, she seems to be interested in the most plausible of those stories, not in ones that involve Lewisian miracles.2 The weak historiocentric principle however seems to be no less at odds with our intuitions in those cases in which we engage in forward counterfactual reasoning. Whereas in some cases it may be irrelevant how in the closest A-world the truth of A comes about, there are cases in which the causal chain that leads to the occurrence of the event described in the antecedent has an influence on whether the event described in the consequent occurs. A safety inspector who finds out that a sprinkler is not working, for example, is likely to conclude that if a fire had broken out the flames would have propagated quickly without being committed to any particular way in which the fire would have broken out in the counterfactual scenario. As far as she is concerned, the fire could have broken out as a result of a miracle or as a result of the carelessness of a smoker 16

(at least insofar as the way in which the fire starts has no influence on how quickly it would propagate). However, this is not always the case. In many cases, the way the event described in the antecedent comes about is relevant to the way we evaluate the counterfactual in question and, in those cases, we do not want A to come about as a result of a miracle. A detective who is working on the theft of a diamond, for example, might reason: ‘If the diamond was stolen by someone with no access to the keys, there would be signs of forced entry’. In this case, how A comes—how a thief with no access to the keys would have got to steal the diamond—seems to be crucial to the truth of the counterfactual and, in this case, we do not want the truth of the antecedent to come about as a result of a miracle. The most plausible scenarios in which someone with no access to the keys stole the diamond seem ones that involve the thief picking the door lock or breaking in through one of the windows, and not the one in which the alternative thief finds herself miraculously teleported inside the room and steals the diamond. In general, the idea the closest possible A-world is one in which A is true as a result of a small miracle may not conflict too strongly with our intuitions when the miracle that makes A true is unobservable and inconspicuous. Most of the examples usually discussed in the literature are examples that require miracles of this kind (involving inconspicuous unobservable processes such as the misfiring of a neuron). However, for most counterfactual conditionals, the miracle it would take to make A true seems to be more conspicuous and counterintuitive than that. I take it that most people who have any intuitions at all about these matters would tend to think that the closest possible world in which I am wearing a blue sweater now is the one in which I decided to wear one this morning and not one in which the colour of my sweater has miraculously changed from red to blue one millisecond ago and the closest possible world in which you are writing this

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paper now is one in which you have come to write it and not the one in which you have become me one millisecond ago.3 The advocates of the Lewisian analysis may well argue that, if we have any such intuitions, it is them, not the weak historiocentric principle, that are mistaken. I do not deny that these intuitions may be mistaken. What I deny is that arguments proposed by Lewis in favour of the weak historiocentric principle are strong enough to persuade us that, if our intuitions are at odds with it, it is our intuitions that should be abandoned. The assumption that the actual world is characterized by a temporal asymmetry of counterfactual dependence plays a crucial role in the grand scheme of Lewis’s philosophy. Lewis famously analysed causation in terms of counterfactual dependence and, as I have mentioned, if we accepted Lewis’s analysis of causation without accepting that our world is characterized by a temporal asymmetry of counterfactual dependence, we would have troubles explaining why there is no backward causation in our world. However, if we do not accept Lewis’s analysis of causation, we do not need to assume that an asymmetry of counterfactual dependence characterizes our world and we do not need to reject our intuitions about how things might have gone otherwise without Lewisian miracles.

Acknowledgements I would like to thank Robert C. Bishop, Nancy Cartwright, Michael Martin, James Stazicker and the anonymous referees for this journal for many useful comments on previous drafts of this paper. References Bennett, Jonathan. (1974) “Counterfactuals and Possible Worlds”, Canadian Journal of Philosophy, Vol. 4, pp.381–402. 18

Bennett, Jonathan (2003) A Philosophical Guide to Conditionals, Oxford, Oxford University Press. Elga, Adam (2001) “Statistical Mechanics and the Asymmetry of Counterfactual Dependence”, Philosophy of Science, Vol. 68, pp.S313–S324. Fine, Kit (1975) “Review of Counterfactuals”, Mind, Vol. 84, pp.451–458. Lewis, David (1973a) Counterfactuals, Blackwell, Oxford. Lewis David (1973b) “Causation”, Journal of Philosophy, Vol. 70, pp.556–567. Lewis, David (1979) “Counterfactual Dependence and the Time’s Arrow”, Noûs, Vol. 13, pp.455–476.

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Notes

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Adam Elga has argued that “[…] the existence of apparent traces of an event (together with the laws, and

together with the absence of evidence that those traces have been faked) falls far short of entailing that the event occurred” (Elga 2001, S324). His argument differs from mine, among other things, in that mine does not make any (explicit) assumptions about the nature of the actual laws and the sensitivity of thermodynamically irreversible processes to changes. More importantly Elga’s conclusion is stronger than the one I wish to draw, as my argument does not preclude that a wide enough set of traces of an event may be a determinant of it in the actual world. What my argument shows is rather that, if determinants are properly understood, it is implausible to assume that an event has more determinants in the future than in the past. 2

Note that I do not thereby mean to deny that we usually find it harder to engage in backward counterfactual

reasoning than in its forward counterpart. There seem to be many ways in which the pilot could have reached the decision not to press the button and, in many cases, it does not seem possible to give a unique answer to questions such as ‘What would have had to happen for the pilot to decide not to press the button?’. But, first, the situation here is not entirely different from the one involving forward counterfactual reasoning. One might argue that there are many answers also to the question ‘What would have happened if the pilot decided not to press the button?’. Would some other member of the crew have pressed the button? Or would no bomb have been dropped on Hiroshima? Second, the fact that it is more it more difficult for us to find true of backward counterfactual conditionals than it is to find true forward ones does not imply that there are more true forward counterfactual conditionals than backward ones. The difference between forward and backward counterfactual dependence may well be epistemic rather than ontic. 3

The advocate of the weak historiocentric principle might want to argue that, in those cases, A is true in the

closest A-world as a result of an earlier small miracle. For example, one in which a neuron has “misfired” in my brain this morning and I have decided to wear my blue sweater rather than the red one. The problem with this line of reasoning is that, if that world is the closest A-world, then a significant number of backward counterfactual conditionals seem to be true.

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