2. Causation in the Mentaculus

Albert wants to show why we are “likely to be in a position to influence much about the future and next to nothing about the past” (Reference Albert and Wilson2014, 165). In context, it is clear that Albert uses “influence” to mean “cause.” To understand his explanation, we must first come to grips with his framework for causal analysis. This runs as follows: causal statements are cashed out in terms of a factual statement plus a counterfactual statement, and an entity called the “Mentaculus” gives probabilistic verdicts on these.Footnote ² In what follows I lay this all out, starting with causal statements. This isn’t exactly how Albert presents his account, but I believe it is a fair reconstruction.

Suppose in our world, some particular event x occurs (I’ll always assume this), and we wish to know whether or not it causes some other particular event y in our future/past. In Albert’s account, as in Lewis (Reference Lewis1973a, Reference Lewis1973b), x causes y if and only if (iff) both of the following causal criteria are satisfied:

• Criterion 1: y occurs in our world.

• Criterion 2: Had $\neg x$ obtained, $\neg y$ would have obtained.

Criterion 1 is a kind of ground-zero requirement for causation because it establishes that the relevant events actually occur in the first place. Meanwhile, Criterion 2 is the definitive feature of a counterfactual analysis of causation. As Lewis himself recognized, this analysis faces various difficulties and requires some refinement in order to get around them. Two particularly salient problems are preemption scenarios and backtracking counterfactuals.Footnote ³ But because these issues aren’t directly relevant for us and would only complicate things, I shall set them aside.

In summary, a causal statement is determined by a factual statement (Criterion 1) and a counterfactual statement (Criterion 2). So, what dictates their truth values? Within the context of classical statistical mechanics, these are determined by the trajectories picked out by the relevant microstates in the universe’s phase space Γ. This is straightforward in the case of Criterion 1: it is satisfied when the actual current microstate $m_0$ time-evolves forwards/backwards under the dynamics to satisfy y. But what is the “relevant microstate” in the case of Criterion 2? Similarly to Lewis (Reference Lewis1973b), Albert (Reference Albert and Wilson2014, 163) consults our closest possible world, which he interprets as the nearest nomologically possible microstate $m_\star$ to $m_0$ that satisfies $\neg x$ (as measured by distance in Γ). Criterion 2 is then satisfied when $m_\star$ time-evolves forwards/backwards to satisfy $\neg y$ .Footnote ⁴ This sums up the truth conditions for causal statements.

Although these truth conditions are conceptually clear, they are epistemically opaque. We can’t literally envisage microstates, much less microstates of the entire universe, and we certainly can’t track their trajectories in Γ. Instead, we must make do with probabilistic verdicts on the causal criteria given by the “Mentaculus.” This entity is a combination of three ingredients:

1. 1. The universe’s fundamental dynamical laws. For simplicity, these are taken to be Newton’s deterministic laws.

2. 2. The “Past Hypothesis,” the posit that the universe began in an extremely low-entropy macrostate $M_{PH}$ . Because Albert (Reference Albert2000, chap. 6) regards this as a law, all nomologically possible microstates are consistent with this posit.

3. 3. The “Statistical Postulate,” a probability distribution that is uniform (according to the Lebesgue measure) over $M_{PH}$ ’s microstates.Footnote ⁵

The result is a uniform distribution over trajectories in Γ, which Albert regards as the universe’s nomologically possible trajectories. By conditionalising the Mentaculus on the actual macrostate $M_0$ or on the counterfactual macrostate $M_\star$ (where $m_0 \in M_0$ and $m_\star \in M_\star$ ), we obtain y’s respective probabilities in the actual or counterfactual world, given all macroscopic evidence in that world.Footnote ⁶ The procedure for finding these probabilities is the same in both cases:

1. i. Apply a uniform distribution over $M_0$ or $M_\star$ (this satisfies the Statistical Postulate).

2. ii. Discard any microstates that didn’t evolve from $M_{PH}$ (this satisfies the Past Hypothesis). This leaves us with the nomologically possible sets of present microstates $N_0 \subset M_0$ or $N_\star \subset M_\star$ . These are just macrostates conditionalized on $M_{PH}$ .

3. iii. Time-evolve $N_0$ or $N_\star$ forwards/backwards under the dynamics to the time of the consequent.

4. iv. Determine the proportion of $N_0$ or $N_\star$ that find themselves in a macrostate in which y occurs. There may be multiple such macrostates, but I shall gloss these as $N_y$ .

5. v. This gives $\Pr (y \mid N_0)$ or $\Pr (y \mid N_\star )$ , that is, the chances of y occurring in the future/past of $N_0$ or $N_\star$ .

This provides us with probabilistic handles on the causal criteria as follows: $\Pr (y \mid N_0)$ is the chance of Criterion 1 being satisfied, whereas $\Pr (y \mid N_\star )$ is the chance of Criterion 2 being violated. When $\Pr (y \mid N_0) \approx 1$ and $\Pr (y \mid N_\star ) \approx 0$ , both causal criteria are probably satisfied, and x probably causes y.

3. The Possibility of Backward Causation

We’ve now identified the conditions under which causation occurs and our means of epistemic access to these conditions via macroscopic evidence. With this groundwork in place, we’re ready to see how it yields a causal arrow and why this may occasionally point backwards.

In order to derive the causal arrow, we must first acknowledge that the world exhibits a record asymmetry. At this point, two questions naturally arise. First, what is a record? This is notoriously hard to answer in a precise way. But for our purposes, we can stick with what seems to be Albert’s own view: records are localied macrostates that are highly informative about other times,Footnote ⁷ and it just so happens that these “other times” always lie in our past.

Second, what explains the record asymmetry? According to Albert (Reference Albert2000, chap. 6), it is the fact that the Mentaculus contains a Past Hypothesis but no analogous “Future Hypothesis.” For our purposes, the details and difficulties of this explanation aren’t relevant,Footnote ⁸ and I am simply going to take it as read. The implication is that not only the universe’s actual macrostate $N_0$ but also the counterfactual macrostate $N_\star$ contain records of the past and not the future. Through piecemeal observations of our world’s records—which, recall, are localized macrostates—we are able to partially reconstruct $N_0$ and $N_\star$ , allowing our credences to roughly track the Mentaculus probabilities.

If we grant the foregoing, the causal arrow drops out as follows: As we saw, whether or not x causes y depends on the two causal criteria. If we take Criterion 1 for granted (i.e., both x and y occur in our world), then the question hinges on Criterion 2. This is a counterfactual statement that we gauge via the Mentaculus. Because of the record asymmetry, the Mentaculus gives different answers depending on whether x precedes y, or vice versa, as shown in the following paragraphs.

When x precedes y, Criterion 2 is a forward counterfactual. To evaluate this, we time-evolve $N_\star$ forwards and gauge the proportion that lands up in $N_y$ , yielding $\Pr (y \mid N_\star )$ . Because $N_0$ lacks records of the future, it lacks records of y. But because $N_\star$ mimics $N_0$ except in satisfying $\neg x$ , $N_\star$ generally also lacks records of y. It can therefore easily happen that $\Pr (y \mid N_\star ) \approx 0$ . In such circumstances, Criterion 2 is probably satisfied, and so x probably causes y.

When y precedes x, Criterion 2 is a backward counterfactual. To evaluate this, we time-evolve $N_\star$ backwards and gauge the proportion that lands up in $N_y$ , yielding $\Pr (y \mid N_\star )$ . Because $N_0$ contains records of the past, it generally does contain records of y. But because $N_\star$ mimics $N_0$ except in satisfying $\neg x$ , it generally also contains records of y. This implies $\Pr (y \mid N_\star ) \approx 1$ . In such circumstances, Criterion 2 is probably violated, and so x probably doesn’t cause y.

In summary, here’s how the causal arrow emerges in Albert’s account. When Criterion 1 is satisfied, x causes y iff Criterion 2 is satisfied. When x precedes y, Criterion 2 is a forward counterfactual; this may well be probable, so x can easily cause y. But when y precedes x, Criterion 2 is a backward counterfactual; this is generally improbable as a result of records, so x probably doesn’t cause y.

As Albert (Reference Albert and Wilson2014, 165–66) observes, the causal arrow that drops out of this isn’t absolute; there are certain scenarios where it probably points backwards. To illustrate this, he offers the following example, first discussed by Douglas Kutach.

Suppose Atlantis existed in our past (y) and that I just kept my fingers still (x). Does x cause y? Because Criterion 1 is satisfied, we must turn to Criterion 2. Because y obviously precedes x, Criterion 2 is a backward counterfactual, so we determine it as follows: time-evolve $N_\star$ backwards to antiquity, and gauge the proportion that lands up in an Atlantis-containing macrostate $N_y$ . By hypothesis, $N_0$ happens to lack records of Atlantis, and because $N_\star$ mimics $N_0$ except that I just clicked my fingers ( $\neg x$ ), $N_\star$ also lacks records of Atlantis. This implies $\Pr (y \mid N_\star ) \approx 0$ , which means Criterion 2 is probably satisfied. Therefore, my finger-resting probably causes Atlantis existence. If we generalize from this example, there are certain scenarios where it’s probable that we cause events in the past.

Incidentally, this example could be generalized a step further. Although the antecedent here happens to involve human action, this doesn’t actually do any important work in the argument. My finger-resting is just a generic present event that could be interchanged for virtually anything, from a leaf falling off a tree to a soap bubble bursting. Therefore, the real upshot is that there are certain scenarios where it’s probable that present events in general cause past events; our doing so is merely a special case of this. But because agency will become important in section 6, I shall stick to examples whose antecedents are human actions.

Kutach’s example poses a clear challenge to Albert’s account: there are certain situations where we can probably cause past events, and yet we never observe backward causation. How can these ideas be reconciled?

To this end, Albert (Reference Albert and Wilson2014, 166) draws a key distinction between (a) the chance that backward causation is in play and (b) the chance we assign to it being in play, and he rightly points out that these may diverge. This is apparent in the Atlantis case, as follows: On the one hand, we saw that the value of item (a) is 1. This is because it was stipulated that Atlantis existed in our past (i.e., that Criterion 1 is satisfied). However, we don’t have direct epistemic access to this fact. Instead, our credence comes from conditionalising the Mentaculus on the universe’s current macrostate, and because this lacks putative records of Atlantis, it will seem like $\Pr (y \mid N_0) \approx 0$ . This makes it seem like Criterion 1 isn’t satisfied, making the value of item (b) negligible. So, even when backward causation is highly probable, we’re none the wiser—thus eliminating any verifiable counterexamples to the orthodox view that backward causation is rare/nonexistent.Footnote ⁹

4. The rampancy of backward causation

Albert’s response is good as far as it goes. However, it runs into a different problem. Regardless of whether or not we observe backward causation, we take this phenomenon to be extremely rare or nonexistent. Albert doesn’t explicitly flag this as an important feature of causation that he needs to respect. Nevertheless, he seems to acknowledge this implicitly, stressing at various points that we are “likely to be in a position to influence much about the future and next to nothing about the past” (Reference Albert and Wilson2014, 165). In order to be palatable, Albert’s causal account must satisfy the idea that backward causation is rare/nonexistent. At face value, however, it violates this idea, as I explain in the following paragraphs.

In arguing that we can unverifiably cause Atlantis’s existence, Albert makes a key hidden assumption: most nomologically possible microstates lacking records of Atlantis didn’t contain that city in their past. Without this assumption, we’d have no reason to expect only a tiny proportion of $N_\star$ to time-evolve backwards into $N_y$ , and hence we’d have no reason to expect $\Pr (y \mid N_0)$ to be minuscule, which was the rationale for saying Criterion 2 is probably satisfied in that scenario. Moreover, we’d have no reason to expect only a tiny proportion of $N_0$ to time-evolve backwards into $N_y$ , and hence we’d have no reason to expect our credence in Atlantis existence to be low, which was the rationale for saying backward causation is unverifiable.

Presumably, this is just a special case of a much more general assumption, which we can express as follows:

Fidelity Assumption: If a nomologically possible region $N_i$ lacks records of y, then $\Pr (y \mid N_i) \approx 0$ .

This tells us that if some event occurred but has no records in $N_0$ or $N_\star$ , then the Mentaculus ascribes that event a low probability in both cases. It would then follow a fortiori that if Atlantis existed but has no records in $N_0$ or $N_\star$ , then the Mentaculus ascribes that city’s existence a low probability in both cases.

If the Fidelity Assumption is indeed integral to Albert’s reasoning, then Atlantis vulnerability to backward causation is just one instance of a wider fact: all unrecorded past events are vulnerable to backward causation. As I will explain, this implies something radical about the frequency of this phenomenon.

If the chance of any given event leaving behind no records is miniscule, then there would rarely/never be unrecorded events in our past, so backward causation would be rare/nonexistent, in accord with common sense. There is certainly a large class of major events for which this is clearly true, such as the existence of a city, the eruption of a volcano, or the impact of a large asteroid, all of which we’d expect to leave behind many records. However, it’s not obviously true of minor events like a stone rolling off a cliff, a Neanderthal’s cry, or a carp splashing in a lake. On the contrary, one would ordinarily think such events have a high chance of leaving behind no records—at least after an appreciable period of time. Any such event would be subject to backward causation by later events. But because the past is chock-a-block with minor events, this suggests that backward causation is not just possible, but rife.

For clarity, let’s see how my objection takes shape with an example. Suppose sometime during the Tang dynasty, a particular carp made a particular splash at a particular time in the Yangtze River (y), and suppose that a moment ago, I kept my fingers still (x). Does x cause y? Because Criterion 1 is satisfied, we must examine Criterion 2 using the Mentaculus: time-evolve $N_\star$ backwards by hundreds of years and find the proportion that lands up in the splashing-carp macrostate $N_y$ . Because $N_0$ lacks records of the carp’s splash, and because $N_\star$ mimics $N_0$ except that I just clicked my fingers ( $\neg x$ ), $N_\star$ also lacks records of the splash. This implies $\Pr (y \mid N_\star ) \approx 0$ , which means Criterion 2 is probably satisfied. Therefore, my finger-resting probably causes the carp to splash.

Just as in the Atlantis case, the Fidelity Assumption entails that our credence in the splash is low, so it won’t seem like my finger-resting causes it. But with a multitude of minor events in our past, it seems we can be confident that there is a vast array of anonymous past events caused by everything we do in the present.Footnote ¹⁰

Rampant backward causation follows as a corollary of Albert’s causal account plus a commonsense idea about how records vanish, and it contradicts the standard view that backward causation is rare/nonexistent. To deal with this, we face a trilemma: either give up the view that backward causation is rare/nonexistent, revise our ideas about vanishing records, or abandon Albert’s causal account altogether. In the next section, I motivate option two.

5. The Dispersion Mechanism

In this section, I propose a mechanism whereby an event’s records persist even though they appear to vanish. I shall start by clarifying the statistical relationship between events and their immediate records. Then, by applying these ideas iteratively for later times, I will develop a picture of how events relate to their more temporally remote records.

Any event C raises the chance of a potential record of it, such as A:

(1) $$\Pr ( A \mid C ) \gt \Pr ( A \mid \neg C ).$$

For example, a splashing carp raises the chance of the formation of a circular wave. However, we know from experience that C doesn’t guarantee A:

(2) $$\Pr ( A \mid C ) \lt 1.$$

In our example, the wave could be suppressed by a sheet of glass or a well-orchestrated gust of wind. What, then, does guarantee A’s occurrence, prior to that event?

In a deterministic system, every event has a “determinant” at every other moment of time, a “minimal set of conditions jointly sufficient, given the laws of nature, for the fact in question” (Lewis Reference Lewis1979, 474). A determinant is a time-slice of the event’s past or future light cone.Footnote ¹¹ A’s prior determinant is therefore C plus some very complex, far-reaching, microscopically specified set of “background conditions” $U_A$ :

(3) $$\Pr ( A \mid C \land U_A) = 1.$$

This is illustrated in Figure 1.

Figure 1. Record A drawn with its prior determinant, “C plus $U_A$ ” (the time axis runs from left to right). Solid lines represent causal correlations.

From experience, it seems plausible that C generally leaves behind multiple records, even though no particular item is guaranteed. This implies that the $U_i$ conditions are not mutually exclusive, and they may be numerous. We can incorporate this into our example by imagining that in addition to $U_A$ leading to the circular wave A, there also exists $U_B$ , which leads to a curious heron B. This is illustrated in figure 2.

Figure 2. Records A and B drawn with their prior determinants, “C plus $U_A$ ” and “C plus $U_B$ ,” respectively. The dotted line represents a noncausal correlation.

So, given C, multiple records tend to form, depending on which $U_i$ conditions happen to obtain. But if we make the assumption that $U_i$ conditions are uncorrelated, the records that end up forming will also be uncorrelated—that is, uncorrelated given C.Footnote ¹² The upshot is that in the wake of C, the records that actually materialize will seem to us to be randomly selected from the set that potentially could have materialized, which is to say the set normally associated with C.

To understand why this is significant, let’s reiterate this logic to see how events like C relate to their more temporally remote records. By construing one of these records (say, A) as a recordable event in its own right, we can give it the same treatment as C itself. This again produces various new records, depending on which $U_i$ conditions obtain. For example, D (a startled dragonfly) might result if $U_D$ obtains, whereas E (a wobbling reed) might result if $U_E$ obtains. This is shown in figure 3. Whereas A is a “first-generation” record of C, we can think of D and E as “second-generation” records of C.

Figure 3. Second-generation records D and E, together with all background conditions that they depend on.

It’s easy to see the pattern emerging: D, for instance, might cause F (well-fed frog) if $U_F$ obtains, and it might cause G (awestruck fisherman) if $U_G$ obtains. This is shown in figure 4. Whereas F and G are immediate or “first-generation” records of D, they are “third-generation” records of C.

Figure 4. Third-generation records F and G of C, along with all background conditions that they depend on. For simplicity, I’ve omitted the second-generation record E (which branches off from A) and the third-generation records it yields.

This “dispersion mechanism” suggests that later-generation records become harder to utilize than early-generation records for two reasons. First, they are more “motley” and hence harder to recognize as records of the original event. Second, even if these records could be recognized as such, they’re less reliable in their own right. Let me unpack these claims in turn.

What I call the “motleyness” of later-generation records is a by-product of two things that happen over time. On the one hand, the range of possible later-generation records of C becomes larger. This can be appreciated by filling in my omission in figure 4 (see caption). On the other hand, the chance of any given later-generation record becomes smaller because its formation hinges on a longer list of $U_i$ conditions obtaining. For example, whereas A hinges on $U_A$ alone, F hinges on $U_A$ , $U_D$ , and $U_F$ . Taken together, these two factors (“more diverse” and “less certain to appear”) entail that later-generation records have a miscellaneous, motley character, making them less obviously symptomatic of the original event. This is clear in our example: we all recognize a circular wave as indicating a splashing fish, but who can say the same about a well-fed frog?

Meanwhile, the unreliability of later-generation records can be understood as follows: In order to be reliable, a putative record of C must have a veridical genealogy stretching back to that event. However, later-generation records have longer genealogies. This is clear from Figure 4: A only depends on the genuine occurrence of C, whereas F depends on the genuine occurrences of D, A, and C. Therefore, when we trace back their origins, later-generation records have more opportunities to be spurious than early-generation records. Our example helps illustrate the contrast: whereas a circular wave misleads us about C if it’s caused by a falling pine cone (and not the splashing carp), a well-fed frog misleads us about C if the frog ate a mosquito (and not a dragonfly), or if the dragonfly was startled by a swan (and not the wave), or if the wave was caused by a pine cone (and not the carp).

So, here is a short summary of the foregoing. Events generally produce multiple records, none of which is guaranteed, and because $U_i$ conditions are uncorrelated, those records that actually materialize seem randomly realized from the set of possibilities. By reiterating this logic for each of these records, we obtain a picture in which C’s late-generation records are motley and unreliable. This means that even long after an event, records still remain, even though they seem to have vanished.

For clarity, let’s see how this blocks backward causation. Suppose there’s an event y in our past. What’s the probability of a present event x causing it? This is high when the causal criteria are satisfied, and because Criterion 1 is satisfied, we must turn to Criterion 2. However, y occupies the role of C in this picture, and it therefore leaves records in the present via the dispersion mechanism. Because $N_\star$ also contains these records, $\Pr (y \mid N_\star ) \approx 1$ , and so Criterion 2 is probably false. This means x probably doesn’t cause y. Because this logic applies irrespective of whether y is a major or minor event, there isn’t a vast backlog of past events subject to backward causation. Hence, this phenomenon is genuinely rare/nonexistent after all.

One might raise the following objection. According to this picture, a given very late-generation record of y will be extremely unreliable. Therefore, when we conditionalize the Mentaculus on this record, this will raise the probability of y only marginally. But in order for it to be unlikely that a present event x can cause y, we require $\Pr (y \mid N_\star ) \approx 1$ ; that is, we require y’s counterfactual probability to be high. How can this be achieved?

The answer is that although records become less reliable with time, this is counterbalanced by the fact that they become more numerous. This follows from the fact that events leave behind multiple records; because this holds true for records themselves, we would expect the sum total of C’s records to mushroom with each iterative generation. Again, this is apparent in Figure 4. So, granted that conditionalising on any single very late-generation record raises y’s probability only marginally, conditionalising on all of them raises this value significantly. Because $N_\star$ embeds the whole lot, $\Pr (y \mid N_\star ) \approx 1$ still stands. So, even long after y has occurred, the chance of a present event x causing it will remain low.

This section comes with a caveat. The dispersion mechanism rests on the notion that events do in fact leave behind multiple first-generation records. However, I did not prove this; I merely stipulated it as plausible. A sceptic might therefore push back by arguing that this isn’t true of certain microscopic events—say, a particular Martian dust particle falling in the distant past— which are therefore vulnerable to backward causation. If this doubt is well founded, what would it bode for my account?

My response is that microscopic events like these are not the sorts of ordinary events that usually appear in counterfactuals. Indeed, it looks like the degree to which an event might feasibly fail to leave behind records—and hence fail to be protected from backward causation—is the degree to which it doesn’t feature in our standard causal discourse. So, even in this pessimistic scenario, my proposal would still block backward causation of ordinary minor events like splashing carps—and hence still benefit Albert’s account, which at face value only avoids backward causation of major events like sunken cities.

6. Implications for control

What does it mean for us to control something? It seems clear that in order to control an event, we need to cause it in the first place. At the same time, there are many things that we cause but do not control: happy accidents like roulette wins, unhappy accidents like wine spillages, and the innumerable events that we bring about through our daily activities but aren’t even aware of. This implies that whatever control amounts to, it must be some sort of a narrow species of causation. So, if it turned out that we can control the past, this would be even more surprising than if we could merely cause it.

Back in section 3, we saw that Albert defended his account by claiming backward causation is unverifiable. However, some have countered this by describing scenarios where our awareness of this phenomenon is a built-in feature. They then go on to argue that in such circumstances, we can not only cause past events but also control them. In this section, I shall use the dispersion mechanism sketched earlier to argue that in these situations, backward causation probably isn’t happening in the first place, so these alleged instances of backward control fall at the first hurdle.

Our first task is to pin down what it might take to control an event. There are few who doubt that causation is a necessary condition for control. The sufficient conditions, however, are less clear-cut. According to Frisch (Reference Frisch, Hüttemann and Ernst2010), these amount to “causation plus epistemic access to the consequences.” According to Albert (Reference Albert and Wilson2014) and Fernandes (Reference Fernandes, Loewer, Winsberg and Weslakeforthcoming), these amount to something stronger: “causation plus profitability of the consequences.” The two examples that follow purport to satisfy these two sets of sufficient conditions (respectively) and thereby show how Albert’s account allows situations where we can control the past. Let’s look at these in turn.

The first case, from Frisch (Reference Frisch, Hüttemann and Ernst2010), runs as follows: Suppose I’m playing the piano, and a certain melody appears in the score twice, where it’s followed by two different endings. So, the score proceeds as follows: melody, first ending, melody, second ending. Now, during my performance, I can’t remember whether I played the melody once or twice. However, I know from experience that I always play this song correctly. This means that when I play the first ending, this is a reliable record of my having played the melody once, and when I play the second ending, this is a reliable record of my having played the melody twice. Let’s also assume that which ending I decide to play is the only record of how many times I played the melody.

For argument’s sake, imagine I play the first ending (x). This makes it highly likely that I played the melody just once (y), and so $\Pr (y \mid N_0) \approx 1$ . x causes y iff the causal criteria are satisfied, and because Criterion 1 is probable, the key question is whether or not Criterion 2 is probable. But this is probable, for had I played the second ending ( $\neg x$ ), it would be highly likely that I played the melody twice ( $\neg y$ ), and so $\Pr (y \mid N_\star ) \approx 0$ . Because the causal criteria are probably satisfied, x probably causes y. Because there are no records relevant to y besides the antecedent itself, Albert’s barrier to backward causation is overcome. Moreover, unlike in the Atlantis or carp scenarios, it’s part and parcel of the situation that I’m aware of this probable causal influence. This is because the records responsible for causal influence are my own actions, and I’m aware of when I perform these. If the sufficient conditions for control are “causation plus epistemic access to the consequences,” then my decision to play the first or second ending in the present allegedly controls how many times I played the melody in the past.

Albert’s (Reference Albert and Wilson2014) response to this example is that even if we have epistemic access to the consequences of our actions, this doesn’t count as control because we can’t profit from this knowledge. This brings us to Fernandes, (Reference Fernandes, Loewer, Winsberg and Weslakeforthcoming) example, which attempts to satisfy this stronger condition. I lay this out next.

Imagine I am seated in a room that has a persistent fly buzzing around it, and there is a video camera that records the fly’s location at $t_1$ . Additionally, this video camera is connected to a screen that reveals the fly’s location a moment later at $t_2$ . This apparatus was rigged up by a sadistic scientist who, upon observing the screen at $t_2$ , gives me a reward iff the fly buzzes past my face at $t_1$ . But as it happens, I am an expert fly-swatter, which means my swatting at $t_2$ is a reliable record of a fly buzzing past my face at $t_1$ , and my remaining still at $t_2$ is a reliable record of a fly not buzzing past my face at $t_1$ . In this scenario, the only records of the fly’s location at $t_1$ are my behavior and the image on the screen.

Now, let’s suppose that a fly buzzes past my face (y) at $t_1$ , and I swat at it (x) at $t_2$ . Does x cause y? Criterion 1 is satisfied by hypothesis. To probe Criterion 2, we consider the implications of me not swatting ( $\neg x$ ) at $t_2$ : in all likelihood, this would mean the fly didn’t buzz past my face ( $\neg y$ ) at $t_1$ , so $\Pr (y \mid N_\star ) \approx 0$ . As in Frisch’s example, both causal criteria are probably satisfied, so my swatting probably causes the fly to buzz past my face. But this time, whether or not I swat has an extra implication: it determines the image on the screen, and hence it determines whether or not I get a reward. As in the piano case, my awareness of backward causation is built into the scenario. But this time, my action ( $\neg x$ ) causes other present records of whether or not y occurred, from which I may profit. So, if the sufficient conditions for control are “causation plus profitability of the consequences,” then my decision to swat or not swat in the present allegedly controls the fly’s location in the past.

Most discussions about whether or not these scenarios involve backward control relate to the sufficient conditions: what these are and whether or not they’re satisfied.Footnote ¹³ It’s generally taken for granted that backward causation—a necessary condition—is in play. However, I shall deny this basic premise by appealing to the dispersion mechanism. This means we can discount these two alleged instances of backward causation while sidestepping this more in-depth debate about the sufficient conditions for control.

The previous two examples share a key similarity: backward causation is allegedly in play because $N_0$ contains no records of the consequent that also feature in $N_\star$ (in the piano case, this is because the only record is my action; in the fly case, this is because the only records are my action plus other records it causes). If such records existed, they would cement the matter of whether or not y occurred, preventing its probability from varying much between $N_0$ and $N_\star$ and thus obstructing backward causation/control.

However, precisely such records generally do exist in the present. Most significantly, if my present actions are genuine records of what I did a few moments ago, then these cannot simply pop out of nowhere. They must have physical precursors that have persisted since that time—presumably, records that have been stored in my brain. But the dispersion mechanism suggests that there will probably be many other records at this time: light leaving the window, air currents, DNA traces, and so on. These are often relatively motley and unreliable, hence why we tend to ignore them when envisaging scenarios like the ones described earlier. But they probably exist all the same. Therefore, whether or not I play the second ending or swat will probably not cause past events because this will be fixed (with high likelihood) by these many records in the present. So, backward causation/control is unlikely in both scenarios.

It is tempting to respond as follows: When evaluating counterfactuals, the explicitly stated antecedent $\neg x$ isn’t the only respect in which $N_\star$ differs from $N_0$ . We almost always have to flesh out $N_\star$ with additional alterations. At the bare minimum, some gravitational fields must be redrawn to account for the fact that the antecedent entails a different matter distribution from our world—however slight.Footnote ¹⁴ Therefore, perhaps $N_\star$ is not just a world in which I act differently in the present but also a world in which all records—including those in my brain—indicate a different past than the one indicated by $N_0$ .

The problem, however, is that this is asking for an awfully large gulf between $N_0$ and $N_\star$ . In asking for all records of my melody-playing or the fly’s location to be different, we’re not just asking for a world in which I act differently in the present. We’re also asking for a world in which my brain’s contents are different, the light that left my window is different, the air currents are different, and so on. So, even if we grant that antecedents bring with them some extra changes (e.g., redrawn gravitational fields), a world this different from our own seems like a poor candidate for qualifying as $N_\star$ .Footnote ¹⁵

Of course, one is free to simply stipulate a scenario in which the dispersion mechanism fails and there are genuinely no other records besides the ones Frisch and Fernandes describe. In these highly unusual circumstances, backward causation would indeed be likely, and my proposed obstacle to backward control would be lifted. However, we generally wouldn’t know whether or not this situation obtains because the sorts of records I’ve been describing are motley and unreliable. So once again, we run into a familiar distinction: even when the chance of backward causation is high (as in this instance), we’d be none the wiser, so Albert’s original unverifiability defense rearises.