TRUMPING OR SIMULTANEOUS PREEMPTION Another kind of example that the Ludovician causal chain response cannot handle is preemption by trumping (first proposed by Jonathan Schaffer 2000). Suppose event E is produced simultaneously by two processes of two distinct kinds K and K′. In “Causation as Influence” (Lewis 2000), David Lewis uses orders by two officers of different and comparable ranks, such as simultaneous and conflicting orders from a captain and a sergeant to a private, to illustrate this type of situation. Whenever orders of these two kinds conflict, the order of kind K (from the superior officer) always wins. In the actual case, the two orders have exactly the same propensity: to produce E. Let's suppose, for example, that both the captain and the sergeant simultaneously order the private to fire. In such cases, the captain's order is the only cause of the private's actions, despite the fact that the two processes culminate at the same instant, with no preempted intermediaries. The sergeant's order is preempted by being trumped by the captain.2
1C. LEWIS'S HYBRID COUNTERFACTUAL THEORY. Before we move on, there is one historical complication to mention. David Lewis's own Counterfactual Theory of Causation (in Lewis 1973a) may not in fact have been a version of Causal Explanationism. Lewis posited the existence of events as the relata of causation. The causal connection between two events, C and E, is then analyzed by means of a counterfactual conditional:
Simple Ludovician Counterfactual Theory: C immediately causes E if and only if had C not occurred, E would not have occurred.
Since Lewis recognizes causation as involving a connection between things, namely, events, Ludovicians could respond to the problem of causal linkage by simply adding some further link between the two events, a link of causal priority:
Hybrid Ludovician Theory: C (immediately) causes E if and only if C is causally prior to E and, if C had not occurred, E would not have occurred.
The causal priority relation could then be thought of as some asymmetric connection between events, not to be analyzed in terms of counterfactuals.
Ludovicians could respond to the problem of linkage in another way, by way of event fragility. The Ludovician theory with fragility analyzes the causal connection between two events in terms of an asymmetric necessitation between the two events, considered as tokens rather than types. The idea is that this very event (the effect) couldn't have existed except in a world in which it results from that every event (the cause). Hence, if the cause had not existed, it would have been impossible for the effect to exist. This kind of counterfactual dependency would work even in cases of overdetermination and of preemption, including late preemption and trumping.
However, this fragility defense is not available to Causal Explanationists, since it requires some kind of fundamental tie between events to serve as the ground of the asymmetric necessitation of causes by effects. If Ludovicians fail to posit such a fundamental tie, then they must posit brute necessary truths linking the propositions that affirm the existence of the disjoint events. For example, in the case of trumping preemption, Ludovicians would have to suppose that the effect is fragile, that the very same effect could not have occurred in the absence of the trumping order. However, when we ask why the effect is tied in this way to the trumping order and not to the trumped order, the only plausible answer is that the trumping order is the cause and the trumped order is not. Hence, fragility cannot provide Ludovicians with a non-circular solution to the problem of linkage.
27.1.1.2 Objection 2: The Problem of Causal Direction or Asymmetry.
The problem of causal direction or asymmetry charges that Causal Explanationism (in all of its forms) provides an inadequate account of the asymmetric direction of causation, from prior to posterior.
Deductive and probabilistic relations are independent of causal direction. For example, there are many cases in which we can deduce a cause from its effects (e.g., deducing the length of a flagpole from the length of its shadow). Similarly, an effect can raise the probability of one of its causes.
Counterfactuals may be more help. David Lewis (Lewis 1979b) argued that the Counterfactual Theory does provide an account of causal direction, since it is generally not true that if an event hadn't occurred, its cause would not have occurred. According to Lewis, all forward-tracking conditionals (from absence of cause to absence of effect) are true, while all backward-tracking conditionals (from absence of effect to absence of cause) are false.
Lewis argued that there are many cases in which conditionals of the form, ‘If A had happened, B would have happened’, are true when A occurs before B, but very few such conditionals are true when B happens before A. Thus, the truth-values of these conditionals can provide a basis for distinguishing time's direction, and thus for determining the direction of causal influence.
How does Lewis get this result, given that the fundamental laws of nature are all time-reversible, and given that his semantics for the conditional includes no explicit temporal bias? The result is supposed to follow from the way the arrangement of occurrent facts in our world interacts with Lewis's priorities for deciding closeness of possible worlds to our own. Lewis suggests four criteria for determining the closest possible worlds, for the purposes of evaluating counterfactual conditionals:
(1) It is of the first importance to avoid big, widespread, diverse violations of causal law.
(2) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails.
(3) It is of the third importance to avoid even small, localized violations of law.
(4) It is of little or no importance to secure approximate similarity of particular fact.
Recall the semantics for the counterfactual conditional discussed in Section 4.1. A conditional of the form ‘p []-> q’ is true in the actual world w just in case q is true in all of the worlds in which p is true that are closest to the actual world. (If there are no maximally close worlds, then it is enough if q is true in all of the p-verifying worlds that are closer to the actual world than some reference point.) In a conditional of the form ‘p []-> q’, p is the antecedent and q is the consequent. Thus, to evaluate such a conditional, we check if the consequent is true in all of the closest antecedent-verifying worlds.
Forward-tracking counterfactual conditionals with actually false consequents can often be true, since the closest world to the actual one in which the antecedent is true will be a world that matches the actual world throughout the past and right before the occurrence of the antecedent, the antecedent is realized as a result of a minor miracle, and the world thereafter evolves according to this world's natural laws. However, backward-tracking counterfactual conditionals with actually false consequents will rarely, if ever, be true, since meeting criterion 2 will force us to preserve an exact match with the actual world throughout the past, forcing the actually false consequent to remain false in the closest possible worlds.
However, this strategy for securing temporal direction and thereby causal asymmetry is problematic. Lewis has built into his application of criteria 1 and 2 a bias toward matching the past. We could instead consider a world that matches the actual world throughout the future, verify the antecedent by producing a small miracle immediately after its occurrence, and then evolve the history of the world backward, in accordance with the laws of nature. The past of such a world will be radically different from the actual past, just as the future of Lewis's preferred worlds are radically different from the actual future.
The crucial question, then, is which world has the smaller miracle: the world w1, with a past like the actual past and a miracle immediately before the antecedent's occurrence, or world w2, with a future like the actual future and a miracle immediately after the antecedent's occurrence? It is not at all easy to say. It certainly seems easier to figure out what kind of miracle is required in w1 than in w2, and that may give us some (fairly weak) reason for thinking that the w1-miracles are smaller than w2-miracles. For example, if our conditional is, ‘Had Nixon pushed the
button, there would have been thermonuclear war’, we have a pretty good idea how to verify the antecedent: produce a miracle in Nixon's brain, causing certain relevant neurons to fire that don't fire in the actual world. It's much harder to figure out exactly what miracle would be required in the immediate future of Nixon's button-pressing that would be needed to verify the button-pushing when we evolve the resulting processes backward.
However, Alexander Pruss (2003) argues that if there is such an asymmetry, it is an anthropocentric asymmetry. Most counterfactuals are forward-tracking rather than backtracking simply because it is the forward-tracking ones that are of most interest to us. It may be that which propositions or facts our languages express impose this asymmetry on the counterfactuals of natural languages, but from a God's eye point of view, the entire set of possible propositions is innocent of any such bias. Hence, at the end of the day, the counterfactual theory of temporal direction is a subjective, anthropocentric one, very similar to accounts, like von Wright's (1971), that define temporal direction in terms of our contingent human abilities to do some things by doing other things.
In addition, Lewis's account doesn't work in cases of probabilistic causality. In the deterministic case, some violation of the laws of nature is required, so a late and small miracle is to be preferred over an early and large one. However, in the probabilistic case, we could verify the antecedent without any violation of law. Shouldn't the avoidance of a miracle be worth a small degree of backtracking? Douglas Ehring (1997) considers a case where we have the following links: C-(50%)-B-(100%)-D-(50%)-E. What would be the closest non-D world? Lewis must say a world where both C and B occur, and then a miracle prevents the occurrence of D. However, wouldn't a world in which C but not B occur be at least as close? Such a world avoids miracles altogether. This would mean that the backtracking conditional ‘If D had not occurred, B would not have occurred’ would come out as true, by Lewis's criteria (see also Elga 2001).
OTHER EXPLANATIONIST ACCOUNTS There are several other accounts of causal direction that Causal Explanationists might offer. There are four accounts that have been most popular: temporal asymmetry, the asymmetry of kaon decay, the asymmetry of entropy, and Reichenbach's account of conjunctive forks. Let's consider these one at a time.
2A. TEMPORAL ASYMMETRY. Here is a fairly simple account of the direction of causation (suggested by David Hume): causes always occur before their effects. This makes the direction of causation depend on a prior or more fundamental direction of time. There are several objections to this account:
Objection 1. The problem of the directionality of time is no easier to solve than the problem of the directionality of causation. Physics is (in its fundamental laws) perfectly time-reversible (except perhaps for kaon decay—see 2c below). In fact, if there is a direction to time, it seems plausible to think that the direction of time depends on the direction of causation, and not vice versa.
Objection 2. It seems plausible that in many cases the cause and effect are simultaneous. In fact, we shall see in the next section that it is plausible that all cases of discrete causation are instantaneous, with the action of the cause and the passion of the effect's being simultaneous.
Objection 3. It seems possible for there to be cases of temporally reversed causation, where the cause is later than the effect. This happens quite often in science fiction and fantasy stories involving time travel or the precognition of the future. Some philosophers have proposed that time-reversed causation actually occurs at the quantum level. A decision to observe a certain property of a particle here and now affects the past of the particle in such a way as to indirectly bring about a change far away at the same time as the observation.
2B. ENTROPY. Another very popular account of the direction of both time and causation involves an appeal to entropy. The Second Law of Thermodynamics states that the total entropy, or disorder, of an isolated system always increases. We see many examples of this. Whole eggs are succeeded by broken eggs, but never vice versa. Tornados tear houses apart; they never assemble houses.
However, modern physicists do not generally consider the Second Law of Thermodynamics to be a fundamental law of physics. Following the work of Ludwig Boltzmann (1844–1906), most scientists and philosophers consider the Second Law to be only statistical in nature, specifying what happens in most cases, not all. Since ordered situations (situations with low entropy) are so rare, they are always more likely to be followed by situations with higher entropy. However, in the whole history of the world, there are an equal number of cases of low-entropy states arising from high-entropy states as there are of low-entropy states decaying into the more common high-entropy states.
On this standard view, the increase in entropy we see around us is merely an artifact of the fact that our local universe began with the Big Bang in such an unusually low-entropy condition. If the world consists of many such universes, then there may be just as many that start in a high-entropy condition and evolve toward extremely low entropy as there are universes like ours that start out in the unusual low-entropy condition and evolve toward higher entropy. If that's not the case, we need some further explanation of why universes must start out, as ours did, in such an orderly condition (see Price 1996 for more details).
2C. KAON DECAY. When we stated earlier that the fundamental laws of physics are time-reversible, we were over-simplifying somewhat. In fact, there is a difference between the actual and the time-reversed versions of many physical processes. If we know, for example, which particles are negatively charged and which are positively charged, we can tell which version of a process is actual and which is time-reversed. A time-reversed electron acts exactly as an ordinary positron (the positively-charged anti-particle of the electron) would. However, charge is itself perfectly symmetrical. A process in which both charge and time are simultaneously reversed would be indistinguishable from an actual process.
There is, though, a very rare and short-lived particle, the kaon, which decays in a way that violates the charge-time symmetry that is respected by all other physical processes. Phil Dowe (2000) has suggested that this charge-time asymmetry in kaon decay could be the fact that distinguishes the forward from the backward direction of time.
However, kaon decay, like all physical processes without exception, does satisfy a somewhat weaker symmetry principle: the charge-time-parity principle. If we simultaneously reverse time, charge, and left- vs. right-handedness, then we cannot distinguish kaon decay from kaon formation. Since parity (left- and right-handedness) are themselves intrinsically similar, the charge-time asymmetry of kaon decay does not pick out a unique direction to time. If kaon decay had occurred in the opposite direction, the only difference would have been that our universe would have been composed mostly of anti-matter instead of matter.
In any case, it seems implausible that the direction of causation depends on the occurrence of a single exotic and extremely rare kind of change. Causal asymmetry is both ubiquitous and local or intrinsic in character.
2D. CONJUNCTIVE FORKS. Hans Reichenbach (1958) suggested that the direction of time can be grounded in certain patterns of statistical correlation that exist in nature. Causal direction is to be defined in terms of the structure of conjunctive forks, making use of Reichenbach's principle of common cause.
Principle of Common Cause. If the joint probability of (A&B) is greater than the product of the probabilities of A and B, and if C is a proposition such that the joint probability of (A&B) given C is equal to the product of the conditional probabilities P(A/C) and P(B/C), then A, B, and C form a conjunctive fork (Reichenbach 1958).
The Conjunctive Fork Theory of Causal Direction. If propositions A, B, and C form a conjunctive fork, then C is causally prior to and causally connected to both A and B.
The direction of time is determined by the predominant direction of causation. The temporal direction D corresponds to the earlier-than relation if and only if most causes stand in the D relation to their effects. The
Conjunctive Fork Theory has been defended and further developed by Wesley Salmon (1984) and by Spirtes, Glymour, and Scheines (1993).
Frank Arntzenius (1993, 2010) has argued that the Conjunctive Fork Theory suffers from many scientific counterexamples, including quantum-mechanical correlations, correlations due to co-existence laws (like electromagnetism, gravitation or Pauli's exclusion principles), and correlations occurring in a deterministic universe. The theory only works when we can assume two things: an initial state of absolute, uncorrelated chaos, and spatial separation between the correlated properties. Thus, like the appeal to entropy, the appeal to Reichenbach's conjunctive forks depends on an apparently contingent and unexplained fact of our world's history, namely, its beginning in a condition in which certain properties are uncorrelated. The asymmetry of conjunctive forks is limited and derived, not universal and fundamental.
The Atlas of Reality Page 97
