Lecture 4


The Causal Theory Of Explanation, Part II

As we discussed last time, Salmon sought to replace the inferential view of explanation, which faces the asymmetry and irrelevance problems, with a causal theory, which postulates that an explanation is a body of information about the causes of a particular event. Today we will discuss Salmon's view in detail, as well as the related view of David Lewis.

Salmon's theory of causal explanation has three elements.

(1) Statistical Relevance - the explanans (C) increases the probability of the explanandum (E), i.e., pr(E|C) > pr(E).

(2) Causal Processes - the explanans and the explanandum are both parts of different causal processes

(3) Causal Interaction - these causal processes interact in such a way as to bring about the event (E) in question

This leaves us with the task of saying what a causal process is. Basically, Salmon's view is that causal processes are characterized by two features. First, a causal process is a sequence of events in a continuous region of spacetime. Second, a causal process can transmit information (a "mark").

Let us discuss each of these in turn. There are various sequences of events that are continuous in the required sense--e.g., a light beam, a projectile flying through space, a shadow, or a moving spot of light projected on a wall. An object that is sitting still, e.g., a billiard ball, is also deemed a causal process. Each of these is a continuous process in some sense but not all of them are causal processes--e.g., the shadow and light spot. Let's look at an example that makes this clearer. As some of you may know, relativity theory says that nothing can travel faster than light. But what is the "thing" in nothing? Consider a large circular room with a radius of 1 light year. If we have an incredibly focused laser beam mounted on a swivel in the center of the room, we can rotate the laser beam so that it rotates completely once per second. If the laser beam is on, it will project a spot on the wall. This spot too will rotate around the wall completely once per second, which means that it will travel at 2p light-years per second! Strangely enough, this is not prohibited by relativity theory, since a spot of this sort cannot "transmit information." Only things of that sort are limited in speed.

Salmon gives this notion an informal explication in "Why ask 'Why'?" He argues that the difference between the two cases is that a process like a light beam is a causal process: interfering with it at one point alters the process not only for that moment: the change brought about by the interference is "transmitted" to the later parts of the process. If a light beam consists of white light (or a suitably restricted set of frequencies), we can put a filter in the beam's path, e.g., separating out only the red frequencies. The light beam after it passes through the filter will bear the "mark" of having done so: it will now be red in color. Contrast this with the case of the light spot on the wall: if we put a red filter at one point in the process, the spot will turn red for just that moment and then carry on as if nothing had happened. Interfering with the process will leave no "mark." (For another example, consider an arrow on which a spot of paint is placed, as opposed to the shadow of the arrow. The first mark is transmitted, but the second is not.)

Thus, Salmon concludes that a causal process is a spatiotemporal continuous process that can transmit information (a "mark"). He emphasizes that the "transmission" referred to here is not an extra, mysterious event that connects two parts of the process. In this regard, he propounds his "at-at" theory of mark transmission: all that transmission of a mark consists in is that the mark occurs "at" one point in the process and then remains in place "at" all subsequent points unless another causal interaction occurs that erases the mark. (Here he compares the theory with Zeno's famous arrow paradox. Explain. The motion consists entirely of the arrow being at a certain point at a certain time; in other words, the motion is a function from times to spatial points. This is necessary when we are considering a continuous process. To treat as the conjunction of the discrete events of moving from A halfway to C, moving halfway from there, and so on, leads to the paradoxical conclusion that the arrow will never reach its destination. Transmission is not a "link" between discrete stages of a process, but a feature of that process itself, which is continuous.

Now we turn to explanation. According to Salmon, a powerful explanatory principle is that whenever there is a coincidence (correlation) between the features of two processes, the explanation is an event common to the two processes that accounts for the correlation. This is a "common cause." To cite an example discussed earlier, there is a correlation between lung cancer (C) and nicotine stains on a person's fingers (N). That is,

pr(C|N) > pr(C).

The common cause of these two events is a lifetime habit of smoking two packs of cigarettes each day (S). Relative to S, C and N are independent, i.e.,

pr(C|N&S) = pr(C|S).

You'll sometimes see the phrase that S "screens C off from N" (i.e., once S is brought into the picture N becomes irrelevant). This is part of a precise definition of "common cause," which is constrained by the formal probabilistic conditions. We start out with pr(A|B) > pr(A). C is a common cause of A and B if the following hold.

pr(A&B|C) = pr(A|C)pr(B|C)

pr(A&B|¬C) = pr(A|¬C)pr(B|¬C)

pr(A|C) > pr(A|¬C)

pr(B|C) > pr(B|¬C)

(The first condition is equivalent to the screening off condition given earlier.) These conditions are also constrained: A, B, and C have to be linked suitably as parts of a causal process known as a "conjunctive" fork.

(Consider the relation between this and the smoking-lung cancer, and leukemia-atomic blast cases given earlier.)

This does not complete the concept of causal explanation, however, since some common causes do not "screen off" correlated by (causally) independent events. Salmon gives Compton scattering as an example. Given that an electron e- absorbs a photon of a certain energy E and is given a bit of kinetic energy E* in a certain direction as a result, a second photon will be emitted with E** = E - E*. The energy levels of the emitted photon and of the electron will be correlated, even given that the absorption occurred. That is,

pr(A&B|C) > pr(A|C)pr(B|C).

This is a causal interaction of a certain sort, between two processes (the electron and the photon). We can use the probabilistic conditions here to analyze the concept: "when two processes intersect, and both are modified in such ways that the changes in one are correlated with changes in the other--in the manner of an interactive fork--we have causal interaction." Thus, a second type of "common cause" is provided by the C in the interactive fork.

Salmon's attempt here is to analyze a type of explanation that is commonly used in science, but the notion of causal explanation can be considered more broadly than he does. For example, Lewis points out that the notion of a causal explanation is quite fluid. In his essay on causal explanation, he points out that there is an extremely rich causal history behind every event. (Consider the drunken driving accident case.) Like Salmon, Lewis too argues that to explain an event is to provide some information about its causal history. The question arises, what kind of information? Well, one might be to describe in detail a common cause of the type discussed by Salmon. However, there might be many situations in which we might only want a partial description of the causal history (e.g., we are trying to assign blame according to the law, or we already know a fair chunk of the causal history and are trying to find out something new about it, or we just want to know something about the type of causal history that leads to events of that sort, and so on). Lewis allow negative information about the causal history to count as an explanation (there was nothing to prevent it from happening, there was no state for the collapsing star to get into, there was no connection between the CIA agent being in the room and the Shah's death, it just being a coincidence, and so on). To explain is to give information about a causal history, but giving information about a causal history is not limited to citing one or more causes of the event in question.

(Mention here that Lewis has his own analysis of causation, in terms of non-backtracking counterfactuals.)

Now given this general picture of explanation, there should be no explanations that do not cite formation about the causal history of a particular event. Let us consider whether this is so. Remember the pattern of D-N explanation that we looked at earlier, such as a deduction of the volume of a gas that has been heated from the description of its initial state, how certain things such as temperature changed (and others, such as pressure, did not), and an application of the ideal gas law PV = nRT. On Hempel's view, this could count as an explanation, even though it is non-causal. Salmon argues that (1) non-causal laws allow for "backwards" explanations, and (2) cry out to be explained themselves. Regarding the latter point, he says that non-causal laws of this sort are simply descriptions of empirical regularities that need to be explained. The same might occur in the redshift case, if the law connecting the redshift with the velocity was simply an empirical generalization. (Also, consider Newton's explanation of the tides.)

Let's consider another, harder example. A star collapses, and then stops. Why did it stop? Well, we might cite the Pauli Exclusion Principle (PEP), and say that if it had collapsed further, there would have been electrons sharing the same overall state, which can't be according the PEP. Here PEP is not causing the collapse to stop; it just predicts that it will stop. Lewis claims that the reason this is explanatory is that it falls into the "negative information" category. The reason that the star stopped collapsing is that there was no physically permissible state for it to get into. This is information about its causal history, in that it describes the terminal point of that history.

There are other examples, from quantum physics, especially, that seem to give the most serious problems for the causal view of explanation, especially Salmon's view that explanations in science are typically "common cause" explanations. One basic problem is that Salmon's view relies on spatiotemporal continuity, which we cannot assume at the particulate level. (Consider tunneling.) Also, consider the Bell-type phenomenon, where we have correlated spin-states, and one particle is measured later than the other. Why did the one have spin-up when it was measured? Because they started out in the correlated state and the other one that was measured had spin-down. You can't always postulate a conjunctive fork. This should be an interactive fork of the type cited by Salmon, since given the set-up C there is a correlation between the two events. However, it is odd to say the setup "caused" the two events when they were both space-like separated! We will consider these problems in greater detail next week.