Causality and Explanation: A Reply to Two Critiques* Wesley C. SalmonH Department of Philosophy, University of Pittsburgh and Universitiit Konstanz This paper discusses several distinct process theories of causality offered in recent years by Phil Dowe and me. It addresses problems concerning the explication of causal pro- cess, causal interaction, and causal transmission, whether given in terms of transmission of marks, transmission of invariant or conserved quantities, or mere possession of con- served quantities. Renouncing the mark-transmission and invariant quantity criteria, I accept a conserved quantity theory similar to Dowe's-differing basically with respect to causal transmission. This paper also responds to several fundamental construc- tive criticisms contained in Christopher Hitchcock's discussion of both the mark- transmission and the conserved quantity theories. 1. Introduction. The June 1995 issue of Philosophy ofScience contained two penetrating discussions of my views on causality and explanation. In "Causality and Conserved Quantities: A Reply to Salmon", Phil Dowe correctly states that we already agree on much, but that impor- tant differences remain. The first part of this reply (§2-7) explores fur- ther the similarities and differences between our two theories; it focuses entirely on our process theories of causality. In "Salmon on Explana- tory Relevance", Christopher Read Hitchcock raises problems con- cerning the nature and role of causality in scientific explanation that *Received February 1996. ·!·Send reprint requests to the author, Department of Philosophy, University of Pitts- burgh, 1001 Cathedral of Learning, Pittsburgh, PA 15260. ti should like to express my gratitude to the Alexander von Hmnboldt Foundation for support of research embodied in this paper and to the University of Konstanz for pro- viding a congenial environment in which to carry it out. My thanks also go to Paul Hoyningen-Huene and Johanna Seibt for helpful and clarifying comments on the issues here addressed. I am most especially grateful to Phil Dowe, Christopher Hitchcock, and Philip Kitcher for their insightful contributions to the discussion of causal explanation. Philosophy of Science, 64 (September I 997) pp. 461 -477. 0031-8248/97/6403-0004$2.00 Copyright 1997 by the Philosophy of Science Association. All rights reserved. 461 462 WESLEY C. SALMON apply just about equally to Dowe and me. These are addressed in the second part (§8-11 ). All three of us agree that, in one way or another, process theories of causality are important and viable. I hold, more- over, that such a theory provides an answer to Hume's famous question about the nature of causal connections. 2. Directionality: Temporal and/or Causal. In sketching a bit of back- ground for the mark-transmission criterion for distinguishing causal processes from pseudo processes (Salmon 1994, 302-303), I pointed out that Reichenbach had maintained that the mark method was ca- pable of establishing a time direction, but that Griinbaum had refuted that claim. I went on to state my earlier view that "the mark method provided a criterion for distinguishing between causal processes and pseudo processes, without any commitment to time direction" (ibid.). Unfortunately, although I intended to retain this neutrality with respect to direction in making the transition from the mark transmission cri- terion to the transmission of invariant (or conserved) quantities crite- rion, I failed to do so in the crucial DEFINITION 3: A process transmits an invariant (or conserved) quantity from A to B (A # B) if it possesses [a fixed amount of] this quantity at A and at B and at every stage of the process between A and B without any interactions in the half-open interval ( A,B j that involve an exchange of that particular invariant (or conserved) quantity. (Ibid., 308) As Dowe points out, the phrase "from A to B" obviously implies a direction. He also mentions the need for an only if condition in the definition. Both flaws can be repaired by slight reformulations (as in- dicted by emphasis). Moreover, for reasons that will become clear in §9-the corollary formulated in that section depends on conserva- tion-! now wish to follow Dowe in formulating the criteria in terms of conserved, rather than invariant, quantities. A process transmits a conserved quantity between A and B (A # B) if and only if it possesses [a fixed amount of] this quantity at A and at B and at every stage of the process between A and B without any interactions in the open interval (A,B) that involve an exchange of that particular conserved quantity. This reformulation should be substituted for the previous DEFINITION 3. Dowe distinguishes two types of asymmetry, causal and temporal. I agree that the two need not coincide. It is not a priori impossible for some causal processes to transpire in a direction contrary to the direc- tion of time; for example, there is nothing logically absurd in Richard Feynman's interpretation of the positron as an electron moving back- CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 463 ward in time. Moreover, the "transactional" interpretation of quantum mechanics, cited by Dowe, cannot be ruled out a priori just because it appeals to "backward causation." Like Dowe, I want to adhere to a causal theory of time, and this commitment precludes defining causal direction in terms of temporal direction. It does not, however, preclude "backwards in time causation" if a great preponderance of causal pro- cesses go in the same direction. It was not my intention in Salmon 1994 to introduce either temporal direction or causal direction; such asymmetries require separate treat- ment in terms of conjunctive forks, increase of entropy, or neural K- meson decay (see, for example, Dowe 1992b). I do not believe there is any residual difference of opinion between us on this issue. 3. The Conservation of Conserved Quantities. In formulating DEFINITION 3, I intended to convey the condition that any conserved quantity that characterizes a causal process retains a constant value as long as there is no causal interaction with another process involving an exchange of that quantity. (The bracketed insertion makes this supposition ex- plicit.) The fundamental idea is that a fixed amount of the conserved quantity is transmitted by the process in question; it doesn't have to be replenished from another source such as the spotlight that illumi- nates a spot on a wall. I assumed that Dowe intended a similar stipu- lation about conserved quantities in causal processes. It seemed rea- sonable to suppose that on his view conserved quantities are conserved overall in interactions involving exchanges of such quantities, and that their values remain constant in the absence of such interactions. Com- menting on this point, Dowe says, Of course, if we are talking about conserved quantities this obvi- ously must be true. However, there are pragmatic difficulties: ac- tual causal processes do not operate in the absence of interactions. A body moving under the action of a field, for example, is really a string of interactions. In reality most causal processes attenuate, as there is loss of energy to the environment. It seems that if we wish to accommodate the standard types of causal processes (e.g., Salmon's example of the moving baseball) then we will have dif- ficulties with this requirement. In theory, causal processes do pos- sess a fixed amount of energy, say, in the absence of interactions, but in practice such a requirement renders useless the notion of a causal process, as opposed to an interaction. For this reason the CQ [conserved quantity] theory does not require that a causal pro- cess possess a constant amount of the relevant quantity over the entire history of the process. (1992b, 331) 464 WESLEY C. SALMON Appearances to the contrary notwithstanding, there is little, if any, disagreement here. In presenting my theory of causal processes and interactions, I am talking in theory. I want to understand what is fun- damentally involved in causal transmission and interaction. The prag- matic problems are not at issue. In the vast majority of cases I would analyze what Dowe considers a single causal process into a large num- ber of distinct but connected processes. The difference is mainly ter- minological. When it comes to practical investigation of actual processes prag- matic considerations determine the level of analysis. For some purposes the motion of a molecule of a gas between collisions with other objects (other molecules, Brownian particles, or walls of containers) may be considered a single causal process; for other purposes the motion of a baseball from a bat to a window (in spite of innumerable collisions with molecules in the atmosphere) may be regarded as a single causal process. I think we gain greater philosophical insight into causality by operating at a rather rarified theoretical level, recognizing, of course, that we must often descend from such abstract heights when it comes to practical investigations. There are many empirical methods for dis- covering and identifying causal processes. Lest anyone believe that I have completely lost contact with physical reality in discussing extended causal processes without causal interac- tions, it should be noted that the mean free path of photons in inter- galactic space is estimated in terms of very large numbers oflight years. Such photons are causal processes, and the mean free path is the av- erage distance between causal interactions with other processes. This fact may actually aid us in understanding why the night sky is dark (Olbers' paradox). 4. Causality and Fields. As we know, flying baseballs and other projec- tiles fall toward Earth with the same acceleration as Newton's apple. Ignoring for now the issue of action-at-a-distance, we should note that classically speaking there is a continuous interaction between two mu- tually gravitating bodies. In my past discussions of causal interactions, thinking in terms of causal interactions connected by causal processes, I have treated interactions as discrete occurrences. This approach has neglected the causal significance of fields-gravitational, electromag- netic, or whatever-a point Dowe raises in the preceding quotation. The issue need not detain us, however, for there is no need to deny the existence of a continuous series of interactions. In this context, we may go back to air resistance and wind, regarding them for practical pur- poses as results of a continuous series of interactions with a homoge- neous medium, neglecting the particulate character of the atmosphere. CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 465 Where atmospheric effects are concerned we are making an idealizing simplification; with classical gravitation we are not. Does an object like a baseball or a bullet then fail to qualify as a causal process? Suppose it is moving in a vacuum and is subject to no external forces~i.e., Newton's first law applies. It is often said that in Newtonian mechanics (in contrast to Aristotelian physics) such uni- form motion needs no explanation; only changes of states of motion require explanation. I would say that such an object constitutes a causal process not subject to any interaction. This is the explanation~it is a particular type of causal process that is just doing its own thing without external interference. Now consider an object falling freely toward Earth in a vacuum. According to classical physics it is changing its state of motion, and the gravitational force explains this change; in my terms we would refer to a continuous series of interactions between this object and Earth's gravitational field. Considered from the standpoint of general relativ- ity, however, the worldline of this object is a geodesic in spacetime. This is the relativistic analogue of Newton's first law. It has been rightly said that, while Newton's theory requires an explanation of the apple's falling, relativity requires instead only an explanation of its stopping when it hits the ground. On my view any such falling object is a single causal process that is free from interactions. This point applies to pho- tons as well as to material particles. As far as explanation of such motion is concerned, it suffices to specify the spacetime metric. Action- at-a-distance is not involved; the moving particle responds to the local spacetime structure. Electromagnetic phenomena are different. According to our best contemporary theory, quantum electrodynamics, the electromagnetic force is mediated by exchanges of photons. This means, in my terms, that whenever a photon is emitted or absorbed by a charged particle we have a causal interaction. Thus a charged particle undergoing ac- celeration in an electromagnatic field consists of a series of causal pro- cesses standing between frequent causal interactions. It is analogous to a baseball moving through air. For most practical purposes we can, of course, idealize the situation and treat the electromagnetic field as con- tinuous, much in the same manner as we treated the air as a continuous medium above. Action-at-a-distance is excluded from the account of the motions of charged particles. It may be that the gravitational force is mediated by spin-two un- charged particles known as gravitons, in somewhat the same way as the electromagnetic force is mediated by photons, but it is too soon to say whether this is a correct account. We do not yet have a unified theory of gravitation and electrodynamics. 466 WESLEY C. SALMON 5. Transmission. The fundamental point on which Dowe and I do ac- tually disagree also concerns DEFINITION 3. Dowe says that it is unnec- essary; I claim that it is indispensable. The issue concerns the concept of transmission, and it is centered on the final clause of the definition, "without any interactions ... that involve an exchange of that partic- ular conserved quantity." In support of my view I invited consideration of a paradigmatic case of a pseudo process, namely, a spot of light moving across a wall. In earlier writings (e.g., Salmon 1984, 145-146) I had argued that the spot possesses energy, but the energy is not trans- mitted; therefore, mere possession of (a fixed quantity) of energy is not a sufficient condition for the status of causal process. Dowe replied (1992a, 127) that the bright spot does not possess energy; instead the illuminated patch of wall has it. Taking Dowe's point, I then suggested that the patches of the surface layer of the wall that absorb the energy would qualify collectively as a causal process with respect to Dowe's criterion. Dowe responds that such a "gerrymandered aggregate" does not really qualify as a thing that can possess conserved quantities. So, we are left with the problem of determining what kinds of "things" can possess conserved quantities and what kinds of "things" cannot. I ad- dress this question in §6. Before discussing that issue, I must comment on Dowe's assertion that "Salmon's account in terms of the transmission of an invariant quantity is itself vulnerable to this objection. For according to that ac- count, transmission amounts just to regular appearance ... if counter- examples such as the rotating spotlight [spot] count as cases of regular possession then they count also as cases of transmission" (Dowe 1995, 327). This criticism is untenable precisely because it overlooks the clause in DEFINITION 3 that precludes outside interactions. The spot of light traveling around the wall exists by virtue of constant illumination from the central spotlight. The energy that appears in the successive patches of the surface of the wall is present only because it is constantly being supplied by an outside source. These are cases in which some- thing is present in all of the intermediate stages of a (pseudo) process, but it is not "present without any interactions ... that involve an ex- change of that particular conserved quantity" (DEF. 3). From my point of view the crucial question regarding causal processes is what they do on their own without outside intervention. My answer is that they transmit something---e.g., conserved quantities, information, or causal influence~and it is by virtue of such transmission that events at A and B (DEF. 3) are causally related. Dowe gives a different answer. 6. Gerrymandered Aggregates vs. Objects. Dowe lays his cards on the table when he says, "there is implicit in the CQ [conserved quantity] CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 467 theory a restriction on what counts as an object. This now needs to be made explicit. I take it that an object must be wholly present at a time in order to exist at that time" (Dowe 1995, 329; Dowe's italics). Ac- cording to Dowe, "time-wise gerrymanders" do not fulfill this require- ment. He invites consideration of the following putative object x (ibid., 328): for t1 s; t < t2 ; xis the coin in Dowe's pocket for t2 s; t < t3 ; x is the red pen on Dowe's desk for t3 s; t < t4 ; x is Dowe's watch It is intuitively clear, for example, that at time T (t2 < T < t3 ) the pen part of x is present but the coin part and the watch part are absent. One reason for this intuitive clarity is the obvious spatiotemporal dis- continuity of x. Since I take causal processes to be spatiotemporally continuous, I am not tempted to regard x as a causal process (though each of the three pieces is). Dowe allows that the spot of light is an object (1995, 329), but it is not the kind of object that possesses conserved quantities. It has size, shape, and speed; it does not have energy, momentum, or electric charge (ibid., 327). I agree. Thus, the spot is not a causal process ac- cording to the conserved quantity theory. Moreover, he argues, neither is the portion of the surface of the wall that is illuminated by the mov- ing spot oflight a causal object; it is a time-wise gerrymander-inPhilip Kitcher's term, a piece of "spatiotemporal junk." It fails the criterion of being wholly present at any given moment in its 'history'. I disagree. Given that this four-dimensional 'object' has a continuous worldline, of which we may take a slice at any moment, I would ask why that time-slice is not wholly present in Dowe's sense. Dowe responds by distinguishing two different ways of viewing ob- jects, namely, (1) as three-dimensional entities having temporal histo- ries or (2) as four-dimensional entities whose totalities include a tem- poral dimension as well as three spatial dimensions. An object of the former type can be wholly present at any given moment of its history; an object of the latter type has temporal parts that are wholly present at various moments, but (given that it has nonzero duration) it is not wholly present at any particular moment. Dowe opts for the first ap- proach, which is certainly legitimate; I do not have a strong preference as long as we are clear about which of them is being adopted. For purposes of this discussion it does not really matter, because, as Dowe explicitly states, in either manner of speaking the key point is the same. Regarding the first alternative, one needs a way of determining whether a given putative object is wholly present at a given time; this requires 468 WESLEY C. SALMON a relation of identity over time, as one easily sees in connection with time-wise gerrymanders. Dowe says, "the CQ theory identifies genuine causal objects according to the possession of certain properties at a time, and identifies genuine processes over time via the additional pre- sumption of a relation of identity over time" (1995, 330). Regarding the second alternative, he says, "the CQ theory takes identity over time as primitive" (ibid.). On either approach he is using the concept tra- ditionally called genidentity without offering an analysis of it. The concept of genidentity is not intuitively easy. Consider the spacetime portion of wall surface that is illuminated by the moving spotlight, each part of the surface belonging to it only during the time that it is actually illuminated. One might say that this is not a gen- identical object because it does not consist of the same molecules at different times in its history. But consider also my body. It has been said-whether truly or not I do not know-that the human body un- dergoes a complete change of cells in any seven year period. If this is true I have undergone about ten complete replacement cycles in my three score and ten years of life; yet, although my body has undergone many changes from birth to its present stage, I consider myself to have possessed the same body. A similar consideration applies to a boat that has been repaired so many times that no original piece remains in it. Things are even worse in the quantum domain. As Feynman (1965, Sec. 3-4) explains, when two identical particles collide and recoil from each other, it is impossible in principle to determine which outgoing particle is genidentical with which entering particle. The concept of genidentity breaks down. This fact has empirical consequences in the probabilities for scattering at various angles. 7. Transmission vs. Genidentity. The upshot of the foregoing discussion is that I have offered a concept of causal transmission, analyzed in terms of the "at-at" theory, for which Dowe has traded an unanalyzed concept of genidentity. This is not, I think, an advantageous exchange. To be sure, as I acknowledged above, the analysis that I gave in Salmon 1994 was faulty. I believe, however, that DEFINITION 3 as given above is correct. Taken in conjunction with DEFINITION 1: A causal interaction is an intersection of world-lines that involves exchange of a conserved quantity, and DEFINITION 2: A causal process is the world-line of an object that transmits a non- zero amount of a conserved quantity at each moment of its history (each spacetime point of its trajectory), CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 469 it yields a criterion that is impeccably empirical, and thus it provides an acceptable answer to the fundamental problem Hume raised about causality. (In §9 a corollary of these definitions will be spelled out ex- plicitly to deal with a putative counterexample given by Hitchcock). The aim, which I hope to have achieved, is to make clear the fashion in which causal influence is propagated throughout our world. 8. The Mechanical Philosophy. In his penetrating discussion, "Salmon on Explanatory Relevance", Christopher Read Hitchcock concludes, "In the new mechanical philosophy [Salmon's], as in the old, the ex- planatory store contains nought but geometric properties" (1995, 319). This, he says, is not enough to capture the concept of explanatory relevance. In support of his claim about the early mechanical philos- ophers he cites Eduard Dijksterhuis's statement, "The only properties recognized as explanatory principles were the size, the shape, and the state of motion of corpuscles, supplemented by characteristics of their aggregates that could also be defined geometrically" (ibid., 318). Al- though this remark applies correctly to Descartes, it does not properly apply to all other early mechanical philosophers, some of whom in- cluded mass (or weight) among the primary properties of objects. Given mass, we can substitute "quantity of motion" for "state of mo- tion," thereby adding momentum, "a concept acceptable to mechanical philosophers" (Westfall 1971, 134). This line of development culmi- nated in the work of Newton-who first clarified the concept of mass, carefully distinguishing it from weight-in whose hands the old me- chanical philosophy became a powerful explanatory engine (ibid., 143). Hitchcock's claim about my theory of causal explanation is more fully justified, for I have appealed, thus far, only to a complex network of causal processes and causal interactions. In Salmon 1984 I employed a mark-transmission criterion to distinguish causal processes from pseudo processes, and a similar criterion to distinguish causal inter- actions from mere intersections of processes. The result was a geomet- rical structure. There is nothing wrong with this sort of geometrical approach as long as its limitations are recognized. It furnishes some- thing like a model of a telephone network that exhibits the lines of communication and the connections. (As I shall explain in §10, even information about the bare network can be useful in eliminating faulty explanations.) With the "at-at" theory of causal propagation, which was included in that presentation, it also provides an account of trans- mission. It does not, however, reveal anything about the messages that are sent. Having identified the skeleton, we now need to make a transition analogous to the introduction of mass in the old mechanical philoso- 470 WESLEY C. SALMON phy. As Hitchcock observes, "The intuitive relation of explanatory relevance does not hold between regions of space-time; it holds between the properties instantiated in certain regions of space-time (or perhaps between the propositions that certain properties are instantiated in cer- tain regions of space-time)" (1995, 310, Hitchcock's emphasis). In Salmon 1994 I adopted a version of Phil Dowe's (1992) conserved quantity theory, in which I tentatively opted for invariant quantities, but the result was, as before, a geometrical network. It was just that different criteria were offered as the defining characteristics of causal processes and causal interactions. A major part of the motivation for this change was an aversion to counterfactuals. I was seeking com- pletely objective causal concepts; counterfactuals are notoriously context dependent. However, the conserved quantity theory has an additional benefit; it does tell us something crucial about what is trans- mitted by causal processes and what is modified in causal interactions, namely, conserved quantities. The conserved quantity theory does not tell us what quantities are conserved; for that information we must appeal to empirical science. However, given conservation of linear momentum, we can easily see why a baseball traveling from a bat to a window can (for many prac- tical purposes) be regarded as a single causal process, ignoring colli- sions with molecules in the atmosphere. We can see why the collision of the baseball, rather than collisions with molecules in the air, explains the breaking of a window. In some situations wind and air resistance do make a practical difference; in such cases collisions of a ball with molecules in the air are a significant factor. We can go further. Ap- pealing to the Bernoulli effect-a consequence of the conservation of energy-we can show why spinning balls follow various curved trajec- tories. In such cases we treat collisions with atmospheric molecules statistically; it is not necessary to detail the trajectories and collisions of individual molecules. 9. Some Counterexamples. Hitchcock offers the following counterex- ample to the conserved or invariant quantity view of causality I gave in Salmon 1994: Suppose that a shadow is cast on a metal plate that has a uniform nonzero charge density on its surface. The shadow then moves across the plate in such a way that the area of the plate in shadow remains constant. The shadow then possesses a constant quantity of electric charge (a quantity that is both conserved and invariant) as it moves across the plate. The shadow is not participating in any causal interactions as it moves; in particular it is not being born- CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 471 barded with photons as is the spot of light in a similar example discussed by Salmon (1984, 308). By definition 3, the shadow trans- mits the charge, and by definition 2, it is a causal process. (Hitch- cock 1995, 314-315) As Hitchcock points out, however, the mark method would easily han- dle his example. If one were to change locally the amount of charge where the shadow falls at one moment, the change would not be trans- mitted as the shadow moves on. Should we, therefore, retreat from a conserved quantity criterion to the mark criterion? Before deciding this issue we must consider a counterexample to the mark criterion offered by Philip Kitcher: Imagine that a vehicle equipped with skis is sliding on an ice rink and casting a shadow. A projectile is thrown in such a way that it lands at the edge of the shadow with a horizontal component of velocity equal to that of the shadow of the vehicle. Because the projectile lies across the edge there is an immediate distortion of the shadow shape. Moreover, the distortion persists because the projectile retains its position relative to the vehicle (and to its shadow). (Kitcher 1989, 464) I confess that I too had been vaguely troubled for some time about cases of the following sort until Kitcher's example forced me to focus upon them directly. Suppose a truck, traveling along a road on a sunny day, casts a shadow on the smooth berm. The truck collides with an overhang- ing tree branch, leaving a permanent dent in the roof of the truck and a permanent scar on the branch. This is a causal interaction; both causal processes, the truck and the branch, are modified in ways that persist beyond the locus of intersection. Both are marked and they transmit their respective marks. When the truck encoun- ters the branch the truck's shadow does so as well. Given the de- formation of the roof of the truck, the shape of its shadow is also modified-i.e., marked-and that modification persists beyond its intersection with the branch. Moreover, had the intersection with the branch not occurred, the shadow would have traveled along the berm with an unchanged shape. Thus, the shadow qualifies as a causal process by MT, the mark-transmission criterion, (Salmon 1984, 148) Dowe would be untroubled by either of these examples, because they cut only against the mark criterion, not against Dowe's conserved 472 WESLEY C. SALMON quantities theory. I take the same attitude, regarding the class of such examples as one more reason for abandoning the mark criterion. Hitchcock was not making a case for a retreat to the mark criterion; instead, he says, I suggest that the conserved quantity theory is best viewed as aug- menting rather than replacing the mark-transmission theory. Nei- ther theory provides a reductive analysis of the concepts of causal process and interaction, and neither provides infallible rules for detecting causal processes and interactions. Rather, each provides guidelines for recognizing causal processes and interactions, as well as reasons for thinking that these concepts are presupposed by physical science. (Hitchcock 1995, 316, his emphasis) Hitchcock's view appears to reflect sound reason. He seems to have shown how, according to my 1994 conserved or invariant quantity criterion, a shadow can transmit a quantity~electric charge~that is both conserved and invariant. Kitcher seems to have shown how, ac- cording to my 1984 mark criterion, a shadow can transmit a mark. I am not, however, prepared to abandon the conserved quantity theory. Dowe will readily reject Hitchcock's example on the ground that shadows do not have electric charges; in this case, the charge be- longs to the metal plate. This response is, I believe, correct. Shadows have such properties as shape, size, velocity, and relative darkness/ lightness, but none of these is a conserved quantity. This claim is as well supported by empirical evidence as is the assertion that flying base- balls have linear and angular momentum. In Salmon 1994 I block re- sort to the claim that shadows qualify as causal processes by virtue of having an electric charge equal to zero. I therefore maintain that the conserved quantity theory can cope adequately with Hitchcock's coun- terexample as he has formulated it. Were Hitchcock to amend the example by attributing the charge in question to that portion of the surface of the plate that is in shadow, but only as long as it is in shadow, Dowe would reject the "object" in question as a time-wise gerrymander~a piece of "spatiotemporal junk." Failing to qualify as an object, it cannot be an object possessing an electric charge (see Dowe 1992, 1995). I cannot endorse this response because, as I have argued above, it invokes an unanalyzed notion of genidentity~a concept I consider highly problematic. How can one then respond to the reformulated example? Informally we want to say that electric charges are carried by particles like elec- trons and protons; they are transmitted between different spatiotem- poral regions by the movement of such particles. This involves the passage of electric charges from one locale to another, thereby aug- CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 473 menting the electric charges already there. The same consideration ap- plies to the intermediate spacetime locations-that is, the electric charge in question must vacate its location at one stage of the process and appear at the other stages of the process at the appropriate times. Otherwise, the electric charge would not be a conserved quantity. Consider some other examples. Suppose that a bullet collides inelas- tically with the bob of a ballistic pendulum. When the intersection (an interaction) occurs, the linear momentum in the region of the intersec- tion is the vector sum of the momenta of the two objects. When two billiard balls collide elastically the momentum of the combined system equals the sum of the momenta of the two subsystems in the region of interaction. When two light waves intersect, the energy in the region of intersection equals sum of the energies of the two waves. This is not an interaction; although there is a superposition-usually called "in- terference"-the waves continue beyond the intersection as before,just as if nothing had happened. There is no exchange of energy or any other conserved quantity. Although the point of the preceding two paragraphs follows logi- cally from the fact that the quantities in question are conserved, I shall formulate it explicitly as a COROLLARY: When two or more processes possessing a given conserved quantity intersect (whether they interact or not), the amount of that quantity in the region of intersection must equal the sum of the separate quan- tities possessed by the processes thus intersecting. In the reformulated version of Hitchcock's example, this means that, if the region of the surface in shadow were transmitting electric charge, the charge density in the portion of the surface that is in shadow would have to be augmented as the shadow passes over it, and then reduced as the shadow goes beyond. This condition is not fulfilled, however, because the uniform charge on the surface of the plate is present re- gardless of the shadow and regardless of its presence in any particular area that happens to be in shadow at any other moment. Looking at the surface of the plate relativistically from its own frame of reference, we can say that its vertical world-worm (not a worldline, because it is spatially extended) retains a uniform charge distribution. Smaller vertical world-worms, representing portions of the surface equal in extent to the area of the shadow, but at rest in this frame of reference, also exhibit constant uniform charge distributions. These constant uniform charge distributions are no different in the spacetime regions where the nonvertical world-worm of the moving shadow in- tersects them. This shows that the portion of the surface defined by the 474 WESLEY C. SALMON motion of the shadow is not transmitting any electric charge; the elec- tric charge is being transmitted by the plate. 10. Counterfactuals and Statistical Relevance. As Hitchcock points out, my earliest criticisms of Hempel's "covering law" models of explana- tion focused on their failure to capture the relation of explanatory relevance (Salmon 1965, 1971). Many years later, Kitcher and I (1987) offered the same criticism of Bas van Fraassen's "pragmatics of expla- nation." Now, ironically, Hitchcock levels the same charge against my causal theory of explanation, whether formulated in terms of the mark criterion or in terms of the conserved quantity theory. The argument is, roughly, that this theory does not give an adequate basis for deter- mining which properties possessed by causal processes and interactions are pertinent to a given outcome and which are not. This is the fun- damental gap in the exclusively geometrical approach; as I acknowl- edged above, the criticism is sound. A map of causal processes and interactions can be useful, however, in weeding out irrelevant factors that are not present at the right place and time. Consider an example first given by Ellis Crasnow. A certain busi- nesswoman usually arrives at her office about 9:00 A.M., makes herself a cup of instant coffee, and settles down to read the morning paper before starting her daily work. From time to time, however, she arrives at her office promptly at 8:00A.M., meets a colleague from another site, and both are served cups of freshly brewed coffee upon arrival. On the mornings when she arrives at 9:00 A.M. she takes the 8:00 bus from home, but when she arrives at 8:00 she takes the 7:00 bus. The taking of the 7:00 bus thus fulfills statistical conditions (Reichenbach's con- junctive fork) that partly characterize a common cause of the coinci- dence of the availability of the freshly brewed coffee and the arrival of her colleague. Catching the earlier bus is not the common cause, how- ever, because appropriate causal connections do not exist. The 7:00 bus is a causal process connecting her boarding of it to her 8:00 arrival, but there is no similar connecting process relating her taking of the earlier bus to the brewing of the coffee prior to her arrival. The actual common cause is a telephone appointment made by her secretary the preceding day. This is one type of example that emphasizes the need to consider actual causal connections furnished by causal processes in addition to statistical relevance relations. Many cases of causal preemption can be handled similarly. Consider again the baseball and the window. Suppose that a well-hit ball is trav- eling on a trajectory that would surely strike and break a certain win- dow pane, if the glass were intact when the ball arrived. As it happens, however, a stray bullet shatters the window just prior to the arrival of CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 475 the ball. In this case, the ball never intersects with the window pane, and thus plays no part in the explanation of the breaking of the win- dow. (The baseball players may, however, face a difficult problem in convincing the homeowner that they were not responsible.) Another example, mentioned by Hitchcock (1995, 305, 316), is John Jones' explanation of his avoidance of pregnancy on the basis of his consumption of oral contraceptives. We can obviously rule out this explanation on grounds of statistical irrelevance, but what about causal processes and intersections? Normal pregnancy occurs when a sperm and an egg unite in a certain way (an instance of a /c-type interaction) in a human body. Since Jones does not possess ovaries he cannot pro- duce eggs, and such an interaction cannot occur. He cannot become pregnant by implantation of a fertilized egg because he possesses no uterus. Again, the required interaction cannot occur. Sperm and eggs are complex causal processes, but they do transmit such classically con- served quantities as mass. While Hitchcock does not advocate a counterfactual theory of causal or explanatory relevance, he does claim that counterfactual con- siderations are near at hand in explanatory contexts. When an expla- nation is offered it is pertinent to consider what would have happened if the explanans had not obtained. For example, when asserting that a window was shattered because it was struck by a baseball travelling at a considerable velocity, we presumably have in mind that the window would not have broken if the intersection with the baseball had not occurred. This is, I think, a relatively unproblematic counterfactual statement because it is supported by well-established assertions of sta- tistical relevance. (We assume no stray bullets intrude.) At the time the window pane broke numerous atmospheric molecules were colliding with it, but window panes very seldom shatter under those circum- stances (unless the wind velocity is extremely great, in which case there would be no ballgame in the vicinity). At the same time, sounds from the mouths of the players would be reaching the window, but again, windows seldom shatter when only shouts from ballplayers impinge. These are not speculations; they are reports of observed relative fre- quencies. We can give a more sophisticated answer in terms of mo- mentum conservation, as sketched above, but the physical assertions here invoked have enormous empirical support. My main motivations in working out a theory of causal explanation as a successor to my theory of statistical explanation were the convic- tions, first, that causality is an essential ingredient in scientific expla- nation, and second, that causal relations cannot be explicated wholly in terms of statistical relations. These points still seem sound. In Salmon 1984 I characterized scientific explanation as a two-tiered structure, con- 476 WESLEY C. SALMON sisting of statistical relevance relations on one level and causal pro- cesses and interactions on the other. As a result of Hitchcock's analysis, I would now say (1) that statistical relevance relations, in the absence of connecting causal processes, lack explanatory import and (2) that connecting causal processes, in the absence of statistical relevance re- lations, also lack explanatory import. In various discussions I have focused on (1) to the virtual neglect of (2). As the preceding discussion of the baseball breaking the window shows, this was a mistake. Both are indispensable. The relationship between counterfactuals and statistical relevance is quite close. If P( BIA. C) =I' P( BIA.-,C), then (given background con- ditions A), in the absence of C, we can say that if Chad been present the probability of B would have been different. This is statistical rele- vance. The probabilities to which I am referring are objective; in this context I am not considering subjective or personal probabilities. As- sertions of such objective probability relations must be based directly or indirectly on empirical evidence. Such probability statements are either true or false, without regard to contextual features. There is, of course, an epistemic question. If we appeal to relations of statistical relevance as above, we must consider whether A. C constitutes a ho- mogeneous reference class, or whether there are other factors D, E, F that are also relevant to the occurrence of B. In cases of statistical explanation the question of homogeneity of reference classes assumes great importance (see Salmon 1984, Ch. 3), but such questions are open to empirical investigation. If B obtains, but A.-,C-> -,B, then we can say that B would not have occurred if C had not. The counterfactual is a limiting case of statistical relevance; if such a statement is true A.-,C is automatically a homogeneous reference class. Counterfactuals, like statistical rele- vance relations, are often effectively tested by controlled experiments. If, however, counterfactuals must be evaluated by comparing intuitions concerning the nearness of possible worlds, then I think they are un- suited for the explication of causality or scientific explanation. 11. Philosophical Methodology. In the course of his discussion, Hitch- cock remarks, "in these post-positivistic times we do not expect there to be any specifiable set of observable conditions that is both necessary and sufficient for the presence of causal processes and interactions" (1995, 313-314). His skepticism regarding the possibility of reductive analyses of these concepts is expressed in a passage quoted above. He does not thereby condemn the search, because its pursuit may lead to a more accurate characterization of causal processes and interactions. Such a result is unquestionably desirable. My attempt to answer Hitch- CAUSALITY AND EXPLANATION: A REPLY TO TWO CRITIQUES 477 cock's counterexample is partly motivated, however, by the hope, per- haps vain, that reductive analyses within the framework of the logical empiricist (not logical positivist) program can be given. I take comfort in Hitchcock's view that even unanswerable counterexamples are not necessarily fatal to the philosophical enterprise of understanding cau- sality and its role in scientific explanation. REFERENCES Dowe, P. (1992a), "Wesley Salmon's Process Theory of Causality and the Conserved Quan- tity Theory", Philosophy of Science 59: 195-216. ---. (1992b), "Process Causality and Asymmetry", Erkenntnis 37: 179-196. ---. (1995), "Causality and Conserved Quantities: A Reply to Salmon", Philosophy of Science 62: 321-333. Feynman, R. eta!. (1965), The Feynman Lectures on Physics, vol. III. Reading, MA: Addison- Wesley. Hitchcock, C. (1995). "Discussion: Salmon on Explanatory Relevance", Philosophy of Sci- ence 62: 304--320. Kitcher, P. (1989), "Explanatory Unification and the Causal Structure of the World", in P. Kitcher and W. Salmon (eds.), Scientific Explanation, Minnesota Studies in Philos- ophy of Science, Vol. XIII. Minneapolis: University of Minnesota Press, pp. 410-505. Kitcher, P. and W. Salmon (1987), "Van Fraassen on Explanation", Journal of Philosophy 84: 315-330. Salmon, W. (1965), "The Status of Prior Probabilities in Statistical Explanation", Philosophy of Science 32: 137-146. ---. (1971), "Statistical Explanation", in Salmon eta!., Statistical Explanation and Sta- tistical Relevance. Pittsburgh: University of Pittsburgh Press, pp. 29-87. ---. (1984). Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press. ---. (1994). "Causality Without Counterfactuals", Philosophy of Science 61: 297-312. Westfall, R. S. (1971), The Construction of Modern Science: Mechanisms and Mechanics. New York: John Wiley & Sons. Article Contents p. 461 p. 462 p. 463 p. 464 p. 465 p. 466 p. 467 p. 468 p. 469 p. 470 p. 471 p. 472 p. 473 p. 474 p. 475 p. 476 p. 477 Issue Table of Contents Philosophy of Science, Vol. 64, No. 3 (Sep., 1997), pp. 377-524 Front Matter Quantities, Magnitudes, and Numbers [pp. 377-410] Divisive Conditioning: Further Results on Dilation [pp. 411-444] Two Faces of Intentionality [pp. 445-460] Causality and Explanation: A Reply to Two Critiques [pp. 461-477] Contextualism and Nonlocality in the Algebra of EPR Observables [pp. 478-496] Placebo Control Treatments and the Evaluation of Psychotherapy: A Reply to Grunbaum and Erwin [pp. 497-510] On an Inconsistency in Constructive Empiricism [pp. 511-514] Book Reviews Review: untitled [pp. 515-516] Review: untitled [pp. 516-517] Review: untitled [pp. 517-519] Review: untitled [pp. 519-521] Review: untitled [pp. 521-523] Back Matter [pp. 524-524]