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The Gravitational Field as Cause

April 3, 2014

[This post is taken from an early draft of Christopher G. Weaver’s paper entitled “Against Causal Reductionism” now entitled “Fundamental Causation”]

    Channeling, to some degree, Bertrand Russell (1912-1913), Jonathan Schaffer (2008) insisted that there is no room for causation in proper scientific practice. Science only requires natural laws and unfolding history (one physical event after the other). He remarked:

…causation disappears from sophisticated physics. What one finds instead are differential equations (mathematical formulae expressing laws of temporal evolution). These equations make no mention of causation.30 Of course, scientists may continue to speak in causal terms when popularizing their results, but the results themselves—the serious business of science—are generated independently.[1]

       Considerations such as those in the quoted pericope above quite naturally breed an argument for causal reductionism, the view that obtaining causal relations are not a part of the world’s fundamental structure, and that as a consequence causal facts reduce to (are nothing above and beyond) a species of non-causal facts. For Schaffer would add that if sound scientific practice can proceed without causation, making use instead of natural nomicity and history solely, then causal reductionism is true. Thus, causal reductionism is true.

      I find Schaffer’s justification for the claim that praise worthy scientific practice does without causation to be problematic. I would argue that with respect to extremely empirically successful theories arrived at on the basis of sound scientific practice, the notion of causation shows up primitively and indispensably in the respective interpretations of the underlying formalism of those theories. In the present post, I have space only to explore one such scientific scientific theory, viz., the general theory of relativity (GTR).

      In GTR, the principle of equivalence (PE) implies that inertial mass just is gravitational mass.[2] What is more, the effects of gravity fade away in coordinizations (or systems of coordinates) that are locally inertial inside some gravitational field, given PE. The evolutions of systems not appearing in gravitational fields are described by the same equations which depict the evolutions of said systems in gravitational fields, provided that the equations are generally covariant (no privileged coordinate system or local Lorentz frame).[3] All of the above indicates that the laws of GTR reduce to those of STR given a flat metric, and that the effects of gravity are not sensed by observers experiencing free fall.[4] We also know from Einstein’s (PE) that gravitation is strongly related to the curvature of spacetime.[5] Einstein’s equation details the relationship, though it says a bit more since it also describes the relationship between the stress-energy tensor (Tab) and the Riemann curvature (R) of space.[6] Famously, the equation also “…relates the spacetime geometry to…matter distribution.”[7]

       The gravitational field represented by the Lorentzian metric (gab),

“…interacts with every other one and thus determines the relative motion of the individual components of every object we want to use as rod or clock. Because of that, it admits a metrical interpretation.”[8]

Geodesics of (gab) correspond to worldlines of objects. These geodesics are paths of “of the” curved “spacetime metric”.[9] The metric  itself can be measured through the use of clocks and rods.[10]

      I believe that the best interpretation of Einstein’s equation indicates that the gravitational field causally influences both photons and massive bodies (the causal language was already explicit in the excerpt from Rovelli above). In fact, the Lorentzian metric of Einstein’s equation is commonly interpreted as the field which causally influences objects constraining their movement, determining their relative motions, and even coupling with and influencing all other fields. Moreover, its behavior is quite different from the behavior of other fields since (quoting Hawking) “…it shapes the arena in which it acts”.[11] This gravitational field has also been described as a “causal field” by philosophers of science.[12] Furthermore, gravitation, say the physicists, is that “which affects every particle in the same way.”[13] And this understanding of spatial curvature or gravitation as causally interacting and influencing “matter in relativity, via Einstein’s equation, is regarded as fundamental by itself.”[14] My understanding of the matter is completely consonant with Einstein’s own interpretation of his work, as Pooley commented:

The idea that affine structure plays a quasi-causal role in explaining the motions of bodies figures significantly in Einstein’s criticism of Newtonian mechanics and SR and in his subsequent understanding of GR.[15]

…the fact that it [Newtonian absolute space] acted without being acted upon was held up as problematic [by Einstein]; a ‘defect’ not shared by the spacetimes of GR (Einstein, 1922, 61-62).[16]

So I believe GTR gives us a good reason for believing that causation shows up in correct interpretations of the mathematical formalism of highly successful physical theories.

      No doubt the causal reductionist will question my interpretation of the formalism. She will ask, “is it not true that the presence of massive bodies interacts (perhaps causally) with the self-same field?” Is not the famous dictum of John A. Wheeler the claim that “spacetime tells matter how to move; matter tells spacetime how to curve”?[17] Does this not suggest that if there are real obtaining causal relations involved, then the gravitational field causes a material body to behave x-ly, while the material body’s behaving x-ly causes the field to behave y-ly? Does this not breed a circle? Should we not prohibit such causal circles?

       I do not find these questions to be very troubling. The gravitational field is present even in the absence of all material bodies, as Harvey Brown noted,

Once it is recognized that gmn is an autonomous field (or fields) in its own right, nothing in Mach’s philosophy implies that its dynamical behaviour or very existence, must be determined by the presence of (other kinds of) matter.[18]

Again, the gravitational field does not owe its very existence to the presence of material bodies (sorry relationalists). Spacetime curvature and geometric structure is prior.[19] I confess to such priority because it’s the very existence of the gravitational field which causally influences the behavior of fields and fundamental particles both massive and massless. I therefore avoid a causal circle since what material bodies influence is the inertial structure of spacetime, not its existence. Oliver Pooley made this clear, the “[i]nertial structure, as encoded in gab, is influenced but not determined by the matter content of spacetime.”[20] So the existence of the gravitational field causally influences particles and fields by constraining their trajectories, and determining their relative motions while the presence of material bodies influences the inertial structure of spacetime.

     Carl Hoefer (2009, pp. 703-704) has argued that if GTR implied that there are certain obtaining causal relations, or if it’s best interpretation requires the use of causal notions, the reductionist should not be worried, for GTR is not itself a fundamental physical theory. GTR’s picture of the world is not the quantum mechanical picture of the world, and the thought is that GTR will have to yield to QM in ways that would rub out any attempt to understand the causal activity of the gravitational field as fundamental physical activity. But I could very well argue that in string theory the graviton plays a causal role. I could also argue that in the context of certain string theories, the interactions of branes are best interpreted as causal interaction involving the exertion of causal influence on one another in a way that is not exactly circular or symmetric. Unfortunately, space constraints prohibit me from trotting out such interpretations, but I do believe there remains a promising response to Hoefer’s worry that can be expressed in a sound bite (not really). Look back to my characterization of Schaffer’s argument for causal reductionism. Notice that one of the premises of the argument states that sound scientific practice implies causal reductionism. That premise does not say that such practice must be peculiar to fundamental physical investigation solely. Obviously, sound scientific practice is what physicists leaned on when developing GTR. And GTR is of course an extremely successful physical theory, and that is precisely why any quantum theory of gravity must recover its predictive success. Thus, Hoefer’s complaint should not worry the anti-reductionist about causation.

      Causal reductionists will no doubt judge my appeal to GTR to be cheap and shallow. They will insist that the authorities I have invoked are merely describing matters with a particular gloss. Surely we can do without causal talk.

      In the absence of both a successful reductive analysis of causation and a correct reductive metaphysical theory of the causal relation, I do not see why we should believe that causal talk in the work of physicists should be understood as redundant and imprecise talk. One cannot dismiss such causal language without providing a worthy proxy or substitute for it. The appropriate substitute arrives at the end of a careful reductive analysis of causal facts and an ontological reduction of the causal relation. The problem is that after a great many years of trying, attempts to reductively analyze and ontologically reduce causation have pretty much universally failed. As two foremost experts on the topic, L.A. Paul and Ned Hall concluded:

After surveying the literature in some depth, we conclude that, as yet, there is no reasonably successful reduction of the causal relation. And correspondingly, there is no reasonably successful conceptual analysis of a philosophical causal concept. No extant approach seems able to incorporate all of our desiderata for the causal relation, nor to capture the wide range of our causal judgments and applications of our causal concept. Barring a fundamental change in approach, the prospects of a relatively simple, elegant and intuitively attractive, unified theory of causation, whether ontological reduction or conceptual analysis, are dim.[21]

I therefore conclude that the direct argument for causal reductionism from sound scientific practice is undercut by a proper understanding of the gravitational field.


* I would like to thank Tom Banks and Aron C. Wall for their comments on an earlier version of this piece. Any mistakes that remain are mine.

[1] Schaffer (2008, p. 92). See also Hitchcock (2007); and Norton (2007a), (2007b). Bertrand Russell said, “In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula.” Russell (1912-1913, p. 14)

[2] Zee (2013, p. 258). There are strong and weak forms of this principle for which see Brown (2005, pp. 169-172). Ciufolini and Wheeler (1995, p. 13) discuss three versions of the principle.

[3] Weinberg (2008, p. 511).

[4] Misner, Thorne, and Wheeler (1973, pp. 312-313).

[5] Penrose (2005, p. 459).

[6] It, of course, says even more than this.

[7] Wald (1984, p. 68).

[8]Rovelli (1997, p. 194)

[9] Wald (1984, p. 67).

[10] Brown (2005, p. 160).

[11] Hawking (1996, p. 5).

[12] Hoefer (2009, p. 687), though Hoefer does not believe there is bona fide causation in GTR.

[13] Hawking and Ellis (1973, p. 2).

[14] Geroch (1978, p. 180) emphasis mine.

[15]Pooley (2013, p. 541) See Einstein (1916, pp. 112-113)

[16]Pooley (2013, p. 541)

[17] As quoted by Wheeler and Ford (1998, p. 235), quoting John A. Wheeler.

[18] Brown (2005, pp. 159-160) emphasis mine.

[19] And here I’m agreeing (at least in part) with Balashov and Janssen,

“Does the Minkowskian nature of spacetime explain why the forces holding a rod together are Lorentz invariant or the other way around?…Our intuition is that the geometrical structure of space(-time) is the explanans here and the invariance of the forces the explanandum” Balashov and Janssen (2003, p. 340).

[20] Pooley (2013, p. 541).

[21] Paul and Hall (2013, p. 249).


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5 Comments leave one →
  1. April 6, 2014 12:19 pm


    I doubt that either Russell or Jonathan think that “there is no room for causation in scientific practice.” After all Russell sketched a positive account of causation and Jonathan has also investigated accounts of causation. Both likely think that scientists could not get along without using causal notions. A more charitable understanding of their view is that causation is not a fundamental relation in physics in the way for example, that mass, distance, metric, quantum state, and so on are fundamental. Their point is that none of the equations of fundamental physics (e.g. the Einstein Field equations, Schrodinger’s equation) include a term that refers to causation. These equations specify regularities in the patterns of fundamental quantities and relations none of which is or obviously corresponds to causation. And these equations are temporal symmetric. “Causation”, as it occurs in special science laws (e.g. certain viral infections cause skin rashes) and ordinary descriptions of macro phenomena (poor visibility caused the plane crash) relate local events to each other whereas the fundamental equations relate global patterns (e.g. the state at one time to states at other times.) And causation is temporally asymmetric. Causation is like “measurement” in quantum mechanics. It is indispensable in describing what physicists are doing when testing theories but it is (or should) not (be) an element of the fundamental ontology or ideology of the theory. Rather, a comprehensive fundamental theory should have the wherewithall to provide an account of causal locutions used by physicists in explaining and testing their theories just as it should provide an account of measurement interactions. More generally, it should have the wherewithall to explain causal notions as they occur in the special sciences and ordinary talk just as it should be able to account for other macro phenomena. This is the reductive project that Russell, Jonathan, Lewis, and many others have been engaged in. While so far this project hasn’t been entirely successful in capturing the nuances of our intuitive conception of causation (but mainly for reasons involving features of our ordinary causal locutions that are unrelated to scientific uses) Russell’s and Jonathan’s observation that causation doesn’t occur in the fundamental laws provides a motivation for the project if not a guarantee of its success.

    One more point. Some philosophers like a more metaphysically loaded conception of laws of fundamental laws than only that they specify patterns and sometimes use causal sounding notions in their metaphysics; for example, saying that laws “produce”, “guide” “constrain” or “shape” the evolution of events. Sometimes, as Chris’ quotes show, physicists adopt these locutions as well. But this is to take a stand on the metaphysics of laws and is a matter of philosophical dispute. In any case, whatever metaphorical locutions like “produce” mean in characterizing the operation of laws this is not causation as it occurs in the special sciences and ordinary talk. Someone who prefers this metaphysics of laws still faces the issue of providing an account of our ordinary notion of causation.

    Barry Loewer

  2. April 6, 2014 2:13 pm

    Thank you Barry. As usual your comments are important and substantive. Let me try to address them point by point, and with all due respect.

    [I’ve removed my earlier comments since I believe the essence of my response is capture completely by what follows. Thanks again for the reply.]

    Reply: Suppose that causal reductionism is true, and that Lewis’s (2004) reductive counterfactual covariance theory of causation holds. On this supposition, all causal talk (even in the interpretations of physical theories) reduces to talk of counterfactual covariance (to some vague extent) between distinct events. Causal relations are those more fundamental relations. This entails that causal talk can be done away with even in the interpretations of fundamental physical theories since it reduces generally. The same point would hold if a great many of the other reductive accounts (Lewis (1973); Dowe (2000) etc….and let’s not forget that Schaffer’s (2005) contrastive account is not reductive (see on this Paul and Hall (2013, p. 22)) held. So it really is true that if you’re reductionist in Schaffer’s sense you can do away with causal talk in the correct interpretations of fundamental physical theories.

    Now what I’m up to is this: (a) I try to show that there are good candidate physical theories whose best interpretations involve explicit reference to obtaining causal relations or to causes influencing or producing effects. GTR is a very good example, for in not a few standard texts on GTR interpretations of the Lorentz metric’s role in the theory are described in explicit causal terms. Einstein himself interprets his theory in this way. (b) I then report the fact that causal reductionists have no successful reductive theory of causation (nor do they have a reductive analysis of causation)….this is the consensus view on the matter. In the absence of a reductive story….how do you do away with the causal talk? Now it seems to me that you’re suggesting that you have reason to think its properly done away with because (as Russell and Schaffer note on your reading)…there is no term in the fundamental equations of fundamental physical theory which refers to a causal relation. This seems like a non-sequiter. That a term which refers to the causal relation does not appear in such equations is neither necessary nor sufficient for sufficiently buttressing the premises of Schaffer’s direct argument for causal reductionism.

    First, that it is not necessary: The equation which describes a simple harmonic oscillator in CM (an instance of F = MA) uses a term ‘f(t)’ which is interpreted as a term that explicitly refers to a cause (though not a causal relation) (see Smith (2013)). If that is the proper understanding of the referent of that term, then one has in the formalism of a theory that is a deliverance of sound scientific practice a bona fide causal notion. This example should, and I think you’d agree, be taken seriously as a potential defeater for Schaffer’s premise that sound scientific practice only requires history and natural nomicity (no causation). So that there’s no term in the relevant batch of equations which refers to a causal relation is irrelevant.

    Now sufficiency: It may be true that with respect to some particular foundational physical theory TP, absent from the formalism of TP is the notion of a cause [or some term referring to a causal relation]…that fact does nothing to motivate the claim that TP should not be interpreted in such a way that it requires an appeal to the notion of causation. A predominate way of understanding the very structure of TP involves demarcating between the formalism of that theory and the interpretation of that formalism. Interpretations constitute the ontology of theories. I would argue that with respect to extremely empirically successful theories arrived at on the basis of sound scientific practice, the notion of causation shows up primitively and indispensably in the respective interpretations of the underlying formalism of those theories even if no term in the formalism has as its extension a cause or the causal relation. Appearance in the correct interpretation is enough to motivate anti-reductionist replies to Schaffer’s argument.

    Schaffer’s key premise suggests that the results of sound scientific practice require natural laws and history (again no causation). On your reading the results would be the formalism strictly. But that’s clearly wrong-headed. GTR isn’t just the Einstein equation…the result is also the accompanying interpretation….for only the two together constitute the theory…the theory is the result. I do not know how to understand Einstein’s equation as a result without some type of interpretation of the formalism.

    Main Point: The formalism of GTR when properly interpreted strictly implies that the gravitational field causally influences fields as well as particles. That no term appears in the equations which explicitly reference an obtaining causal relation is irrelevant. Think, for example, of modal interpretations of QM. Some of these interpretations use the same formalism of (say) Copenhagen interpretations of QM though some of them rub out the projection postulate. But (and this is crucial) (a) such interpretations nonetheless usually strictly imply that there are instances of actualization. Moreover, (b) the interpretations can even feature necessity operators! Nothing in the assumed standard formalism explicitly references either bit of the interpretation. This is particularly the case in modal-Hamiltonian interpretations in which there are interpretational postulates added to the interpretation of the theory. These postulates bring in additional physical content which outstrips the bare formalism. The addition of that content is justified by the attempt to secure the benefits of the theory considered in entirety. Again, “the serious business of science”, the results, are not just the formalisms, but the theories built on the formalisms. Such theories include substantially more physical content than the formalisms of the physical theories in question. Such additional physical content includes, in the GTR case, causation.

  3. April 7, 2014 12:20 pm

    Hey Chris,

    I have a nitpicky point and a more substantive one:

    Nitpicking: In your final paragraph you argue that the fact that we currently do not have a successful reductive account of causation requires us to take causation as fundamental. But this is an argument from ignorance–the current lack of a reductive account isn’t reason by itself to doubt that there is such an account; it’s reason to continue searching for such an account. We would need additional reason to think no account can be successful.

    Substantive: We might have additional reasons to think that causation is fundamental to GTR, but I’m not convinced; you argue that the proper interpretation of GTR requires us believe that the field causally influences objects, but I’m not sure we must take this to be fundamental; to interpret a scientific theory like GTR, we need merely to say what the formalism represents. For GTR, this requires us to say what the stress-energy tensor corresponds to (roughly, matter/energy distribution) and what the Ricci tensor corresponds to (roughly: spacetime curvature). The equation expresses a relationship between these. Is this relationship causal? It might be, but I don’t see why an interpretation needs to say anything either way. And I think that the causal reductionist can accept that this relationship is causal, but claim that it’s not fundamental: the fundamental facts are the distribution of matter and the curvature of spacetime.

  4. April 9, 2014 2:35 pm

    Thanks for your comments Mike.

    “In your final paragraph you argue that the fact that we currently do not have a successful reductive account of causation requires us to take causation as fundamental. But this is an argument from ignorance–the current lack of a reductive account isn’t reason by itself to doubt that there is such an account; it’s reason to continue searching for such an account. We would need additional reason to think no account can be successful.”

    I believe you have misunderstood my reasoning, for if your reading of my post is correct there is no particular justification for invoking an interpretation of the Lorentzian metric as representing a causal field. All one need do is point out that there’s no reductive account of the causal relation and no successful reductive conceptual analysis either. If I were claiming that causal anti-reductionism followed from that alone, I would be susceptible to a stronger criticism than yours, viz. this one: We do not have a reductive account of the ontology of a parking meter, nor do we have a successful reductive analysis of our concept of a parking meter, would it not follow from the imagined argument that we should be anti-reductionists about parking meters? Reductio ad absurdum.

    No. I’m not after a case for causal anti-reductionism. I’m simply deflecting an argument for causal reductionism by rejecting the premise that sound scientific practice proceeds by an appropriation of natural nomicity and history alone. A proper interpretation of GTR requires causal-talk. Therefore, one can’t get along doing sound scientific study without appropriating obtaining causal relations. Schaffer was wrong. If, however, one had up one’s reductionist sleeve a nifty ontological reduction of that relation, or if one could reductively analyze it away, then my response might be in trouble. However, there is no such trick. The argument then, is as follows:

    (1) If the correct interpretation of GTR appropriates causal-talk and such causal-talk cannot be ontologically reduced or reductively analyzed away, then sound scientific practice requires causation.
    (2) The correct interpretation of GTR appropriates causal-talk and such causal-talk cannot be ontologically reduced or reductively analyzed away.
    (3) Therefore, sound scientific practice requires causation.

    Notice the conclusion is not that causal anti-reductionism is true.

    One can therefore substantively respond by either (a) proffering a reductive theory or analysis of causation, or by (b) explaining precisely why it is that the correct interpretation of GTR does not appropriate causal talk. The responses so far have been, (i) Russell and Schaffer should not be moved by your claim since the formalism does not have a term which represents an obtaining causal relation, and (ii) all the formalism of GTR does is report on precisely how physical events are lawfully related, it reports on how one physical event follows the other. That’s it.
    Response (ii) begs the question. Response (i) transmutes Schaffer’s (2008) argument into something it (arguably) isn’t, and even if it were the correct reading, it assumes that the results of the “serious business of science” are merely the formalisms of theories. I’ve noted that that’s not right in my response to Barry Loewer. You’ve added a bit of flavor to the mix by stating:

    “[a] to interpret a scientific theory like GTR, we need merely to say what the formalism represents. [b] For GTR, this requires us to say what the stress-energy tensor corresponds to (roughly, matter/energy distribution) and what the Ricci tensor corresponds to (roughly: spacetime curvature). The equation expresses a relationship between these.”

    I disagree. Let me give you just a few examples which highlight why any interpretation of GTR worth its salt should do more than report on what the bits of formalism of GTR represent.

    First, consider the principle of general covariance which is most definitely a part of the correct interpretation of the theory that is GR. That principle says that both the quantities which fall out, by derivation, of the Lorentzian metric, and the Lorentzian metric itself are the unique and privileged collection of quantities that may appear in the laws of GTR (Wald (1984)). That’s it. No more, no less. Now that principle appears nowhere in the formalism of GTR (how can it, it’s about what can appear in the formalism…). But again, standard texts such as Robert Wald’s General Relativity (p. 68) treat the principle as part of a correct interpretation of the theory. The principle qualifies the nature of the laws of GR. I should add that this principle is the reason why I have focused on a causal interpretation of the gravitational field (what’s represented by the Lorentzian metric), since one can easily see how according to GTR that field is regarded as fundamental. If it behaves causally, a fundamental entity of the theory behaves causally. And so I found your reading of what I’m up to to be imprecise. I’m not necessarily vying for a causal interpretation of just how it is that matter influences (but does not determine) the gravitational field. The Ricci tensor and its relationship to the stress energy tensor is not of vital and central importance to me. The entity represented by the metric is (Wald (1984, p. 286)).

    Second, consider the fact that any verisimilar interpretation of GTR should include a statement of energy conservation. (After all, the law of energy conservation shows up in all other physical theories.) But it is well known that in GTR one cannot even represent gravitational field energy or gravitational energy density. Thus one cannot obtain an expression of total or global energy conservation. What theoreticians typically try to do in order to admit into GTR an energy conservation law for isolated systems (different from a global law) is treat an isolated system as a special relativistic particle (see Wald (1984, pp. 285-297). Pause. What in the formalism of GTR represents the law of energy conservation with respect to an isolated system? What in the formalism represents the four velocity of such a relativistic particle? What in the formalism of GTR represents the isolated system? I take it that the formalism of GTR involves all of that mathematical equipment needed to (a) usher in a topology of open sets which yields topological structure and a topological space which itself breeds a manifold (given that one finesses a few things such as the relations holding between coordinate charts). (b) Define a metric over the manifold so as to secure a Riemann manifold. Add in (c) Einstein’s equation and formulae related to that equation (as in Wald (1984, pp. 66-74 sect. 4.3 entitled “General Relativity”) so as to obtain mathematical backbone of GTR (see Carroll (1997)). Again, what in this equipment represents the law of energy conservation as it is typically understood in the general relativistic context? What represents the isolated systems (or relativistic particles) in the statement of that law in the general relativistic context? Interpretations are chunky, they go above and beyond mere reports on what each bit of formalism means.

    Carroll, S. (1997).

    Wald, R.M. (1984). General Relativity. Chicago, IL; University of Chicago Press.

  5. Thomas Blanchard permalink
    April 15, 2014 10:26 am

    Hi Chris,

    One remark on your last point about the failure of attempts to reduce causation. It’s important here to distinguish two kinds of things that people mean by “causation” and accordingly two sorts of reductive projects :

    1. Often by causation people simply mean non-backtracking counterfactual dependence. That’s the sense of “cause” that causal decision theorists have in mind when they say you should act for the sake of outcomes you can cause; it’s also the kind of relation represented in the “causal graphs” familiar from the work of Pearl and others. Here one project is to reduce this sort of counterfactual dependence to fundamental physical features of the world – the challenge being that, as we know since Russell, it’s hard to see how time-asymmetric counterfactual dependence between local events can be grounded in physics in light of the time-symmetry and globality of fundamental physical laws. That’s the sort of project in which Albert and Loewer among others are engaged, I take it.

    2. The second kind is so-called “actual causation”, the sort of relation that underlies our ascriptions of blame and moral responsibility, and the one that holds between the preemptor and the effect in cases of preemption. The second project is to reduce this causal relation to something else, perhaps complicated patterns of counterfactual dependence (a la Lewis or Yablo) or processes (a la Dowe).

    Hall and Paul in their book are solely concerned with the second project, and as they point out all attempts to carry it out have failed in one way or another. But there are good reasons to be more optimistic about the first project. Although there are still details to be worked out I think it’s fair to say that the work of Albert, Loewer, Price etc. gives us a good sense of the kind of time-asymmetric, local counterfactual dependence relation that’s relevant for decision-making and manipulation emerges from fundamental physical features of the world.

    Now even if you’re right that causation shows up in GTR, it seems to me that it’s going to be the first kind of causal relation, i.e. claims about the gravitational field causally influencing photons and massive bodies are simply claims about the counterfactual dependence of the latter on the former. Or at least I see no reason in your post to think otherwise. But if that’s correct I think we have good reasons to think that the kind of causation that shows up in GTR isn’t fundamental since we have a good sense of how it emerges from fundamental physical laws and history.

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