Is There a Problem with Mental Causation?
[Draft: 1/30/02]
Brian Beakley
Philosophy Department
Eastern Illinois University

"To appreciate the exclusion problem, we do not require much heavy-duty metaphysics – overarching doctrines about mental anomalism, "strict laws" in causal relations, a physical/mechanical conception of causality, token physicalism, and the rest.  It arises from the very notion of causal explanation and what strikes me as a perfectly intuitive and ordinary understanding of the causal relation."
-- Jaegwon Kim (Kim 1998: 66-7)

I. Introduction. The last two decades have witnesssed the philosophical resurrection of a issue presumed dead since the heyday of reductive materialism: the problem of whether (and if so, how) mental states can have any causal influence on the world, and most especially our own behavior.  While such a problem cannot arise for reductive materialism – where the mental just is the physical – the case is presumed to be more troublesome for functionalism.  For though the functionalist may well be (indeed, typically is) a materialist, he does not follow the reductive materialist in identifying (i.e, “reducing”) mental properties to physical properties; and this split, it is feared, leaves the mental properties inert – all the “causal work” being done by the physical properties.   Physical properties, we are told, “causal exclude” mental properties, and so functionalism must bring epiphenomenalism in its wake.  

Essential to defining both “epiphenomenalism” and “causal exclusion,” of course, is the concept of cause.  But those expecting this crucial concept to be analyzed rigorously in these epiphenomenalist arguments will, I submit, be disappointed – indeed, as I stress below, it is a consistent, if somewhat surprising, feature of these arguments that the concepts of causation and causal exclusion are nowhere even discussed at much length.  More importantly, I argue, expectations that the missing analysis could anyhow be  inserted into these arguments without event, are all the more badly dashed: on any of several going accounts of causation and causal exclusion, the functionalist epiphenomenalist finds no support for his cause, and in the worst case finds the very concept of functionalist epiphenomenalism reduced to absurdity.  If my analysis of these cases is correct, it suggests that the missing discussion of causation in the epiphenomenalist arguments is not an innocent shortcut, but an oversight necessary for functionalist epiphenomenalism to have ever seemed reasonable in the first place. 

II. Functionalist Epiphenomenalism.

While arguments for functionalist epiphenomenalism are at this point legion, I focus here on well-known presentations by Ned Block (Block 1990), Frank Jackson and Philip Pettit (Jackson and Pettit 1988, 1990), and in numerous writings by Jaegwon Kim (e.g., Kim 1989b; Kim 1993; Kim 1998).  These arguments proceed in subtly different ways, but their common core is simplicity itself.  Functionalism (or what Block terms “cognitive science”)(Block 1990: 146) here involves two familiar theses: the view that mental properties supervene upon their physical bases (Block 1990:146; Jackson and Pettit 1990: 199; Kim 1989b: 275ff.), and the concomitant thesis of the multiple physical instantiability of such mental properties (Jackson and Pettit 1990: 206; Block 1990: 146; Kim 1989b: 271ff.).  Causation, meanwhile, is taken to involve properties possessed by objects and events, in the sense that one event causes another only by virtue of having the right sort of properties (Jackson and Pettit 1990: 197; Block 1990: 140; Kim 1989b: 270, 279).  To this is added the uncontroversial further observation that only a small portion of properties present in any instance of causal interaction are causally relevant—and hence that the vast remainder will be excluded as causally irrelevant – or “screened off,” as Block somewhat presciently puts it (Block 1990: 149; Jackson and Pettit 1990: 198-9; Kim 1989b: 281).

But these reasonable concessions cannot of themselves strip mental states of their causal power; epiphenomenalism ensues only if the supervenient mental properties are among those ruled out as causally relevant. The crucial missing link here is a principle of causal-explanatory exclusion, and a demonstration that mental properties fall before that principle. Concerning how to establish the causal irrelevancy of properties, Jackson and Pettit cite “an attractive answer... that we do so by completely explaining the effect in terms of properties distinct from that property or set of properties” (Jackson and Pettit 1990: 198).  Hence if one set of properties is relevant to the occurrence of an event (in “completely explaining” it), then any other (distinct) set of properties will be causally irrelevant.  Kim makes a case for this same principle: if one event “completely explains” the effect, then all other purported causes are revealed as imposters (Kim 1989a: 239) – barring which we are landed in causal overdetermination, which Kim variously labels “an instrinsically unstable situation,” and simply “absurd” (Kim 1989a: 246; Kim 1989b: 281).  And while Block does not mention such a principle of causal-explanatory exclusion by name, it seems clear he has effectively the same strategy in mind: like Kim, he stresses that an unacceptable causal overdetermination arises in the wake of multiple causes of the same event (Block 1990: 158-9).

III. A Note on Supervenience.

Before proceeding I must make clear a point about the concept of “supervenience” that I will rely on in the following arguments.  As Jaegwon Kim has emphasized, “supervenience” picks out not a unique relation, but a family of such, differing significantly among themselves.  He distinguishes between (at least) two different “strengths” of supervenience.  A property A weakly supervenes on property B iff:

N (x)(y) ( [Bx  By]  [Ax  Ay] ) ,

(where “N” is a necessity operator).  Where A weakly supervenes on B, then, B indiscernibility in each  world entails A indiscernibility in that world (for all possible worlds)(Kim 1984a:58-9).  As Kim points out, on this view A’s and B’s need not line up in the same way across worlds (even across “nearby” worlds), as long as they do so systematically within each world.  But since, in a discussion of causal powers, philosophers often wish to make counterfactual claims about supervenience, weak supervenience may prove to be too-weak supervenience (Kim 1984a: 60; Kim 1989b: 276-8; Kim 1990: 143).  Kim introduces a more demanding condition of strong supervenience which seems a better fit for functionalist purposes.  A property A strongly supervenes on property B iff:

N (wi)(wj)(x)(y) ( [Bx in wi  By in wj] 
					[Ax in wi  Ay in wj]) ,

where “wi” and “wj” are quantifiers ranging over possible worlds.  If A strongly supervenes on B, cross-world B-indiscernibility entails cross-world A-indiscernibility (Kim 1984a: 65).  Here supervenience claims will be counterfactual-supporting (as long as the necessity operator it represents at least some sort of “physical” or “nomological” necessity). 

Since the supervenience of the mental on the physical is here tied up with questions of causality, and concepts of causation are, as we shall see, often explicated in terms of counterfactual conditionals, I will proceed with Kim on the assumption that the supervenience relation intended by all of these authors is at least as strong as Kim’s strong supervenience. Kim later argues that a particular form of strong supervenience may be what is needed in functionialism – viz. mereological supervenience, where wholes supervene on their constitutive parts (Kim 1993b: 166-9). . But so long as mereological supervenience is a more strongly specified form of strong supervenience, my assumption that the relation involved is at least as strong as strong supervenience will prove unproblematic.  The assumption is not entirely innocent, all the same. For as Kim notes, there remains the possibility that some weaker supervenience relation might suffice (Kim 1993b: 169-171). But to discuss supervenience and causation at all, some clear concepts or other must be used; and Kim’s strong supervenience (if not something stronger) seems most congenial to the type of functionalism(s) examined here. While this may leave open some weaker-supervenience escape-hatch from my argument, the burden will anyhow be upon the epiphenomenalist to make good on this possibility.

Having adopting strong supervenience as a standard, it is convenient here to point out one of the “subtle differences” of strategy I mentioned above.  Simply put, there is disagreement among these writers as to the proper metaphysical “strength” of the necessity operator employed in the definition of supervenience.  Block, adapting a Ramsey-sentence functionalism from David Lewis, takes supervenience to be a logical relation.  A functionalist theory of mind on Block’s view is a ‘Ramseyfied’ theory, where the theoretical terms for properties are replaced by variables interconnected only by their causal relations; but these variables are bound by existential quantifiers rather than figuring in the definite descriptions of Lewis’ approach (hence, in fact, returning to Ramsey’s original model). This existentially quantified theory will still hold true of all the situations the definite descriptions would, but also cases where more than one set of properties are causally connected in the way the theory states.  This, Block concludes, permits the multiple instantiability essential to functionalism, and so qualifies these Ramseyfied theories as properly functionalist accounts of mind (Block 1990: 156; see also Block 1980: 174-5).  Note that the supervenience relation holding between functional and base theories is on this view easily characterized: it is summed up by the rule of Existential Generalization.  For in any case where base properties are interconnected in the way specified by the functional theory, the existentially generalized theory structure of Block’s functionalism will be true.  So on Block’s approach the supervenience  relation should apply wherever the laws of logic do. 

For Jackson and Pettit, supervenience is likewise a logical relation (Jackson and Pettit 1990: 207).  Kim, by contrast, does not assume such a strong supervenience relation in making his case, noting simply that “the necessity involved here is standardly taken to be at least nomological necessity – so that if the mind-body supervenience holds, it holds in all worlds that share with our world the same fundamental laws of nature” (Kim 1998: 39).

We could again safely adopt the assumption that the necessity involved must be at least that of “nomological necessity” – thus leaving the possibility for it to wax stronger – and for the most part I will do so without discussion.  But in certain cases – particularly, in analysis of counterfactuals and causation – we will see how this parting of ways can make a signficant difference

IV. A Concept of Causation?

Having set the bar for a minimum concept of supervenience attributable to the authors here, the natural follow-up is to settle on the concept(s) of causation afoot in the same arguments.  I should stress how central this task is: since causation is (literally) one of the defining concepts of epiphenomenalism, we should strictly only be as confident about an epiphenomenalist conclusion as we are that we are employing an adequate theory of causation.  And while I will push this point from one angle in what follows, it bears passing mention that difficulties in understanding causation – particularly at the deepest physical level, where many of our authors feel it truly operates – could also spell trouble for epiphenomenalism.  So, for instance, if it is true, as Wesley Salmon suggests (Salmon 1984: 278-9), that the peculiarities of quantum physics are currently intracable on any going model of causation, then a certain paradox arises in arguing that true causation is found only on that level.  For in that case, true causation would wind up rather like the Kantian thing in itself: a mundane relation holding among ordinary objects is jettisoned as illusory, in favor of a strange and perhaps intractable posit.  I will not pursue that paradox here, however, as I think independent problems of causation await the epiphenomenalist arguments, regardless of our account of quantum physics.

Important as causation is to epiphenomenalism, it is a bit surprising that none of our authors are entirely clear on what model of causation they have in mind. Complicating matters further, to the degree that mention is made of a model of  causation, the authors differ on what that model should be. Jackson and Pettit might seem to provide an account of causation in their principle of causal-explanatory exclusion.  When we causally exclude a property (or set of properties), they explain, 

...we do so by completely explaining the effect in terms of properties distinct from that [candidate] property or set of properties. (Jackson and Pettit 1990: 198)

But this “rule” antecedently presupposes an understanding of what it is to “completely explain” something.  If we assume, as Jackson and Pettit seem to, that a completely explanatory set of properties is a causally efficacious set, then there can be at most one completely explanatory set for each explanandum event (for if there were more than one,  each set, though completely explanatory, could nonetheless be excluded by any of the others).  Beyond this, however, their notion of a complete explanation is left undefined, and so, by association, is their rule of causal exclusion.  

In an extensive discussion of causal-explanatory exclusion, Kim states at the outset: “My central considerations will not depend on any special features of reasons and causes, or mind and matter” (Kim 1989a: 239; see also Kim 1984b: 99).  And while his account of causal-explanatory exclusion also relies critically on the concept of a “complete independent causal explanation,” he is candid about lacking an account of what this is: “I should say right now, though, that I shall not be offering general definitions of these notions, but depend rather on the discussion of specific cases to generate reasonably cohesive senses for these terms” (Kim 1989a: 239).  But at times Kim does allow various preferences concerning models of causation.  Laws seem to hold a special place in his judgment, as he claims that “the nomological conception of causation, in its many variants, is still ‘the received view’” (Kim 1991: 288);  indeed, in one statement of his epiphenomenalist indictment of functionalism he says: “We shall assume here a broadly nomological conception of causality….”: (Kim 1993: 351).  (More than once, in fact, Kim adds that laws are the defining feature of a science: Kim 1985: 194; Kim 1998: 33, n. 4.)  But Kim also appeals frequently to counterfactuals to illustrate cases of causation (e.g., Kim 1989b: 281); and more than once Kim alludes approvingly to Wesley Salmon’s later spatio-temporal process model of causation (1984b: 93, 102; 1998: 45, and n. 28).  

Block considers two different types of models (though neither employing the “complete explanation” of the other authors): nomological (law-based) and counterfactual approaches (Block 1990: 149).

Now, if the concept of causation were settled independently – say, in the philosophy of science – we could instead adopt those results here and proceed.  But things are not so simple: if there is room for disagreement over supervenience, there is more for causation. So I cannot in fairness make the sort of simplifying minimal assumption for causation which I did for supervenience.  Instead, I will deal with models of causation by cases.  In the next section I deal with perhaps the most prominent model of causation in philosophy of science today (though one neglected by all of our authors) – viz., the probabilistic treatment of causation; in subsequent sections I consider models of causation appealing to counterfactual conditionals, spatio-temporal “processes,” and laws.

V. Causal Conundra I: Probabilistic Causation

The point of developing an account of causation here is, of course, in the service of developing the corollary concept of causal exclusion needed in epiphenomenalist arguments – what Block calls “screening off” (Block 1990: 149). Happily, both causation and screening off are explicated in various probabilistic accounts of causation. At the heart of such accounts is the notion of statistical relevance, discussed prominently by Hans Reichenbach (Reichenbach 1956) and Welsey Salmon (Salmon 1970).  Explicating a simple form of statistical relevance, Salmon distinguishes between prior and posterior (or conditional) probabilities for an event (or event-type): while the bare probability of rain on any given day may be 10%, the probability of rain given that local atmsopheric pressure is dropping is 75%.  Expressing this formally (where R = “rain occurs” and A = “atmospheric pressure drops”), we have:

p(R) = .10
p(R, A) = .75  .

And while the notion of conditional probability is intuitively obvious enough, it is a guiding theme of this paper that intuitive obviousness is no match for formal precision.  So let us note here that conditional prob. can be mathematically defined using only simple (i.e., prior) probabilities, as so:

p(X, Y) = p(X & Y) / p(Y)  .

Innocent as this mathematical definition of conditional (or posterior) probability may seem, we must keep it well in mind; for it will provide the foundation for the argument developed later in this section.

Given prior and posterior probabilities, the concept of statistical relevance is equally simple to define: 

Y is statistically relevant to the occurrence of X iff p(X) ¹ p(X, Y)

In the previous example, the probabilty of rain given a drop in atmospheric pressure is different from the simple (i.e., prior) probability of rain. Here a drop in atmospheric pressure “makes a difference” to the chances of having rain — so a drop in pressure is statistically relevant to the occurence of rain.  If the posterior probability is greater than the prior, the factor is positively relevant; if lower, it is negatively relevant (Salmon 1971: 10ff.).  Positive relevance is the type of statistical relevance of interest in building an account of explanation: the cause raises the probability of the effect, and in the limit case (where the cause raises the probability of the effect to 100%), the cause guarantees, or determines, the effect.

But statistical relevance in this bare form is a demonstrably inadequate measure of what truly “makes a difference”.  For instance, in cases where my barometer is working perfectly well, its needle will fall whenever there is a drop in atmospheric pressure; so a drop of the barometer needle would be just as statistically relevant to rain as will the drop in pressure.  Letting B = “barometer needle falls,” we have: 

p(R, A) = p(R, B) = .75  .

To block such spurious factors, Salmon (following Reichenbach) proposes the screening off rule.  In the face of competing factors X and Y, both of which may be statistically relevant to Z, we say that X screens off Y from Z iff:

p(Z, X&Y) = p(Z, X) ¹ p(Z, Y)  (Salmon 1970: 55).

Informally: if Z is just as likely given X alone as it is given both X and Y, but it isn’t as likely given Y alone as it is given X&Y, then X has screened off Y from Z — i.e., has revealed Y to be a spurious cause of Z, compared to X.  In the case of the barometer needle, the probabilty of rain given only a drop in atmospheric pressure (while holding the barometer needle up) is the same as the probabilty of rain given a drop of both pressure and barometer needle; whereas the probability of rain is considerable lower given only a falling barometer needle (by pushing it down), with no drop in pressure.  Put more succinctly:

p(R, A) = p(R, A&B) ¹ p(R, B)  .

Hence the falling barometer needle is correctly screened off as a spurious factor in the occurence of rain. 

(As a bit of a bonus, this account already provides a simple concept of the “complete cause” employed by some of the epiphenomenalist authors, since the collection of  all statistically relevant factors fully explains the effect.  Note, though, that while in ideal cases these factors may provide sufficient conditions for the effect – one reading of “complete cause” which Kim suggests – nothing within the statistical relevance approach demands this.  That is, an indeterministic universe may often provide only factors positively relevant to the effect, but no collection of factors guaranteeing or determining it.) 

Now it must be said, positive statistical relevance and (statistical) screening off are not generally taken as an adequate account of causation and causal explanation.  The real importance of positive statistical relevance and screening off lies rather in the fact that in one form or another these concepts form the core of practically every probabilistic account of causation.  I back this claim with a brief overview of some well-known probabilistic accounts of causation.  

Among the early writers on the subject, both Hans Reichenbach and Patrick Suppes built accounts of causation out of positive relevance, in the form used in the examples above (Reichenbach 1956: 204; Suppes 1970: 12).  Strictly speaking, for Suppes a temporally prior, positively relevant event is only a “prima facie cause”; it is a genuine cause if it is a prima facie cause not screened off by a yet earlier event (where Suppes’ account of screening off is essentially the same as the one given above) (Suppes 1970: 21; see also Salmon 1980: 61).  And while Reichenbach builds an account of common causes out of the statistical relevance measure, and shows how these can screen off correlated effects of that cause, this account is, as Salmon shows, reducible to the account of screening off which we already have (Reichenbach 1956: 158-60; Salmon 1980: 60-1). 

While I.J. Good’s “causal calculus” (Good 1961-1962) does not set down specific quantitative conditions on probabilistic causality, it is in general, a function of  p(E), p (E, F), and p(E, ~F).  And when Good provides specific examples of his general conditions, he employs a comparison of p(E, F) to p (E, ~F): his function Q(A: B) is defined as log [p(~A, ~B)/ p(~A, B)] [Salmon 1980: 53] (Good 1961-2 I: 316-17; Salmon 1980: 52).

Later writers provide more or less complicated variations on, and additions to, the notion of (positive) statistical relevance.  Mellor endorses a straighforward positive relevance account like Suppes (Mellor 1988: 227 ff.), while Paul Humphreys instead compares p(E, C) to the p(E) in some specified “neutral state” (Humphreys 1989: 37ff.).  And while van Fraassen declines to give a precise definition of his “favoring” relation, at least in the example he proffers it amounts to p(E, C), compared not to p(E), but to the probabilty of E given each of the other members of the “contrast-class” of the explanation-seeking “Why?”-question (van Fraassen 1980: 148), and this across all partitions, following Cartwright’s examples; (Cartwright 1979; VF 1980: ).  And he adds, as a further condition on being genuinely explanatory, that the factor (typically) not be screened off “in the Reichenbach-Salmon sense of ‘screens off’: P screens off A from B exactly if the probability of B given P and A is just the probability of B given P alone”  (ibid.: 150).  

The point to keep in mind is this: if the functionalist epiphenomenalist signs on to any of these probabilistic accounts of causation, his concepts of causation and screening off will be built out of the positive statistical relevance relation.

A relevant question at this point is how to put these probabilistic concepts into communion with the modal idiom of functionalist “strong supervenience”. Issues surrounding the link between probability and modality are complex and contentious, so the task is non-trivial; and assumptions I make here are correlatively not without risks.  That said, I will proceed on an extremely simple (and hopefully minimal) assumption sufficient to make my point.  In what follows I will assume that: if B’s are necessarily A’s, then in a given world p(A, B) = 1.00, if the probabilitiy is defined at all in that world.

This simplifying principle immediately permits a type of probabilistic ‘projection’ of the supervenience relation onto the actual world.  For concreteness, consider first a simple population (or “world”) of 100 objects, 20 of which have a supervenient mental property A (for propositional attitude).  Property A must supervene on one or another B (physical base) property. Suppose further that A is multiply instantiated, supervening here on three different B properties: 

p(A) = .2
p(B1)  = .12
p(B2) = p(B3) = .04  .

Call this little scenario “Situation M” (for multiple instantiability). Note that, by translating modality into probability according to my above principle of modal projection,  the distrubution of A-instances with respect to B-instances in Situation M is indeed consistent with strong supervenience: every instance of a base property is invariably accompanied by an instance of the supervenient property:

p(A, B1) = p(A, B2) = p(A, B3) = 1.00  ,

and so 

p(-A, B1) = p(-A, B2) = p(-A, B3) = 0

But Situation M exhibits supervenience alone, whereas we are interested in the combination of supervenience and causation.  So we supplement Situation M to include a bit of caused behavior: let the A be (the property of) deciding to move one’s arm, and each of the B’s be a physiological (property of an) event (e.g., a brain event) on which that mental event supervenes.  And suppose that such physiological events cause the  moving of the arm (or – at  the risk of bogging down natural discourse in property talk – “the property of  moving one’s arm”) – call this C.  This is a more complex version of Situation M,  Situation M*.  For simplicity, suppose the behavior (C) invariably follows the mental state (A) (though, as we will see, nothing will change if we lower that probability).

p(C, A) = 1.00

And suppose that A is positively relevant to C, i.e., that p(C) < p(C, A):

p(C) = .2

Now in Situation M* we can state very precisely what is involved in a B-event’s truly causing C, and screening off A from C.  If our probabilistic model of causation is built out of positive statistical relevance, B’s causing C will involve, at a minimum, B’s being positively relevant to C.  (It might of course require more than that, depending on how our probabilistic model of causation is embellished; but it will require at least that.)  And from the probabilities stated so far, the required relation of positive relevance holds between each of the B’s and C:

p(C, Bi) > p(C), for every Bi

Moreover, we have stated formally a screening off relation in terms of statistical relevance.  Recall that for any Bi – for concreteness, consider a situation with B1 – to screen off A with respect to bringing about C, we need:

p (C, B1) = p(C, B1&A) ¹ p(C, B1&~A)  .

We may hesitate over whether B screens off A with respect to C; for perhaps it is a little unclear what values some of these conditional probabilities will take in this situation.  But here our mathematical definition of conditional probability comes to the rescue – for recall that conditional probability can be defined out of simpler, nonconditional probabilities:

p (X, Y) = p (X & Y) / p (Y)  .

Now we have all the clues we need.  By spelling out the conditional probabilities in the previous equation, we can state conditions for B’s screening off A with respect to C in the situation depicted in Figure 2, and in a way that only appeals to the nonconditional probabilities of properties in  Situation M*.  This is easy to calculate:

[p(C& B1)/p(B1)] = [p(C& B1&A)/p(B1&A)] ¹ [p(C& B1&~A)/p(B1&~A)]

This is what we’d need to find in order for the physical properties to screen off the mental properties with respect to some behavior.  

Now we must focus on that right quotient, [p(C&B1&~A)/p(B1&~A)]; what is its value in Situation M*?  Thanks to strong supervenience, we know that the denominator, p(B1&~A), is 0 – there is no way of having the base, B1, without the supervenient property A.  And since the result of dividing any number by 0 is undefined, [p(C& B1&~A)/p(B1&~A)] is undefined.  There is no number that could fill the required right blank in our final screening-off equation.  So in a case like Situation M* – a situation, that is, where mental properties strongly supervene on physical properties, and are multiply instantiated in them – we cannot fulfill the formal requirements for the physical property to screen off the mental with respect to some bit of behavior.  The proposed screening off is mathematically incoherent.  

Note that nothing important turned on the A-property being instantiated in B1: thanks to strong supervenience, p(A, Bi) = 1.00 for all Bi, so the same results ensue when A is instantiated in any other Bi.  For the same reason, the number of different  B-properties we chose would likewise make no difference to the result: so long as p(Bi) > 0 for each Bi, p (A, Bi) = 1 by strong supervenience; hence p(Bi&-A) = 0; hence p(C& Bi&-A) /p(Bi&-A) is undefined, and the probabilistic conditions for screening off are not satisfied. Nor will value of p(C,A) (and so p (C, Bi)) affect the outcome – using 1.00 in this case was simply an expository convenience.  (Though in order to have a genuine case of causation in these models, p(C, A) will still need to be greater than p(C).)  Given our probabilistic version of strong supervenience, no such variation would yield the probabilities needed to satisfy the formal definition of screening off.

This is a point worth stressing, since (I will argue) something like it recurs in counterfactual models of causation as well: if we assume strong supervenience of the mental on the physical; and if we also assume a concept of screening off which depends on having the physical base without the supervenient mental; then claiming the physical  screens off the mental lands us in incoherence.  For consider: supervenience insures that we never have the physical without the mental; whereas the physical causally screening off the mental demands that we sometimes do have the physical without the mental.  But as this little formal exercise illustrates, we can’t have it both ways.  And this provides an  initial cautionary note for anyone worrying about functionalist epiphenomenalism.

VI. Causal Conundra II: Counterfactuals and Causation

I turn next to the counterfactual model of causation, developed most famously by David Lewis.  

It is worth noting that not all our authors are equally fond of the counterfactual approach.  True, the counterfactual model of causation is one of two that Block recognizes; and Jackson and Pettit do appeal crucially to counterfactual considerations in []. But Kim, by contrast, exhibits a peculiar love-hate relationship with counterfactuals.  On the one hand, he often falls into the counterfactual idiom when illustrating causal exclusion.  Yet he has also been a critic, early and late, of the counterfactual model of causation exemplified in Lewis’ work.  As an early critic of Lewis’ account, Kim has noted that many counterfactual relations, of just the sort Lewis depends on, are clearly non-causal; so that counterfactual dependence is itself no sure sign of causation (Kim 1972: ) .  And more recently, Kim has reaffirmed his scepticism concerning appeal to counterfactuals in an analysis of causation (Kim 1998: ).  

Without assessing Kim’s criticisms, I would add here that, of all the accounts of causation surveyed here, the counterfactual approach strikes me as least likely to yield a clear conclusion in favor of epiphenomenalism – if only because, as it stands or falls on our counterfactual intuitions, it can rely on no clear intuitions concerning what comes of physicalism, strong supervenience, and functionalism taken together.  Quite simply, I submit that none of us have any intuitions about such abstruse metaphysical principles, and that approaching functionalist mental causation through this avenue nonetheless may at best amount to bobbing for quasi-intuitions.  

Not unrelated to this, perhaps, it needs stressing that, even if Lewis is correct in analyzing our concept of causation – so that, in any case where we take A to cause B, we likewise believe the appropriate counterfactuals hold between A and B – the fact remains that such counterfactuals only analyze the proposition that causation holds.  If the counterfactuals are based on nothing but intuitions, then they can provide evidence only for a belief in causation, but not that such a belief is objectively correct.  (Analogy: even if positive statistical relevance provided an analysis of our concept of causation – in the sense that, if we believe A caused B, then we believe A is positively relevant to B – we don’t base our belief that A is positively relevant to B on our intuitions about positive relevance, but on objective facts.)  Now, there is no reason in principle why a counterfactual analysis of causation couldn’t be buttressed with an account of how counterfactuals are objectively established.  But in questions, e.g., of physicalism and strong supervenience, the existing discussion in the philosophy makes no pretense of finding empirical evidence for such metaphysical principles.   And without any such basis, or even a method of making our commitments precise – as we had in the probabilistic approach – counterfactual adjudication of functionalist epiphenomenalism threatens to devolve into a unremunerative festival of alleged intuitions.  Nonetheless, in the interest of thoroughness – as well as to spell out in detail why I think my concerns are well-motivated – I turn here to the consequences we might expect of functionalist epiphenomenalism, taken within a counterfactual framework.

Lewis argues for a straightforward link between counterfactual conditionals and the notion of causal dependence, via the intermediate concept of counterfactual dependence.  C counterfactually depends on A, for Lewis, if both of the following counterfactuals are true:

(i) If A had occurred, C would have occurred; and 
(ii) If A had not occurred, C would not have occurred (Lewis 1973a: 166-7)

And counterfactual dependence can be extended to classes of events: for a family of mutually exclusive propositions A1, A2, ..., and a family C1, C2, ..., of equal size, if all the counterfactuals (A1 > C1), (A2 > C2), ..., are true (using “>” here to stand for the counterfactual conditional operator), then the C's depend counterfactually on the A's.  As Lewis notes, this resembles our use of "depends" tout court ("C depends on A"), and he cites ordinary examples such as the barometer reading depending (counterfactually) on the atmospheric pressure, and my visual sensations depending (counterfactually) on the scene before me. (Lewis 1973a: 165).  In such a case of systematic counterfactual dependence, Lewis concludes, we can say that the C’s causally depend on the A’s –  that is, where the A-event is the conditio sine qua non for the C-event, all else being equal (Lewis 1973a: 166-7).  A series of causally dependent conditions – where C causally depends on A, D causally depends on C, etc. – constitutes what Lewis calls a "causal chain"; and "one event is a cause of another iff there exists a causal chain leading from the first to the second" (Lewis 1973a: 167).

Concerning whether one counterfactual – say, A > C – is true in favor of its opposite, A > ~C, Lewis’ now familiar answer relies on comparisons of similarity to the actual world.  The counterfactual “If A had occurred C would have occured" is true in our world iff some possible world where “A” and “C” are true is more similar to the actual world than any possible world where “A” is true and “C” false (Lewis 1973a ; 1973b: 10).  (If “A” is true in the actual world, then the ‘counterfactual’ is determined by whether “C” is actually true, since no world will so resemble the actual world as itself; Lewis 1973a: 164).  So, for example, in the case of a normal, dry, unstruck match in the presence of sufficient oxygen, it is less of a departure from the actual world to conclude that the match would have lit if struck, as this preserves, inter alia, the fact that there was sufficient oxygen, that the match was not wet, and the regularity (in this world) that struck dry matches light when sufficient oxygen is present; the opposing counterfactual (“if the match had been struck, it would not have lit”) calls for a sacrifice of one of these conditions (on top of the unstruckness of the match), and so differs more from  the actual situation.

On this view, rain depends on drop in atmospheric pressure, because both counterfactuals hold: if the atmospheric pressure drops, rain ensues (or is at least more likely); but if atmospheric pressure doesn’t drop, rain does not ensue.  And rain (happily) does not causally depend on a drop of the barometer needle, as we see from the second counterfactual: if atmospheric pressure doesn’t drop, then – all things (including drop in barometer needle) remaining as similar as possible to actuality – rain doesn’t ensue.  So we can say that the atmospheric pressure counterfactually screens off the barometer needle from the rain.  And in general, if B and C are candidate causes for effect A, and only B bears the requisite pair of counterfactual relations to A, we can on this model say that B screens off C from A.   

However, the situation is more complex in, e.g., the flagpole example, now infamous in the philosophy of science: a vertical flagpole with height h, in the presence of the sun with angle of elevation a from the horizon, cast a shadow with length l.  Surely we feel that the height of the flagpole is causally relevant to the length of the shadow, but not vice versa;  yet if the background conditions are held constant, the flagpole height and shadow length covary. Here it might seem that counterfactual conditionals hold in both directions, and that the shadow should be just as causally relevant to the flagpole’s height, according to the counterfactual analysis of causation – an unintuitive result.  In such a case Lewis bites the bullet, arguing that if a cause c and effect e covary in this way,

The proper solution... I think, is flatly to deny the counterfactuals that cause the trouble.  If e had been absent, it is not that c would have been absent....  Rather, c would have occurred just as it did but would have failed to cause e.  It is less of a departure from actuality to get rid of e by holding c fixed and giving up some or other of the laws or circumstances in virtue of which c could not have failed to cause e rather than to hold those laws and circumstances fixed and get rid of e by going back and abolishing its cause c (Lewis 1973a: 170).  

So with the flagpole example we might, for example, conclude that if the shadow had not had length l, the flagpole would still have had height h, but the sun would have had a different elevation in the sky.  But Lewis is not opposed in principle to violating laws as well in the counterfactual situation, and in fact proposes a hierarchy of difference a world could bear to the actual world, in terms of its effect on degre of similarity with the actual world.  For purposes of  similarity, Lewis holds, the first priority is that the counterfactual world “avoid big, widespread, diverse violations of law”; second in importance, the counterfactual world must optimize perfect agreement of particular fact; third, that world must avoid even small violations of law; and last in importance, that world must optimize approximate match of particular fact (Lewis 1979: 47-8).

Now consider a case of putative mental causation: mental property A strongly supervenes upon three different brain-properties, B1, B2, and B3.  And suppose further that a behavioral effect – an event with behavioral property C – causally depends on the presence of certain brain-state properties – in this instance, say, the presence of B1.  Then, by Lewis’ criteria, the actual world trivially supplies one of the needed counterfactuals: 

(C1) If the B1-event (brain event) had occurred (and it did), the C-event (behavior) would have occurred (and it did). 

Furthermore, by hypothesis (that C causally depends on B1), the B1-event is a counterfactually-sustaining necessary condition for the behavioral effect C, in Lewis’ sense: if the B1-event had not occurred, the behavioral effect C would not have occurred.

(C2) If the B1-event (brain event) had not occurred, the C-event (behavior) would not have occurred.

What more would the functionalist epiphenomenalist need to add to this picture, to have B1 screen off A from C?  Clearly, he would need A not to sustain this pair of counterfactuals with respect to C.  Now, since the mental state and the behavior did occur, we already have (trivially) that: 

(C3) If the A-event (mental state) had occurred (and it did), the C-event (behavior) would have occurred (and it did).

So the crucial ingredient to block the causal dependence of C on A, is this final counterfactual:

(C4) If the A-event (mental state) had not occurred, the C-event (behavior) would still have occurred.

Within this counterfactual model of causation, the case for functionalist epiphenomenalism hangs on our accepting (C4).

Should we accept (C4)?  It doesn’t look like either Block, or Jackson and Pettit, can.  For recall, they hold supervenience to be a logical relation, hence one holding in all possible worlds.  But then since, by hypothesis, A supervenes on B1 here, any possible world with B1 in this situation must be a possible world with A as well.  Here’s why that’s a problem: to accept (C4) is to accept that the world most similar to the actual world, but without A in this situation – call that world “W4” – is a world where C is still present.  But in accepting (C2), we accepted that: the world most similar to the actual world, but without B1 in this situation – call this world “W2” – is a world without C present in this situation.  Now I ask: which world is more similar to the actual world: W4 (lacking A but keeping C),  or W2 (lacking both B1 and C)?

Any appearance of incommensurability between the two worlds is an illusion – they can be perfectly well compared, thanks to strong logical supervenience.  Given logical supervenience, any possible world without A is a world without B1 as well.  So W4 is a world without B1, but still with C.  And since both W2 and W4 are worlds without B1, my question can be rephrased: which is more similar to the actual world – a world where neither B1 nor C are present (W2), or a world where B1 isn’t present but C still is (W4)?  But we already answered that question, when we accepted (C2): W2 is the world without B1 most similar to the actual world, and so W2 is more similar to the actual world than W4.  Hence the world without A, most similar to the actual, is a world without C either.  But then we must reject (C4) in favor of its negation:  

(CN4) If the A-event (mental state) had not occurred, the C-event (behavior) would not have occurred.

And in that case A is not causally irrelevant to C after all, so B1 does not screen off A from C after all.

For someone embracing supervenience as a logical relation, the only way to avoid this conclusion is to insist that W2 – the B1-less world most similar to actuality – is not, as I have assumed, a world without A after all.  But to hold that is then to accept the counterfactual:

(C5) If  the B1-event (brain state) had not occurred, the A-event (mental state) would still have occurred.

That’s not impossible, given the multiple instantiability of A as one of our basic functionalist premises.  But it insists on a particular reading of (C2) as most natural – viz., one involving (C5) in the bargain; and on reflection, (C5) hardly seems motivated.  For consider: on the functionalist scheme in question, the A-property must be instantiated by some base property in that counterfactual situation. So to accept (C5) along with (C2) is to say: 

In the actual world, this brain state did occur, and this mental state supervened on this brain state, and this behavior ensued; but in the most similar world where this brain state didn’t occur, a different state would have occurred instead, and the same (type of) mental state would still have supervened on this new state, but this new state would not have brought about the behavior in question.

The functionalist epiphenomenalist who takes supervenience to be a logical relation must insist that this is indeed what we would naturally accept, in accepting (C2).  So, for example, if I decide to drink my cup of coffee, and this deciding supervenes on a certain of my brain states, and that brain state causes my reaching out and picking up the cup, we should say: if this brain state hadn’t occurred, I would indeed still have decided to drink the cup of coffee – but the decision would then have supervened on some other brain state, which would not have led to my picking up the cup.  We would have to say that such a counterfactual situation would be less of a departure from actuality than one where I didn’t have the original brain state, and so didn’t have the supervening mental state either, and so didn’t drink the coffee.  So we would have to accept this counterfactual judgment:

(C6) If I had not had the brain state which in fact led me to pick up the coffee, I would still have decided to pick up the coffee, but I would nonetheless not have picked up the coffee.

And we would likewise have to say such a situation, with a causally ineffective surrogate supervenience base, is less of a departure from actuality than one where the original brain state is swapped for an equally causally effective surrogate supervenience base, which brings about my lifting the cup – that is, we would also have to accept the following counterfactual:

(C7) If I had decided to pick up the coffee, but that decision had supervened on some other brain state, then I would not have picked up the coffee. 

Now, as far as I can tell, there is no reason to think either (C6) or (C7) are judgments people would hold by virtue of taking a brain state to have caused some behavior – not even if they are functionalists; so there is likewise no reason to believe people would accept (C5), which has (C6) and (C7) as consequences.  Kim, for instance, seems to reject (C5) outright, judging that if the actual supervenience base hadn’t occurred, no other one would have taken its place (Kim 1998: 43).  If that is correct, and these counterfactuals are unacceptable, then this escape hatch is closed for those espousing supervenience as a logical relation; and so the screening off of mental states by brains states is blocked for the functionalist.

But what if the supervenience relation is not taken to be a logical relation – if strong supervenience holds only with some sort of ‘nomological’ necessity, as is alleged for the laws of science?  We are at first faced with the same sort of argument made in the previous section. In light of strong supervenience, a situation without mental state A must (with modal force) be a situation without physical base B1 as well.  So the most similar world without A should also be a world without B1, and hence without C as well – undermining (C4), and epiphenomenalism with it.

But if the modal force of supervenience is weakened, then we could accept (C4), if we accept that the A-less situation most similar to actuality is one where the B1-event still occurs, and causes C.  Strong supervenience is violated in that case, yes – but not in a logically impossible way; and Lewis does, after all, allow the most similar world to break actual laws, so this consequence is not disastrous of itself.  Is strong supervenience with weakened modality the salvation of functionalist epiphenomenalism?

In this case, we have something of a modal duel between counterfactuals (C2) and (C4):

(C2) If the B1-event (brain event) had not occurred, the C-event (behavior) would not have occurred.

(C4) If the A-event (mental state) had not occurred, the C-event (behavior) would still have occurred.

For, note first that, in order to keep (C2), a violation of certain laws must be rejected as too dissimilar from actuality – specifically, violation of whichever laws are involved in brain states causing behavior (presumable physiological, and ultimately physical laws).  But in order to accept (C4), a violation of certain laws must not be rejected as too dissimilar from actuality – specifically, violation of  the law of strong supervenience.  So we must here not only accept a ‘nomological’ modality weaker than logical necessity (or even “broadly logical/conceptual” necessity), but moreover grades of nomologicality, whereby supervenience is nomological, but less so than the laws of, say, physics.  But we are nowhere presented with any motivation for such a stipulation (other than to save the very epiphenomenalism viewed as troublesome by all our authors).  Recall how Kim – the only one of our authors to premise a non-logical supervenience relation – described the modality involved: “the necessity involved here is standardly taken to be at least nomological necessity – so that if the mind-body supervenience holds, it holds in all worlds that share with our world the same fundamental laws of nature” (Kim 1998: 39).  This puts supervenience perfectly on a par with the “fundamental laws of nature” in our world – hence yielding a perfect standoff between our counterfactuals. 

Finally, note that Lewis explicitly presents his counterfactual model as an account of single-case causation, with causal regularities consisting of systematic single-case couterfactual dependences.  But in this respect, there is a deceptive artificiality in the above attempts to decide on the general issue of epiphenomenalism by focusing on a single case of the physical property B1 causally excluding the functional property A from an effect.  For such a single case may involve only a single miracle, on Lewis’ account; but for the general epiphenomenalist claim to go through (that is, in the most similar possible world involved in counterfactually ‘excluding’ all mental states), supervenience would need to be violated across the board (i.e., throughout the universe).  That would constitute an inestimably large number of miracles – or, effectively, a single enormous miracle.  And note: equating a large concatenation of small miracles in this way is not a bit of sleight-of-hand on my part, but part of Lewis’ metric of comparative similarity. 

A big miracle consists of many little miracles together, perferably not all alike.  What makes the big miracle more of a miracle is not that it breaks more laws; but that it is divisible into many and varied parts, any one of which is on a par with the little miracle (Lewis 1979: 56).

But then the general epiphenomenalist claim is in direct violation of Lewis’ prime directive in comparative similarity: “avoid big, widespread, diverse violations of law”.  So, beyond the difficulties with uncooperative intuitions already considered, we must add: taken as the general view that it is, it seems epiphenomenalism should be rejected by the basic principle of Lewis’ model.

Reviewing, I conclude that such a counterfactual approach to causation offers slim hope indeed to the functionalist epiphenomenalist; and perhaps the best that can be said on his behalf is that we have no definite counterfactual intuitons legislating against epiphenomenalism – if only because we have no definite counterfactual intuitions on the topic at all.  Such is, however, an impressively thin reed on which to hang the entire epiphenomenalist endictment of functionalism.

VII. Causal Conundra III: Causal Processes

Although I have frequently cited Salmon as an expositor of probabilistic causation, in fact he did not long remain satisfied with bare probability and statistics, and in his later works he adds further, non-probabilistic criteria on causation.  This later work is itself worth noticing here, as Kim occasionally alludes to this view as the sort of view he finds amenable to his discussions of mental causation (Kim 1984b: 93; Kim 1998: 45, n. 28).  Salmon proposes buttressing the “statistical base” of the above models with an account of the physical processes exhibiting these probabilistic relations – the idea being, very roughly, that only certain kinds of statistically-related events and processes should count as genuinely causal: “although statistical relevance relations provide evidence for causal relations, causal relations are not appropriately analyzable in terms of statistical relevance relations” (Salmon 1984: 185-6). In developing further criteria to properly characterize the genuine causal interactions, the focus in Salmon’s account is shifted from events – specifically, causes and effects – to causal processes (Salmon 1984: 23).  The idea here is that if causal processes are aptly characterized, then events of causal interaction can be specified in a derivative way, as the intersection of two (or more) causal processes (Salmon 1984: 182-3).  

Following Reichenbach, Salmon takes mark transmission to be the defining quality of a causal process.  A car traveling through space constitutes a causal process, because intersection with the path of another car (another causal process) can leave marks (e.g., dents in the car) that are preserved by the car until another interaction with a causal process (e.g., a moving hammer in an auto repair shop).  By contrast, the car's shadow, moving alongside the car, is only a pseudo-process, since 'marks' imposed on the shadow (e.g., change of shape as the shadow passes over a rock) are not preserved by the shadow (it returns to its original shape once it passes back to smooth pavement, without having to be hammered back into this shape like the car)(Salmon 1984: 144).

Crucial to being a genuine causal process, then, is that marks are preserved, or “propogated” as Salmon phrases it.  The term “propogation” might itself suggest causal activity, and hence appear to render the account of causality circular (since causal processes would then be defined by appeal to the constituent causal processes of mark propogation).  But Salmon makes clear that propogation of a mark involves only the process having that mark at each space-time point of its history subsequent to its intersection with another process – what he terms the “at-at” view of propogation (Salmon 1984: 148).  From this we see that genuine causal processes are continuous spatio-temporal lines that can incur marks through intersections with other such processes (the events which we traditionally term “causes”).  

Note finally that, since statistical relevance relations still count for Salmon as evidence of causal processes (relations which the underlying causal processes explain – Salmon 1984: 209), the statistical version of screening off discussed in a previous section lives on in this model.  However, Salmon suggests a second type of “screening off,” in discussing special types of common causes.  In many common cause “forks,” the common cause C will statistically screen off one effect, A, from another, B – that is, will establish, purely statistically, a “barrier” to interaction between A and B.  But in some common-cause forks (the “interactive forks”), the common cause will not statistically erect such a barrier to interaction – i.e., judging purely from the statistical relations in these cases, A and B might be causally interacting. Armed with an account of ‘markable’ causal processes, however, Salmon argues that even here we can show how a common cause C insures that neither A nor B causes the other – thus “causally screening off” each from the other.

Suppose we mark the process that connects C to A at some point between C and A.  …the mark will not be transmitted to the process connecting C to B.  Similarly, a mark imposed upon the process connecting C to B will not be transmitted to the process connecting C to A.  This means that no causal influence can be transmitted from A to B or from B to A via C.  C constitutes an effective causal barrier between A and B, even if A and B exhibit the sort of statistical correlation [characteristic of an interactive fork] (Salmon 1984: 176-7). 

Such “causal screening off” amounts, of course, to a lack of spatio-temporal causal processes between A and B which could transmit a mark from one effect to the other – and here, even without any statistical screening off.

Now, will supervening mental states and events count as causes on this model, or are they instead “screened off” by genuine physical causes? The statistical relevance component of Salmon’s later model has been addressed in a previous section.  In terms of figuring in causal processes, mental states (and computational states generally) certainly undergo changes through interaction with the world (and with other such states), and these changes are subsequently preserved.  So it appears that mental states (or processes) can be marked through causal interactions, and can propagate these marks over time. 

But perhaps that conclusion seems too fast.  A critic could object that any “marks” preserved by supervening mental processes owe their preservation through their continued supervenience on physical processes – rendering the mental processes mere pseudo-processes, like the car’s shadow or the moving light disk.  This is certainly the picture of supervening mental states some philosophers of mind have adopted (e.g., Segal and Sober 1991); but I think Salmon’s model of pseudo-processes is especially unsuited to such cases of supervening mental events/processes.  Note first that Salmon’s pseudo-processes are slices of several different causal processes – but each such slice, in Salmon’s examples, is causally produced by, or a causal propogation of, earlier stages of that causal process.  Now, supervening events are not causally produced by their supervenience bases, since – as all our authors recognize – supervenience is not causation (Block 1990: 140, 159; Jackson and Pettit 1990: 207; Kim 1984b: 103; Kim ).  And propagation, in Salmon’s usage, involves a later stage of a process having the same structure as the earlier stage; whereas supervenience is not a matter of preserving structure over time – not least because supervenience is a non-temporal relation.  In fact, Kim himself stresses this point in an earlier paper, where he appeals to Salmon’s causal process model.  Drawing a distinction between causal relations among supervening events, and pseudo-causal connections between, e.g., a mirror image of a causal interaction, Kim states: 

The difference between the two cases is this: macrocausal relations are supervenient causal relations – supervenient upon microcausal relations – whereas cases like Edwards’s mirror images are not.  This can be seen by reflecting on the fact that in a perfectly straightforward sense, mirror images, symptoms of a disease, and so on are causal effects of the underlying process – they are not mereologically supervenient upon those processes.  This is the theoretical difference between the two cases: some epiphenomenal causal relations are supervenient causal relations, and these are among the ones that are “real”; there are also cases of epiphenomenal causation that do not involve direct causal connections, and these include ones in which the events involved are successive causal effects of some underlying process (Kim: 1984b: 103).

And while Kim’s later discussions of supervenient causal powers have not retained the compatibilism of this passage, he does not, I think, ever explain what error he sees in this earlier statement of why supervenient processes do not qualify as psuedo-processes.

It is important to note as well that in this last passage Kim has shifted from bare strong supervenience to a specific version of that relation, viz. mereological supervenience.  Mereological supervenience is, briefly, strong supervenience of macro-level properties on micro-level properties  (Kim 1984b: 96-7; 101-102).  This is a version of strong supervenience which Kim continues to recommend in his later writings, since it offers to move beyond the symmetrical covariance relation of strong supervenience alone, to an asymmetrical (and hence perhaps “genuinely explanatory”) “dependence” relation  (Kim 1993b: 166-9; 1998: ) – a move recommended likewise by Segal and Sober in their discussion of functionalist epiphenomenalism (Segal and Sober 1991: ). As a specific form of strong supervenience, it is moreover perfectly compatible with both my assumptions about supervenience at the outset, and the general functionalist outlook of non-reductive materialism.  And such a move is particularly fruitful in a discussion of Salmon’s causal process model, since it brings out especially strikingly how poorly that model of causation lends itself to epiphenomenalist ends.  

For consider: if we suppose that mental properties and events are macro-properties and   –events strongly supervening on physical micro-properties and –events, then supervening mental states will obey physical regularities, or “laws,” to the exact degree that the physical “base” states do – that is, will obey such laws entirely.  Whereas, as Salmon stresses, a defining feature of pseudo-processes is that they can violate physical laws: a shadow can move faster than the speed of light, whereas no genuine causal process can.  So again, supervening mental events do not at all seem to fit Salmon’s characterization of pseudo-processes.  Moreover, adopting mereological supervenience insures that alleged cases of mental causation, on a functionalist scheme, do indeed exhibit spatio-temporal continuity in the processes involved, as Salmon’s “at-at” mark propagation requires. For if supervening functional properties are properties of a larger whole, which supervene on the properties of the smaller parts, then the spatial continuity holding on the lower, "parts" level must be preserved on the macro-level of the wholes.  That is: under strong mereological supervenience, there is no way of introducing a spatio-temporal discontinuity at a higher (“functional”) level without introducing spatio-temporal discontinuity at the lower base level.  So to the observation of Section V, above – that statistical screening off off the mental by the physical is blocked – we can here add that Salmon’s non-statistical, ‘spatio-temporal’ screening off likewise does not apply to the mental with respect to the physical.

It seems, then, that a simple compatibilism between supervening mental events and causation ensues from Salmon’s later model – once again spoiling hopes for a functionalist epiphenomenalism.  

VIII. Causal Conundra IV: Laws

Lastly, we consider approaches to causality and causal explanation by way of laws.  This is one of the two approaches Block considers (and the one that he argues is most susceptible to functionalist epiphenomenalism); and Kim has also appealed to laws as crucial to understanding causation (not to mention science generally).

The main problem in getting clear on a law-based approach to epiphenomenalism is that everything will turn on how laws are identified, and what types of laws we permit.  On the first point, consider that if laws are explicated through appeal to statistical regularities or counterfactuals, then this approach devolves into one of the previous two considered.   In his early work on statistical relevance, Salmon notes that the statistical generalizations appealed to count as laws (Salmon 1971 postscript: 78-9).  Whereas Hempel, for one, adapted a point by Nelson Goodman to argue that laws will be precisely those generalizations which are counterfactually supporting (Hempel 1965: 339); and this account of laws is happily advanced by many philosophers of mind precisely when discussing functionalism and multiple instantiability (see, e.g., Fodor 1974: 133;  Pylyshyn 1984: 210).  But then on either of these approaches, worries about laws linking the mental to effects will turn on worries about which statistical or counterfactual relations hold between the mental and the effects – and so should reduce to one or the other of the cases already considered.

On the second point – which kinds of laws are needed to link the mental to the effects – Block raises an objection which merits passing comment.  The law (or “nomological”) approach to causation is, he argues, especially vexed, because even if the mental is linked to the effect in question by a genuine law, that law might not be a causal law – the idea being that there is more than one type of law, but that of course causation on this approach must be a matter of causal laws (Block 1990: 146).  This will not be a problem for counterfactuals, he adds, and he takes this as a point in favor of the counterfactual approach (Block 1990: ).  But that seems flatly wrong.  For Kim has noted, in response to Lewis’ counterfactual approach to causation, that neither does every counterfactual dependence constitute causal dependence (Kim 1972b: ); and Lewis is himself careful to distinguish causal from non-causal counterfactuals (Lewis 1979: 34-5; in “Causal Explanation”[Lewis 1986a]).  This should be obvious, after all: supervenience is itself spelled out modally, and is taken to license counterfactuals; but the counterfactuals in question will not be causal counterfactuals, since the supervening mental state is not caused by its physical base.  So, for what it is worth, it appears that an appeal to laws does not merit the special objections Block raises.

Block does cite a model of laws which, atypically, is not spelled out in terms of one of the earlier relations covered – a model developed by Paul Horwich (Block 1990: ). And since it is one of the approaches to causation which Blocks explicitly considers, I want for purposes of thoroughness to pause over it here.

Horwich calls his account of causation “neo-Humean,” in the sense that it explicates causation in terms of regularities, or “laws”.  For Horwich,  “basic laws” determine the basic links in a causal chain:

In general, as we continue to interpolate events between determining events, we encounter relations that are more and more basic.  In the limit we find relations of determination by means of the most basic laws, and these we identify with the elementary links in a determination chain (Horwich 1987: 134).

But he does not insist that only such a basic link counts as a cause of an event, only that a cause be linked to an effect by a chain of such basic links:

A direct cause of some effect is an essential part of an antecedent condition whose intrinsic description entails, via basic laws of nature, that the effect will occur.  And causation in general involves a chain of direct causation.  That is to say, C causes E if and only if there are some events, e1, e2, …, eN, such that C directly causes e1, e1 directly causes e2, …, and eN directly causes E (Horwich 1987: 133). 

Indeed, Horwich explicitly describes his law-based account of causation as “defining causation in terms of chains of direct determination via basic law” (Horwich 1987: 135). And in order to insure the proper causal structure of the direct determination” employed here, Horwich imposes two further “global constraints”:

(1) require that causes precede their non-simultaneous effects, and (2) maximize causal continuity (so that causal priority in one part of the chain may be ‘smoothly’ extended to adjacent parts) (Horwich 1987: 136).

Now note, so long as “basic laws” can include those chaining links of mental causation, nothing in this account so far poses a problem for the causal powers of the supervenient mental.  So the question becomes: what can count as a genuine law, and particularly a basic law, on this account?  Horwich follows Goodman in arguing that laws must be “projectible,” in the sense that for a law that “All A’s are B’s,” “the observation of A’s that are B’s provides reason to believe that unobserved A’s are B’s”; and he offer this preliminary criterion of projectibility:

…a plausible preliminary view of the matter (Goodman 1955; Horwich 1982) is that hypotheses are projectible when they employ terms that are natural (that is to say, entrenched words  such as “green” rather than ‘defined’ words such as “grue”), and when they are nevertheless syntactically simple (like “All A’s are B’s”, and unlike “All A’s are either sampled and B or unsampled and –B”).  Given some such account of projectibility, Goodman’s account of laws reduces to the idea, roughly speaking, that laws are naturally simple generalizations (Horwich 1987: 164).

Taking that last sentence at face value, it seems Horwich’s laws are more like sentences than regularities; but perhaps we should read him as asserting simply that laws must be describable in terms of syntactically simple generalizations using natural terms.  In any case, Horwich recommends sharpening the projectibility criterion of laws, in light of “inductive generalizations” in natural terms still not qualifying as laws (e.g., “Every match in this box is dry”).  Genuine laws, for Horwich, are those projectible generalizations (or regularities so described) that can only be explained (if at all) in terms of other laws (Horwich 1987: 166).

But note again, generalizations (or regularities) linking supervening mental causes to their effects (perhaps by a chain of law-governed links) pose no special problem for any of these criteria: our current mental terms (or their replacements in future cognitive science) could be just as “natural” and non-gerrymandered as the terms of physics.  And the explanantion of these laws via laws of physics would be by way of the (modally-enforced) regularities of supervenience – hence explaining these laws, if at all, only through other laws, in accordance with Horwich’s criteria.

Since the key to epiphenomenalist arguments against functionalist mental causation is the notion of  “screening off,” or “causally excluding” a putative cause, it is worth noting comments Horwich provides on such screening off – and this precisely in terms of epiphenomena, and the familiar barometer example:

One virtue of defining causation in terms of chains of direct determination is that we are able to avoid confounding cause and effect with mere epiphenomena.  The latter are events that are nomologically related, not because one cause the other but through being common effects of  the same cause.  In such cases an event may determine a later event and yet not cause it.  For example, …a change in the barometer reading does not cause the storm.  Schematically, cases in which A and B are epiphenomenal effects of C… are distinguishable by the existence of relations of determination between some earlier event C, and A, and between C and B.  Thus the determination chain between A and B passes through C.  So the only way for A to cause B would be for A to cause C and C to cause B.  Therefore, given the absence of backwards causation, it must be that C causes A and B (Horwich 1987: 135).

The account is certainly familiar (even providing the “fork” which Block sees also in supervenient causation), and does the nice service of pointing out the link Horwich sees between a “nomological” relation and “determination” – the epiphenomenon determines the effect exactly when there is a law connecting them.  However, the sort of epiphenomena Horwich sees being excluded by his account here are causal effects of a common cause, whereas nothing about supervenience says that mental states are caused by their “supervenience base”. This difference is important, since it is Horwich’s temporal condition on causes that excludes the epiphenomenon here: the common cause is temporally prior to the epiphenomenon in Horwich’s example, and – barring backward causation – the epiphenomenon cannot for that reason be the true cause of the effect.  But supervening events are not temporally preceded by their base events according to the functionalist (nor, again, are they causal effects of their bases), so Horwich’s temporal condition of causation will not block them in the way the atmospheric pressure would for the barometer.  So Horwich’s account of laws, causation, and causal exclusion (while sketchy, by his admission) does not, from what we can tell of it, lend any support to an epiphenomenalist argument.

IX. Probabilistic Supervenience and the Return of Functionalist Epiphenomenalism.

In case my presentation seem entirely negative, let me point out that not every statement of functionalist epiphenomenalism need suffer the same fate as the ones canvassed above. 
The problem stemmed, as we saw, from the combination of causation and supervenience.  So if epiphenomenalism is not sustained by any of the causal models canvassed above, a diehard epiphenomenalist has two obvious options: set out an alternative model of causation, or an alternative model of supervenience.  I have nothing to offer here toward a new model of causation and causal explanation. But strong supervenience can, I think, be modified in a fairly obvious way permitting an epiphenomenalist loophole – resulting in what I call probabilistic supervenience.  In the same way that the treatment of causation moved from a deterministic ideal to a probabilistic form, we can weaken the hold that the base has on supervenient properties and events, stipulating, for instance, that the mental supervenes on the physical only with a certain (significantly, non-1.00) probability.

While unorthodox, the idea is not without precedent.  The emergentist philosopher of mind Arthur Lovejoy makes a useful distinction between two types of “emergence” the mental can exhibit with respect to the physical:

[W]e must first of all distinguish between indeterminist and determinist theories.  The former declare that there are instances of emergence which are reducible to no causal law; no fixed occasions can be formulated upon which they invariably occur.  The hypothesis of “undetermined evolution” to which Professor Dreisch has referred is, I take it, a theory of this sort….  The determinist kind of theory declares that whenever certain specific occasions appear a specific variety of emergent uniformly arises (Lovejoy 1927: 25-6; cited in Horgan 1993: 559).

Now this discussion concerns emergence rather than supervenience, but a parallel concept can work for supervenience in both cases. Strong supervenience in this case is deterministic supervenience, where the mental invariably accompanies its physical base; whereas probabilistic supervenience constitutes a weaker (“indeterministic”) link whereby the mental events only supervene on the physical a certain percentage of the time (and there is, perhaps, no further story to be told about this link).

Probabilistic supervenience amounts, in brief, to a surrender of my earlier principle for probabilistically ‘projecting’ strong supervenience onto a world – i.e., the principle that if A supervenes on B, then p(B, A) = 1.00.  In a case where A probabilistically supervenes upon several different bases Bi, p(C, A&-Bi) ¹ 0 (by virtue of  multiple instantiation); and p(C, Bi&-A) ¹ 0 (by virtue of probabilistic supervenience).  Here we can satisfy the probabilistic definition of screening off, allowing Bi to screen off A from C.  (Obviously the same sort of modified supervenience relation could be translated into counterfactual/modal  terms, by having A supervene on Bi with something less than necessity, and so licensing law-perserving counterfactuals about situations with Bi but not A.)

I don’t say probabilistic supervenience is the sort of supervenience that would satisfy many functionalists; but it does seem to me one of few strategies that holds out much hope for functionalist epiphenomenalist arguments, even in light of a detailed theory of causation. To the degree that probabilistic supervenience is itself implausible, however, adopting it as an alternative premise in epiphenomenalist arguments may again render such arguments uncompelling.

X. Conclusion.

Finally, as a bit of additional benefit to be drawn from a largely negative survey, I want to close by drawing an important moral for the philosophy of mind, which epiphenomenalist worries illustrate rather starkly.  Note one last time, that in all the arguments studied here, the concepts of causation and causal exclusion were for the most part left unanalyzed, simply assumed as something uncontroversial and intuitive.  At best only fleeting reference is made even to the type of model being assumed, and at worst no mention is made at all.  Throughout, no effort is taken to explain how the details of any model of causation (and causal exclusion) figure into an argument for epiphenomenalism, nor does such analysis appear even to be recognized as important.  At bottom, the entire discussion of epiphenomenalism has uncritically assumed that the notion of causation is thoroughly intuitive, and so thoroughly unneeding of further analysis.  That assumption, I suggest, is the downfall of functionalist epiphenomenalism.

Not coincidentally, I think, all of these authors do nonetheless share a common family of  metaphors for causation.  Jackson and Pettit explain that “what drives the behavior is the physiological nature of the various states, not the functional roles they fill” (Jackson and Pettit 1990: 199; also 207). When discussing how syntactic processing screens off semantic properties, for example, Block tells us likewise that “[t]he syntactic properties of the representations do the causal work, and the semantic properties come along for the ride” (Block 1990: 145). And the “work” metaphor, in particular, recurs throughout Kim’s writings on functionalist epiphenomenalism: “The exclusion problem, then, is this: Given that P is a sufficient physical cause of P*, how could M also be a cause, a sufficient one at that, of P*?  What causal work is left over for M, or any other mental property, to do?” (Kim 1993: 354)  In the wake of the causal powers of the physical, Kim later asks, “what causal work is left for [mental property] m to contribute?” (Kim 1998: 37).  And taking that to be something of a rhetorical question, he concludes: “It is difficult to see how M and P together can pack any more causal power than M alone or P alone” (Kim 1998: 44).  The ‘work’ metaphor itself finds additional work as Kim turns to Block’s example of a “second-order property”: “…if the color of the cape is, in and of itself, a sufficient cause of the anger… what further causal work is left for its provocativeness?”  (Kim 1998: 53).  And likewise: “…given the color of the cape as a full cause, there is no additional causal work left for its provocativeness, or anything else.” (Kim 1998: 53)

Now, as long as discussions of functionalist epiphenomenalism remain on the level of intuitive metaphors, it is easy for such epiphenomenalism to seem like a genuine possibility.  My point here has been that when our philosophical arguments move beyond metaphors, to a detailed analysis of causation and causal exclusion, the reasonableness of these epiphenomenalist worries is no longer so obvious.  In that way, functionalist epiphenomenalist worries are an especially useful cautionary reminder for all of contemporary ‘analytic’ philosophy of mind.