Sungho Choi has criticised Michael Strevens’s counterexample to David Lewis’s final theory of “token” causation, causation as “influence.” I argue that, even if Choi’s points are correct, Strevens’s counterexample remains useful in revealing a shortcoming of Lewis’s theory. This shortcoming is that Lewis’s theory does not properly account for degrees of causation. That is, even if Choi’s points are correct, Lewis’s theory does not capture an intuition we have about the comparative causal statuses of those events involved in Strevens’s counterexample (we might, for example, intuit that Sylvie’s ball-firing is as much/more/less a cause of the jar’s shattering as/than is Bruno’s ball-firing).
Sungho Choi (2005, 106–113) has criticised Michael Strevens’s (2003, 4–7, 11–17) counterexample to David Lewis’s (2000) final theory of “token” causation, causation as “influence” (hereafter, “CaI”). I argue that, even if Choi’s points are correct, Strevens’s counterexample remains useful in revealing a shortcoming of CaI. This shortcoming is that CaI does not properly account for degrees of causation. This paper proceeds as follows. Section 1 articulates CaI. Section 2 articulates Strevens’s counterexample to CaI, and Choi’s criticism of Strevens’s counterexample. Section 3 argues that, even if Choi’s points are correct, CaI does not capture an intuition we have about the comparative causal statuses of those events involved in Strevens’s counterexample (we might, for example, intuit that Sylvie’s ball-firing is as much/more/less a cause of the jar’s shattering as/than is Bruno’s ball-firing).
1 CaI
CaI involves three ideas. The first idea is the “alteration” of an event. Consider this event E: the vase’s shattering. Lewis defines an “alteration” of E as “either a very fragile version of E or else a very fragile alternative event that is similar to E, but numerically different from E” (2000, 188, emphasis mine).
To elucidate, an event is considered “fragile” if we impose stringent conditions for its occurrence (if we say that any change in one of its details turns it into a numerically different event) (Lewis 2000, 185–186). One alteration of E is E’s actual alteration: exactly when and how the vase shattered. The other alterations of E are un-actualised (one example: the vase shattering one millisecond later, and into more pieces).
The second idea is “influence.” Let C and E be two single, distinct, actual events. Lewis holds that C “influences” E iff
there is a substantial range C1, C2, … of different not-too-distant alterations of C (including the actual alteration of C) and there is a range E1, E2, … of alterations of E, at least some of which differ, such that if C1 had occurred, E1 would have occurred, and if C2 had occurred, E2 would have occurred, and so on. (Lewis 2000, 190)
Idea three concerns the relationship between influence and causation. According to Lewis, C is a cause of E iff C directly influences E, or there is a chain of stepwise influence (hereafter, “i-chain”) leading from C to E (that is, a sequence of (actual) events C, D1, D2, …, Dn, E, such that C influences D1, D1 influences D2, …, D(n-1) influences Dn, and Dn influences E) (Lewis 2000, 191; see also Lewis 1973, 563).
Let’s observe CaI in action. Consider this scenario: Sylvie throws a rock at a vase. Beside her, Bruno laughs. Here, CaI delivers the intuitive result that Sylvie’s throw is a cause of the vase’s shattering, while Bruno’s laughter is not. This is because Sylvie’s throw has substantial direct influence on the vase’s shattering. That is, there are many different, not-too-distant alterations of Sylvie’s throw (e.g. her throwing one millisecond later/with slightly more force) upon which alterations in the vase’s shattering (i.e. the vase’s shattering one millisecond later/into more pieces) counterfactually depend. Bruno’s laughter, however, has no substantial direct influence on the vase’s shattering. Maybe one distant alteration of Bruno’s laughter is so infectious that it delays Sylvie’s throw (and hence, the vase’s shattering) by a second. Nevertheless, no not-too-distant alteration of Bruno’s laughter appears to alter the vase’s shattering.1 Moreover, one cannot identify any i-chain leading from Bruno’s laughter to the vase’s shattering.
2 Strevens’s counterexample to CaI; Choi’s criticism
Here is Strevens’s counterexample to CaI (2003, 4–7, 11–17):
SCE. At time \(t_{1}\), and using identical rifles, Sylvie and Bruno fire at a jar intrinsically identical, minute lead balls. Sylvie, who never misses, shoots so that her ball will ricochet two times prior to striking the jar. Bruno shoots directly at the jar. The balls, however, collide in mid-air at time \(t_{c}\). Consequently, they perfectly exchange trajectories and spin (we thus take the motion of the balls to be that of two point particles; this admittedly requires something like a fortuitous gust of wind at \(t_{c}\)) (2003, 5, fn. 2). Stipulate moreover that the speeds of the two balls are always identical (and extremely high). Ultimately, Sylvie’s ball shatters the jar, and Bruno’s ricochets, then flies through thin air.2
Let SF stand for Sylvie’s firing, BF for Bruno’s firing, and JS for the jar’s shattering. For two reasons, Strevens argues that CaI delivers this unintuitive result: SF is not at all a cause of JS. First, SF has no substantial direct influence on JS (2003, 4–5, 12–13). After all, hold fixed BF, and consider an alteration of SF in which Sylvie fires one millisecond earlier/later, or one in which her rifle points one degree to the left/right. Given the properties of both balls, these alterations result in: no collision \(\rightarrow\) Bruno’s ball striking the jar (before Sylvie’s ball finishes ricocheting) \(\rightarrow\) no alteration to JS. Second, there appears no i-chain leading from SF to JS (2003, 5–7, 13–14). This second point, however, is where Choi (2005, 110–113) most seriously disagrees.
Referring to Figure 2, and using both Choi’s and Lewis’s terminology (Choi 2005, 110–111; Lewis 1986a, 244–249), let D1 and D2 be the (fragile) events whose occurrence conditions consist of all the intrinsic and spatio-temporal properties satisfied by the region that Sylvie’s ball occupies at, for D1, time \(t_{2}\) before \(t_{c}\), and for D2, time \(t_{3}\) after \(t_{c}\).
Strevens claims that D1 has no substantial influence on JS. After all, alter, say, the spatio-temporal properties of Sylvie’s ball at \(t_{2}\). This results in: no collision \(\rightarrow\) no alteration to JS. Strevens also claims: SF has no substantial influence on D2. After all, alter, say, the timing, or direction of SF. This results in: no collision \(\rightarrow\) the occurrence condition of D2 being satisfied by Bruno’s ball (Strevens notes that, on Lewis’s metaphysics, it isn’t a violation of the occurrence condition of D2 if the ball at D2’s spatio-temporal region loses the property of “belonging to” Sylvie (2003, 7); said property, after all, is extrinsic).
Choi, however, claims that Strevens is twice mistaken. (i) D1 does influence JS. After all, alter the mass, or shape, of Sylvie’s ball at \(t_{2}\). Admittedly, if \(t_{2}\) were, say, right after \(t_{1}\), then these alterations result in: Sylvie’s ball taking a different post-\(t_{2}\) trajectory (balls of different mass/shape encounter different amounts of air resistance) \(\rightarrow\) no collision. However, stipulate that \(t_{2}\) is right before \(t_{c}\). Then, neither alteration prevents the balls’ collision. Both, however, alter the manner of the collision, and resultantly the manner of JS. Furthermore, (ii) SF does influence D2. After all, alter the surface properties, or electrical charge, of the ball Sylvie fires. Neither alteration prevents the balls’ collision. Both, however, in altering an intrinsic property of Sylvie’s ball at \(t_{3}\), alter D2.
Combining (i), the fact that D1 influences JS, with the (safe) claim that SF influences D1, and combining (ii), the fact that SF influences D2, with the (safe) claim that D2 influences JS, Choi concludes that there are (at least) two i-chains leading from SF to JS—one “via” D1 (i-chain1), and one “via” D2 (i-chain2). Thus, CaI delivers the intuitive result that SF is a cause of JS, and “[SCE] spells no trouble whatsoever for [CaI]” (2005, 113).
3 CaI, SCE, and Degrees of Causation
I think, however, that even if Choi’s points are correct, SCE still spells some trouble for CaI. In what follows, I argue that, even if Choi’s points are correct, CaI does not capture an intuition we have about the comparative causal statuses of SF and BF. Thus, insofar as my argument succeeds, SCE remains useful in revealing the failure of CaI to properly account for degrees of causation.3 4
Here is the intuition I have in mind:
Comparative Intuition. SF is (at least) as much a cause of JS as is BF.5
I think that Comparative Intuition is, and should be, held as strongly as is the (absolute) intuition that SF is a cause of JS. A question arises: what buttresses our intuition in Section 1 that Sylvie’s rock-throw is a cause of the vase’s shattering, while Bruno’s laughter is not? One answer is the following: informed (only) of Sylvie’s rock-throw, I can predict, explain, and blame someone for the vase’s shattering. Informed (only) of Bruno’s laughter, I can do none of these things. However, and to use Jonathan Schaffer’s terminology, note that “the core epistemic, explanatory, and ethical connotations of causation” (2001, 12–13, emphasis mine) are no more present in the claim that “BF caused JS,” than they are in the claim that “SF caused JS.” Suppose the jar were a national treasure. First, and to endorse Lewis’s view that we don’t ordinarily consider events fragile (2000, 185–186; 1986b, 198), comparing a scenario in which I’m informed (only) of BF with one in which I’m informed (only) of SF, it’s not as if I can only predict JS (here taken as a non-fragile event) in the former. Second, consider the question, “Why did the jar shatter?” It is likely that most would find the answer “Because Sylvie fired” to be no more lacking than the answer “Because Bruno fired.” Third, it’d be surprising if Judge blamed Bruno more than she did Sylvie. More likely, liability for the jar’s damages would be apportioned equally.
Nevertheless, two considerations might motivate
Counter Intuition. BF is more a cause of JS than is SF.
Consideration1 is this asymmetry: had Sylvie not fired, nothing about JS would have changed. However, had Bruno not fired, the jar would’ve shattered slightly later, and in a slightly different manner. Consideration2 is that JS occurred at a time, and in a manner more (and, in fact, exactly) in line with Bruno’s, rather than Sylvie’s, intention.
If, however, Consideration1 and Consideration2 are what motivate Counter Intuition, then Counter Intuition is misleading. Consider this scenario:
Unlucky President. At time \(t_{1}\), AssassinH and AssassinR poison President’s coffee. AssassinH uses poison H, which will induce heart failure at time \(t_{4}\). AssassinR uses poison R, which will induce respiratory failure at time \(t_{5}\). At time \(t_{2}\), President drinks her coffee. At time \(t_{3}\), however, poison H and poison R interact in President’s system—poison H neutralises the respiratory-failure-inducing elements of poison R; poison R neutralises the heart-failure-inducing elements of poison H. But President isn’t so lucky—she happens to be fatally allergic to some other element e of poison H. Element e induces in President respiratory failure at \(t_{5}\), and she dies.
Considerations parallel to Consideration1 and Consideration2 are present in Unlucky President. In Unlucky President, we have Consideration1*, which is this asymmetry: had AssassinH not poisoned President’s coffee, nothing about President’s death would have changed. However, had AssassinR not poisoned President’s coffee, President would’ve succumbed to heart failure at \(t_{4}\), and not respiratory failure at \(t_{5}\). In Unlucky President, we also have Consideration2*: President’s death occurs at a time, and in a manner more (and, in fact, exactly) in line with AssassinR’s, rather than AssassinH’s, intention. However, does either Consideration1* or Consideration2* push us to think that “AssassinR’s poisoning caused President’s death”? No. Most intuitively, AssassinH’s poisoning caused President’s death. This shows that considerations like Consideration1 and Consideration2 aren’t substantially relevant to causation. Thus, if Counter Intuition is motivated by Consideration1 and Consideration2, then Counter Intuition should be suppressed.
Comparative Intuition, then, is justifiably strong. But I now argue that CaI violates this intuition: it counts SF as (significantly) less a cause of JS than is BF.
What determines how much a cause BF is of JS? On CaI, it is (roughly) the amount of influence that BF has on JS (Lewis 2000, 92). What determines this amount? Centrally, it is the size of the range of alterations to BF that lead to changes in JS. Accounting for those types of alterations that Strevens and Choi consider, there are (at least) four types of alterations to BF that lead to said changes: alterations to the timing and direction of BF, and to the mass and shape of the ball Bruno fires.
What determines how much a cause SF is of JS? Because SF has no substantial direct influence on JS,6 CaI must appeal to i-chain1/i-chain2. For each of these i-chains, however, CaI is silent on whether the determinant is (A) the amount of influence that SF has on D1/D2 (the amount of influence present in “link”1 of the i-chain), (B) the amount of influence that D1/D2 has on JS (the amount of influence present in “link”2 of the i-chain), or (C) some weighted average of [(A)+(B)]. Nevertheless, let’s first determine (A) and (B):
“Link”1 of i-chain1 (At least). six types of alterations to SF lead to changes in D1 (alterations to the timing and direction of SF, and to the mass, shape, surface properties and electrical charge of the ball Sylvie fires);
“Link”2 of i-chain1 (At least). two types of alterations to D1 lead to changes in JS (alterations to the mass and shape of the ball at D1’s spatio-temporal region);
“Link”1 of i-chain2 (At least). two types of alterations to SF lead to changes in D2 (alterations to the surface properties and electrical charge of the ball Sylvie fires);
“Link”2 of i-chain2 (At least). four types of alterations to D2 lead to changes in JS (alterations to D2’s spatio-temporal properties (this counts for two), and to the mass and shape of the ball at D2’s spatio-temporal region).
Let the “strength” of an i-chain “link” be the amount of influence present in that “link.” I now claim that, for i-chain1 and i-chain2, CaI must say that what determines how much a cause SF is of JS is the strength of the i-chain’s weaker “link.” This follows from my next, more general, claim that if an event C is a cause of another event E because there is a (two-“link”) i-chain leading from C to E, then how much a cause C is of E supervenes upon the strength of said i-chain’s weaker “link.” I will now evidence the just-mentioned general claim by constructing one (two-“link”) i-chain in each of two causal scenarios. I will then show that, in these i-chains, varying the strength of the stronger “link” (while holding fixed that of the weaker “link”) doesn’t vary our intuitions about how much C is a cause of E. Varying the strength of the weaker “link” (while holding fixed that of the stronger “link”), however, does. The first i-chain I construct will possess i-chain1’s strong-weak pattern of influence (i.e. C (SF) has no substantial direct influence on E (JS); C strongly influences some intermediate event D (D1); D weakly influences E). The second will possess i-chain2’s weak-strong pattern of influence (i.e. C (SF) has no substantial direct influence on E (JS); C weakly influences D (D2); D strongly influences E).
Scenario 1. Divorce. Only two things elicit in Wife hatred for Husband (the first significantly more so than the second): (1) the memory of their first fight, which occurred in the rain; (2) the memory of their second fight, which occurred in the fog. Wife, nevertheless, has fallen for Paramour. Thus, she has decided that she will file for divorce from Husband on Thursday afternoon. On Wednesday afternoon, Husband goes on a drinking binge. Late Wednesday night, Husband arrives home. His drunkenness annoys Wife, and the two fight in their driveway. Because fog happens to descend, the fight is so serious to Wife that it (temporarily) lays her thoughts of Paramour to rest, and independently drives her to file for divorce on Thursday afternoon.
We can construct a strong-weak i-chainDivorce with these three events: (C) Husband’s drinking binge on Wednesday afternoon; (D) the fight late Wednesday night; (E) Wife’s filing for divorce on Thursday afternoon. (1) C has no substantial direct influence on E—altering whether or not/how/what/how long Husband drinks changes nothing about Wife’s filing for divorce. (2) C strongly influences D—altering whether or not/how long Husband drinks changes whether or not/at what time the fight occurs. (3) D weakly influences E—altering whether or not/how long Wife and Husband fight changes nothing about Wife’s filing for divorce. However, if the fight had occurred in the rain, then Wife would’ve filed for divorce, say, earlier.
Does strengthening i-chainDivorce’s stronger “link” (C’s influence on D) make us intuit that C is more a cause of E than before? No. Add to Divorce that the fight’s topic is sensitive to the type of alcohol that Husband consumes—this doesn’t make us intuit that Husband’s drinking binge is more a cause of Wife’s filing for divorce than before. But what if we strengthen i-chainDivorce’s weaker “link” (D’s influence on E)? Add to Divorce that the timing of Wife’s filing for divorce is sensitive to whether or not (but not the extent to which7) Husband is drunk during the fight (perhaps Wife takes sober fights most seriously, and would’ve filed for divorce earlier if Husband had been sober during the fight8)—contrary to before, this does make us intuit that Husband’s drinking binge is more a cause of Wife’s filing for divorce on Thursday afternoon (and not, say, early Thursday morning).
Scenario 2. Resolve. Colonel is testing Recruit’s resolve. Recruit possesses a button which, if pressed, activates a light which Gunman takes as a signal to shoot Prisoner. Gunman will only ever shoot at time \(t_{2}\). Also, iff Recruit doesn’t press the button by time \(t_{1}\), Colonel will shoot Prisoner at \(t_{2}\). The following three events occur: (C) Recruit presses the button at \(t_{1}\); (D) Gunman fires at \(t_{2}\); (E) Prisoner dies at \(t_{3}\).
\(C\)-\(D\)-\(E\) form weak-strong i-chainResolve: (1) C has no substantial direct influence on E—altering whether or not/how/when Recruit presses the button changes nothing about Prisoner’s death at t3. (2) C weakly influences D—altering how Recruit presses the button changes nothing about Gunman’s firing at \(t_{2}\). And neither does having Recruit press the button before \(t_{1}\). However, if Recruit hadn’t pressed the button (by \(t_{1}\)), Gunman wouldn’t have fired. (3) D strongly influences E—altering whether or not/how Gunman fires changes whether or not/how Prisoner dies.
Consider these two possible additions to Resolve: (1) Gunman possesses many rifles to choose from, each of which inflicts death differently; (2) Recruit possesses another button which, if pressed, prevents Gunman’s firing (Colonel will nonetheless shoot Prisoner at \(t_{2}\) if this button is pressed9). Again, only that addition which strengthens the i-chain’s weaker “link” (addition (2)) makes us intuit that C is more a cause of E than before.
There is evidence, then, that in (two-“link”) i-chains, how much C is a cause of E supervenes upon the strength of the i-chain’s weaker “link.” Consequently, unless one (a) reasonably explains why this doesn’t apply to i-chain1 and/or i-chain2, or (b) denies that the causal status of C has something to do with i-chains (or counterfactual dependence in general), then how much SF is a cause of JS supervenes upon the strength of “link”2, for i-chain1, and “link”1, for i-chain2.
This result, however, likely forces CaI to (counterintuitively) count SF as (significantly) less a cause of JS than is BF. After all, four types of alterations to BF count towards the influence that BF has on JS. Only two types of alterations to D1 count towards the influence that D1 has on JS. And only two types of alterations to SF count towards the influence that SF has on D2. Certainly, it remains possible that for, say, i-chain2, the total number (as opposed to the number of types) of alterations to SF that lead to changes in D2 is greater than the total number of alterations to BF that lead to changes in JS. But this would be surprising. Why think, for example, that there are (significantly) more surface properties that Sylvie’s ball might have had, than there are angles at which Bruno might have fired? It also remains possible for the defender of CaI to try to identify more types of alterations to SF that lead to changes in D2. This strategy, however, can only be a stopgap, unless it can be shown that, for each such newly-identified type of alteration to SF, there is no not-too-distant, hitherto-unidentified, type of alteration to BF that leads to changes in JS. Showing this would be difficult. After all, there appear many examples of the latter (e.g. altering properties like the muzzle velocity and barrel length of Bruno’s rifle will affect the travel of his ball).
I end by blocking one last maneuver that the defender of CaI might perform. Consider:
“Threshold” Operation of CaI. Causation isn’t a scalar relation. That is, there are no degrees of causation—either an event C is a cause of another event E, or it isn’t. Thus, if the strength of the weaker “link” of i-chain1/i-chain2 determines anything, it’s simply whether or not SF is a cause of JS. That said, in both i-chains, said strength meets that minimum amount of influence \(x\) required to establish causation. So there is a sense in which CaI does capture Comparative Intuition—SF is “as much” a cause of JS as is BF in that neither firing can be said to be more or less a cause than the other. (On “Threshold” Operation, then, any influence that C has on E exceeding \(x\) is ignored.)
Besides its diverging from Lewis’s writing10, there are (at least) two reasons to reject “Threshold” Operation.
First, causation is plausibly a scalar relation. After all, this appears to be the “common sense”, or “ordinary”, view. For one thing, Hitchcock and Knobe offer experimental evidence for their claim that “ordinary causal judgments of subjects” come in degrees (2009, 602). For another thing, Michael Moore argues that the law treats causation as scalar (2009, 71, 118–123; see also Braham and van Hees 2009, 324). Thus, in tort law, the idea of “degrees of causal contribution” is both taken as sensible, and employed widely. We see this especially in negligence cases in which the doctrine of divisible harm is invoked so as to apportion liability amongst several defendants according to the degree of causal contribution each makes to some indivisible harm (Moore 2009, 118–119). In one such case11— Moore v. Johns-Manville Sales Corp 781 F 2d 1061 (5th Cir 1986)—liability for each plaintiff’s asbestosis was apportioned according to the degree to which each (defendant) manufacturer’s (asbestos-containing) products caused the plaintiff’s asbestosis (i.e. each defendant’s “degree of relative causation”). Therefore, if we think that our concept of causation should accord with how causation is employed “ordinarily,” we should also think that causation is a scalar relation.
Second, determining the value of \(x\) appears impossible. After all, \(x\) cannot be some one particular value. This is because we can easily conceive of one pre-emption case in which (the event intuited as) the pre-empting cause doesn’t exhibit \(x\) amount of influence on the effect, and another pre-emption case in which (the event intuited as) the (non-causal) pre-empted alternative does (see Dowe 2000, 6–7). One may then suggest that one determine \(x\) on a case-by-case basis. This, however, would require one to establish some standard set of case features relevant to determining \(x\) (so as to ensure that our determinations of \(x\) are not ad hoc). At this point, however, I simply cannot see what these features might be.