Casting a Shadow on Lewis’s Theory of Causation
A Shadowy Puzzle:
In the above diagram L is a distant light source, A and B are two opaque rectangular objects with equal width. If only A had been present, it would have cast the shadow R+S on the ground; and if only B had been present, it would have cast the shadow S. In the situation above, P is the shadow A casts on B (which coincides with the area of B facing A).
Question: Clearly, the shadows R and P are caused by A. But which one of A and B is causally responsible for the shadow S?
(1) B cannot be causing S, because B is not receiving any light, as A blocks the light from reaching B. And an object which doesn’t have any light impinging on it cannot cast any shadow.
(2) A cannot be causing S, because A’s casting S is prevented by A’s casting P on B. And an object can cast only one shadow in the presence of one light source. In this case, A’s full shadow due to L is R+P; so we cannot claim that A casts S in addition to casting P.
(3) Since neither A nor B is causally responsible for S, we can’t say A and B overdetermine S. For in overdetermination situations, there are two or more causes each of which is causally responsible for the same effect. Nor can we say that one of A and B is preempting the other and itself causing S—for neither is a cause of S.
Then what is causing S?
My answer to this puzzle is that it is A, despite the considerations in (2). Clearly, A is what is causing the dark region (umbra) behind A, by blocking the light coming from L. (B has no share in bringing about that dark region, as B doesn’t receive any light.) The presence of the ground (represented by the long horizontal line in the figure) that intersects with the dark region leads to the casting of the shadow R+S on the ground. Hence, it is A that is causally responsible for S.
B is a “back-up cause” of S: If A hadn’t been present, B would have cast S. It follows that we do have a case of preemption here, after all: A preempts B from causing S.
Another interesting feature of the situation in the diagram is that it seems to pose a problem for David Lewis’s well-known counterfactual analysis of causation.1 Although, as I argued, the presence of A is causally responsible for (or is “a cause” of) the shadow portion S, we don’t have a series of actual events running from A to S that constitute a chain of counterfactually dependent events from A to S, which Lewis’s analysis requires. The presence of B blocks completion of such a chain. Take, for example, the events:
d1: the presence of the dark region between A and B
d2: the presence of the dark region to the right of B,
and consider the counterfactuals:
If A had not been present, then d1 would not have occurred
If d1 had not occurred, then d2 would not have occurred
If d2 had not occurred, then S would not have been present.
These counterfactuals fail to entail a chain of counterfactually dependent events in Lewis’s sense, because the second counterfactual is false: even if d1 had not occurred, d2 would still have occurred thanks to the presence of B.
Hence the situation above appears to constitute a counterexample to Lewis’s 1973 analysis of causation. And this case doesn’t seem to be assimilable to the other problematic cases for that analysis, such as “late preemption” and “trumping preemption.” (To give a name to them, we might call the kind of cases exemplified in the diagram “overshadowing preemption.”)
To illustrate how the improved theory Lewis offered in 20002 works, let me give the example of how this new theory is supposed to take care of trumping preemption cases. An example of trumping preemption was given by Jonathan Schaffer:
… the major and the sergeant stand before the corporal, [and they] both shout “Charge!” at the same time, and the corporal decides to charge.[.] Orders from higher-ranking soldiers trump those of lower rank. I hope you agree that the major’s order, and not the sergeant’s, causes the corporal’s decision to charge….3
Lewis thinks that his improved theory can handle Schaffer’s example. According to the new criteria Lewis added, first we imagine altering the trumping factor while keeping the trumped factor the same, and see if there will be any change in the effect. Secondly, we imagine altering the trumped factor while keeping the trumping factor the same, and see if the effect will be any different. Lewis argues that in the first case there will be a change in the effect (e.g. if the major were to shout “Charge in 5 minutes from now!”, instead), whereas in the second case there will be no change in the effect (e.g. if the sergeant were to shout “Charge in 5 minutes from now!”, instead). Thus we can conclude that the major’s shouting, rather than the sergeant’s, is a cause of the soldiers’ charging, according to Lewis.
But this ploy wouldn’t work in our case. In our example, suppose we lowered the height of A, while we kept B unaltered. The effect S wouldn’t change. Secondly, suppose we increased the height of B while A remained unaltered. The effect S would thereby change—it would become a taller shadow. Consequently, we must conclude that the presence of A isn’t a cause of S, contrary to our verdict above.
1 David Lewis, “Causation,” Journal of Philosophy, 70(1973), pp.556-567.
2 David Lewis, “Causation as Influence,” Journal of Philosophy, 97(2000), pp.182-197.
3 Jonathan Schaffer, “Trumping Preemption,” Journal of Philosophy, 97(2000), pp.165-181; see p.175.
Written by Erdinç Sayan
August 12, 2012 at 1:31 am
Posted in Metaphysics
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