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the desert. He has two enemies, Zack and Mack: Zack aims to poison him by putting
poison in his water-bottle; Mack aims to cause him to die of dehydration by
punching a hole in his bottle. Both these events occur. The water runs out of Fred s
bottle and Fred dies of dehydration. Thus, Mack s punching a hole in Fred s bottle
caused his death, even though there is no simple counterfactual dependency of death
on Mack s holing the bottle. Structurally the case can be shown by Figure 7.4.
Nevertheless, we recognize that there is a process of the right kind from the holing
to death. By isolating this process from its actual context we can make that depend-
ency manifest. A simple way of doing this is to suppose that the preempted cause had
not occurred. If there had been no poisoning, then the holing-death process would still
Analysing chancy causation 125
holing
death
poisoning
Figure 7.4
have obtained. Moreover, the dependency  had there been no holing, there would
have been no death  would have held under those conditions. Thus, one might argue,
holing was the cause of death for this reason. But can t one argue equally in the oppo-
site direction that had there been no holing, then there would still have been a
poisoning and a death, and moreover a dependency of the latter on the former? The
answer is no; there is no completed process in this case. If there had been no holing,
then the poisoning-death process would have been completed, that is, events that actu-
ally did not occur would have to have occurred to get the effect; had the holing and
these events not occurred, there would have been no death. That is the asymmetry, and
why poisoning is not a cause whereas holing is. We can sum up the theory thus:
The Embedded Dependency  ED  account: (c caused e) iff
[1] O(c) and O(e).
[2] There are events, conditions or states, f  possibly non-obtaining such
that:
a. (¬O(f) > (O(c) & O(e))) b. (¬O(f) > (¬O(c) > ¬O(e))).
[3] No non-obtaining event, condition or state, g, is such that:
a. (¬O(f) > O(g)) b. ((¬O(f) & ¬O(g)) > ¬O(e))12.
The idea is that the causation is ultimately based on counterfactual dependency.
That is given in [2b]. For the dependency to reveal itself we cut out the alternative
paths leading to the effect. But the paths must be complete in the actual world, a
fact guaranteed by [3]. We apply the ED account to the poisoning case as follows 
here poisoning, holing and death are the three events concerned. It is the case that
(holing caused death) since:
[1] O(holing) and O(death).
[2] There is an event, poisoning, such that:
a. (¬O(poisoning) > (O(holing) & O(death)))
b. (¬O(poisoning) > (¬O(holing) > ¬O(death))).
[3] No non-occurring event, condition or state, g, is such that:
a. (¬O(poisoning) > O(g)) b. ((¬O(poisoning) & ¬O(g)) > ¬O(death)).
In contrast it is not the case that (poisoning caused death) since although [1] and [2]
hold, [3] does not:
126 Stephen Barker
[1] O(poisoning) and O(death).
[2] There is an event, holing, such that:
a. (¬O(holing) > (O(poisoning) & O(death)))
b. (¬O(holing) > (¬O(poisoning) > ¬O(death))).
But there is some event, g, say, poison enters George such that:
¬O(poison enters George)
((¬O(holing) & ¬O(poison enters George)) > ¬O(death))
The idea here is that the chain from poisoning to death is incomplete, and a neces-
sary condition for causation fails to obtain. Completion would have come about
only if there had been no holing of George s bottle.
That is the ED theory in essence.13 ED involves no step-wise chains of depend-
ence; it requires dependency of effect on cause, under the hypothetical conditions.
Late preemption
We have looked at early preemption above. Take a case of late preemption, as in
Figure 7.5.
In this case, black circles are fired neurons  B*, A* and so on mean that B, A, and
so on have fired  and light grey circles unfired neurons, with arrows indicating
stimulatory connections, and reverse arrows inhibitors. In this case, the A* E*
process occurs, but is faster than the B* E* process. If E* occurs before C*, the
former inhibits the latter. A* causes E*, but if A* had not occurred, it is not the case
that E* would not have occurred, since E* would have occurred later. Lewis s step-
wise dependency approach, which can cope with early preemption, fails here: D*
depends on A* but E* does not depend on D*.
The ED account applies straightforwardly. That is (A* causes E*) because:
[1] O(A*) and O(E*).
[2] There is an event, B*, such that:
a. (¬O(B*) > (O(A*) & O(E*)))
b. (¬O(B*) > (¬O(A*) > ¬O(E*))).
[3] No non-occurring event, condition or state, g, is such that:
a. (¬O(B*) > O(g)) b. ((¬O(B*) & ¬O(g)) > ¬O(E*)).
B
C
E
D
A
Figure 7.5
Analysing chancy causation 127
In terms of Figure 7.5, the conditions required by ED amount to isolating the A* E*
chain by supposing B* has not occurred, and noting that it is complete. In contrast,
if we isolate the B* E* chain by supposing A* does not occur, we find that it is
incomplete. The event C*, which is non-occurring, must occur for B* to cause E*.
Frustration: preempted causes with completed causal paths?
It might be objected that this ED account is doomed since it cannot deal with
preemption in which the causal process of the preempted cause is complete. Are
there such cases? Noordhof (1998a) argues there are. His example is shown in
Figure 7.6.
A fires at time 0 and B fires at 1. It takes 2 units of time for the impulse from B to
reach D, and 4 units for A s impulse to reach D via C. Intuitively the cause of D s [ Pobierz całość w formacie PDF ]