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(1986) develops a detailed account of event distinctness. What ought to be
apparent (but is never discussed) is that the same problem can arise for cases of
prevention: we also want to avoid saying that my raising my arm prevented my arm
from going down, that my saying hello prevented me from remaining silent, and
so on. Although we have counterfactual dependence in each of these cases, we fail
to have genuine prevention. The reason again involves a failure of distinctness: my
raising my arm is not distinct from the failure of my arm to go down. Some may
find this particular formulation jarring: how can an occurrent event fail to be
distinct from an event-absence? No matter, we can just introduce some different
terminology: my raising my arm and my arm s going down are contrary events,
where contrariety is to be explicated in terms of logical and spatiotemporal exclu-
sion in the spirit of Lewis (1986). The key point here is that a counterfactual theory
of causation is already committed to a notion of contrary events. We may now use
this notion to re-formulate our rule: two events are to be represented as different
values of the same variable if they are contrary; as values of different variables if
they are distinct but not contrary.13 In Back-up Assassin, the novice s shot and the
back-up s shot are not contraries; hence they must be represented as values of
different variables, and the one could (in principle) cause or prevent the other.
Let us illustrate the rule with a further example, taken from Cartwright (1979).
Weed. A weed in a garden is sprayed with a defoliant. This decreases the
chance that the weed will survive from 0.7 to 0.3. Nonetheless, the weed
survives.
Intuitively, spraying the weed with defoliant did not cause it to survive. Note,
however, that the probabilities are identical to those in Back-up Assassin. What is
the difference between the two cases, such that we regard one to be a case of
causation, the other not? In order to answer this question we must look at the equa-
tion(s) and graph that characterize Weed.
Here is a natural attempt to provide a representation: Let S' be a variable that
Routes, processes and chance-lowering causes 147
takes the value 1 if the weed is sprayed, 0 if it is left alone; and let V' take the value
1 if the weed survives, 0 if it dies. Then we can represent the situation using Equa-
tion 3 and Figure 8.2, adding primes to the variable names.
Is this the correct representation? Or should the representation look more like
Figure 8.1 and equations 1 2? In order for the latter to be correct, we would have to
include one more variable in the model. We might try to do this in the following
way: let A' take the value 1 or 0 according to whether the weed is sprayed or not, B'
take the value 1 or 0 according to whether the weed is left alone or not. Using these
variables, the analogues of equations 1 and 2 seem to capture the relevant facts. But
this representation clearly violates our rule: A' = 0 and B' = 1 represent events that
are not distinct, while A' = 1 and B' = 1 represent events that are contrary.
Alternately, we might note that spraying the plant affects its chances of survival
by affecting its state of health shortly after the spraying. Let S' and V' be defined as
above, and let H = 1 or 0 according to whether the plant is healthy or not, one day
after being sprayed. In order to make the case parallel to that of Back-up Assassin,
suppose that the weed will be healthy just in case it is not sprayed. That is, suppose
that the equation expressing the relationship between S' and H is:
(4) H = 1 S'
Now, however, there are (at least) two different ways in which we can write the
second equation so as to preserve the appropriate probabilities. We could write it
on the model of equation 2:
(5) Ch(V' = 1) = 0.3S' + 0.7H 0.21S'H
or we could write it more simply:
(5') Ch(V' = 1) = 0.3 + 0.4H
Both entail that the plant has a 0.3 chance of surviving if it is sprayed, 0.7 if it is
not. There is an important difference, however: Equation 5 implies that the plant s
chance of survival depends upon whether or not it is sprayed, even when its later
state of health is held fixed; Equation 5' does not. This is an empirical matter, not
settled uniquely by the description of the scenario. Nonetheless, Equation 5'
seems vastly more plausible: spraying the weed affects its chance of survival only
by affecting its subsequent health. If the plant were sprayed, but were (miracu-
lously) healthy the next day, its chance of survival would be 0.7, not 0.79. The fact
that it was sprayed, in addition to being healthy, would not give it an extra chance
to survive one that it would not have had if had not been sprayed. To slightly
abuse some familiar terminology: the state of the plant s health screens off
spraying from survival.14
The graphical representation of Weed, as characterized by Equations 4 and 5', is
shown in Figure 8.3. This figure shows clearly that there is only one route from the
148 Christopher Hitchcock
' '
S H V
Figure 8.3
spraying to the plant s survival. It is possible to interpolate variables along this
route, but doing so does not create distinct routes from S' to V'. The causal structure
depicted in Figure 8.2 can be embellished, but not fundamentally altered. Since
there is only one route from spraying to survival, and spraying lowers the proba-
bility of survival, it follows that spraying must lower the probability of survival
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