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body, missing all bones, and continues on across the room, into your friend s
skull, and kills her.Your firing your gun at the gunman (C) lowered the chance of
your friend dying (E). It was very likely that he would have killed her since his
gun was loaded, working, he fully intended to do it, he was a good shot, and she
stood still not 5 metres away. Your firing your gun was unlikely to kill her since
the gunman stood between you and her and the bullet was most unlikely to pass
through the man s body. Moreover, since the gunman hasn t seen your gun, you
are a good shot, and the gunman stands about 5 metres away, there is a good
chance that you can kill him before he shoots. So your firing your gun lowered the
chance of your friend dying even though it caused her death as it happened.
It follows that P(E|C & K)
background factors such those given in the previous paragraph, and for the
frequentist this is made true by the fact that in similar situations the victim s life is
more often saved than ended this way. It also follows that chC(E)
because the chance that my shooting gives E is greater than the chance the same
circumstances without my shooting gives E.
There are various strategies to save the chance-raising theory of causation, short
of denying the intuition that my shooting caused her death. In this paper I will
consider three, which, following Salmon, I will label as follows: (1) Fine-grain
the cause , where one more closely specifies the cause event, for example, as my
shooting the gun in precisely the direction that I did; (2) Fine-grain the effect ,
where one more closely specifies the effect, for example, as her being killed by a
bullet of the type that belongs to my gun (and not that of the gunman); and (3)
Interpolating causal links where one identifies an intermediate event D between
the cause and the effect such that there is a chain of chance-raising C D E, for
example, accounting for the bullet emerging from the gunman. In what follows I
will consider each of these strategies in turn, providing versions of the counter-
example which are not amenable to these strategies.
30 Phil Dowe
Fine-grain the cause
If we more adequately specify the cause, according to this strategy, we will find
that the cause does raise the chance of the effect. Take C' to be my shooting in
exactly the direction that I did. Then P(E|C' & K) > P(E|~C' & K) simply because
my shooting in that exact direction, unknown to me, did make it very likely that
the bullet would pass through the gunman. For the same reasons, Mellor s
approach gives chC'(E) > ch~C'(E) (although the strategy is not available to a
factualist, because that I fired the gun and that I fired the gun in the direction I did
are distinct facts).
We need to note that in general it is necessary to fine-grain the circumstances to
the same extent as the cause. It will not do to specify the cause as C' if the back-
ground K is specified only roughly. For example if we think of K including the fact
that the gunman stood between me and the victim, this in itself may not be a fine
enough description to give the desired chance relations. We need to specify exactly
where and how he stood in order to make it sufficiently probable that the bullet
would pass through. This fine-graining of the background is already built into
Mellor s account, where the circumstances S include all the local facts that
there are.
We should next ask, to what degree should we fine-grain the cause? What facts
about my shooting should be included in the cause? We have already seen that the
chance relations can be reversed by more closely specifying the cause, and indeed
in principle they can be reversed back again by yet more closer specification. And
the question is not only how far should we fine-grain? but worse, why isn t our
answer to that question arbitrary and question-begging? It would be arbitrary if
we have no reason to prefer the adopted degree of fine-graining to any other, and
question-begging if we choose a level of fine-graining just because it gives the
desired result.
One obviously non-arbitrary answer would be always to fine-grain completely
in other words, specify everything that is true about the cause, say C* (with an
appropriate restriction to local factors, or the like, so as to exclude properties such
as eventually has effect E ).
However, this answer faces a dilemma. Either our situation is deterministic or it
isn t. By deterministic I mean that the state of the world at the time of the cause,
together with the laws of nature, fixes the state of the world at the time of the effect,
and, conversely, the state of the world at the time of the effect, together with the
laws of nature, fixes the state of the world at the time of the cause. This means that
P(E|C* & K*) = 1 where K* includes everything (local) about the situation in
which C occurs at the time of C, and chC*(E) = 1, if C is what Mellor calls a total
cause (if it is not, then the conjunction of C* with whatever else makes up the total
cause gives E a chance of 1).
Suppose on one hand the situation is deterministic. Then P(E|C* & K*) =1and
chC*(E) = 1. But we also need to know P(E|~C* & K*) and ch~C*(E). Take the
frequency version. Here the problem is that it may well be that the conjunction of
Chance-lowering causes 31
~C* & K* is physically impossible, in other words that P(~C* & K*) = 0. The
reason is that, in a deterministic world, factors which are part of C* may have as a
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