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we allow C to qualify as a candidate for a neutralizer for itself. And yet surely
being purely negatively causally relevant to an event implies being causally rele-
vant to it. Thus, one must impose a constraint on being a candidate for a neutralizer
that yields that C must not qualify as a neutralizer for itself.
But this is not enough, since in general this sort of trivialization holds not only for
C itself, when considered as a candidate for a neutralizer for itself and A, but also for
many events C* that imply C, or, more precisely, that yield C with probability 1
(given WA), when considered as candidates for neutralizers for C. Such a C* that
yields C with probability 1 (given WA) is too a stable screener for A and C. If we then
confine the restriction on neutralizers, the occurrence time of which pertains all the
way to the upper end of the occurrence time of C in such a way that it excludes only
C itself, then, for any A and C, consider an informational expansion of C. An infor-
mational expansion of C would be, for instance, a conjunctive expansion of the form
B.C, where B is an (actual) intermediate event (for A and C). Select B so that A is not
a cause of B. Then, for the kind of case under discussion here, A is also not a cause of
B. C A is not a cause of C since A is purely negatively causally relevant to C. I f we
impose a restriction on candidates for neutralizers so as to exclude only C itself, then
such B. C would qualify as a neutralizer for A and C since B. C screens off A from C
in a stable way. So the account faces trivialization since, again, if A is not a cause of
C, A would always come out as causally irrelevant to C.
Hence an appropriate constraint on neutralizers, when allowing the occurrence
time of neutralizers to stretch all the way up to the upper end of the occurrence time
of C, is:
(8) A neutralizer E for A and C must fulfil: P(C/E.WA)
Condition (8) rules out C as well as any C* that yields C with probability 1 (given
WA) as neutralizers for A and C. Making sure that C does not qualify as a neutral-
izer for A and C is crucial when A has purely negative causal relevance to C, but is
harmless or not objectionable in the other cases, namely the cases in which A is
Probabilistic cause 175
causally irrelevant to C or has some positive causal relevance to C. I f A has some
positive causal relevance to C, A is a cause of C, and thus C would not qualify as a
neutralizer for A and C on our analysis of causal relevance without any further
constraints. If A is causally irrelevant to C, then, if we see to it that C does not
qualify as a neutralizer for A and C, we can expect that there is some intermediate
event other than C that serves as a neutralizer for A and C. This is since in cases of
causal irrelevance that are not cases of probabilistic irrelevance, the motivation
for expecting the presence of a neutralizer anyhow hinges on the expectation that
there are intermediate events other than A or C that attest to the would-be causal
relevance of A to C being neutralized; and if there is one such neutralizer, then
often there is more than one.
Elsewhere31 I argued that a corresponding constraint must hold also vis--vis the
possibility that the occurrence time of a neutralizer extends all the way down to the
lower end of the occurrence time of A, namely, a constraint to the effect that for E
to be a neutralizer for A and C, it must be the case that P(A/E.WA)
argued that an even stronger constraint is well motivated, to the effect that the
occurrence time of neutralizers must not stretch all the way down to the lower end
of the occurrence time of A. I will not, however, elaborate on this issue here.)
However, we need to be more precise about the relation between the temporal
edges of C and of a neutralizer-candidate E. The time to which C pertains must
include, but need not coincide with, the occurrence time of the C-event. Thus, the
time to which C pertains, its pertinence time, in other words tC may extend beyond
the actual occurrence time of the C-event. (This is so since the sentence C may
have a temporal quantifier such as during T or even, more emphatically, some
time during T .) Since we proceed here in terms of narrow individuation of events,
we may replace the terminology of the time to which the sentence that determines
the event pertains with the notion of the specified occurrence time of the narrowly
individuated event in question. These two notions come down to the same thing, and
must be distinguished from the notion of the actual occurrence time of the event in
question. That is, if the C-event in question is not temporally fragile (and is actual
here we are concerned only with actual events), we may contrast its actual occur-
rence time, the interval throughout which it in fact occurred or took place, with its
specified occurrence time the temporal component of the C-event. (An event can
be specified as temporally fragile by a phrase such as exactly at t that specifies its
occurrence time.) One may thus distinguish between temporally fragile events,
where the specified occurrence time coincides with the actual occurrence time, and
cases where C is temporally non-fragile, so that the actual occurrence time of C
does not overlap with, but is included in, its specified occurrence time.32
The difference between fragile and non-fragile events plays a significant role in
counterfactual analyses of cause such as Lewis s, and in particular in the case of
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