[ Pobierz całość w formacie PDF ]
simply dissipate. Yet note that a causal-relevance neutralizer need not be the event
that cuts off would-be causal chains from A to C even when such chains are cut off.
The role of a causal-relevance neutralizer is to secure that no would-be causal
chains15 from A proceed all the way to C, thereby securing the absence of causal
relevance.
3 Candidates for causal-relevance neutralizers
A causal-relevance neutralizer E, which secures causal irrelevance of A to C
(despite probabilistic relevance), must, I suggest, screen off A from C; that is, it
must fulfil:
Probabilistic cause 169
(6) P(C/A.E.WA) = P(C/~A.E.WA)
An event E satisfying (6) is a screener for A and C.16
As an illustration, consider Example 3.
Example 3
Consider a pipe that leads from a main tap (faucet) to a pool. This main tap can be
in only one of two positions: in one position it allows water to flow freely through
the pipe, whereas in the other position it doesn t allow any water to flow through
the pipe. Furthermore, the pipe has at an intermediate point its own separate tap
that also controls the water flow through it. This intermediate tap also has two
positions, of the same sort as in the main tap. Assume that it was in the open posi-
tion. The main tap was originally closed. But then x switched the main tap to the
open position (A). And indeed, the pool filled up (C). Assume that the chance, as
of tA, of further interventions regarding the positions of the taps (other than A) is
small. Hence there is ab initio probability increase for A and C (and thus there is a
null differentiator for them), and A is therefore probabilistically relevant to C.
Assuming that there are no other pertinent unexpected aspects of the story took
place, A is also intuitively causally relevant to C as well as a cause of C.
Now let us move to a variation in which, unlike the previous version, immedi-
ately after A, in an unrelated development, E occurred: the intermediate tap was
closed. Consequently, no water originating from the main tap reached the pool.
Yet, it started to rain around that time, and the rain filled up the pool. We can
assume further that, as of tA, and given E, the chance of C given A vs. ~A is the
same. Assume also that no other pertinent unexpected occurrences took place.
Intuitively, then, A was not a cause of C, and indeed, as it turned out, in view of E, A
ended up being causally irrelevant to C. E is indeed a screener for A and C, and, I
suggest, under circumstances akin to the rough specification of the above sort, E is
also a main component of a causal-relevance neutralizer for A and C (see E' on
p. 170).
Yet the mere presence of a screener E need not yield a stable ex post facto proba-
bilistic equality, since a screener may have a differentiator for it. But, I suggest, a
causal-relevance neutralizer for A and C must also screen off A from C in a stable,
that is, unreversed, way. That is, there must not be any other intermediate event F
that undoes this screening-off. In other words, there must not be an intermediate
event F such that:
(7) P(C/A.E.F.WA) `" P(C/~A.E.F.WA)
If E is a screener for A and C, fulfilling (6), for which there is no intermediate F,
fulfilling (7), then the probabilistic equality of (6) is indeed stable. Call such a
screener E (satisfying (6)) for which there is no such F satisfying (7) a stable
screener for A and C. A stable screener, then, yields stable probabilistic equality.17
170 Igal Kvart
To illustrate, let us move now to a still further variation of Example 3 above, in
which, in addition to the story of the last variation, the following F occurred: the
intermediate tap was re-opened (at time t). t was later than A and E but well before
C. (Recall: A was: x switched the main tap to the open position; E was: the interme-
diate tap was closed.) Given that the intermediate tap was re-opened, there would
be water flow from it to the pool, given A, and A thus intuitively would end up
being causally relevant to and a cause of the actual C (which was: the pool filled
up).18 In this variation, E, despite being a screener for A and C, was not a stable
screener, since F is a differentiator for E (vis-à-vis A and C). A screener that is not
stable falls short of securing causal irrelevance.
If, however, as in the previous version, neither F nor any other differentiator for
E occurred, then E is a stable screener for A and C. As noted, in such a case, under
the circumstances, A would end up being causally irrelevant to C, and E is, as I
suggested, a main component of a causal-relevance neutralizer for A and C. This
requirement, that a candidate for a causal-relevance neutralizer for A and C be a
stable screener for them, reflects a probabilistic approach to causal relevance,
viewed as a probabilistic phenomenon. And indeed, an extension E' of E is a stable
screener for A and C and also a causal-relevance neutralizer for them, where E' is:
the intermediate tap was closed and remained so.19
Consider again Example 2 in Section 2 in which, intuitively, A (Enemy 1
released his dog at t1) ended up being causally irrelevant to C (x was injured). Yet
there is a null differentiator for A and C, and thus A was probabilistically relevant
to C. But E (an avalanche completely blocked the entrance to the cave at t1 + dt)
was a stable screener for A and C: given E, it makes no difference to the probability
of C whether A or ~A took place, and there is no differentiator for E (vis-à-vis A and [ Pobierz caÅ‚ość w formacie PDF ]
zanotowane.pl doc.pisz.pl pdf.pisz.pl karpacz24.htw.pl
simply dissipate. Yet note that a causal-relevance neutralizer need not be the event
that cuts off would-be causal chains from A to C even when such chains are cut off.
The role of a causal-relevance neutralizer is to secure that no would-be causal
chains15 from A proceed all the way to C, thereby securing the absence of causal
relevance.
3 Candidates for causal-relevance neutralizers
A causal-relevance neutralizer E, which secures causal irrelevance of A to C
(despite probabilistic relevance), must, I suggest, screen off A from C; that is, it
must fulfil:
Probabilistic cause 169
(6) P(C/A.E.WA) = P(C/~A.E.WA)
An event E satisfying (6) is a screener for A and C.16
As an illustration, consider Example 3.
Example 3
Consider a pipe that leads from a main tap (faucet) to a pool. This main tap can be
in only one of two positions: in one position it allows water to flow freely through
the pipe, whereas in the other position it doesn t allow any water to flow through
the pipe. Furthermore, the pipe has at an intermediate point its own separate tap
that also controls the water flow through it. This intermediate tap also has two
positions, of the same sort as in the main tap. Assume that it was in the open posi-
tion. The main tap was originally closed. But then x switched the main tap to the
open position (A). And indeed, the pool filled up (C). Assume that the chance, as
of tA, of further interventions regarding the positions of the taps (other than A) is
small. Hence there is ab initio probability increase for A and C (and thus there is a
null differentiator for them), and A is therefore probabilistically relevant to C.
Assuming that there are no other pertinent unexpected aspects of the story took
place, A is also intuitively causally relevant to C as well as a cause of C.
Now let us move to a variation in which, unlike the previous version, immedi-
ately after A, in an unrelated development, E occurred: the intermediate tap was
closed. Consequently, no water originating from the main tap reached the pool.
Yet, it started to rain around that time, and the rain filled up the pool. We can
assume further that, as of tA, and given E, the chance of C given A vs. ~A is the
same. Assume also that no other pertinent unexpected occurrences took place.
Intuitively, then, A was not a cause of C, and indeed, as it turned out, in view of E, A
ended up being causally irrelevant to C. E is indeed a screener for A and C, and, I
suggest, under circumstances akin to the rough specification of the above sort, E is
also a main component of a causal-relevance neutralizer for A and C (see E' on
p. 170).
Yet the mere presence of a screener E need not yield a stable ex post facto proba-
bilistic equality, since a screener may have a differentiator for it. But, I suggest, a
causal-relevance neutralizer for A and C must also screen off A from C in a stable,
that is, unreversed, way. That is, there must not be any other intermediate event F
that undoes this screening-off. In other words, there must not be an intermediate
event F such that:
(7) P(C/A.E.F.WA) `" P(C/~A.E.F.WA)
If E is a screener for A and C, fulfilling (6), for which there is no intermediate F,
fulfilling (7), then the probabilistic equality of (6) is indeed stable. Call such a
screener E (satisfying (6)) for which there is no such F satisfying (7) a stable
screener for A and C. A stable screener, then, yields stable probabilistic equality.17
170 Igal Kvart
To illustrate, let us move now to a still further variation of Example 3 above, in
which, in addition to the story of the last variation, the following F occurred: the
intermediate tap was re-opened (at time t). t was later than A and E but well before
C. (Recall: A was: x switched the main tap to the open position; E was: the interme-
diate tap was closed.) Given that the intermediate tap was re-opened, there would
be water flow from it to the pool, given A, and A thus intuitively would end up
being causally relevant to and a cause of the actual C (which was: the pool filled
up).18 In this variation, E, despite being a screener for A and C, was not a stable
screener, since F is a differentiator for E (vis-à-vis A and C). A screener that is not
stable falls short of securing causal irrelevance.
If, however, as in the previous version, neither F nor any other differentiator for
E occurred, then E is a stable screener for A and C. As noted, in such a case, under
the circumstances, A would end up being causally irrelevant to C, and E is, as I
suggested, a main component of a causal-relevance neutralizer for A and C. This
requirement, that a candidate for a causal-relevance neutralizer for A and C be a
stable screener for them, reflects a probabilistic approach to causal relevance,
viewed as a probabilistic phenomenon. And indeed, an extension E' of E is a stable
screener for A and C and also a causal-relevance neutralizer for them, where E' is:
the intermediate tap was closed and remained so.19
Consider again Example 2 in Section 2 in which, intuitively, A (Enemy 1
released his dog at t1) ended up being causally irrelevant to C (x was injured). Yet
there is a null differentiator for A and C, and thus A was probabilistically relevant
to C. But E (an avalanche completely blocked the entrance to the cave at t1 + dt)
was a stable screener for A and C: given E, it makes no difference to the probability
of C whether A or ~A took place, and there is no differentiator for E (vis-à-vis A and [ Pobierz caÅ‚ość w formacie PDF ]