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correlation would be explained, even though there was no common cause, and this would violate the Principle of the Common Cause. Hence, conjunctive forks involving a common effect must, if Reichenbach is right, always be closed forks. All open forks, therefore, must involve a common cause, and so the direction of causation is fixed by the direction given by open forks. 3.2 Objections This is a subtle and ingenious attempt to offer a probabilistic analysis of the relation of causation, and one that appeals only to Humean states of affairs. Unfor- tunately, it appears to be open to a number of decisive objections. 86 Michael Tooley 3.2.1 Accidental, open forks involving common effects The basic idea here is simply this. Suppose that A and B are types of events that do not cause one another, and for which there is no common cause. Then it might be the case that the conditional probability of events of type A given events of type B was exactly equal to the unconditional probability of events of type A, but surely this is not necessary. Indeed, it would be more likely that the two probabilities were at least slightly different, so that the conditional probability of events of type A given events of type B was either greater than or less than the unconditional probability of events of type A. Let us suppose, then, that the second of these alternatives is the case. Suppose, further, that the occurrence of an event of type A is a causally necessary condition for the occurrence of a slightly later event of type E and, similarly, that the occur- rence of an event of type B is a causally necessary condition for the occurrence of a slightly later event of type E. Finally, let us suppose as is perfectly compatible with the preceding assump- tions that the relative numbers of all possible combinations of events of types A, B and E, throughout the whole history of the universe, are given by the following table: E Not-E A Not-A A Not-A B 1 0 18 12 Not-B 0 0 42 28 From this table, one can see that Prob(A) = 61/101, or about 0.604, while Prob(A/ B) = 19/31, or slightly less than 0.613, so that, if the absolute numbers are not too large, there will be nothing especially remarkable about the fact that Prob(A/B) > Prob(A). Next, examining the numbers that fall under E , we can see that we have the following probabilities: Prob(A/E) = 1; Prob(B/E) = 1; Prob(A & B/E) = 1 Hence the following is true: (1) Prob(A & B/E) = Prob(A/E) × Prob(B/E) Similarly, examining the numbers that fall under not-E , we can see that we have the following probabilities: Prob(A/not-E) = 60/100 = 0.6; Prob(B/not-E) = 30/100 = 0.3; Prob(A & B/not-E) = 18/100 = 0.18 Probability and causation 87 So the following three equations are also true: (2) Prob(A & B/not-E) = Prob(A/not-E) × Prob(B/not-E) (3) Prob(A/E) > Prob(A/not-E) (4) Prob(B/E) > Prob(B/not-E) Hence, in a universe of the sort just described, the three types of events A, B and E form a conjunctive fork. Moreover, since there is, by hypothesis, no type of event, C, that is a common cause of events of types A and B, it is therefore the case that A, B and E constitute an open fork. This open fork then defines the relevant direction of causation as the direction that runs from events of type E towards events of the two types, A and B, that are causally necessary conditions for the occurrence of an event of type E. In short, not only is it logically possible to have an open fork that involves a common effect, rather than a common cause, but there is no significant unlikeli- hood associated with the occurrence of such an open fork. The direction of open forks cannot, therefore, serve to define the direction of causation. 3.2.2 Underived laws of co-existence John Stuart Mill suggested that, in addition, to causal laws, there could be basic laws of necessary co-existence that related simultaneous states of affairs. Are such laws possible? If one considers some candidates that might be proposed, it may be tempting, I think, to be attracted to the idea that although there can be laws of necessary co-existence, all such laws are derived, rather than basic, though this idea is far from unproblematic. Thus, consider, for example, a Newtonian world, and Newton s Third Law of Motion that if one body, X, exerts a certain force, F, on another body, Y, then Y exerts a force equal in magnitude to F, and opposite in direction, upon X. This certainly asserts the existence of a necessary connection between simultaneous states of affairs, but is it correctly viewed as a basic law, in a Newtonian universe? Doubts arise, I think, in view of the fact that the funda- mental force laws entail conclusions such as the following: (a) It is a law that for any objects X and Y, and any time t, if X exerts a gravita- tional force, F, onY at time t, then Y exerts a gravitational force, F, onX at time t. (b) It is a law that for any objects X and Y, and any time t, if X exerts an elec- trostatic force, F, onY at time t, then Y exerts a gravitational force, F, on X at time t. (c) It is a law that for any objects X and Y, and any time t, if X exerts a magnetic force, F, onY at time t, then Y exerts a gravitational force, F, on X at time t. 88 Michael Tooley So non-causal laws that are special instances of Newton s Third Law of Motion can be derived from the fundamental force laws, and the latter are, if one treats forces realistically, causal laws. But this is not, of course, a derivation of Newton s Third Law of Motion itself. [ Pobierz caÅ‚ość w formacie PDF ] |