Mellor on the Chances of Effects*
ABSTRACT: In the Facts of Causation (1995), D.H. Mellor includes, as a part of his theory of causation, an account of the chance that a cause gives its effect. He proposes that this chance can be analyzed as a certain kind of conditional, a closest world conditional with a chance consequent. I show that there are problems with Mellor’s account, but also attempt to show how these can be remedied. This analysis highlights important issues concerning the concept of components of single case objective chance.
Mellor takes the chance he is concerned with to be objective single case chance measured by the probability calculus. It is not frequency nor credence, although it has important connections to both frequencies and credences.(1)
According to Mellor facts which have chances can have more than one chance, for example, by having them at different times. Suppose we have two unstable atoms A and B in close proximity, each of which has a low chance of decaying, and suppose that atom A, if it decays, may bombard atom B with its product, thereby driving atom B into a state in which its chance of decaying is quite high- much higher than otherwise (see figure 1). Suppose this in fact happens, and let us consider the chance E that atom B will decay at a later time tE, when an observation will be made. The chance of E changes—increases, in fact—at tb, the time at which B is bombarded. Thus E has two chances, at different times.
Mellor also holds that chances are contingent, but not on the fact that they are "chances of" (in our example, E), since they can exist when that fact does not. Atom B may not decay at t0, but it still had a chance of doing so prior to that time; so the chance existed but the state of affairs that it was about never did. Since chances are contingent, they must therefore be properties of other facts, facts without which they would not exist. The chance E that atom B will decay at time t0 is a property of facts about the structure and nature of that atom, together with facts concerning the nature and proximity of atom A. Mellor writes this chance as "chQ(E)" where Q is the fact or conjunctive fact of which the chance is a property.
Applying this to the case of causation, the chance of the effect is a property not of the effect but of another fact, the cause C or the conjunction of C and S, where S is the circumstances in which C causes E.
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