For all properties F and G, if F is a supervenience base of G, then no event is causally overdetermined by (events that are instances of) F and G.
Like Exclusion, this principle has a tautologous sound to it. When we say that an event is causally overdetermined by two other events, we mean that it has two causes that are independently sufficient for its occurrence. “Independent” here means, surely, at least that it would have been possible for each to occur without the other (and that if one had occurred without the other, it would have brought about the same effect). But it is a straight logical consequence of the definition of supervenience that instances of properties and their supervenience bases are not “independent” in this sense, as the instantiation of the base necessitates the instantiation of the supervening property.
Our evidence that Kim makes use of No Overdetermination is in the section titled “Why overdetermination is not an option”, in which Kim answers the question, Why do instances of mental properties and their supervenience bases not overdetermine their effects? His answer (p. 48):
The usual notion of overdetermination involves two or more separate and independent causal chains intersecting at a common effect. Because of Supervenience, however, this is not the kind of situation we have here. In this sense, this is not a genuine case of overdetermination ...
Since Kim thinks it is “because of supervenience” in the case under consideration, we assume he thinks that supervenience always precludes overdetermination, and that is what No Overdetermination says.
In addition, Kim must also assume some other principles relating supervenience to causation. We believe that he is assuming these:
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