Jaegwon Kim is a prolific and influential writer on the topic of higher-vs.-lower level properties and mental causation. Many of his arguments may be seen as raising the following dilemma: either higher level properties reduce to lower level ones (i.e., their causal powers are identical to the causal powers of their lower level realizers), or higher level properties are epiphenomenal.
But it has always seemed to me that the "subset view" escapes Kim's dilemma. By subset view, I mean the view that higher level properties are a part of their realizers, in the sense that their causal powers are a subset of the causal powers of their realizers. (The subset view occurred to me years ago while reading Kim and listening to his talks. I believe a version of the subset view has been defended by Sydney Shoemaker, though I haven't read Shoemaker's work. I took the term from Gillett and Rives's recent paper in Nous. The subset view as I understand it seems consistent with different views of properties: either properties as individuated by their causal powers, or properties as constituted entirely by their causal powers.)
The subset view escapes Kim's dilemma because being a proper subset of something is not the same as being identical with something, and yet there is no reason why a subset of the causal powers of a realizing property (which is assumed to be causally efficacious) should be epiphenomenal.
But to the best of my knowledge, Kim has not discussed the subset view in print. I was interested his opinion, so I emailed him and asked: do you agree that the subset view is a legitimate alternative to reductionism and epiphenomenalism about properties? If not, why? If you reject the subset view, why do you?
The following is an excerpt from Kim's response (reproduced with permission):
"No, I don't think one can escape the mental causation problem by defining "realization" in the way you describe. From the start, this approach looked to me like an attempt to solve a substantive philosophical problem by definitions. Don't you think it sound too neat and too good to be true? One way to see the problem with it is this, I think: If you define a realizer in the way suggested by the "subset" view, how do you show--what does it take to show--that mental properties have physical properties as their realizers? That is, how does one show that the physical realizes the mental? The subset view looks plausible at first blush, I think, because it is presented with the unspoken assumption in the background (which we normally make under our more or less intuitive and unspecific notion of realization) that the mental is physically realized.
"Consider a mental property M. How does M get to have a physical property, P, as one of its realizers? According to the subset definition, the causal powers of M must be a subset of the causal powers of P. How is that possible? We may assume that most of P's causal powers are powers to cause other physical events but we can allow, at this point, that P's causal powers may include causal powers to cause nonphysical events as well. But for the present strategy to work for the mental causation problem, the causal powers of M must include at least some of P's physical causal powers. This amounts to the supposition that M has causal powers to cause physical events. How do we show that? Well, showing that that is possible, or showing how that is possible, is exactly the problem of mental causation. We seem to be back to square one, and very quickly, in a small circle!"
In the rest of his email, Kim also writes that from his point of view, the subset view as I define it counts as a form of reductionism, and is unlikely to satisfy die-hard nonreductive physicalists.
I agree with Kim that die-hard non-reductive physicalists will not be satisfied with the subset view as I have defined it.
But I am not a die-hard non-reductive physicalist. I am happy to say that the causal powers of higher level properties are physical. In fact, I am happy to say that all causally efficacious properties, higher and lower level, are physical (even those higher level properties, if there are any, that are not identical to (but are "parts" of) lower level properties).
I don't think the subset view is a way of defining our way around a philosophical problem. I find the subset view attractive for independent reasons: it seems to me that the subset view accomodates the existence, robustness, and other characteristics of scientific explanations and generalizations at different levels and does so better than identity-based reductionism. This could be the beginning of a long story, but I'll have to stop here for now.