Humphreys is concerned with the problem posed by the apparent completeness of physics for explanations of the physical combined with the dependence (or supervenience) of the mental on the physical. Adding to this some plausible assumptions about properties and irreducibility of the mental to the physical, the problem is that it is impossible for the mental to do any causal work.
The mental appears to be causally unnecessary because (1) the mental and physical are not identical (according to the commonly held non-reductive physicalism), (2) physical explanations for physical phenomena are complete in that mental explanations are not possible for physical events, (3) the mental depends on the physical so that any mental event has a complete physical explanation. Hence, there is no need for any mental explanation for any mental event since such an event already has a complete physical explanation. Humphreys further claims that this problem is endemic to any type of scientific discourse beyond the most basic physical level. Hence, the problem generalizes to all higher-level sciences and their properties (that is, anything besides physics in which one might plausibly claim that the properties in question are not identical to some set of underlying physical properties). Biology, geology, fluid dynamics, economics are all areas in which higher-level properties (being a mountain, being alive, being an airfoil, being money) are not identical to any set of physical properties (properties in basic physics).
Philosophers have floated all sorts of plausible and implausible responses to this problem. Humphreys's response seems to me the most implausible so far. Humphreys develops a complex symbolization for events that I refuse to discuss since I think the problems with his view are more obvious without the layer of symbols.
Humphreys's solution is that (1) higher-level events are fusions of lower-level events, (2) these lower-level events cease to exist after they are part of this fusion, and, therefore, (3) the fusion does not supervene on the physical since the physical events (lower-level events) no longer exist.
I'll quote just to make clear that I am not making this up (p. 120 of Emergence: Contemporary Readings in Philosophy and Science, edited by Mark Bedau and Paul Humphreys):
[I]t is false to say that i-level [lower-level] property instances [events] co-occur with the (i + 1)st [next higher] level property instance [event]. The former no longer exist when they fuse to form the latter.The solution works by denying that there is a complete physical explanation for the higher-level events since supervenience fails for them. There is no causal exclusion or causal overdetermination for these higher level events--they have same-level causes that are not determined by lower-level events because those lower-level events do not exist once the higher-level event does. This solution, Humphreys thinks, is the only way to have the kind of robust causation at the higher level one needs.
Humphreys has two final claims: (1) there is some evidence that this emergence (i.e. fusion of lower-level events into higher-level events) occurs in the case of quantum mechanics in entangled states of paired particles, for example. (2) It is an open question how often this kind of emergence appears elsewhere in the natural world. Thus, it is an open question whether mental phenomena can be emergent in the requisite way.
Now, seriously, what is one to say to this? It is not a solution to the problem of mental causation since he does not even claim that it applies to the mental. But if it doesn't apply to the mental, then we continue to have the previously described problem of mental causation. So, is there another solution if the mental is not properly emergent? Do we just give up and consider the mind to be epiphenomenal?
But, more significantly, this whole idea that events fuse to form higher-level events and then cease to exist is about as implausible as an idea gets. Supposing that cell biology is emergent on the biochemical level, so that cells (or parts of cells or organelles, or whatever) are fusions of complex biochemicals. That means these biochemicals do not exist once they become part of a cell. If organisms are emergent, then cells cease to exist. If societies are emergent, then individuals cease to exist. If these lower-level entities don't exist, then laws of biochemistry, biology, psychology can no longer apply to them. And organisms cannot even be said to be constituted by cells (post fusion) because those cells no longer exist. We solve the problem of higher-level causation at the cost of giving up all our lower-level science. I don't think I even need to look for problems with this theory; I only have to state the basic view and the absurdity of it is obvious.
Is this as crazy as it looks? I think so. Maybe Humphreys will claim that particles, cells, chemicals still exist but the events of which they are constituents do not. I don't know that such a move would make sense. It seems just as crazy to say that chemicals in cells are not interacting (the event does not occur), they are part of an object that is undergoing a higher-level interaction that is not constituted by lower-level chemical interactions.
The moral I take from this is that (1) philosophers, especially good philosophers, can believe some crazy things if it helps them solve a problem, (2) excessive jargon, abstraction and symbolization can obscure the real meaning of a solution (or even a problem) rather than elucidate it, and (3) there is no third moral. Actually, the third moral might be: common sense is not a prerequisite for publishing philosophy and is probably a detriment to it.
And that's how and why Humphreys's view is the craziest thing I've ever read.