For example, in Philosophy of Mind and Physicalism, or Something Near Enough he discusses the problem of qualia. These are basically the first person experience of things, the "what it is like" to have a particular experience or be a particular entity (a bat, say). So when you experience pain, the qualia is not the firing of C-fibers, it's not the nerve endings, it's not your response to move away from whatever is causing it. The qualia is the pain, the "this hurts" experience. The difficulty in explaining qualia as physical properties is notorious, so much so that some philosophers feel it necessary to deny their existence (I guess the thinking is, if your philosophy conflicts with reality, the problem must be in the latter). The problem of qualia really opens the floodgates to the problems of explaining consciousness in general in terms of physical phenomena and processes.
Another example is where Kim discusses the difficulties in reconciling the causal closure of the physical with mental causation. Mental causation is simply the idea that the mind can cause a physical event (for example, that I can decide to pick up a pencil). But if the physical realm is causally closed, we are led to the problem of causal exclusion. In Mind in a Physical World: An Essay on the Mind-Body Problem and Mental Causation, he writes,
To acknowledge mental event m (occurring at t) as a cause of physical event p but deny that p has a physical cause at t would be a clear violation of the causal closure of the physical domain, a relapse into Cartesian interactionist dualism which mixes physical and nonphysical events in a single causal chain. But to acknowledge that p has also a physical cause, p*, at t is to invite the question: Given that p has a physical cause p*, what causal work is left for m to contribute? The physical cause therefore threatens to exclude, and preempt, the mental cause. This is the problem of causal exclusion. The antireductive physicalist who wants to remain a mental realist, therefore, must give an account of how the mental cause and the physical cause of one and the same event are related to each other. ... Thus the problem of causal exclusion is to answer this question: Given that every physical event that has a cause has a physical cause, how is a mental cause also possible?
Yet another example comes from a passage in Philosophy of Mind where Kim gives some detail about Donald Davidson's anomalous monism, as can be found in his collection, Essays on Actions and Events (which is on my to-read list). The point is that rational processes must follow different rules than (mere) physical processes, and so the former cannot be reduced to the latter.
A crucial premise of Davidson's argument is the thesis that the ascription of intentional states, like beliefs and desires, is regulated by certain principles of rationality, principles to ensure that the total set of such states ascribed to a subject will be as rational and coherent as possible. This is why, for example, we refrain from attributing to a person flatly and obviously contradictory beliefs -- even when the sentences uttered have the surface logical form of a contradiction. When someone replies, "Well, I do and don't" when asked, "Do you like Ross Perot?" we do not take her to be expressing a literally contradictory belief, the belief that she both likes and does not like Perot; rather, we take her to be saying something like "I like some aspects of Perot (say, his economic agenda), but I don't like certain other aspects (say, his international policy)." If she were to insist: "No, I don't mean that; I really both do and don't like Perot, period," we wouldn't know what to make of her utterance; perhaps her "and" doesn't mean what the English "and" means. We cast about for some consistent interpretation of her meaning because an interpreter of a person's speech and mental states is under the mandate that an acceptable interpretation must make her come out with a consistent and reasonably coherent set of beliefs -- as coherent and rational as evidence permits. When we fail to come up with a consistent interpretation, we are likely to blame our unsuccessful interpretive efforts rather than accuse our subject of harboring explicitly inconsistent beliefs. We also attribute to a subject beliefs that are obvious logical consequences of beliefs already attributed to him. For example, if we have ascribed to a person the belief that Boston is less than 50 miles from Providence, we would, and should, ascribe to him the belief that Boston is less than 60 miles from Providence, the belief that Boston is less than 70 miles from Providence, and countless others. We do not need independent evidence for these further belief attributions; if we are not prepared to attribute any one of these further beliefs, we should be prepared to withdraw the original belief attribution as well. Our concept of belief does not allow us to say that someone believes that Boston is within 50 miles of Providence but doesn't believe that it is within 70 miles of Providence -- unless we are able to give an intelligible explanation of how this could happen in the particular case involved. This principle, which requires that the set of beliefs be "closed" under obvious logical entailment, goes beyond the simple requirement of consistency in a person's belief system; it requires the belief system to be coherent as a whole -- it must in some sense hang together, without unexplained gaps. In any case, Davidson's thesis is that the requirement of rationality and coherence is of the essence of the mental -- that is, it is constitutive of the mental in the sense that it is exactly what makes the mental mental.
But it is clear that the physical domain is subject to no such requirement; as Davidson says, the principle of rationality and coherence has "no echo" in physical theory. But suppose that we have laws connecting beliefs with brain states; in particular, suppose we have laws that specify a neural substrate for each of our beliefs -- a series of laws of the form "N occurs to a person at t if and only if B occurs to that person at t," where N is a neural state and B is a belief with a particular content (e.g., the belief that there are birches in your yard). If such laws were available, we could attribute beliefs to a subject, one by one, independently of the constraints of the rationality principle. For in order to determine whether she has a certain belief B, all we need to do would be to ascertain whether B's neural substrate N is present in her; there would be no need to check whether this belief makes sense in the context of her other beliefs or even what other beliefs she has. In short, we could read her beliefs off her brain. Thus, neurophysiology would preempt the rationality principle, and the practice of belief attribution would no longer need to be regulated by the rationality principle. By being connected by law with neural state N, belief B becomes hostage to the constraints of physical theory. On Davidson's view, as we saw, the rationality principle is constitutive of mentality, and beliefs that have escaped its jurisdiction can no longer be considered mental states. If, therefore, belief is to retain its identity and integrity as a mental phenomenon, its attribution must be regulated by the rationality principle and hence cannot be connected by law to a physical substrate.
I've mentioned three issues: the problem of qualia, the problem of mental causation, and the dichotomy between rational processes and physical processes. The difficulty in each case is reconciling some property of the mind with physicalism. One might be tempted to say, with Kim, that we can have Physicalism, or Something Near Enough; the fact that we have a few threads that are left hanging doesn't put the physicalist project in jeopardy. But the "hanging threads" metaphor implies that the threads are on the periphery. These three examples, however, are at the center of the cloth, touching, in some way, every other thread. If one of these threads were removed, the whole thing would unravel.
Next up is Kim's Supervenience and Mind. Wish me luck.
Now forgive me for getting on my hobby horse, but the problem of mental causation and the distinction between rational and physical processes sound strikingly similar to what C. S. Lewis argued a half century earlier. In "Bulverism", he claims that rationality cannot be explained by mere brute physical causality; it requires a "special kind of cause called “a reason.”". Similarly, in the third chapter of Miracles, he points out that there is a difference between a mental event being caused and being grounded. Specifically, it is the difference between it having a non-rational cause (i.e. a physical cause) and having a rational cause. For human rationality to be valid, we have to assume that at least some of our beliefs are rationally caused.
To be caused is not to be proved. Wishful thinkings, prejudices, and the delusions of madness, are all caused, but they are ungrounded. Indeed to be caused is so different from being proved that we behave in disputation as if they were mutually exclusive. The mere existence of causes for a belief is popularly treated as raising a presumption that it is groundless, and the most popular way of discrediting a person's opinions is to explain them causally -- "You say that because (Cause and Effect) you are a capitalist, or a hypochondriac, or a mere man, or only a woman." The implication is that if causes fully account for a belief, then, since causes work inevitably, the belief would have had to arise whether it had grounds or not. We need not, it is felt, consider grounds for something which can be fully explained without them.
But even if grounds do exist, what exactly have they got to do with the actual occurrence of the belief as a psychological event? If it is an event it must be caused. It must in fact be simply one link in a causal chain which stretches back to the beginning and forward to the end of time. How could such a trifle as lack of logical grounds prevent the belief's occurrence or how could the existence of grounds promote it?
(cross-posted at Quodlibeta)