My understanding in regards to the philosophy of the mind is the following problems:
1) Mental Causation: If the 'mind' is fully a result of synapse activity, then the state of the mind can be fully reduced (at least in principle) to the physical state of the brain. Change the state of the brain (e.g., control the firing of a synapse), and you henceforth change human thoughts. Therefore, there should be some rules (called 'bridge rules') which perfectly determine our thoughts. However, if there are these bridge rules, then they should explain the cause of our thoughts. Yet, how can that be the case? A bridge law should be a highly technical neurological or, ultimately physics, related answer which perfectly explains how the flow of electrons in our brain (combined with atomic structures of our brain) are able to explain each and every thought. This doesn't make sense since very often we have a very perfectly suitable explanation for our thoughts - other thoughts. For example, when Phillip asked his tooth pick word puzzles, a few of us started having thoughts of tooth picks. If my thoughts on toothpicks was solely due to internal synaptic activity, then what neurological/physics law can explain why I now have thoughts of toothpicks? You would need to say that such bridge laws are very complex in that they combine large numbers of neurological systems in the brain and that it only appears that other people's thoughts are causing my thoughts. Rather, the cause is my brain's neurological wiring reacting to electrons coming into my optic nerve, sound vibrations coming into my inner ear, etc. The commonsense explanation is eliminated (i.e., we are trying to solve a puzzle), and the replacement explanation is far, far beyond the scientific explanation. In fact, because of quantum indeterminancy (which must be considered since physics ultimately reduces to quantum mechanics), there is the whole dilemma of whether there really is a cause per se of your 'thoughts'. So, the die-hard materialist explanation of using bridge laws moves from having a very simple and straightforward explanation (i.e., we have a mind which is not reducible to material structures and thinks and processes 'thoughts' as a whole), or we have no real solution since extreme reductionism of biological systems to quantum physics is only a far and away dream. Hence, it would seem that there really are no bridge laws of mental to physical. If true, then the physicalist explanation is not an explanation at all!
2) Supervenience and determinism: Along the same lines, if the mental is caused by the physical (i.e., the mental state supervenes on the physical state), then how is it that the mental causes physical states. For example, I can pick up my computer mouse by simply willing myself to do so. If the die-hard physicalist is right, then something physical just happened inside my head which determined that I think the 'thought' (i.e., my brain state changed to a specific pattern), and that pattern led to another pattern (i.e., desiring to pick up the mouse), which resulted in another pattern (i.e., the awareness that I am in fact picking up the mouse by ordering my body members to follow my intention). As you can see, our actions are 100% determined by prior physical states going back to conditions of our prenatal inception. However, such an explanation is counterintuitive since this is not how it feels at all. We pick up objects because we want to pick up those objects. We perform experiments because we think those experiments will benefit our understanding, etc. Such stark deterministic thinking suggests that all concepts, languages, art, music, etc are all chemical and ultimately quantum mechanical. Yet, we cannot reduce such things as language to atomism. So, why should we think that a physical state is able to perform this function? Likewise, why is it so appealing to think that 'we' are responsible for our actions (versus solely our brain chemistry)?
I think that physicalism is a belief system (just like dualism). As a belief system it requires a certain amount of imagination on our part. These reasons do not necessarily mean that physicalism is wrong, but I do think that some type of holist answer is required in order to rescue a physicalist project. The problem is, though, I am not sure how different a holist physicalist answer is from a dualist response. The mere requirement for holism is that a phenomena cannot be reduced to its components. However, I don't think that current physicalist explanations are ready to accept that this might be the case. I think we are creatures seeking explanation, and that's the one thing that our universe might not be so willing to provide. At best, we are looking for a kind of approximate explanation (e.g., molecules, when in fact these structures can be understood as a collection of atoms, etc).
Warm regards, Harv