Does comparing neurons firing with beliefs/desires involve a type distinction that renders belief/desires irreducible to patterns of neuron activity?
I don't think it does, but I do think that the difference in scale between a neuron firing and an entire belief forming makes the reduction very difficult, and possibly pointless. It's a bit like reducing the spray of water out of a garden hose to the movement of individual water molecules. It's very difficult, given that each water molecule's motion contributes only an infinitesimal amount to the movement of the water as whole. Furthermore, even if you could map particular interactions between water molecules to specific motions of water droplets or the water stream as a whole, would you learn anything new thereby? Would it help solve any of the problems you're interested in? A lot of the time, it's better to work at higher levels of abstraction.