Ian, there's nothing wrong with reductionism.

Overly simplistic reductionism is wrong, e.g., if you divide a computer into individual bits, each of which can be in one of two states, then you can't explain the operation of the computer in just the states of its bits. However, that reduction omitted an important part, the interconnections of the bits--how each affects the others. When you reduce a computer to individual bits and their immediate relationships with other bits, you can indeed explain the whole computer's operation, completely. (It just becomes unwieldy to do so.)

"I mean if you list all the actions that it's parts can do alone, the combined thing can have actions that aren't in that list."

What are these "actions that aren't in that list"? They are still aggregations of interactions that take place at a lower level, but we assign meaning to them. The extra "actions" are in our interpretations of the whole, not in the parts or the whole itself.