Temporal causation versus hierarchical causation
It seems to me we use the term cause in two very different ways that are completely independent of each other, and that confusing these for each other results in a lot of problems.
Temporal causation
One way we use the term cause is in discussions about events causing other events. I push the button and this causes the engine to start. This is past event to future event causation. When we talk about causal determinism, this is what we are discussing. Here's a hopefully somewhat uncontroversial definition of determinism for the purpose of discussion.
Causal Determinism: The idea that the past state of the world at some time necessitates specific future states of the world at all later times, as transformed according to natural law.
I say causal determinism, to differentiate it from logical determinism or any other senses. Actually the broader point I'm making here isn't really to do with determinism versus indeterminism, but I'm using this to establish one sense in which we use the term cause. We use it the same way when we talk about indeterminism in relationships between temporal events though.
Hierarchical causation
Another way we talk about causation is in terms of bottom up or top down causation, basically something like reductionism and weak emergence, versus top down or strong emergence. The conclusion I've come to is that this is a completely different concept. I'm not even entirely sure it has any common features with the idea of causal determinism at all.
I came to this conclusion observing some people talking about the relationship between causal determinism and beliefs about the neurological basis of mental processes, such as making decisions. I realised that what seems to happen is people seem to rotate the concept of past-to-future causation into the hierarchical dimension, as though microphysical processes such as chemical reactions in the brain cause thoughts in the way that ball A hitting ball B causes ball B to hit ball C. I don't believe that's the way to think about emergence at all.
Emergence isn't a temporal process, it's a hierarchical or structural one. It's looking at the exact same activity happening at the same time at different degrees of detail. The temperature of a gas is the motion of the gas molecules, it's not something that is caused by their motion in the sense that a gas molecule hitting another causes the other one to be deflected. Likewise the temperature of the gas isn't something that causes the molecules to move a certain way. Viewed this way, causation in the event-to-event sense is a completely different concept. In fact confusing these is pernicious. Even talking about the relationship between the microphysical and macro descriptions in causal terms leads to fundamental misconceptions. I don't think we should be talking about what I'm calling hierarchical causation at all. We need other terms.
I won't go further into what I think those misconceptions are, or what I think about emergence now. Maybe another time. For now I'd be interested to see how others think about this. I'm coming to believe that the fact we use cause in both these senses is a significant problem.