Often in debates about emergence, an opposition is set up between (strong) emergence and reductionism. These are seen as incompatible alternatives.
In particular, if one believes in downward causation, or perhaps some kind of non-causal influence (emanationism ) going from higher-level to lower-level phenomena, then, in the usual framing of the discussion, this is seen as contradicting scientific reductionism, which holds that the causal interactions within the lowest level totally causally determine the behaiviour of the higher level. (Whether or not we can predict the behaivour at the higher-level from the lower-level is a separate question.)
However, I've often wondered if there could be a view analogous to compatibilism in the free will debate which attempts to affirm both strong emergence and causal reductionism.
We can consider how that might go by considering Conway's Game of Life. In this game, there are certain apparently emergent structures such as gliders which move across the grid and seem to have various effects on other structures that they locally interact with. However, in this case, there is also an obvious sense in which causal reductionism is true since we know from how the game is build that deterministic rules governing sequential updates to individual pixels generate all the observed behavior.
Nevertheless, one could deny that gliders and other game of life structures are merely epiphenomenal. A neo-Platonist might hold that these structures are emanations of Forms in a higher level of existence and this claim would not have to contradict the claim that, at the material level, their behavior is causally determined by the pixels and update rules.
Of course, the details of such a view are vague, and I'm not attempting to defend it here. My question is whether there are any articulate modern defenders of something like this. I guess I would call it non-causal or emanationist strong emergence (although it might have a totally different name in the literature).
As an aside, if such view of emergence is viable, then a form of compatibilism about free will might end up being a special case of this type of emergence. This is hinted at in Stephen Wolfram's discussion of cellular automata and free will in A New Kind of Science.
Nevertheless, one could deny that gliders and other game of life structures are merely epiphenomenal. A neo-Platonist might hold that these structures are emanations of Forms in a higher level of existence and this claim would not have to contradict the claim that, at the material level, their behavior is causally determined by the pixels and update rules.
I think this idea is completely relevant, and I choose to call it "middle emergence". It's not strong emergence, because there's no downward causal force, but the emergent "stuff" still has some kind of ontological realness to it.