Marc,
I was very glad to see your last-year's essay on the list of prize-winners, and your new one lives up to expectations. Again you give an excellent overview of the issue by combining remarkably various viewpoints into a clear and engaging narrative. I particularly liked the paragraph on "basic chemistry," since I imagine it's generally assumed there's no "strong emergence" here, just quantum physics at work - and yet even if we could describe complex molecules and chemical reactions strictly in terms of physics, why would we want to?
You're certainly right that we need to distinguish between "epistemological" and "ontological" ways of being fundamental. As the above example illustrates, chemistry may well be ontologically nothing but physics, yet for the sake of explanation and understanding, it's much better to give "laws of chemistry" in their own higher-level language.
But you're also right that this distinction is not really so clear. If we look at the case of biology, it's not just a question of what level of explanation is most helpful. Ontologically, what's going on in living organisms is not just very complex physics; it's very complex physics in the service of self-replication, which doesn't happen at any lower level. I have no doubt that everything organisms do is done by molecular physics. And though it's not at all clear how life began, I see no reason to think it can't be explained by physics and chemistry. Yet the ability of self-reproducing organisms to evolve is something entirely new... both ontologically and epistemologically.
This makes me doubt whether there's any point to the debate over "strong emergence." I think the problem is that physicists and their philosophical attendants tend think only in terms of structure, not function. Structurally, every level up to the neural networks of the brain may be "derivable" from lower levels, but radically new kinds of functionality clearly appear at higher levels of structure.
My current essay tries to show that functional emergence is relevant in physics as well. As you explain so nicely, the quest for a fundamental physics has uncovered a bizarre combination of theoretical structures that are very far from simple or self-evident. I take "fine-tuning" as pointing toward a functional explanation for all this, in terms of what's required for a universe to be able to make any information definable and measurable.
That connects with your "metaphysical" discussion of "all=nothing", since your "infinite ensemble of all abstractions" seems strangely like the "chaos of all possible happening" I take as a starting-point. And by the way, your one-sentence summary of your last-year's essay took my breath away. You "explained why it is reasonable to consider that a physical world is simply an abstract structure that contains self-aware sub-structures: what makes such a world physical is the contemplation of its mathematical structure by these sub-structures." Wow! This is conceptual imagination of a very high order... not apparently derivable from anything more pedestrian.
Of all the "overview" essays here, this is definitely the most fun, and gave me most to think about. So thanks!
Conrad