Isn't there still an asymmetry, in that all brains are made of atoms, but few atoms are part of brains, etc? Basically in some sense the higher levels are more rare and fragile than the lower levels.

At one time I would have labelled the top Emergent and the bottom Fundamental, but David Deutsch convinced me that even this was a mistake. A mind of arbitrary power, given only the bottom row, could deduce all the others—granted. But finally I said to myself: could not this same mind, given only the complete row for Physiology, deduce the contents of Chemistry no less readily? The blue line has no direction

I very much like the post and think that the way of thinking and the diagrams are excellent. Furthermore, I'm not even sure you'd have to change much if you come to agree with what I say here. However, I'm not ready to agree with this statement quoted. I admit insufficient expertise in what I'm about to say, and would happily have someone explain to me I'm simply wrong, but I think that many different lower-level mathematical models can correspond to the same surface-level observations. Sean Carroll I think supports this claim in this talk (with the relevant stuff starting at 21:40 although it's a good talk all over). I think a correct example of this would be: knowing the thermodynamics of a system doesn't define all the positions and velocities of all the different particles. Lots of different lower levels could be true (but only one of them is). So the blue line sorta does have some direction, even though I agree that this 'emergence' talk is unnecessary... And now I realise I'm confused again. Hmm.

Your post is an illuminating attempt to explicate some usually implicit concepts.

I sort of agree with your first diagram, that it is only human thinking that overlays a direction, or any kind of linkage, on the human-made collection of abstractions. But you lose me after that.

David Deutsch convinced me that even this was a mistake. A mind of arbitrary power, given only the bottom row, could deduce all the others—granted.

This is a highly contentious speculation (Deutsch, like Penrose, is fond of them), and I am not aware of any experimental evidence for it, so I refuse to grant it until I see some. Well, I suppose there is a tiny bit of it, where advances in physics let people design new chemical processes, or when understanding biology better lets us predict some behavior patterns.

I am far more comfortable with the more pedestrian definition of reductionism, where the arrows of human analysis of these abstractions point downward, and the secondary arrows of synthesis point upward, together forming "explanations", and, if we are lucky, testable predictions, when your secondary upward arrows lead to something not yet observed.

I don't understand your description of the "causation" meta-abstraction. "Meta" because it seems to connect towers of abstractions together somehow. One hint is that you describe it by "how" instead of "what", and, if I cut through your gratuitous use of pathos and evocative imagery, you seem to say that both abstraction towers and meta-abstraction connections between the abstraction towers are required for robust knowledge.

Furthermore, you seem to describe the breaks in your [what x how] mental framework as supernaturalism, which makes sense in the context, I suppose.

Better, then, to unlabel the blue line entirely, and when someone wants to know what ontological difference exists between the higher rows and the lower, say "Mu." ... Reductionism proper is just this: noticing that green arrows are always present, and always point up.

There's a tension here: green arrows are a property of our maps, but to the extent that our maps are accurate, they do actually reflect the territory. So sure, the green arrows are always present and always point from physically smaller to physically larger, but what are the ontological determinants of the arrow head positions, i.e, why are the rows where they are?

It often occurs in physics that from a small number of seemingly obvious and simple propositions, a great deal of far-ranging consequences can be deduced. This discussion brings up an example: the seemingly simple and obvious propositions are (i) that an element of a row is composed of a large number of components of the row immediately below; and (ii) our minds pick out rows by virtue of some kind of apparent "systematizability" or "model-ability".

From this we can deduce that there is an important ontological property which distinguishes a row from the one immediately below. It is the property of macrostate reproducibility, that is, if there is an accurate model of macrostate (i.e., upper row) quantities, then the fine details of the microstate (i.e., row immediately below) just don't matter -- we can automatically infer that almost anything that can happen at the microstate level will lead to that same description at the macrostate level.

The paradigmatic example is thermodynamics, in which all of the important information about the microstate (particle momenta and positions) is captured by a few macrostate variables (e.g., pressure, volume, temperature, chemical potential, etc.). Empirically, it is observed that knowledge of the values of only a subset of the macrostate variables suffices to predict the values of the remaining macrostate variables. We can use that empirical observation plus an accurate model of the microstates to create an accurate model of macrostates as follows: (i) create a probability distribution over the microstates by maximizing entropy subject to the constraint that the predictive subset of macrostate variables are fixed; (ii) take expectations over this probability distribution to predict the remaining macrostate variables.

The point: when someone wants to know what ontological difference exists between the higher rows and the lower, one trivial observation (upper rows are compositions of lower ones) and one mildly more subtle anthropic one (our minds distinguish rows on the basis of some kind of systematizability) provide enough information to give a much better answer than "Mu". This perspective gives a better definition of reductionism too: reductionism is the process of discovering which details of the microstate matter for accurate macrostate modeling, and which can be ignored.

I really like the imagery in your explanation, but I am not entirely clear on what the golden threads symbolize here. Would it be fair to say that the golden threads are the explanations of how a law or model on a lower level of abstraction causes the observations on a higher level?

Also, I don't really think you could deduce the entire structure of the blue line given by any one point as you seem to imply.

If you are given the physics of a universe, there might be several possible types of physiology, and for every such physiology there might be several different types of neural circuitry. Similarly you could say that there are still some degrees of freedom left over when some arbitrary psychology is given; it might be possible to have human-like cognition within the framework of purely newtonian physics, or we might be able to have a mind with the same morality but vastly different circuitry.

Of course you gain information about the entire blue line when you are given a single point, but it does not seem sufficient for crafting a complete model to know a lot about, say, the moral values of humans or the mental states of earthworms.

Adopting naturalism leaves a lot of questions unanswered; likewise adopting reductionism. One issue you haven't touched on is whether there is always a reductive relation between causal relations on different levels, or whether there can be independent laws at difference levels.