I've read all of the posts from Reductionism 101 and Joy in the Merely Real and enjoyed my time. But I think that a brief critique of reduction was misunderstood as anti-reductionist and Savanna-Poet-like. Which cannot be further from the intention behind it. In fact, in many ways I intended to highlight those very ideas that Eliezer brought up! 

Reduction is one of the best tools we have to approach the way things are. That is not my beef. My beef is with compartmentalizing the way things are into "real things" and acting as if everything can be knowable and acted upon rationally. As if everything around us was "already explained" by "the Science!". In fact, to stop acting as Savanna Poets as that leads to fixations on our beliefs and cognitive dissonance inside. 

First things first, the emptiness of inherently existing nature is not a nihilistic stance at all! It is only a call to question our inbuilt epistemology and ontology with regard to the "real". Understanding that all our compartmentalizing is inherently empty. Not false in the absolute sense! But in a sense: "All models are wrong, but some are useful." Yes, quarks too shall pass. That is, opening thinking up for Joy in Discovery. It also stresses out that everything around us can be known only in dependence, in relational structure. If it were not for emptiness of essence, knowledge in itself would be impossible! Think about "misunderstanding by essence", how to change that which is immutable. So to highlight that quarks are really "quarks". Even if experimentally confirmed with five sigma accuracy. They are still our little rainbows! 

Secondly, I tend to disagree that the following (simplified) definition of reduction is severely flawed:

Reduction is an operation of reason by the observer to extract the most relevant relations from the observed.

from a brief critique of reduction

As we understand everything based on a relational structure, that's how we make things intelligible. Think about the Special Relativity. Einstein examined simultaneity of events and proposed the constant speed of light. That's a change in relations. Or about the General Relativity - he equated "curvature" and stress tensors to come up with gravity as a curvature of spacetime. Again - relational structure. (More on that below.)

Further I will comment on some of Eliezer ideas that caught my eye with respect to the content of a brief critique of reduction and explore where it branches from them. Hopefully it will clarify misunderstandings. 

In Reductionism it is stated: 

And reductionism is not so much a positive hypothesis, as the absence of belief—in particular, disbelief in a form of the Mind Projection Fallacy.

It is so only in the light of Mind Projection Fallacy, but not entirely so. As no idea can be set as an absolute truth (in other words, to have an essential character). We carry with us some definite ontology concerning the way things are and its relational structure. And we think in terms of that ontology. Few examples. Einstein didn't introduce new ontic elements in Special and General relativity (except for convenient mathematical structures). But used existing. He redefined relations between them. Pauli and Dirac introduced new elements based on observation or even pure math. But that all was done in relational structure, in dependence on other things. What's important - it was not done independently of existing relations. 

In Dissolving the Question, Wrong Questions and Righting a Wrong Question the author reflects on what it is for a question to be unanswerable and therefore to be dismissed. But I would argue that there are no stupid or wrong questions! Even if they are unanswerable. As Exupéry said: 

If you want to build a ship, don't drum up the men to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea.

The question is really like a coal that smokes and gives off heat until it leads to a discovery or better questions. As Richard Feynman shares: 

Another thing that my father told me–and I can’t quite explain it, because it “was more an emotion than a telling–was that the ratio of the circumference to the diameter of all circles was always the same, no matter what the size. That didn’t seem to me too unobvious, but the ratio had some marvelous property. That was a wonderful number, a deep number, pi. There was a mystery about this number that I didn’t quite understand as a youth, but this was a great thing, and the result was that I looked for pi everywhere. 

Richard Feynman, What is Science?

Yes, that was about pi not about angels on a pin. But who knows what questions are "right" and what are "wrong"? Who can manage to handle such responsibility to decide where will they lead a curious mind? 

Further in Righting a Wrong Question the author writes:

If your belief does derive from valid observation of a real phenomenon, we will eventually reach that fact, if we start tracing the causal chain backward from your belief.

But how to decide the reality of the phenomenon when exploring uncharted territories? Neutrinos were once a postulated mathematical curiosity until observed. Here my beef is that the author presupposes an inherent reality to ontology that was built around previous experience. Takes it for absolute instead of conventional. 

If what you are really seeing is your own confusion, tracing back the chain of causality will find an algorithm that runs skew to reality.

But that may be a necessary unavoidable step when you are exploring the unknown!

Either way, the question is guaranteed to have an answer.  You even have a nice, concrete place to begin tracing—your belief, sitting there solidly in your mind.

Questions are not guaranteed to have an answer! Think about Gödel's incompleteness theorems and extrapolate from there. There are valid results that are not provable from formal systems. What if question hits some of those areas? That can be applied to belief systems as well. But that's just an example. 

Further in The Quotation is not the Referent: 

Similarly, the notion of truth is quite different from the notion of reality.  Saying "true" compares a belief to reality.  Reality itself does not need to be compared to any beliefs in order to be real.  Remember this the next time someone claims that nothing is true.

Here happens the reification of reality or attributing the concept with essence. That is "reality" = reality. But the very concept of reality depends on the observer (unitary or collective). So nobody knows any reality in the absence of the observer. As a concept it is useful in its areas but the attempt to reify it is a fallacy. As a concept it is dependent and as such empty of essence (again, not in absolutist sense, not non-existing, not unimportant or nihilistic as in "nothing is true", but fits in a relational structure which has to be taken in mind if one is to avoid the fallacy of reification). In short, it has its place. 

Further in Think Like Reality: 

Reality has been around since long before you showed up.  Don't go calling it nasty names like "bizarre" or "incredible".  The universe was propagating complex amplitudes through configuration space for ten billion years before life ever emerged on Earth.  Quantum physics is not "weird".  You are weird.  You have the absolutely bizarre idea that reality ought to consist of little billiard balls bopping around, when in fact reality is a perfectly normal cloud of complex amplitude in configuration space.  This is your problem, not reality's, and you are the one who needs to change.

The phrase "reality is a perfectly normal cloud of complex amplitude in configuration space" assumes a model which reifies "amplitudes" and "configuration space" (not mentioning reality as such). While in fact these are our current best understanding of phenomena. 

Human intuitions were produced by evolution and evolution is a hack.  The same optimization process that built your retina backward and then routed the optic cable through your field of vision, also designed your visual system to process persistent objects bouncing around in 3 spatial dimensions because that's what it took to chase down tigers.  But "tigers" are leaky surface generalizations - tigers came into existence gradually over evolutionary time, and they are not all absolutely similar to each other.  When you go down to the fundamental level, the level on which the laws are stable, global, and exception-free, there aren't any tigers.  In fact there aren't any persistent objects bouncing around in 3 spatial dimensions.  Deal with it.

That's exactly what the concept of emptiness from a brief critique of reduction means. There are no tigers! Spot on. 

Intuition is only a model by another name: poor intuitions are shocked by reality, good intuitions make reality feel natural.  You want to reshape your intuitions so that the universe looks normal.

Again, spot on and a brief critique of reduction agrees with that here: 

Generally, the bigger the entropy of the observed, the higher trouble for the observer. As his coarse-grained ontology does not correlate with all the details the observed requires. So this leads to higher processing load and less time to respond thus forcing the observer to many contradictions he cannot handle. That is only one of scenarios the rationality breaks down and irrational instinctive behavior becomes prevalent.

Further from Think Like Reality: 

Surprise exists in the map, not in the territory.  There are no surprising facts, only models that are surprised by facts.  Likewise for facts called such nasty names as "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird".  When you find yourself tempted by such labels, it may be wise to check if the alleged fact is really factual.  But if the fact checks out, then the problem isn't the fact, it's you.

Again, spot on. We are discarding reification of all those "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird". What I argue about is that we should not stop there but remember that our current categories will one day appear as childish as anthropomorphizing and emotional language of old. 

Further in Reductionism: 

The notion here is a subtle one.  It's not just the notion that an object can have different descriptions at different levels.

It's the notion that "having different descriptions at different levels" is itself something you say that belongs in the realm of Talking About Maps, not the realm of Talking About Territory.

As I read it, here again the reification of the realm of territory comes into being. Rationally we can only talk about maps. It doesn't mean we cannot talk about what lies beyond the known, but what lies beyond the known is either a rational extrapolation or suprarational intuition (or simply a hunch). 

This, as I see it, is the thesis of reductionism.  Reductionism is not a positive belief, but rather, a disbelief that the higher levels of simplified multilevel models are out there in the territory.  Understanding this on a gut level dissolves the question of "How can you say the airplane doesn't really have wings, when I can see the wings right there?"  The critical words are really and see.

Spot on. And I agree when it is rephrased like that concerning the belief (see above). It's exactly stopping the reification process. 

Further in Explaining vs. Explaining Away

I think that when physicists say "There are no fundamental rainbows," the anti-reductionists hear, "There are no rainbows."

Spot on! Stopping reification. It's exactly what I mean when write that things have no essence and are empty in essence (not absolutely!). There is no fundamental rainbow. And to stress it out that a brief critique of reduction is not anti-reductionist:

The observer which faces overwhelming complexity of the observed by default is using its best tool - rationality and reduction. 

It just attempts to highlight that reduction (as everything else, like rainbows) has its limitations. It is in itself a dependent phenomenon and hence without essence. Just as a reminder. 

Again from Explaining vs. Explaining Away:

Actually, Science emptied the model of air of belief in haunts, and emptied the map of the mine of representations of gnomes.  Science did not actually—as Keats's poem itself would have it—take real Angel's wings, and destroy them with a cold touch of truth.  In reality there never were any haunts in the air, or gnomes in the mine.

I would say that explaining and explaining away are closer than it may seem. "In reality there never were any haunts in the air, or gnomes in the mine." I.e. they were there as mental episodes and could be registered by fMRI as such and that would concern the model of the brain and cognitive science. 

Further in Fake Reductionism:

There is a very great distinction between being able to see where the rainbow comes from, and playing around with prisms to confirm it, and maybe making a rainbow yourself by spraying water droplets—

—versus some dour-faced philosopher just telling you, "No, there's nothing special about the rainbow.  Didn't you hear? Scientists have explained it away.  Just something to do with raindrops or whatever.  Nothing to be excited about."

Wholeheartedly agree. Again, to stress out that a brief critique of reduction is not anti-reductionist. 

Further in Joy in the Merely Real:

Why, things that are mundane, of course.  Things that are normal; things that are unmagical; things that are known, or knowable; things that play by the rules (or that play by any rules, which makes them boring); things that are part of the ordinary universe; things that are, in a word, real.

Again, the only beef is with reification of "normal", "ordinary" and "real". There are states of consciousness where all disappears. Are they ordinary? Are they real? Do they have no value if they reduce suffering and train the brain in new modes of perception? That are all open questions! I do not attempt to deny the use of words and their value. Only the tendency to reify. To anchor in them as absolutes. 

Which is to say that everything—everything that actually exists—is liable to end up in "the dull catalogue of common things", sooner or later.

With that I disagree as exactly the principle of computational irreducibility shows that we are only capable to "catalogue" things only in pockets of reducibility. That does not mean that all is reducible. It simply is not. Again, it is not denying the value of reduction, but only to highlight its limitations. 

Further in Bind Yourself to Reality: 

It's about binding yourself to reality.

Reification of reality. Besides that, how to bind oneself to something unknown? And who is the binder? 

Further in If You Demand Magic, Magic Won't Help:

If I were transported into one of those fantasy novels, I wouldn't be surprised to find myself studying the forbidden ultimate sorcery—

—because why should being transported into a magical world change anything?  It's not where you are, it's who you are.

Who am I? Really. Does it depend on my capacity to build better models? Does it define me? Isn't it reification of the "I"? 

If I'm going to be happy anywhere,
Or achieve greatness anywhere,
Or learn true secrets anywhere,
Or save the world anywhere,
Or feel strongly anywhere,
Or help people anywhere,
I may as well do it in reality.

What if reality is gruesome? And the only way out to exercise my thinking is to escape from it? It may be a paradoxical fix. 

Further in Is Humanism A Religion-Substitute?

The choice between God and humanity is not just a choice of drugs.  Above all, humanity actually exists.

The reification of humanity. It is a term. Perhaps, useful. But what does actually exists? There are no tigers, remember? 

Further in The Sacred Mundane:

That capacity—to really, really, without defense, admit you were entirely wrong—is why religious experience will never be like scientific experience.  No religion can absorb that capacity without losing itself entirely and becoming simple humanity...

Actually, we've approached religious experiences scientifically and have found a lot. You may find an example in Myths about Nonduality and Science by Gary Weber.

In closing remarks I would like to express gratitude for you forum and it's interesting nature. It makes me think and reflect, and I like that. It all was written in a friendly manner and hope it reads in the same way. I hope all the examples that are provided are enough to understand what was meant in my little post on reduction and clarify all matters.