"it" isn't a single theory.

The argument that Everettian MW is favoured by Solomonoff induction, is flawed.

If the program running the SWE outputs information about all worlds on a single output tape, they are going to have to be concatenated or interleaved somehow. Which means that to make use of the information, you gave to identify the subset of bits relating to your world. That's extra complexity which isn't accounted for because it's being done by hand, as it were..

By far the best definition I’ve ever heard of the supernatural is Richard Carrier’s: A “supernatural” explanation appeals to ontologically basic mental things, mental entities that cannot be reduced to nonmental entities.

Physicalism, materialism, empiricism, and reductionism are clearly similar ideas, but not identical. Carrier's criterion captures something about a supernatural ontology, but nothing about supernatural epistemology. Surely the central claim of natural epistemology is that you have to look...you can't rely on faith , or clear ideas implanted in our minds by God.

it seems that we have very good grounds for excluding supernatural explanations a priori

But making reductionism aprioristic arguably makes it less scientific...at least, what you gain in scientific ontology, you lose in scientific epistemology.

I mean, what would the universe look like if reductionism were false

We wouldn't have reductive explanations of some apparently high level phenomena ... Which we don't.

I previously defined the reductionist thesis as follows: human minds create multi-level models of reality in which high-level patterns and low-level patterns are separately and explicitly represented. A physicist knows Newton’s equation for gravity, Einstein’s equation for gravity, and the derivation of the former as a low-speed approximation of the latter. But these three separate mental representations, are only a convenience of human cognition. It is not that reality itself has an Einstein equation that governs at high speeds, a Newton equation that governs at low speeds, and a “bridging law” that smooths the interface. Reality itself has only a single level, Einsteinian gravity. It is only the Mind Projection Fallacy that makes some people talk as if the higher levels could have a separate existence—different levels of organization can have separate representations in human maps, but the territory itself is a single unified low-level mathematical object. Suppose this were wrong.

Suppose that the Mind Projection Fallacy was not a fallacy, but simply true.

Note that there are four possibilities here...

1. I assume a one level universe, all further details are correct.

2. I assume a one level universe, some details may be incorrect

3. I assume a multi level universe, all further details are correct.

4. I assume a multi level universe, some details may be incorrect.

How do we know that the MPF is actually fallacious, and what does it mean anyway?

If all forms of mind projection projection are wrong, then reductive physicalism is wrong, because quarks, or whatever is ultimately real, should not be mind projected, either.

If no higher level concept should be mind projected, then reducible higher level concepts shouldn't be ...which is not EY's intention.

Well, maybe irreducible high level concepts are the ones that shouldn't be mind projected.

That certainly amounts to disbelieving in non reductionism...but it doesn't have much to do with mind projection. If some examples of mind projection are acceptable , and the unacceptable ones coincide with the ones forbidden by reductivism, then MPF is being used as a Trojan horse for reductionism.

And if reductionism is an obvious truth , it could have stood on its own as apriori truth.

Suppose that a 747 had a fundamental physical existence apart from the quarks making up the 747. What experimental observations would you expect to make, if you found yourself in such a universe?

Science isn't 100% observation,it's a mixture of observation and explanation.

A reductionist ontology is a one level universe: the evidence for it is the success of reductive explanation , the ability to explain higher level phenomena entirely in terms of lower level behaviour. And the existence of explanations is aposteriori, without being observational data, in the usual sense. Explanations are abductive,not inductive or deductive.

As before, you should expect to be able to make reductive explanations of all high level phenomena in a one level universe....if you are sufficiently intelligent. It's like the Laplace's Demon illustration of determinism,only "vertical". If you find yourself unable to make reductive explanations of all phenomena, that might be because you lack the intelligence , or because you are in a non reductive multi level universe or because you haven't had enough time...

Either way, it's doubtful and aposteriori, not certain and apriori.

If you can’t come up with a good answer to that, it’s not observation that’s ruling out “non-reductionist” beliefs, but a priori logical incoherence"

I think I have answered that. I don't need observations to rule it out. Observations-rule it-in, and incoherence-rules-it-out aren't the only options.

People who live in reductionist universes cannot concretely envision non-reductionist universes.

Which is a funny thing to say, since science was non-reductionist till about 100 years ago.

One of the clinching arguments for reductionism.was the Schrödinger equation, which showed that in principle, the whole of chemistry is reducible to physics, while the rise of milecular biology showeds th rreducxibility of Before that, educators would point to the de facto hierarchy of the sciences -- physics, chemistry, biology, psychology, sociology -- as evidence of a multi-layer reality.

Unless the point is about "concretely". What does it mean to concretely envision a reductionist universe? Pehaps it means you imagine all the prima facie layers, and also reductive explanations linking them. But then the non-reductionist universe would require less envisioning, because byit's the same thing without the bridging explanations! Or maybe it means just envisioing huge arrays of quarks. Which you can't do. The reductionist world view , in combination with the limitations of the brain, implies that you pretty much have to use higher level, summarised concepts...and that they are not necessarily wrong.

But now we get to the dilemma: if the staid conventional normal boring understanding of physics and the brain is correct, there’s no way in principle that a human being can concretely envision, and derive testable experimental predictions about, an alternate universe in which things are irreducibly mental. Because, if the boring old normal model is correct, your brain is made of quarks, and so your brain will only be able to envision and concretely predict things that can predicted by quarks.

1. "Your brain is made of quarks" is aposteriori, not apriori.

2. Your brain being made of quarks doesn't imply anything about computability. In fact, the computatbolity of the ultimately correct version of quantum physics is an open question.

3. Incomputability isn't the only thing that implies irreducibility, as @ChronoDas points out.

4. Non reductionism is conceivable, or there would be no need to argue for reductionism.

The Deutsch-Yudkowsky argument for the Many Worlds Interpretation states that you can take the core of Quantum Mechanics -- the Schrödinger wave equation, and the projection postulate -- remove the projection postulate (also known as collapse and reduction ), and end with a simpler theory that is still adequate to explain observation. The idea is that entanglement can replace collapse: a scientist observing a superposed state becomes becomes entangled with it, an effectively splits into two, each having made a definite observation.

Moreover Yudkowsky, following David Deutsch, holds the many worlds interpretation to be obviously correct, in contrast to the majority of philosophers and physicists, who regard the problem of interpreting QM as difficult and unsolved.

This has some problems.

(Which are to do with the specific argument, and the level of certainty ascribed to it. To say that you cannot be certain about a claim is not to say it is false. To point out that one argument for a claim does not work is likewise not to say that the claim itself is false. There could be better arguments for these versions of many worlds, or better many worlds theories, for that matter).

The Problems.

The first thing to note is that there is more than one quantum mechanical many worlds theory. What splittng is...how complete and irrevocable it is ... varies between particular theories. So does the rate of splitting, so does the mechanism of splitting.

The second thing to note is that many worlders are pointing at something implied the physical formalism and saying "that's a world"....but whether it qualifies as a world is a separate question from whether it's in the formalism , and a separate kind of question, from whether it is really there in the formalism. One would expect a world, or universe, to be large, stable, non-interacting, and so on . It's possible to have a theory that has collapse , without having worlds. A successful MWI needs to jump three hurdles: empirical correctness, mathematical correctness and conceptual correctness -- actually having worlds

The third problem to note is that all outstanding issues with MWI are connected in some way with quantum mechanical basis....a subject about which Deutsch and Yudkowsky have little to say.

Coherence versus Decoherence

There is an approach to MWI based on coherent superpositions, and a version based on decoherence. These are (for all practical purposes) incompatible opposites, but are treated as interchangeable in Yudkowsky's writings.

Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. (WP)

Coherent superpositions are straightforwardly implied by the core mathematics of Quantum mechanics. They are small scale in two senses: they can go down to the single particle level, and it is difficult to.maintain large coherent superpositions even if you want to. They are also possibly observer dependent, reversible, and continue to interact (strictly speaking , interfere) after "splitting". The last point is particularly problematical. because if large scale coherent superposition exist , that would create naked eye, macrocsopic evidence:, e.g. ghostly traces of a world where the Nazis won. All in all, a coherent superposition isn't a world you could live in.

I said complex coherent superpositions are difficult to maintain. What destroys them? Environmental induced decoherence!

Interference phenomena are a well-known and crucial aspect of quantum mechanics, famously exemplified by the two-slit experiment. There are many situations, however, in which interference effects are artificially or spontaneously suppressed. The theory of decoherence is precisely the study of such situations. (SEP)

Decoherence tries to explain why we don't notice "quantum weirdness" in everyday life -- why the world of our experience is a more-or-less classical world. From the standpoint of decoherence, sure there might not be any objective fact about which slit an electron went through, but there is an objective fact about what you ate for breakfast this morning: the two situations are not the same!

The basic idea is that, as soon as the information encoded in a quantum state "leaks out" into the external world, that state will look locally like a classical state. In other words, as far as a local observer is concerned, there's no difference between a classical bit and a qubit that's become hopelessly entangled with the rest of the universe.

(http://scottaaronson.com/democritus)

Decoherence is the study of interactions between a quantum system (generally a very small number of microscopic particles like electrons, photons, atoms, molecules, etc. - often just a single particle) and the larger macroscopic environment, which is normally treated "classically," that is, by ignoring quantum effects, but which decoherence theorists study quantum mechanically. Decoherence theorists attribute the absence of macroscopic quantum effects like interference (which is a coherent process) to interactions between a quantum system and the larger macroscopic environment.(www.informationphilosopher.com)

Decoherent branches are necessarily large, since decoherence is a high level phenomenon. They are also stable, non interacting and irreversible...everything that would be intuitively expected of a "world". But there is no empirical evidence for them (in the plural) , nor are they obviously supported by the core mathematics of quantum mechanics, the Schrödinger equation.

We have evidence of small scale coherent superposition, since a number of observed quantum effects depend on it, and we have evidence of decoherence, since complex superposition are difficult to maintain. What we don't have evidence of is decoherence into multiple branches. From the theoretical perspective, decoherence is a complex , entropy like process which occurs when a complex system interacts with its environment. But without decoherence, MW doesn't match observation. So there is no theory of MW that is both simple and empirically adequate, contra Yudkowsky and Deutsch.

The original, Everettian, approach is based on coherence. (Yudkowsky says "Macroscopic decoherence, a.k.a. many-worlds, was first proposed in a 1957 paper by Hugh Everett III" ... but the paper doesn't mention decoherence^[1]) As such, it fails to predict classical observations -- at all -- it fails to predict the appearance of a broadly classical universe. If everything is coherently superposed, so are observers...but the naturally expected experience an observer in coherent superposition with themselves, is that they function as a single observer making ambiguous, superposed observations ... not two observers each making an unambiguous , classical observation, and each unaware of the other. Such observers would only ever see superpositions of dead and living cats, etc.

(A popular but mistaken idea is that full splitting happens microscopically, at every elementary interaction But that would make complex superpositions non-existent, whereas a number of instruments and technologies depend on them -- so it's empirically false).

Later, post 1970s, many world theorists started to include decoherence to make the theory more empirically adequate, but inasmuch as it is additional structure, it places the simplicity of MWI in doubt. In the worst case, the complexity is SWE+decoherence+preferred basis, whereas in the best case, it's SWE alone, because decoherence is implicit in SWE, and preferred basis is implicit in decoherence. Decoherentists hope to show that the theory can be reduced to core QM, such as the Schrödinger equation, but it currently uses more complex math, the "reduced density matrix". The fact that this research is ongoing is strong evidence that the whole problem was not resolved by Everetts's 1957 paper. In any case, without a single definitive mechanism of decoherence, there is no definitive answer to "how complex is MWI".

And single-universe decoherence is quite feasible. Decoherence adds something to many worlds, but many worlds doesn't add anything to decoherence.

So, coherent superpositions exist, but their components aren't worlds in any intuitive sense; and decoherent branches would be worlds in the intuitive sense, but decoherence isn't simple. Also, theoretically and observationally, decoherence could be a single world phenomenon. Those facts -- the fact that it doesn't necessarily involve multi way branching, and the fact that it is hard to evaluate its complexity because there is not a single satisfactory theory for it -- means it is not a "slam dunk" in Yudkowsky's sense.

The Yudkowsky-Deutsch claim is that there is a single MW theory, which explains everything that needed explaining, and is obviously simpler than its rivals. But coherence doesn't save appearances , and decoherence, while more workable, is not known to be simple. So neither theory has both virtues

here he argues directly against “To be able to determine the future in a way that is itself determined falls short of being able to steer to a future of your choosing.”

Not really, because he is only saying , in typical compatiblist fashion, that you can bring about future in accordance with your desires ...which are determined. There is still no unpredictable turning point when you make a choice ... and therefore no steering to one of a number of physically possible futures...just a bunch of clockwork that's all inevitable.

I think he actually had different attitudes about different kinds of FW, although he isn't fully explicit about it

Maybe you are referring to this passage.

My position might perhaps be called “Requiredism.” When agency, choice, control, and moral responsibility are cashed out in a sensible way, they require determinism—at least some patches of determinism within the universe. If you choose, and plan, and act, and bring some future into being, in accordance with your desire, then all this requires a lawful sort of reality; you cannot do it amid utter chaos.

But choice..choice between options, any of which could possibly occur..is incompatible with determinism, because determinism means there is only ever one possible (and therefore necessary) outcome ... even if determinism is useful in other ways. You can still have a deterministic decision making process...but it is only some clockwork gets you to an outcome that was predetermined before you were born.

A libertarian choice is an actual fork in the road, and a Laplace's Demon wouldn't be able to see past it.

So, he thinks that compatibilist FW is as good as libertarian FW, because he thinks they both involve the same notion of choice...but they aren't.

Also, "utter chaos" isn't the only alternative to strict determinism. That would be false dichotomy. Lawful probabilistic causation is a thing.

He also argues against FW, in the sense of libertarian free will. Above , he argues for compatibilist free will. As usual, its not much of a consolation prize. To be able to determine the future in a way that is itself determined falls short of being able to steer to a future of your choosing.

ETA:

He also seems to think that merely being part of a wider system means you are determined. Nope.

All AI's scheming co-operatively is less likely than on scheming.

On standard physicalism zombies would be conceivable

On standard (non eliminative) physicalism, zombies cannot be conceived without contradiction , because physicalism holds that consciousness is entirely physical, and a physical duplicate is a duplicate simpliciter. So the inconceivability of zombies is not a USP of RM.

The bite of the zombie argument is that zombies are conceivable given physics ... physics does not predict phenomenal properties, so absence of phenomenal properties does not lead to contradiction.

I could also imagine other flavours of Monism (which might be better labelled as property dualism?) for which the intrinsic categorical properties are contingent rather than necessary

Phenomenal "properties" are more necessary under DAT than RM, because they are not even separate properties, but arise from the subjective perspective on the underlying reality.

AI research might end up with similar problems

Might. IABIED requires a discontinuity to be almost certain.