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I guess that is kind of the problem, isn't it? People tend to use words like self-organization (or supernatural) to mean something, without every really thinking about the consequences if it would exist.
Personally I believe that all "stuff" is either naturally generated or artificially created? Which doesn't leave any room for anything "supernatural" to exist, either "supernatural" is just another way to say "not naturally generated"? OR they see it as a (proper) subset (or maybe superset) of the term "natural", maybe for extremely rare occurrences? So what does "supernatural" really mean? Likewise, I dont really know what people think when they talk about "self-organization" as if it was real; To me it's obviously clear that it does not exist.
In many ways it's almost as if self-organization is just a synonym for "supernatural force"... because it is used in almost the same way: Where the mystic appeals to the supernatural to explain away the unknown so too does the quasi-physicalist who makes an appeal to self-organization as if this would explain anything. Neither actually explains anything. It does not answer the how-question. The mystic answers with an "who" and the physicalist with an "what". Neither is all that helpful.
I don't believe in (physical) self-organization, especially at the molecular scale.
Nothing like physical self-organization has ever been observed, all we ever have observed are very limited self-ordering phenomena which don't scale at all.
All known organization is modular and often hierarchically combining modules into larger modules. All known organization is non-trivial.
While the physical parts may allow them to be organized, or rather the parts can be organized in a way which is consistent with the physical properties of the parts and so generate the desired system as a whole so that more is different then just the sum of its parts. This same organization however does not follow from just the physical properties of the parts. The physical properties are required, but insufficient. More is required: "Life is consistent with, but undecidable from physics and chemistry."
The hypotheses of molecular self-organization is without any actual evidence and is inconsistent with experience and logic. And still it is a widely held believe. Is the widespread believe that physical systems can self-organize "insane"?