Stan,
Approximation sweeps away 'fuzziness', and one thing your and my conceptions are completely consistent on is "any system during its development moves from being more vague to becoming more definitely embodied". There are issues in differentiating descriptive, explanatory, and organizational/behavioral 'fuzziness', but it's those "fuzzy bits" that are the main thing approximation sweeps away. But studying the 'fuzziness' is central to finding the half of the universe that physics missed.
My analytical approach interprets it as evidence of the transitional systems which frequently can be found to have periods of implied derivative continuity in their measures, displaying some of their evolving internal dynamic structures. That's what I've been carefully studying for the last many years, but now mostly play with the wordings for to find some way to communicate.
Your grasp of the links to other fuzzy ways of thinking about the subject (it's history and citations) is far superior to mine, and hopefully I'll get a chance to ask you some questions about it shortly. When the research wave called 'fuzzy logic' hit, for example, I never thought it interesting because it seemed to be further interpreting the world as a set of fixed rules with a universal noise machine attached. Maybe I should look closer at that and other approaches. Remember, I'm with Einstein and don't think God rolls dice. God lets things develop on their own from the inside, but that's different from making changes without processes or causation.
Another thing we'd totally agree on is the unique individuality of events, and a third is "As a system hardens into senescence via the accumulation of information to the point of overload, it becomes unable to marshal the requisite variety needed to survive perturbations, and gets recycled". What is specifically meant by some of this remains "fuzzy" to me, to be more fully detailed by reference to the real shapes of things to be observed in their natural stages.
Would you say that opportunity is the principal cause of causal loops?, and so the principal interest of an internalist perspective, whereas opportunity is largely invisible to an externalist perspective and so usually ignored?
I had a nice long conversation on FRIAM with Nicholas Thompson on the meaning of homing systems in nature, and their taxonomies, ending in proposing it as a natural scale of consciousness. To summarize what I got out of it, thermostats have loops, and so an interior, but only a one dimensional awareness of the world. Natural systems with various levels of homeostasis have internal worlds of greater complexity and evident multi-dimensional awareness and responses to their environments. Mammals, consider a mouse strategically scurrying for it's hole and apparently homing to an abstract image, all have precognition on various rather high levels.
Nick initially seemed concerned with whether considering a thermostat to have any measure of consciousness would mean human experience was no longer unique. Part of the idea as it developed, is that having a taxonomic scale of emergent levels for consciousness meant there might be great distances between its ends and branches. fyi I think human consciousness is different in several ways, even if most of the difference traditionally seen comes from the externalist point of view that only humans have anything inside at all.
That somewhat extreme and faulty notion may be, itself, a pointer to one of the things so different about human consciousness. Our mental worlds are so very rich and complete, and compelling, they hardly need any support in reality whatever, i.e. we're able to be self-deceived in profound ways. What's the way around that?... perhaps watching the fuzzy bits in the natural connections, the indelible unique emergence of things. I think once people can observe them it naturally becomes exhausting to try to fake them..., making a stimulating natural bond between mind and reality!
... anyway, that's one of the main things I see missing from approximation... :,)