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"The messiness is only in the eye of the beholder."

Yes, and also the order, too-- at least the order that is conceived. That a particular idea of a particular order TRULY represents the state of reality is a matter of opinion (not necessarily arbitrary or careless opinion-- but still opinion).

I don't know how to escape the fact that order, of some kind, is a fact. Otherwise I could not make my way in the world at all. But no good skeptic denies order in general. I don't either. I just keep asking "which order?" Is there only one possible order that can account for what we see? No conceivable argument can establish that.

Competent skeptics, in my opinion, argue that you can't be certain what the order is. AND, they argue that you don't need certainty, anyway. Just say, "I've decided to treat this as true and here's why I think my way is better." You don't need to say "and it is impossible that a reasonable person could come to any different idea about this". Skepticism is a position that has heuristic value, just as there is heuristic value to being a dogmatist or a religious fundamentalist. I just like the heuristic of skepticism better. I harp on this because it seems that 3/4 of your writing makes a great case for openness, and the remaining stuff seems to sound a note of "Thou must bow to the Great Model that my Friends and I use to explain everything." You could instead talk about the benefits of your model and leave it at that.

I'm combing through your text looking for an argument that justifies giving a privilege to order. I'm not finding it. You keep reasoning from coherence, but coherence is just more induction, and coherence requires that you decide a priori, what constitutes evidence and how much is needed before you stop. To echo your own form of argument, not since George Berkeley and Immanuel Kant has it been acceptable to ignore a priori categories of thought.

Do you really not see the turtle your ideas stand on, or are you thinking that it's turtles all the way down?