Thank you so much for your insightful reply.
I think the article is an attempt to bridge some theories and ideas that scaffold up to the mind.
For one, I'm unsure whether indeterminism about statistical mechanics bears any relevance to brain dynamics. I don't think mainstream brain science seriously considers this. But if indeterminism were true, then I think it would certainly have implications for brain dynamics. This is one part that's kind of indirectly hinted in the article. If interested in this angle, Robert Kane's theory of free will is an interesting theory that incorporates quantum indeterminism.
You're correct about the rest. I've mainly used Godel Escher Bach as my reference to Hofstadter's ideas, but they seem too loose to constitute a theory of the mind. What is your opinion? Do you think his treatment of Godelian undecidability is appropriately analogized to "higher-order thought"?
That said, I think the cleavage between dynamical systems and formal systems must reside in some theory of the mind. My particular take, which is as yet a hazy attempt, is to explore whether quasi "formal" aspects of the mind like language (though by no means a formal system), can be situated in the context of the organism as a dynamical system.
This has two prongs: we want to say that the information the brain hosts is "multiply-realizable", which is like saying the same program can be implemented in different types of hardware, but also we want to say just how that information is hosted or encoded, i.e. how it's dependent on the lower-levels.
And people disagree about this: some say these two strata can't be uncoupled, e.g. information is embodied or is constituted through global variables, and some say that the lower layers of dependence create a semi-independent layer, mental contents, that can be realized differently (the neural substrate being merely incidental).
Would be curious to know what you think? I know I'm still working out my position, and the article aims to probe aspects of this question.