for these things we really cannot unwind entirely, even when we have reason to distrust them.

I've had similar thoughts when reading Hofstadter etc. However, are you saying that strange loops and inductive reasoning are inherent properties of 'thinking minds,' or just of human minds? Is it, by definition, impossible to put to gether an AI that could step back and consider questions like 'why does the universe appear to be simple' without make prior assumptions?