I haven't read Hostadter or the other's arguments, but this comment got me thinking. If the incompleteness theorem is about the limitations of an axiomatic system, why wouldn't it apply to rational thought. If (and it's by no mean certain) rational thought and the human brain have certain rules built into it to process, interpret, and act on information from the outside world, then couldn't these hardwired rules be considered axioms? These axioms are clearly powerful enough to express the integers and so one would conclude that there are certain propositions that are true but cannot be proven by the human brain. Of course, the brain and it's wiring is still a matter of research, and the fact that the brain is a dynamic system with neural connections in constant flux means that the system is not static nor are these "axioms".
> Just because you can create a function to return a row of Pascal's triangle doesn't mean you're a great programmer but if you can't, it almost certainly means you aren't. It's a negative signal filter, nothing more, but an incredibly quick and useful one.
Or as we say in the medical field, this test has high "sensitivity" :)
I took the algorithms class at UCSD a few years ago from Sanjay Dasgupta, one of the authors of that book. At the time the book wasn't finished but we used a draft as the lecture notes. One of the best classes I took. I use that book to this day as a reference for some algorithms.