"Free will? No, free Willie"

Explainin how the world works some times has very little to do with actually "grasping" (for lack of better word) what its like. I've studied basic quantum mechanics at the time and talked to people who studied it at a more advanced level, and they tell me it seems to work just fine as far as describing the world goes. however, I'll be damned if could ever actually grasp the idea of a particle "being" a wave function. actually it isn't - science never bothers with the so-called "essence" of things - it merely describes the connections these undefined things have with other undefined things. and so at its higher level, physics is simply sophisticated mathematics that for some reason (or maybe for no reason at all) seem to be efficient at describing phenomenons. it doesn't mean we can suddenly grasp 12 dimensions just because a mathematical theory of that nature describes something efficiently.

How does the "Cogito" prove anything? You constantly fail to actually prove any of your assertions, other than just reasserting them in different ways.

By the way, concerning that dialogue, I think that this is just another case of someone just saying that he can do something without actually doing it. I don't believe that this person, or any person, can really go up as many levels as he pleases. He can say that he's going up as many levels as you can imagine (and I would say that that's a finite number, as well). If not, then tell me, what insights do you extract from being aware (of being aware)^9 that you couldn't extract from being aware (of being aware)^7?

B. The Principle of Mathematical Induction is an _assumption_ you must make about the natural numbers. It can't be proven from other, simpler axioms (though it is equivalent to the Well Ordering Principle).
But I digress. My point is, that the above dialogue is just a silly game of definitions, with too many implicit assumptions and not enough clear terminology to be useful. I again ask you to tell me of the startling conclusions you've come to by thinking (about thinking)^10 that were impossible to arrive at by thinking (about thinking)^7.