My present understanding is basically that any system of thought can produce statements like "this statement is a lie" and that, while these statements can be resolved by building some metasystem that includes the offending system as a subset, that metasystem will also be capable of generating similar statements.
In essence, yes.
I take this to mean that we are not infinitely intelligent.
Here I take exception. Godel showed, in principle, that even an 'infinitely intelligent' being (whatever that may be) could not utilise a logic system that was both consistent and complete (consistent in not giving rise to inherent falshoods - paradox's, complete in being able to prove every true statement within the system itself). It is not a limitation on intelligence, but upon the notion of logic, or reason, itself.
