there's a tiny book called Godel's Proof that is both short and easy to read. I picked it up in my quest to read everything Hofstadter (he wrote the foreword) a

there's a tiny book called Godel's Proof that is both short and easy to read. I picked it up in my quest to read everything Hofstadter (he wrote the foreword) and thought it made it pretty straight forward. any axiomatic system that's flexible/powerful enough to make some sort of statement about itself will succumb to this method for constructing a paradox - and so all such systems are either inconsistent (paradox is possible) or incomplete (lacks sufficient flexibility to make a statement about itself).