Hewitt is now kind of a crank. When Hofstadter came over for the Symsys thing in Stanford a few years back, Hewitt handed Hofstadter a little sheet of paper saying that mere contradiction allowed axiomatic systems to transcend Godel incompleteness theorems. Hofstadter: "Thanks, Carl." and then he threw it away when Hewitt wasn't looking. I think there's a thread in Lambda the Ultimate.