I know Carl a little from the late 90s. I figured there was a 50% chance he would come up with something historically important, and a 60% chance he was crazy.

I know Carl a little from the late 90s. I figured there was a 50% chance he would come up with something historically important, and a 60% chance he was crazy. (The two options are not quite mutually exclusive.) Indeed, most examples illustrating the Incompleteness Theorem involve self-reference. But, it seems hard to prove anything interesting in a system that precludes self-reference. BTW, the Y Combinator is a way of adding self-reference to a non-self-referential formalism. And we're debating his argument here. Deep.