I seem to be running into topics of conversation that return to mathematical logic in some form or another a lot lately. E.g., Adam Rosi-Kessel and I got to talking about [book: Gödel, Escher, Bach]-type topics recently, namely the connection — if there is one — between consciousness (whatever that is) and self-reference in formal systems. Then there was this blog post today about programs that can print themselves and other topics.

I need to learn me some mathematical logic already, extending (let’s say) all the way from propositional logic through predicate calculus, up to Gödel’s theorem. Anyone have any recommended readings here?