> I'm curious, though, if things like the halting problem actually hold in the absence of (certain types of) self-referential statements. To my (very limited) k

> I'm curious, though, if things like the halting problem actually hold in the absence of (certain types of) self-referential statements. To my (very limited) knowledge, all proofs in these areas rely on them. I mean, if "certain types of self-referential statements" we're banning can include all recursion and (dynamic) loops, then the halting problem is trivial - your program halts.