Just because I mention something doesn't mean I assume you don't know it. This is a public forum and although it's Hacker News I still doubt everyone has heard

Just because I mention something doesn't mean I assume you don't know it. This is a public forum and although it's Hacker News I still doubt everyone has heard of primitive recursive arithmetic. You're the only one making personal statements here. Also I don't know what sort of code I'm supposed to use to make my arguments without offending you, if PRA is the example I think illuminates my point I kind of have to write its name whether you know of it or not. > I said it right there. How could you not know this? When I said "the properties of Peano arithmetic", I meant the presence of addition and multiplication. That's a curious definition of "heavily dependent" on the properties of Peano arithmetic (when the condition is in fact "any integer arithmetic with addition and multiplication"), and I'd argue it would be hazardously confusing to the uninitiated, but that's just semantics. Back to the original point (that the analogy is poor) I don't see how that breaks the analogy at all. Just like there are weaker arithmetics that escape Goedel's theorems (I will not mention their names since that seems to just cause issues), there are weaker models of computation that dodge the halting problem (again I'm sure you know of them, the one I'm thinking of off the top of my head rhymes with schmimative shmecursive shmunctions). > Let me explain it another way: Goedel's theorem is a theorem about math. Math as it was understood in the 18th century. That's what makes it interesting. I think what makes it interesting has nothing to do with the particulars of what people thought math was in the 18th century. I doubt there are any mathematicians from ancient Greece to a thousand years from now that would seriously consider using a logical system incapable of modeling addition and multiplication as a ground-level theory for the majority of mathematics. They probably would be fine with one that only killed off Peano arithmetic, just like we'd be fine with a form of computation that wasn't as limiting as PRFs but didn't happen to be susceptible to Turing's reasoning. It seems just as general by construction, and I doubt it is an accident that Goedel using something so basic. Basically what I'm saying is just like the fact that the Church-Turing thesis has held up and all interesting forms of computation and equivalent to Turing machines, there is an implicit Addition-And-Multiplication-Are-Basic thesis that claims that systems unable to model addition and multiplication in some form are fun to visit but not to live in when you're doing mathematics.