Once you have those properties, the inability of any given computational model (even a super-Turing model) to solve its own halting problem is just a matter of

Once you have those properties, the inability of any given computational model (even a super-Turing model) to solve its own halting problem is just a matter of logic, as schoen said. This seems to assume that logic provides some form of undeniable truth but I am not sure that this is the case. Sure, every system of logic is hopefully consistent and you can use it to derive true statements within it by simply playing a game of symbol manipulation, and in that sense the system is a source of undeniable truth. But when we are using logic to reason about the real world, we need the real world and the logic we use to be compatible. Classical logic works great in the classical world but quantum mechanics seems to push it to its limits. You can certainly still use it if you are careful, but it seems no longer a really good fit once you no longer have your particles either here or there, either spin up or spin down. So logic seems much more like physics if you want to apply it to the real world instead of just using it for the fun of symbol manipulation. There are systems of logic that are useful to describe the world and there are ones that are less useful or probably even ones yielding wrong conclusions about the real world. Long story short, I am not sure that we can conclude that there will be halting problems for super-Turing machines because we can not be sure what kind of logic would be adequate to describe those machines. Not that I consider this a likely scenario or whatever, I just think we have to be more careful when saying something is just a matter of logic.