Exactly, you can't verify a system using that system, so maybe it's not possible to exactly specify all of mathematics and physics within our universe.
Roger Penrose applies this thinking to the problem of consciousness and thinks this points to a special characteristic of humans that we can decide if things are true by 'stepping outside' of a problem, and that no mathematical function can do this. Therefore no computer running a mathematical function can be like us in that way.
Well no, not if it's a consistent system, but why does it have to be consistent? We're not consistent systems and we build systems that aren't consistent all the time, including computer systems.
Roger Penrose applies this thinking to the problem of consciousness and thinks this points to a special characteristic of humans that we can decide if things are true by 'stepping outside' of a problem, and that no mathematical function can do this. Therefore no computer running a mathematical function can be like us in that way.
Well no, not if it's a consistent system, but why does it have to be consistent? We're not consistent systems and we build systems that aren't consistent all the time, including computer systems.