>Even more, NathanÃÂÃÂ¹s list, if it can exist at all, is already an >infinite string and it must be given before the diagonal can be >constructed. > >Which means that any "diagonal" requires an infinite string, the >list, for its definition.
I'm having trouble seeing this point. Why would this same objection not apply to the standard argument showing the reals are not denumerable? It seems to me that Nathan can construct his diagonal as far out as he wants to, one step at a time, just the way the diagonal in the standard argument is constructed, only assuming the availability of an algorithm for translating strings to real numbers.