Arguments that claim something is impossible from an argument related to the halting problem are generally bogus. The halting problem applies only to deterministic systems with infinite state. If you have finite state and determinism, you have to eventually repeat a state, or halt. Note that "very large" and "infinite" are not the same thing here.
Not being able to predict something for combinatorial or noise reasons is a more credible argument.
Not being able to predict something for combinatorial or noise reasons is a more credible argument.