I believe there exist some subset of turing machines that can be proven to run forever. But providing an oracle for the halting problem - of which an upper bou

I believe there exist some subset of turing machines that can be proven to run forever. But providing an oracle for the halting problem - of which an upper bound is one form - makes the Busy Beaver Game computable. To get back to the original topic... a finite brain in finite time can only produce finite output. Both the brain and its output are, like all fully bounded sets, computable.