Correct me if I am wrong, but in Theravada, the idea that a mindstream continues after the death of an arahant, i.e., anupadisesa-nibbana, is refuted.
That is correct.
The official party line is that complete cessation implies cessation of all causal processes, including that of the mind. Those who suggest otherwise, e.g., those who speculate that the mind, consciousness, or mindstream does not cease, are labelled as eternalists.
Right, and Mahayanist consider this to be the extreme of annihilation. But it does not answer my question above.
If I had to hazard a guess, however, and we assume for the moment that (i) the mind is not an emergent property of the brain, (ii) there are no effects that do not have a cause, and (iii) the causes for the continuation of the mind are limitless, then I imagine that a sentient being would continue to cycle in samsara indefinitely. I concede that this point is accepted in Theravada,
but it is the fate of a Buddha’s or arahant’s mindstream that I am questioning here. Earlier you stated that the stream of mind never ceases, that it even continues in the state of Buddhahood. This is where Theravada seems to disagree, and I am unsure of what to think myself.
If the causes if a mindstream were solely afflictive, then with the exhaustion of the karmic share that sustains the life force of the body, and thus the life of a Buddha or an arhat, I might be inclined to agree that the mind stream of a Buddha or an arhat would cease at death, since all causes for its continuance would be exhausted too. However there is a slight problem with this: if the mindstream’s causes were solely afflictive, why does the mind not cease with nirvana in toto? Why does the mind continue after the eradication of all afflictions in a Buddha and an arhat? And if the mind continues after the eradication of the afflictions of a Buddha, etc., why could it not continue after the breakup of the body of a Buddha, etc., albeit in a non-afflicted state? In fact, Peter Harvey’s interesting book, the Selfless Mind, makes this very suggestion on page 250 where he summerizes all of his arguments and findings. I am sure this book is not without its controversy, but it is interesting and recommend it highly.
The Mahayana perspective, of course is that the mind continues on because of all the limitless positive causes the bodhisattva creates in the course of his/her career.
If someone can accept that sentient beings endless wander in samsara, there is no reason that they need to reject the idea that Buddhas can remain endlessly in samsara, other than on purely dogmatic grounds– but certainly not on logical grounds.