Yesterday, we noted that the Gemara does not directly determine the halachah regarding activating electrical circuits on Shabbos. But that does not mean that the Gemara is irrelevant. Rather, a posek decides whether electricity is sufficiently analogous to categories that the Gemara does discuss. Because there can be no exact analogy, this means that ultimately it is a matter of the personal judgment of the posek, which is why there are disputes on the matter. In other words, the halachah cannot be directly or conclusively inferred from the Gemara; but a Posek can exercise his judgment that it is sufficiently - albeit not exactly - analogous to something in the Gemara. As a rough analogy rather than a precise inference (I am not yet sure whether the stress should be on the adjective or the noun - input would be welcomed!), the halachah is ultimately based much more on non-Talmudic considerations rather than on the Gemara itself, even though it may be ultimately rated as falling under a Talmudic category. The recognition of that allows for more incorporation of non-Talmudic-halachic reasoning. For example, one could say that because electricity is not in the Gemara, therefore it is permitted; or, one could say (or subconsciously feel) that because activating electrical circuits destroy the spirit of Shabbos, therefore we will consider it analogous to one of the forbidden melachos.
Now, back to brain death!
In an earlier post, I noted how Rav Shlomo Zalman Auerbach admitted that he was mistaken in attempting to determine the halachah of brain death based on the Gemara regarding the impossibility of delivering a live baby from a woman who dies. What happened here is that Rav Auerbach realized the impossibility of inferring the halachah from the Gemara. One cannot infer that since a brain-dead woman can deliver a healthy child, then brain death is not death - for when the Gemara says that a dead woman cannot deliver a live baby, this was merely describing the reality of 1500 years ago, and it has no bearing whatsoever on the modern question of brain death.
By the same token, one cannot draw inferences from the Gemara in Yoma regarding a person found under a collapsed building, where respiration is ruled to determine whether he is alive. This only tells you (and correctly so) whether with a person found under a collapsed building 1500 years ago, respiration determined whether he was alive; it does not tell you what the ruling is regarding someone brain dead and breathing via a respirator.
What about the Mishnah regarding a decapitated animal being considered dead even if the limbs twitch? Again, one cannot draw any direct inferences to brain death, which is not exactly the same. One can judge that it is sufficiently analogous, but because this is a personal judgment regarding sufficient analogy, there can be - and are - those who disagree.
The Gemara really does not address the situation of brain death at all. How could it? In order to do so, the Gemara would have to differentiate between the functioning of different organs and systems. It would have to reflect an awareness of the differentiate between respiration, circulation and neural activity - and the correct identification of which organs are responsible for each. But 1500 years ago, there was no concept of the difference in these functions, or in keeping part of the body alive while another part has died, let alone correctly identifying the function of each part of the body. Thus, no clear inferences about brain death - either way - could possibly be drawn from anything that the Gemara could conceivably say.
But what we can do is to decide that brain death is analogous to something in the Gemara - either to a case in which someone is considered alive, or to a case in which someone is considered dead. So, we will subsume it under a category in the Gemara. But to determine which, we will have to make a judgment call based on ideas, facts and values. How to do this is a thorny problem, which we have touched upon in the past and to which we may return on a future occasion.