With all your Heart, With all your Soul
Continuing with my elaboration of my reasons for signing up as an organ donor, here is a discussion of the first part of the first of my two reasons. (About a year ago, I noted that when people give two reasons for something, it's usually the second reason which is the real reason, and the first one is a smokescreen. That is not the case here!)
As noted, I have not extensively studied the topic of organ donation - which is why I am explicit about not giving a thoroughly-researched conclusion on the matter. But I have extensively studied the topic of Chazal's knowledge of science in general, and Chazal's view of the kidneys in particular (and I plan to e-publish a monograph on this specific topic in the near future). And this gives two critical insights on the matter, both relating to the fact that the very act of analyzing different passages in the Gemara in order to determine whether Chazal considered life to fundamentally depend upon respiratory, circulatory, or neurological activity, misses the point entirely.
First of all (and this was a point that only occurred to me yesterday, so I am not yet certain of this), as Rabbi Breitowitz notes, in the ancient world there was no practical situation in which there was a differentiation between brain death and cardiac death. All vital systems - respiratory, circulatory, and neurological - would fail at approximately the same time, and there was no way of keeping one system going while another had failed. Thus, the failure of any one of them would be a satisfactory indicator of death. As such, any argument that the Gemara demonstrates Chazal to have conditioned death on a particular one of these systems is in error.
Second, after studying the matter very carefully in Chazal, the Rishonim, and Acharonim, it is abundantly clear to me that that Chazal, consistent with standard belief in the ancient world, mistakenly believed that the mind and free will are housed in the heart (assisted by the kidneys), not in the brain. There was no concept of organ transplants back then, but if there would have been, Chazal would definitely have held that the person's identity and soul is transplanted with the heart and kidneys, not the brain. We today, on the other hand, say that a heart transplant has no religious significance, whereas if a brain transplant would be possible, it would mean a person's mind and soul are being transferred. So even if it can be argued that Chazal considered a person's life to reside in the heart, this is irrelevant, since Chazal were mistaken as to which bodily organ houses a person's mind and soul.
Is there any Posek who agrees that Chazal were mistaken as to which bodily organ houses a person's mind and soul, but says that nevertheless they considered cardiac death to be actual death and were correct to do so? If so, I would like to know about it, because it would challenge my reasoning. But as far as I am aware, no Posek who does not accept brain death as actual death says such a thing. As such, the significance of my following this particular aspect of the topic is not so much that I agree with the reasoning of those Poskim who accept brain death, but more that I disagree with the reasoning of those who do not accept it, as I believe that they are fundamentally in error regarding Chazal's beliefs.
I am convinced that if Chazal would have understood the true nature of the heart and brain, and would have lived in a world where one could distinguish brain death from cardiac death, and where it was possible to save lives by using the organs of someone who is brain dead, they would have urged us to do so.