The first application is kidney transplants. As I noted in my monograph, The Question of the Kidneys' Counsel, Rabbi Eliezer Waldenberg, the famed Tzitz Eliezer and posek for Shaarei Tzeddek Medical Center, had severe reservations about the halachic permissibility/ advisability of kidney transplants. His reason was based on the clear and unequivocal position of the Gemara that the kidneys provide counsel to the heart; hence, there is a danger of the donor’s kidneys counseling the recipient in a harmful manner. Rabbi Ovadiah Yosef discourages receiving kidneys from a non-Jew for this reason.
To most of the readers of this website, it will be clear that the kidneys do not in fact counsel us. Since the halachic rulings of Rav Waldenberg and Rav Ovadiah were based on this mistaken belief, they are therefore invalid. My presumption is that it is for this reason that in the RCA's recent document about organ transplants, it does not mention these views of Rav Waldenberg and Rav Ovadiah in the section on kidney donation.
Now let us turn to the most important application of this principle: brain death, and its resultant ramifications for organ donation. Most (but not all) of those who reach conclusions about the halachic status of brain death, whether for or against, do so by examining the words of Chazal and the Rishonim, from which they draw various inferences. This is the usual halachic procedure - but how is it valid in this case? Chazal had a very, very different understanding than us as to the nature of various aspects of the human body, and they lived in a world in which the medical possibilities were very different. They believed that a person's mind resides in his heart. This is undeniable to any reasonable, honest student; in the same way as the Rishonim and early Acharonim universally acknowledged that Chazal believed the kidneys to provide counsel, they believed the heart to house the mind - after, it is the very same section of the Gemara, discussing the functions of different parts of the body, which describes the heart as receiving the kidneys' counsel and making decisions. See too this fascinating post by R. Josh Waxman concerning the Midrash's explanation of kaveid lev Pharaoh - that his heart became like his liver. Chazal lived in a world where there was no such thing as heart transplants, but if there were, they would have said that the person's identity is transferred with the heart. Chazal lived in a world where circulation was an excellent and sufficient indicator of life, but we live in a world where you can have blood circulation in a person who is quite definitely dead according to all views. Chazal lived in a world where a person's mind and soul were mistakenly thought to relay their force and influence from the heart, via blood and breath, rather than from the brain, via neurons and nerves. That sentence cannot be emphasized enough.
As a result, the very idea of drawing halachic conclusions about brain-death from Chazal's statements relating to life and death is just as mistaken as drawing halachic conclusions about kidney transplants from Chazal's statements about kidney function. Dr. Noam Stadlan said it best, in the second paragraph of a two-paragraph comment on the Hirhurim blog (I have highlighted the most important parts):
At least two shitot exist that have been “rationalized, squared and equated in any fashion with the criteria of death set forth in the Talmud, Rishonim and Acharonim“, namely 1. relying on the Gemara’s determination that the irreversible cessation of breathing, under the proper circumstances is the criterion for death (brainstem death, which is the position of the Chief Rabbinate) and 2. extending the Gemara’s discussion of decapitation, which is the physiological decapitation position. (There are actually others, such as the Rambam’s approach to human treifot where he relies on the medical determinations of the doctors of the time, and the position of Rav Azriel Rosenfeld (found in Tradition in the late 60-s early 70′s) where he states simply that the brain is the seat of the soul and absent a brain there is no life).
A different approach which I alluded to is to realize that the non-neurological circulation based definitions of death do not produce coherent results in this day and age, and in fact with modern techniques circulation is actually rarely irreversibly absent (as long as arteries are present circulation is a possibility). With this realization, it is necessary to go back and try to understand not the details of the positions of the Rishonim and Acharonim, because the details no longer make sense, but the underlying rationale and concept of what it means to be alive or dead, and come to some conclusions with that in mind. For example, you would have to look at what Rashi wrote, and say to yourself, Rashi’s medical knowledge told him that when the heart stopped, everything else in the body ceased to function as well. Doctors told him that a stopped heart never restarted. Since these are no longer a true assumptions, what would Rashi say under these different conditions? Would he still have the same position? One hint is that it seems that most if not all of the poskim in the past used the science of their day (see Rabbi Dr. Edward Reichman’s excellent article on the definition of death in the light of medical history).
Thus, the entire halachic section of the controversial RCA document on brain death and organ donation is fundamentally in error. Without mentioning any of the aspects that I pointed out, the document simply engages in the traditional approach of analyzing inferences from statements of Chazal and the Rishonim, and quoting Poskim who engaged in such a procedure. Yet this is no different from Rav Waldenberg deducing that kidney transplants are problematic since the Gemara says that the kidneys provide counsel. I understand that this is the halachic methodology in the charedi world (except when it is blatant to them that the science of Chazal is incorrect), but a centrist/modern Orthodox rabbinic organization, which accepts the Rishonic view that Chazal were not infallible in scientific matters, should incorporate the ramifications of that principle into our approach to this topic - just as Rav Yitzchak Lampronti and other halachic authorities incorporated it into their analysis of Chazal's ruling about killing lice on Shabbos, and just as the RCA itself would do regarding kidney transplants.