A general note at first, if I may. I am not sure why this question pertains to “Orthodox Jews”, as opposed to all Jews. As an Orthodox Jew, I see each and every Halacha (matter of Jewish Law) as equally binding on every Jew, (except as described below) from the greatest saint or Rabbi, to the most ignorant and assimilated. We all have the same level of obligation without regard to whichever denomination we might choose to affiliate with, or no denomination at all. We are all equally Jewish and bound by our covenant at Sinai.
There are exceptions to what I said above, but not based on denomination. There are some mitzvoth that are only for women, and some that are only for men. There are some that apply only in the Land of Israel. And there are some that apply only to Kohanim or Leviim. While it may be argued that the more one holds oneself out as an observant Jew, the more that is expected of them, that is on the ethical and moral plain, not on the basic legal fact of obligation.
Having said that, I would like to address the question posed.
There is no prohibition whatsoever for any Jew to view a human brain.
There may be issues of whether it is appropriate for the museum to put it on display, not so much because there is anything wrong with its viewing by the public, but rather due to issues of Kovod HaMet, or respecting the dignity of the Dead. (For more reading about this very important topic, please see http://www.nasck.org/ ).
Among the most important rules regarding Kovod HaMet is the very strong insistence that, in virtually all cases, it is vital that the body be buried in its entirety, without missing any body parts. However, from the point of view of Halacha, this rule applies only to Jewish corpses. (The issue of organ donation, which in some cases may be an exception to this rule, is a controversial one in Halacha, and beyond the scope of this question.)
Thus, if the brain was from a non-Jewish person, there would be no reason that a museum could not put it on display for the very worthy objective of promoting science and public knowledge, as long as it done so with dignity and good taste.
The only remaining issue, as I see it, is whether it would be helpful for the Museum to notify Kohanim of the presence of this exhibit. Kohanim, after all, are prohibited from direct contact with a corpse, and are even prohibited from being in the same building as a corpse. (This actually makes my life – as a Rabbi and a Kohen – somewhat difficult, as visits to a hospital contain the very real possibility of being under the same roof as a body in the morgue.)
However, according to most authorities, while a Kohen may not touch a non-Jewish corpse or any removed body parts, a kohen may be under the same roof. (This is the leniency I rely on with hospital visits; I do not have to assume, unless I know otherwise, that there is a Jewish corpse in the morgue.)
Thus for our purposes, even a Kohen may view a brain inside a museum, unless he knows that in fact it is from a Jewish corpse.
Is the museum under any obligation to inform Kohanim that it contains an exhibit with a Jewish brain? Certainly, if there is a significant population of that observant Jews is likely to p[atronize the museum, it would be very helpful to sensitize the staff to the possibility of this question coming up, and to be able to state that there is no problem, as the brain is from a non-Jewish corpse.
As a science museum with an exhibition that has a human brain in it what is our obligation to alert orthodox Jewish visitors to its presence?
It is somewhat out of the ordinary to have Jewish Values Online, which regularly solicits answers from across the Jewish denominational spectrum, address a question such as this one, whose domain is specifically dealing with one denomination, in this case, Orthodox Jews. The most important answer to this question ought to come from an Orthodox respondent.
With all due deference to Orthodox Jewish colleagues, therefore, I will deal with a more general set of implications of the question:
1) The key Jewish concept involving a dead body is k’vod ha-met, “the dignity of the deceased”. This concept leads to various Jewish mandates, such as the prohibition of embalming the body of a Jew, the speedy burial of the Jewish dead, and so on. This concept would militate against the display of a bodily organ.
But this general principle is modified by the following consideration:
2)There is an inherent and voluntarily restriction in the scope of Jewish law: with few exceptions, known in Jewish texts as “the laws of the children of Noah”, Jewish laws are meant to bind only Jews. For example, Judaism considers the prohibition against murder to have been given by God to all of humanity. But most other laws, such as the Sabbath, the dietary restrictions, the laws pertaining to religious ceremonial, are part of the “Sinai covenant”, not the “Noahide covenant”, and they bind only Jews. Therefore, the commandment not to leave a bodily organ unburied would not apply to bodily organs of non-Jews.
3)Jews of priestly descent, “kohanim”, are specifically prohibited from being under the same roof as a Jewish corpse.
4)Education of the public is a worthy goal, and one can readily construct a religious rationale for wishing to educate the public about the human body. We praise God for having created the human with wisdom, and we dedicate a prayer to reflecting upon the intricacy of the human body’s design. This is known as the “asher yatzar” prayer. Even so, it ought to be possible to promote the scientific knowledge and the spiritual appreciation of the human body while still remaining faithful to the general principle that the bodies of the dead deserve speedy burial.
5)It is also a general principle of Jewish law that we must go the extra mile to avoid misleading people. “Keep far from a false matter”—Exodus 23:7. Therefore, since some people’s sensibilities would be affronted by being in the presence of a bodily organ on display—there are both Jews and Gentiles who would feel strongly about this-- the organizers of the science museum ought to post accurate signage outside the display hall. Considering point #3, it would even be correct to post signage outside the museum building.
Balancing these factors, I would argue that a Jew ought not seek to prohibit a science museum from displaying a human organ, but could well communicate to the museum our tradition’s preference for the burial of human body parts and the substitution of molds and other replicas for educational purposes. If the museum opts to put human body parts on display, Jewish values would lead us to urge the museum, minimally, to alert the viewing public of the contents of that display, to allow members of the public to avoid entering that room, if so desired.
I don’t see that a science museum has any particular obligation to alert a specific segment of the population about the contents of an exhibit. I think a museum has some general obligations to ensure that all its exhibits are legally and ethically obtained and treated ethically (e.g. that art or artifacts from other lands or cultures were not stolen or appropriated without permission; that human remains such as mummies are treated with dignity and respect, that modern remains such as skeletons or organs are obtained through voluntary donation and are treated with dignity and respect.) If some exhibits are potentially disturbing to some viewers, either because they might be too young for some exhibits, or because they might have religious or ethical objections, the museum might post a general warning at the entrance to that exhibit to the effect that the exhibit contains items that might be disturbing to some. But as a general rule, anyone coming to a science museum has to know there are going to be various kinds of human remains on display, whether they be mummies or bones or organs or anything else. If this is going to be disturbing to them for any reason, I would think they simply wouldn’t go to such a museum.
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