Gemara

Question: Is the reason for burial to avoid disgrace (of a rotting corpse), or for atonement?

The answer teaches about one who asked (before he died) not to be buried: if we are concerned for disgrace, we do not comply. If it is for atonement, since he does not want it, we honor his request.

Nazir 43b (Rav Chisda citing Rav): A Kohen may not be Mitamei to bury his father if the head was cut off. It says "for his father" - when his father is intact.

Question (Beraisa): " He will be Mitamei for her (his sister)", but not for her limbs. He may return for a bone the size of a barley seed.

Inference: The Mes was lacking (a bone), and he was permitted to be Mitamei for it (and again for the remaining bone)!

Answer: The Beraisa is like R. Yehudah (but Chachamim permit him to be Mitamei only for an intact Mes).

(Beraisa - R. Yehudah): "For her he will be Mitamei", but not for her limbs. He may be Mitamei for a limb that separated after death.

Question (Rav Kahana's Beraisa - R. Eliezer ben Yakov): "For her he will be Mitamei", but not for limbs. This excludes a k'Zayis of flesh of a Mes. He may be Mitamei for her spine, skull, or bones comprising the majority of the stature (i.e. three bones out of the shins and thighs) or of the number (of bones of the body, 248). We learn from the repetition "say... and you will say."

Answer: Also this Beraisa is like R. Yehudah. Rav holds like the following Tana:

(Beraisa): R. Yitzchak's father died in Ninzak. R. Yitzchak did not hear until three years later. R. Yehoshua ben Elisha and four Chachamim expounded "for his father" - he may be Mitamei only for an intact Mes.

Shabbos 93b (Mishnah): If one takes a k'Zayis of a Mes to Reshus ha'Rabim, he is liable;

R. Shimon exempts.

Berachos 5b: R. Yochanan would say (to console mourners) 'this is a bone from my tenth son.'

Rishonim

Rif (Hilchos Tum'ah 1b): A Kohen may be Mitamei for a bone of his father that is the size of a barley seed.

Rebuttal (Rosh Hilchos Tum'ah 7 and Ramban (Toras ha'Adam, brought in Kesef Mishneh Hilchos Evel 2:14)): The Rif means that if one was Mitamei for his father, and a bone was not buried, he is Mitamei again to bury it. We must say that this is like R. Yehudah, who argues with R. Yehoshua ben Elisha and the four Chachamim. However, we rule like was done in practice (they forbade R. Yitzchak to be Mitamei for his father, because the body was not intact)! Also, this was the majority opinion. Also, Rav forbids, and we do not find an Amora who argues with him.

Defense (Kesef Mishneh Hilchos Evel 2:14): R. Yehudah is not a lone opinion. R. Eliezer ben Yakov agrees. Even though R. Yehoshua ben Elisha and the four Chachamim disagree, we follow the two because they appear more regularly in the Gemara. Also, the Halachah always follows R. Eliezer ben Yakov. It seems that Rav Kahana held like the Beraisa he taught (of R. Eliezer ben Yakov). Perhaps in the Rif's text, Rav Chisda said his law himself (not in the name of Rav). Even if he said it in the name of Rav, perhaps it is according to the Tana who argues with R. Yehudah, but Rav himself holds like R. Yehudah. The Gemara says so sometimes. However, since the Rambam, Ramban and Rosh agree, we rule like them.

Rambam (Hilchos Evel 2:14): A Kohen may not be Mitamei for Ever Min ha'Chai of his father, nor for a bone the size of a barley seed.

Ra'avad: The Rif disagrees.

Rambam (Hilchos Evel 12:1): If one commanded 'do not bury me', we do not heed him, for it is a Mitzvah - "you will bury him."

Radvaz: Why didn't the Gemara learn from the verse? Perhaps the verse applies to Stam Mesim, but not to one who asked not to be buried. It is a Safek mid'Oraisa, so we are stringent. Alternatively, we brought proofs that it is due to disgrace, and we do not rely on the rejections.

Radvaz (2:780): Why did the Gemara ask about the reason we bury Mesim? In any case the Torah commands to bury Mesim! It seems that if it is for Kaparah, if one asked not to be buried, we bury him, but he does not get a Kaparah. Perhaps this is why the Rif did not bring this, for it does not affect us. Hash-m knows whether or not he gets a Kaparah!

Poskim

Shulchan Aruch (374:2): A Mes Mitzvah for which one must become Tamei is only if one found the head and majority. If he found the head and majority except for one limb, he becomes Tamei again for that limb.

Source (Beis Yosef DH u'Mah): The Ramban brings this from the Yerushalmi.

Radvaz (8:197): There is a custom to bring bones from Mitzrayim to be buried in Yerushalayim. This is proper. We have a tradition that Techiyas ha'Mesim will be only in the valley of Yehoshafat. Bringing the bones saves the Mes from the pain of rolling through tunnels. However, one must ensure that nothing remains of the Mes (in the old grave). If anything remains, after Techiyas ha'Mesim, the person will be lacking until that remnant rolls to Yerushalayim. Therefore, one must take also the dirt he is in. Then, one may put a new Mes in the grave of the one moved.

Chasam Sofer (EH 2:134): A case occurred in which blood of a Mes was absorbed in dirt. It need not be buried together with the Mes. People were not particular to bury limbs that fell from Mesim together with the Mes (Rashi Mo'ed Katan 5b DH Mishum).

Mishneh Halachos (16:113): Ha'Emek She'elah (YD 97) discusses a man who lost a finger, moved, and died. The father wanted them to send his son's finger to be buried with him. Is this proper, in order that he will not lack a limb at the time of Techiyas ha'Mesim? The Chasam Sofer brings from Rashi that people were not particular to bury limbs that fell from Mesim together with the Mes. The Radvaz teaches a big Chidush (that if anything remains in the old grave, the person will be lacking until the remnant rolls to Yerushalayim). This is another reason not to reinter Mesim. Rashi (Pesachim 68 DH Hachi) says that Mesim will be revived the way they were buried, and afterwards Hash-m wil heal them.

Tosfos Yom Tov (Shabbos 10:5 DH v'Chen): The Mishnah obligates one who takes to Reshus ha'Rabim a k'Zayis of a Mes. Perhaps the Mitzvah to bury is only if there is at least a k'Zayis.

Rebuttal (Mishneh l'Melech Hilchos Evel 14:21, DH Asher): The Yerushalmi (Nazir 7:1) obligates burial only if the head and majority are intact. Perhaps the Mishnah discusses a Mes Nochri. A k'Zayis is useful to feed to a dog.

Gesher ha'Chayim (1:16:2:1,2): Even those who say that the Mitzvah to bury is only if the head and majority were found, they agree that a limb or a k'Zayis of flesh must be buried, if not for the Mitzvah of burial, for one of four reasons. 1) One may not benefit from a Mes. (We bury Isur Hana'ah unless there is a Mitzvah to burn them.) 2) We are concerned lest people become Tamei from it. 3) The body was like the margin or case of Kedushah (the Neshamah), so any part of it so it requires Genizah (burial). 4) Burial of any part of a Mes shows anticipation of Techiyas ha'Mesim.

Kol Mevaser (1:70): It seems that he becomes Tamei again even for part of a limb. R. Yehudah (Nazir 43) requires this even for a bone the size of a barley seed, for one's father! The Rif rules like R. Yehudah, but the Poskim disagree (Beis Yosef Sof Siman 374). Shirei Korban says that Tana'im argue about relatives, but regarding a Mes Mitzvah, all agree to R. Yehudah. The Tur (374) and Shach (1) say so. When the head and majority are intact, one must return to bury even a partial limb or a bone less than a k'Zayis. There was no need to teach that a Kohen may bury these, for these are not Metamei. Rather, we learn that they must be buried.

Note: Perhaps the Chidush is that a Kohen buries them with the rest of the body, and he becomes Tamei from entering the cemetery or opening the coffin!

Kol Mevaser (1:70): It seems that since less than a k'Zayis is not Metamei, one need not bury it. One must bury a bone the size of a barley seed, even though it has no Tum'as Ohel, just like one must bury Nochrim, who have no Tum'as Ohel. Rav Nisim Gaon (Berachos 5b) explains that R. Yochanan's tenth son fell into a boiling cauldron, and all his flesh melted, and only bones remained. Since the head and majority did not remain, there was no Mitzvah to bury even bones with a Shi'ur Tum'ah.