Question: Let them bring the baby to the vessel, as this would not be a transgression of Shabbos at all since a live person carries his own weight!

Answer #1: He is a child who needs his mother, and he must be returned to his mother after the Milah. After he has the Milah he is considered like a person who is tied up (who does not carry his own weight), as he is sick.

Proof: This is as the Gemara says in Yoma (66b) that even Rebbi Nasan would agree that a sick person is different (as he does not carry his own weight, and therefore a person who carries him is deemed to be carrying on Shabbos). Additionally, the mother is considered in danger after birth, and therefore cannot come to the baby after the birth.

Answer #2: It is also possible to answer that since it is easier to bring the vessel than to bring the baby, Rebbi Eliezer permits bringing the vessel in order to hurry to perform the Mitzvah.

Proof: This is as is apparent from the Gemara that says that they once forgot and did not bring a knife from before Shabbos. They brought the knife on Shabbos against his will through yards, roofs, and open empty spaces. It was against his will, as Rebbi Eliezer understands one is even permitted to carry it through the public domain. This implies that Rebbi Eliezer permits carrying through the public domain, which is a Torah prohibition, in order to hurry to perform a Mitzvah. This is despite the fact that one can do the same thing in a way that is only a Rabbinic prohibition.

Observation: The Medrash (Shochar Tov) on the Pasuk, "Lamenatzeach Al ha'Sheminis" expounds on David ha'Melech being happy regarding having a Milah (in the bathhouse where he was otherwise devoid of Mitzvos), as the Medrash understands this Pasuk is referring to Milah that is done on the eighth day (this is how the Maharsha understands Tosfos, see also Maharshal who changes the text of Tosfos).

Observation (cont.): The Pirkei d'Rebbi Eliezer (ch. 29) says regarding the Pasuk, "And Avraham made a large meal on the day "Hegamel Es Yitzchak." The Medrash says that "Hegamel" alludes to "Heh Gimmel Mal" meaning that he gave him a Bris Milah on the eighth day, the numerical value of Heh (5) plus Gimmel (3).

Explanation: He did not give himself over by saying they are Tefilin. (Rabeinu Shmuel)

Question: The Rashba has difficulty with this. We say later (33a) that wherever one finds a positive Mitzvah and a negative Mitzvah, if you can fulfill both you should etc. In our Gemara, he can uphold both by bringing the knife through yards, roofs, and open spaces (that are not public domain). Why should he bring it through the public domain?

Answer: One cannot say that regarding Milah, that the Torah teaches pushes aside Shabbos as we derive later, we do not say this rule. (Why not?)

Question: Later, when the Gemara says that one should even cut the flesh of the Milah even if there is a mark of leprosy on it, we say that this is like Reish Lakish who says that whenever you find etc. (In other words, if we could do the Milah without doing so we would do it in this fashion, despite the fact that there is a Torah derivation that Milah pushes aside cutting the leprosy.)

Question: Why don't we say that the case is where they brought it through a yard that had an Eiruv which would be in accordance with the will of the Chachamim and unlike Rebbi Eliezer who even permits carrying through the public domain?

Answer #1: In such a case Rebbi Eliezer would not have permitted to carry from the public domain, since he could bring it through a yard that had an Eiruv in a totally permitted fashion.

Answer #2: Alternatively, the term "they forgot" does not imply that this was the case. If it had an Eiruv, it would not say "they forgot" but rather that they did not take care to bring it before Shabbos, since it could be brought on Shabbos without transgressing anything.

Answer #2 (cont.): However, since the Gemara concludes that this was done according to Rebbi Shimon it is understandable why it said "they forgot." If they would have remembered they would have brought it before Shabbos, since the Rabbanan argue on Rebbi Shimon.

Implied Question: It also could have said that this was according to the opinion of Rebbi Meir, as they brought it by going over the roofs from roof to roof or through yards from one yard to the next. This is as is apparent in Eiruvin (89a) that Rebbi Meir holds that all of the roofs in a city are considered one domain. The same applies (according to Rebbi Meir) to all of the yards and open empty spaces. (Why didn't the Gemara say it is according to Rebbi Meir?)

Answer: Rather, it said that it is according to Rebbi Shimon because we rule according to Rebbi Shimon.

Explanation: This was the case regarding that knife.

Explanation: This means he is from the House of Shamai.

Proof: This is apparent from the Yerushalmi in Terumos (ch. 5) where the Mishnah (5:4) states that a Sa'ah of impure Terumah that fell into one hundred Sa'ah of pure Terumah, Beis Shamai forbids and Beis Hillel permits etc. The Mishnah continues to say that "after they admitted," Rebbi Eliezer says that he should take Terumah and burn it.

Proof (cont.): The Gemara says that Ben Pazi and Rebbi Aiyvu bar Nagri were sitting and learning this statement, "after they admitted, Rebbi Eliezer says he should take off Terumah and burn it." Who admitted to who? Rebbi Asi says that our Mishnah is saying that after they admitted etc. Isn't Rebbi Eliezer a Shamuti? In other words, Rebbi Asi is saying that since he is from the students of Beis Shamai, we can deduce that Beis Shamai admitted to Beis Hillel. Rabeinu Tam.

Explanation: This means that it is considered as if there is no yard here at all, as the yard is now considered a house. When they did not make an Eiruv, the houses are as if they are not there. (The Gemara therefore asks that Rav's law is not being followed in either case.)

Explanation (cont.): However, the yard is not considered as if it is not there, even though it is forbidden to carry from the yard to the alleyway. Since there is no path that separates between it and the alleyway it is not considered closed. However, houses are considered closed, since the yard separates between them and the alleyway. We only require houses and yard open to it when they did not make a Shituf. However, if they did this it is not required.

Explanation (cont.): The Gemara answers that it is possible that the people in a yard can nullify their domain to one person. This would make it that there is a house that is not considered closed off from the alleyway (as the person who it is nullified to can carry into that yard). He did not say that all of the yards are considered taken away, since the people in the other houses cannot carry into the yard.

Explanation (cont.): The Gemara asks that there is a house, but not houses (and two houses are required to be able to carry from the yards to this alleyway)!

Explanation (cont.): We cannot say that the case is where they nullified their domain to two people, as they would forbid each other from carrying into the yard (if they do not make an Eiruv with each other).

Explanation (cont.): We cannot say that these two people made an Eiruv, as since Rav said they did not make an Eiruv, the implication is that the case is when no Eiruv was made at all.