Gemara

"Ish Iti" - we send the Se'ir ha'Mishtale'ach at any 'Es', even on Shabbos.

Question: What is the Chidush that it is permitted on Shabbos?

Answer (Rav Sheshes): If the goat is sick, the man may carry it.

Suggestion: This is unlike R. Noson, who says that ha'Chai Nosei Es Atzmo (carrying living beings is not a Melachah).

Rejection: It is even like R. Noson. R. Noson agrees about a Ba'al Chai that is too sick to walk (we do not say ha'Chai Nosei Es Atzmo).

Shabbos 94a - Mishnah: If one was Motzi a live person on a bed, he is exempt even for the bed, for it is Batul to the person.

Suggestion: This is like R. Noson, and unlike Chachamim:

Beraisa: If one was Motzi to Reshus ha'Rabim an animal or bird, alive or slaughtered, he is liable;

R. Noson says, he is liable if it was slaughtered and exempt if it was alive, for ha'Chai Nosei Es Atzmo.

Rejection: Our Mishnah is even like Chachamim. They argue only regarding carrying animals and birds, which resist being moved. They agree about carrying people.

Question (Rav Ada bar Ahavah - Mishnah): (It is forbidden to sell a large (work) animal to a Nochri, lest on Shabbos the Yisrael show how to make it work, or lest the Yisrael come to rent or lend and transgress letting his animal rest on Shabbos.) Ben Beseira permits to sell a horse.

Beraisa: Ben Beseira permits a horse because it is normally used for (carrying people,) a Melachah for which one is not Chayav Chatas.

R. Yochanan: Ben Beseira and R. Noson say the same thing.

Summation of question: If Chachamim agree about carrying people, Ben Beseira's law has nothing to do with the argument of R. Noson and Chachamim!

Answer: R. Yochanan learns from a horse special for carrying hunting birds (the Chachamim who argue with R. Noson obligate for this. Ben Beseira permits all horses).

R. Yochanan: R. Noson agrees about a living being that was tied up (we do not say ha'Chai Nosei Es Atzmo).

Question (Rav Ada bar Masnah): Persians are (wrapped in wide garments and are too delicate to walk,) like people who are tied up, and R. Yochanan taught that Ben Beseira holds like R. Noson! (Ben Beseira allows selling horses even to Persians, who will ride on them. This shows that he exempts even for tied beings!)

Answer: Persians can walk; they are merely haughty. A certain sergeant ran 12 Mil on foot when the king got angry at him!

141b - Rava: If one was Motzi a live child with a wallet around his neck, he is liable for Hotza'ah of the wallet;

Question: He should also be liable for the child!

Answer: Rava holds like R. Noson, who says ha'Chai Nosei Es Atzmo.

128b - Beraisa #1: One may Medadeh animals and birds (hold them and force them to walk) in a Chatzer, but not in Reshus ha'Rabim;

A woman may Medadeh her son in Reshus ha'Rabim. There is no need to say that it is permitted in a Chatzer.

Avodah Zarah 16a (Beraisa - Ben Beseira): One may sell a horse, because it does not do Melachah for which a person would be liable;

Rebbi forbids a horse for two reasons. It is like a weapon (it tramples fallen soldiers in war) and it is considered a work animal (when it grows old, people make it turn a millstone).

R. Yochanan: The Halachah follows Ben Beseira.

Rishonim

Rambam (Hilchos Shabbos 18:16): If one was Motzi an animal or bird, even if it is alive, he is liable. However, a live person is not considered a load unless he is tied up or sick.

Rambam (ibid. 20:4): One may sell a horse to Nochrim, for it is used solely to carry people, and ha'Chai Nosei Es Atzmo.

Magid Mishnah: The Rambam rules like Ben Beseira, for R. Yochanan taught that the Halachah follows him.

Objection: Pirush ha'Mishnayos says that the Halachah does not follow Ben Beseira! Also, the Mishnah Torah permits only a horse that people ride on. This is like Chachamim, who say that ha'Chai Nosei Es Atzmo applies only to people!

Answer #1 (Tosfos Yom Tov Pesachim 4:2): The Rambam's text of the Gemara (and the Bartenura's; he explicitly says that the Halachah does not follow Ben Beseira) did not say that the Halachah follows Ben Beseira.

Objection (Rashash Avodah Zarah 16a DH Omar R. Yochanan): Even if this is so, the Rambam should rule like R. Noson (who holds like Ben Beseira) because Rava (Shabbos 141b) holds like R. Noson!

Answer #2 (Rashash ibid.): R. Yochanan taught that the Halachah follows Ben Beseira, i.e. the Halachah does not follow Rebbi, who (in that Beraisa) forbids a horse because it is a weapon and it pulls a millstone when it is old. If R. Yochanan meant that we say ha'Chai Nosei Es Atzmo even regarding animals, his Pesak would have been taught on the Mishnah. Rava holds like R. Noson and Chachamim. The Gemara attributes Rava's law to R. Noson because R. Noson explicitly said that ha'Chai Nosei Es Atzmo. The Rambam rules like Chachamim, for they are the majority.

Rosh (Shabbos 10:2): If one was Motzi a live person on a bed he is exempt even for the bed, since it is Batel to him. If one was Motzi a tied up person he is liable.

Rashi (Shabbos 93b DH Es ha'Chai): A living being makes itself lighter.

Rebuttal (Tosfos Shabbos 94a DH sheha'Chai): One is liable even for carrying a light load! The exemption is not because he did not do the Melachah himself, i.e. Ploni helped carry himself, because Ploni could not have done the entire Melachah himself! Rather, they did not carry living beings for the Mishkan, therefore one is exempt for this.

Question: Why do Chachamim exempt for (carrying) people and say that one is liable for animals?

Answer (Korban Nesan'el 10:6): All agree that one is liable for things that were not carried in the Mishkan. They exempt for something which helps to carry itself, for this is unlike what was carried in the Mishkan. Chachamim hold that animals do not help (rather, resist) to be carried.

Note: Tosfos explained how R. Noson can explain why they did not carry a live Chilazon, Tachash or ram. Perhaps Chachamim disagree about this, and say that live beings were carried for the Mishkan! Tosfos did not explain why R. Noson did not directly say that one is exempt because live beings were not carried in the Mishkan. Presumably, he explains why it is reasonable to distinguish like this. Carrying a live being is not a significant Melachah because it could have walked itself.

Poskim

Shulchan Aruch (OC 308:41): A woman may be Medadeh a child even in Reshus ha'Rabim, as long as she does not drag him. He must step, and one of his feet must be on the ground at all times.

Mishnah Berurah (153): We do not forbid to be Medadeh, for even if she would pick him up, this is forbidden only mid'Rabanan. If the child is sick, then ha'Chai Nosei Es Atzmo does not apply, so we decree against being Medadeh lest she transgress mid'Oraisa.

Kaf ha'Chayim (251): If someone can walk, carrying him in a Karmelis is Shevus of Shevus. It is permitted if there is a great need or even a slight illness.

Shmiras Shabbos k'Hilchasah (18:51): If a sick child needs to go to a doctor, if he knows how to walk but it is difficult for him, one may carry him even in a proper Reshus ha'Rabim. In a Karmelis one may carry a child even if he cannot walk. Whenever one may carry a child it is permitted to carry him in a stroller. However, one may not carry a child holding anything or with anything in his pocket; when using a stroller, everything else must be removed from it.

Note: Shmiras Shabbos k'Hilchasah cites Mishnah Berurah 328:102 for his source. The Mishnah Berurah relies on the third opinion in 328:17, which allows things that are not 'Nismach l'Melachah'. It is not clear that carrying in Reshus ha'Rabim is not 'Nismach l'Melachah'. If the child is too young or sick one is liable for carrying him!