Gemara

23b (Mishnah): If a man incited a dog or snake to bite, he is exempt.

Opinion #1: The inciter is exempt, but the owner of the dog or snake is liable.

Inference: An animal's mouth is unlike the damager's yard. If not, the owner would be exempt!

Rejection #1 (and Opinion #2): No, even the inciter is exempt.

Rejection #2 (and Defense of Opinion #1): The owner is liable when the animal stuck out its teeth to bite (the damage occurred outside its mouth).

24a - Question: If Levi incited Reuven's dog to bite Shimon, what is the law? Surely, Levi is exempt. Is Reuven liable?

Can he say 'I didn't do anything!' Or, since he knows that his dog can be incited, he should not keep it aroud!

Answer (R. Zeira - Mishnah): If an animal does not gore when children play with it, it is Tam.

(Inference): If it gores other oxen (when incited by children), it is liable!

Rejection (Abaye): No. If it gores when incited, it is Mu'ad, but it is exempt for that goring.

(Mishnah): If a man incited a dog or snake to bite, he is exempt.

Suggestion: The inciter is exempt, but the owner of the dog or snake is liable.

Rejection: No, even the inciter is exempt.

(Rava): Even if you will say that when Levi incited Reuven's dog to bite Shimon, Reuven is liable, if it bit Levi, Reuven is exempt.

This is because if one party does something abnormal, and another party acts abnormally and damages the first, the second party is exempt.

Support (for Rava - Rav Papa - Reish Lakish): If a cow was crouching in a Reshus ha'Rabim, and another cow was walking, and the walking cow kicked the crouching cow, it is exempt;

If the crouching cow kicked the walking cow, it is liable.

(Rava): I say that even in the first case, it is liable. The walking cow may walk over the crouching cow, but it may not kick it.

39a (Mishnah): An Itztadin ox (one that is trained to gore in stadiums) is not killed - "when it (an ox) will gore (...it will be stoned)", not when it is incited to gore.

55b (Beraisa - R. Yehoshua): There are four things for which one is exempt b'Yedei Adam, but liable b'Yedei Shamayim: breaching a fence in front of Reuven's animal, bending Reuven's crop in front of a fire; hiring false witnesses, and not testifying when one knows testimony that could help Reuven.

Rishonim

Rif: Rava does not support himself from Reish Lakish's law, for Rava obligates even in the first case.

Question (Nimukei Yosef DH v'Aska): Why is this different than an Itztadin ox, which is exempt due to "when it will gore", not when it is incited to gore.

Answer #1 (Ro'oh, cited in Nimukei Yosef): An Itztadin ox is different. It is very used to doing so. It has no Da'as at all. It gores like its nature whenever it is incited. A dog has Da'as. Sometimes it is incited and it does not bite. We do not apply to it "when it will gore", but not when it is incited to gore.

Answer #2 (Ritva, cited in Nimukei Yosef): An Itztadin ox is not killed, but it is liable for damage.

Rebuttal (Nimukei Yosef): (It is exempt.) The ox is forced. It is not merely incited. They pain it! It has no Da'as, unlike a dog.

Note: On 41b, R. Akiva asked why R. Eliezer needed to learn from a verse that a Tam does not pay half-Kofer (since it pays only mi'Gufo and it is stoned). According to the Ritva, perhaps the verse is needed to teach about an Itztadin ox!

Rosh (2:14): The Rif holds that the Halachah is that if Levi incited Reuven's dog to bite Shimon, Reuven is liable. This is because Rava's question is only according to this opinion. The Halachah follows Rava, for he is Basra.

Rambam (Hilchos Nizkei Mamon 2:19): If Levi incited Reuven's dog to bite Shimon, Levi is exempt b'Yedei Adam, but liable b'Yedei Shamayim. Reuven pays half-damage. Since he knows that his dog can be incited, he should not keep it around. If Levi incited it to bite himself, Reuven is exempt. This is because if one party does something abnormal, and another party acts abnormally and damages the first, the second party is exempt.

Ra'avad: If it is Mu'ad, it pays full damage.

Magid Mishneh: I say that even if it is Mu'ad, it pays half damage, since it did not do so by itself, rather, through incitement. For this reason we do not kill an Itztadin ox. Here too, it pays only half-damage. This is why the Rambam did not distinguish.

SMA (CM 395:2): Since it gores only through incitement, this is a Shinuy (unusual).

Migdal Oz: Abaye said that if it gores when incited, it is Mu'ad. The Rambam (agrees. He) writes only what is explicit in the Gemara, not what can be inferred.

Rashi (55b DH Patur): R. Yehudah exempts these four matters because he exempts Gerama in Nezikim.

Poskim

Shulchan Aruch (CM 395:1): If Levi incited Reuven's dog to bite Shimon, Levi is exempt b'Yedei Adam, but liable b'Yedei Shamayim. Reuven pays half-damage. Since he knows that his dog can be incited, he should not keep it around. If Levi incited it to bite himself, Reuven is exempt. This is because if one party acts abnormally, and a second acts abnormally and damages the first, the second is exempt.

Beis Yosef (DH ha'Meshaseh): The Gemara (23b) explained that the inciter is exempt, and the owner is liable. It rejected this to avoid enable saying that an animal's mouth is like the damager's Reshus, but this is not the Halachah.

SMA (1): It is exempt b'Yedei Adam because it is Gerama.

Bach (DH ha'Meshaseh): Also Rashi connotes that that he is liable b'Yedei Shamayim, for he says that this is Gerama. We say (CM 378) that Gerama in Nezikim is forbidden, therefore surely he is liable b'Yedei Shamayim.

Gra (2): Levi is liable b'Yedei Shamayim, like it says in Kidushin 43a (one who told a Shali'ach to murder is Chayav b'Yedei Shamayim), all the more so here (the animal has no Da'as of its own). This is no less than damages (through Gerama that are liable b'Yedei Shamayim) mentioned on 56a.