Commentary for Bava Kamma 4:4

An ox of a competent person that gores an ox of a deaf-mute or incompetent person....

ושל חרש שוטה וקטן שנגח שור של פקח פטור – for we don’t appoint an administrator/guardian for an innocuous ox to collect [damages] from his estate for they are movables, and we stated in the first chapter (Tractate Bava Kamma 14b) an equivalent amount of money teaches that the Jewish court does not need anything other than property from which debts may eventually be collected and we establish this for orphans.

[If] an ox of a person of sound senses gored the ox of a deaf-mute, an insane person, or a minor, [its owner] is obligated.
[If] an ox of a deaf-mute, an insane person or a minor, gored the ox of a person of sound senses, [its owner] is exempt.
[If] an ox a deaf-mute, an insane person or a minor gored, the court appoints a guardian over them, and [their oxen] are testified against in the presence of the guardian. [If] the deaf-mute became of sound senses, or the insane person recovered his reason, or the minor came of age, [the ox] is thereupon deemed harmless once more, according to Rabbi Meir. Rabbi Yose says, “It remains as it was before.”
An ox from the stadium is not liable to be put to death, as it says, “When it will gore” (Exodus 21:28), and not “When others cause it to gore.”
Our mishnah deals with oxen owned by deaf-mutes, insane people or minors that damage oxen owned by adults of sound-mind or are damaged by them. We should note that in the ancient world deaf-mutes were considered to be unintelligent, probably because they had no way of communicating with the outside world. We should remember that in those times the written word was much more scarce and almost all communication and learning was done orally. It is therefore, little surprise, that deaf-mutes were considered to lack intelligence. The three categories of people mentioned are therefore, according to the mishnah, all people who are not capable of fully knowing the consequences of their actions, and therefore cannot be held responsible for them. Thankfully, in the modern world we have developed sign language and other forms of communication (including e-mail and the internet) that have allowed us to learn that people who cannot speak verbally or hear are no less intelligent than those who can.
 Section one deals the ox of a person of sound senses that injures the ox of a deaf-mute, insane person or minor. In this case the owner is obligated the same way that s/he would be obligated if the ox injured any person’s ox.
 Section two deals with the ox of a deaf-mute, insane person or minor that gores another person’s ox. In this case the owner of the injuring ox is not liable. The mishnah considers these people not to be capable of protecting their oxen from injuring others, and therefore they are not liable.
 Section three continues to deal with the problem of oxen that belong to deaf-mutes, insane people or minors from injuring. Although these people are not responsible for their actions, this does not mean that the halakhah does not have the duty to protect the interests of others who are damaged by them. Therefore, the mishnah institutes a process by which the court appoints a guardian over the oxen of the aforementioned people. If the ox should henceforth damage three times, it will become an attested danger (muad) and the guardian will pay full damages from the estate of the deaf-mute, insane person or minor.
 In section three clauses c through e, Rabbi Meir and Rabbi Yose disagree concerning the case where the ox of a deaf-mute, an insane person or a minor was declared by the court to be an attested danger (muad) and then the status of the owner changed to that of an adult person of sound senses. According to Rabbi Meir, the ox’s slate is cleaned and it returns to being a harmless ox (tam). If it should injure again its owner will only be obligated half damages. According to Rabbi Yose, the ox remains an attested danger and if it should injure again its owner will be obligated full damages.
 Section four deals with a stadium ox, what we might call a fighting bull. As is well known, the Romans entertained themselves by throwing slaves and other human beings into pits to fight animals to the death. (Indeed some still find this entertaining). In Exodus 21:28 we learn that oxen are obligated for death if they kill a person. Our mishnah is a midrash on the words, “When it will gore” that begins this verse. According to the midrash, or legal exposition, the verse deals with an ox that gores of its own will and not an ox that is put into the position where human beings are urging it to kill. In this case, the ox is innocent and I might add one should wonder whether those in the stadium aren’t the ones with innocent blood on their hands.

When it becomes accustomed to gore an ox of a deaf, deranged, or minor, to damage people, at that time we appoint to them stewards.

מעמידין להן אפוטרופוסים וכו' – if they (i.e., oxen) are known to be gorers, we appoint for them a guardian/administrator and not to pay one-half damage other than for forewarned oxen, for if it gores again, they pay from the most valuable property and they collect the damages from the land of orphans.

"A stadium"... An ox that people accustom it to do as follows: that this one sends his ox and this one sends his ox and they signal to them with a sound that they are familiar with so that they will try to over power the other ox to see which one of them will win over his friend. And this is not the nature of the ox, rather, the will of their owner. And many sinful people do this with many types of animals and birds.

חוזר לתמותו – for he (i.e., Rabbi Meir) holds that if it (i.e., the animal) left the domain of his masters an entered into the domain of other masters, he returns to his [former status] of innocuousness, for a different domain changes the law of its being “forewarned.”

שור האיצטדין – that is designated for goring and they (i.e., the oxen) are instructed in this.