Answer: The Chidush is the Reisha, which says 'free men, members of the covenant.'

'Free men' excludes slaves. 'Members of the covenant' excludes Nochrim.

The Mishnah needed to teach about both.

Had it taught only about slaves, one might have thought that this is because they have no lineage, but Nochrim have lineage, [so they can be witnesses];

Had it taught only about Nochrim, one might have thought that this is because they have only seven Mitzvos, but slaves have Mitzvos (that women have, so they can be wqitnesses).

(Mishnah): Women are included in damages.

Question: What is the source of this?

Answer (Rav Yehudah): "A man or woman who will do any sin" equates men and women for all punishments;

(D'Vei R. Elazar): "These are the Mishpatim (laws) that you will put in front of them" equates men and women for all Dinim (monetary laws);

(D'Vei Chizkiyah): "And (an ox) will kill a man or woman" equates men and women regarding death.

The Torah needed to teach all of these:

Had it taught only about punishments, one might have thought that this is so she will get atonement, but (monetary) judgments are for men;

Had it taught only about Dinim, one might have thought that this is so she can do business and earn a living, but only men get punishments for atonement, for they are obligated in all the Mitzvos;

Had it taught only about these two, one might have thought that this is for atonement and business, but Kofer (ransom to atone for one whose animal killed someone) would apply only to a man (who was killed);

Had it taught only about Kofer, one might have thought that this is because a life was lost, but in other cases, women are not like men.

(Mishnah): The damager and victim both participate in payments.

(Rav Papa): A Tam that pays half-damage is Mamon (a proper obligation. It is not a fine.)

(Rav Huna brei d'Rav Yehoshua): It is a fine.

Rav Papa holds that oxen are not considered guarded. Really, the owner should pay full damage;

The Torah was lenient, because he was not yet warned to guard it.

Rav Huna brei d'Rav Yehoshua holds that oxen are considered guarded. Really, the owner should be exempt;

The Torah fined him, to encourage him to guard his ox.

(Mishnah): The damager and victim are both involved in payments.

Question: This is like the opinion that half-damage is Mamon. The victim loses half of what he deserves.

According to the opinion that it is a fine, the victim receives what he does not deserve. Can we say he participates in the payments?!

Answer: The Mishnah refers to the decrease in value of a carcass, which the victim suffers.

Question: A previous Mishnah already taught this! 'Payments of damage' teaches that the victim deals with the carcass!

Answer: The Mishnah teaches this about a Tam, and about a Mu'ad. It needs to teach about both.

Had it taught only about a Tam, one might have thought that because the damager was not yet warned to guard his ox, the Torah did not make him lose the decreased value of the carcass (but regarding a Mu'ad, he would lose this);

Had it taught only about a Mu'ad, one might have thought that because he pays full damage, the Torah does not make him suffer the decrease in value of the carcass (but for a Tam, he does).

(Mishnah): The difference between Tam and Mu'ad, is that a Tam pays half-damage (up to) its own value, and a Mu'ad pays full damage, even above its own value.

Question: If half-damage is a fine, the Mishnah should also say that a Tam does not pay due to the owner's admission!

Answer: The Tana did not list all differences.

Question: Surely, he did not omit only one thing. What else did he omit?

Answer: He omitted that only a Mu'ad pays Kofer.

Objection: (Perhaps) our Mishnah is like R. Yosi ha'Glili, who says that a Tam pays half-Kofer!

Question (Mishnah): If one said 'my ox killed Ploni', or 'it killed Ploni's ox', he pays due to his own admission.

Suggestion: This refers to a Tam (this shows that it is Mamon)!

Rejection No, it refers to a Mu'ad.

(Inference): A Tam would not pay due to its own admission.

Question (Reisha): If one said 'my ox killed Ploni's slave' he does not pay due to his own admission.

If (q) is correct, the Mishnah could have distinguished within the first case. He pays due to his own admission for a Mu'ad, but not for a Tam!

Answer: The Mishnah discusses only a Mu'ad.

(Beraisa): The general rule is, any payment more than the damage is not paid due to an admission.

(Inference): Any payment less than the damage is paid due to an admission.

Rejection: No. The inference is that any payment equal to the damage is paid due to an admission.

Question: Do you say that less than the damage is paid due to an admission?

If so, why did the Mishnah say 'any payment more than the damage is not paid due to an admission?' It should have said 'any payment not equal to the damage is not paid due to an admission', to include more or less!

Rav Huna brei d'Rav Yehoshua is refuted.

The Halachah is, half-damage is a fine.

Question: This was refuted. It cannot be the Halachah!

Answer: The refutation was because the Mishnah did not say 'any payment not equal to the damage is not paid regarding the person's admission.' The Mishnah could not say this, for it is not always true;

A tradition from Moshe from Sinai teaches that half-damage of pebbles is not a fine.

Since we say that half-damage is a fine, if a dog ate a sheep, or a cat ate a chicken, this is abnormal (hence a Toldah of Keren), so we do not collect it in Bavel (like all other fines).

This is only if it ate a large sheep or chicken. It is normal for them to eat small ones.

If the victim seized payment, we do not make him return it.

If the victim requested to fix a time to go to Eretz Yisrael to judge the case, we comply. If the damager does not agree, we excommunicate him.

In any case, we excommunicate him until he removes the damager.

(Beraisa - R. Nasan): "Do not put blood in your house" forbids one to have a wild dog or a rickety ladder in his house.

(Mishnah): There are five Tam damagers, and five Mu'ad damagers:

An animal is not Mu'ad to gore, push, bite, crouch or kick;

Shen is Mu'ad to eat food fitting for it. Regel is Mu'ad to break things while it walks;

A Mu'ad ox; an ox that damages in the victim's premises; and man.

A wolf, lion, bear, leopard, Bardelus, and snake are Mu'ad;

R. Elazar says, if they are domesticated, they are not Mu'ad, except for a snake, which is always Mu'ad.

(Gemara): Since it says that Shen is Mu'ad to eat fitting food, this must be in the victim's premises, and it says that a Tam pays half-damage.

This is like Chachamim, who say that Keren pays half-damage in the victim's premises.

Question: The Reisha calls an ox that damages in the victim's premises Mu'ad. This is like R. Tarfon!

Is the Reisha like Chachamim, and the Seifa is like R. Tarfon?!

Answer #1 (Shmuel): Yes!