We are arriving at the final Mishnah of the third chapter of tractate Bava Kamma - Mishnah 11. This Mishnah deals with various scenarios of doubt: how beis din rules when we do not have clear knowledge of what exactly occurred, and we are faced with an issue of Keren damages.
An ox that was chasing after an ox:
The language of the Mishnah is: "Shor shehayah rodef achar shor acher, vehuzak - zeh omer: shorcha hezik, vezeh omer: lo ki, ela besela lakah" - an ox that was chasing after another ox, and it was injured - this one says: "Your ox injured it," and this one says: "No, rather it was injured by a rock." We are presented with two oxen: ox A is chasing after ox B at a distance, and there are no witnesses who see what is happening. Afterwards, it is discovered that ox B has been injured. Even though there is a suspicion that ox A is the one that caused the damage, there is no certainty. The owner of ox B claims that his fellow's ox injured his, while the owner of ox A replies that this is not necessarily the case, and perhaps the ox struck a rock and was injured on its own.
"Hamotzi mechavero alav haraayah":
This is the rule that will accompany us in a large portion of the laws of damages. One who seeks to extract money from his fellow - in our case, B who claims that A owes him - bears the burden of proof. He must bring proof to beis din, presumably through witnesses, that A's ox indeed caused the damage. In the absence of proof, there is no way to obligate A in payment.
This law applies even when B makes a claim of "bari" (certainty) - meaning that he is sure of the matter and saw it with his own eyes - while A only makes a claim of "shema" (perhaps), that he does not know and is not convinced. Even in this scenario, B is unable to obligate A in any payment.
An oath mid'Oraisa and mid'Rabbanan:
Mid'Oraisa, the discussion would end at this point, since there are only three ways to obligate a person in an oath when he does not otherwise owe money to his fellow:
Modeh bemiktzas - a partial admission to the plaintiff's claim.
Ed echad - when a single witness testifies, and not two.
Shevuas hashomerim - the oath of the watchmen, in the context of the laws of guardianship.
However, there is a Rabbinic law called shevuas heses: when B claims with certainty that A owes him money, and A denies this, B can obligate A to swear that he does not owe him. In this way, the matter can be brought to a resolution.
Two that were chasing after one:
"Hayu shenayim rodefim achar echad" - two oxen are chasing after a third ox, and afterwards the third ox is found wounded. The owner of the injured ox sues both owners, but the owner of the first ox deflects him to the owner of the second, and the owner of the second replies that perhaps it was specifically the ox of the first that caused the damage. It makes no difference whether each of them claims with certainty or uses the language of "perhaps"; the point is that each of them dismisses the responsibility from himself. Therefore, both of them are exempt, since the owner of the injured animal does not win a payment unless he brings proof to beis din that the money is due to him.
If both of them belonged to one man:
When the two chasing animals belong to a single owner, and we know clearly that one of them caused the damage, the Mishnah says that both of them are liable. This requires explanation: we are dealing here with damage caused by the horn of a tam (docile) ox, which pays half the damage from its own body, meaning the liability is limited to the animal itself that did the damage. Since it is unknown which of the animals caused the damage, both of them are encumbered for payment, but in practice the decision is left in the hands of the damager, and he will pay from the lesser of the two. Furthermore, if the lesser of the two died or was lost, the damager will claim that his liability is limited to that animal which is no longer here, and the injured party will receive no payment.
One large and one small:
The owner of the damaging animals has two cows, and one of them caused damage. It is unknown which one, but it is known that their values differ. It is in the interest of the injured party to claim from the more expensive cow, since his ability to collect is limited to the value of the animal that caused the damage. As the Mishnah states: "Hanizak omer: gadol hezik, vehamazik omer: lo ki, ela katan hezik" - the injured party claims that the expensive cow caused the damage, and the damager replies that this is not so, but rather the smaller of the two did the damage, and therefore he will not pay from the large one.
One tam and one muad:
In the same way, the damager has two animals: one is a muad (forewarned), which pays full damages without restriction, and the other is a tam, which pays half the damage exclusively from its own body. "Hanizak omer: muad hezik, vehamazik omer: lo ki, ela tam hezik" - the injured party claims that the muad is the one that caused the damage, and the damager denies this and claims that the tam caused the damage. The ruling is: "Hamotzi mechavero alav hara'ayah" - the burden of proof is on the one seeking to extract money from his fellow, and the injured party will not receive any payment beyond what he can prove.
Let us clarify this point, as it will also apply to the next case:
If the injured party claims that one of the damager's animals caused him damage, and even though he does not know which one, he claims at least the value of the lesser of them, then in the case of a tam he will receive payment, assuming the damager admits that one of his animals caused the damage, and the payment will be collected based on the lesser of the two.
However, when the injured party claims with certainty that the expensive animal is the one that caused the damage, and the damager denies this and claims that specifically the lesser one caused the damage, we are faced with a complete denial. The Gemara compares this to the case of "he claimed wheat and he admitted to him regarding barley": when the claimant claims wheat and the defendant replies that he owes nothing but barley, this is an absolute denial of the claim, and the defendant is exempt. The same applies here: the injured party claims from the large animal, and the damager completely denies this and claims that nothing is involved here but the small animal. On a Torah level, this is considered a complete denial, and the rule is that the burden of proof is on the one seeking to extract money from his fellow - without evidence, nothing will be paid. On a rabbinic level, since this is a complete denial, the law of a shevuas hesset (rabbinic oath of denial) applies: the one denying must swear that he does not owe the money, and thereby the matter is resolved. Once he swears that he does not owe from the large cow, he pays nothing.
Two injured animals and two damaging animals:
The last case is a variation on the previous ones: two cows that damaged two cows. The injured party has two cows, one more expensive than the other, and the damager has two cows of different values, and the damager's cows attacked the injured party's cows. The injured party's interest is that the damager's expensive cow damaged specifically his expensive cow, due to the limitation of liability for a tam that pays from its own body. The damager, on the other hand, claims that reality was in his favor: his lesser cow damaged the expensive cow, and vice versa. The exact same principles will apply to these.
As the Mishnah states: "Hayu hanizakin shenayim, echad gadol ve'echad katan, vehamazikin shenayim, echad gadol ve'echad katan. Hanizak omer: gadol hezik et hagadol vekatan et hakatan, vehamazik omer: lo ki, ela katan et hagadol vegadol et hakatan" - the injured party claims that the expensive cow damaged his expensive one, and the lesser one damaged the lesser one; whereas the damager rejects this and claims that his lesser cow damaged the more expensive of the injured party's cows, and his expensive cow damaged the lesser one.
The Calculation:
Let us assume that each party has two cows: one is worth a thousand and the other is worth a hundred. The damager's two cows killed the victim's two cows, and the carcasses have no value at all. The victim's total loss is one thousand one hundred, and half-damages is five hundred and fifty.
If the large one damaged the large one: For the cow that was worth a thousand, he is entitled to half-damages - five hundred, and this can be collected in full, since the damaging cow is worth a thousand. For the cow that was worth a hundred, he is entitled to half-damages - fifty, which is collected from the lesser cow. The total is five hundred and fifty.
If the lesser one damaged the large one: The damage is a thousand and half-damages is five hundred, but the damager's liability is limited to the value of his damaging cow, which is only a hundred. Thus, even though he would legally be entitled to five hundred, he only collects a hundred. And for the death of his small cow he will collect fifty. It turns out that instead of five hundred and fifty he only receives a hundred and fifty - and therefore this is not in his interest.
The Tam and Muad Variation:
In the same way, when instead of two cows of different values, one of them is a Tam and one is a Muad: The Tam pays half-damages and is limited to the value of the animal, and the Muad pays full damages without limitation. The victim, who lost two cows, claims that the Muad damaged his expensive cow and the Tam damaged the cheap one, while the damager rejects this and claims the opposite: The Tam damaged the expensive one and the Muad damaged the cheap one. Here too, the damager cannot be held liable to pay without proof, and on a Torah level this is a dead end for the victim, even if his claim is a definite claim. But as mentioned, with a definite claim the victim can at least obligate the damager to take a Rabbinic oath of denial (Shevuas Hesses).
In summary: In this Mishnah we learned how the court rules in situations of doubt regarding Horn damages. The fundamental rule is "Hamotzi mechavero alav haraayah" - the burden of proof rests on the one seeking to extract money from his fellow, and even a definite claim against a doubtful claim is not sufficient for a monetary obligation. We discussed an ox chasing another ox, two chasing one where both are exempt, and two animals belonging to one owner where both are liened but the collection is made from the lesser one. We also discussed disputes between a victim and damager regarding a large and small animal, a Tam and Muad, and two victims and two damagers - in all of which the collection is limited to what the victim is able to prove. Finally, we saw that a complete denial is judged like "he claimed wheat and he admitted to barley," and on a Rabbinic level the denier can be obligated in an oath of denial (Shevuas Hesses).
With this, the third chapter of Tractate Bava Kamma is concluded.