1) AN OX THAT BURNS A PILE OF GRAIN WITH SPECIFIC INTENT
OPINIONS: The Mishnah (34b) teaches that one must pay for the damages caused by his ox that burned a pile of grain on Shabbos, while a man who burned a pile of grain on Shabbos is exempt from payment. The Gemara explains that just as a man is liable (Misah) for desecrating Shabbos (and is thus exempt from payment) only when he lit the fire on Shabbos for the purpose of using the resultant ashes, the owner of the ox is liable for damages even when his ox lit the fire to use the ashes to sooth a sore on his back.
The Gemara's point is to show that the circumstances in the case of the ox that burns the grain are the same as the circumstances in the case of the man who burns the grain; the ox's owner must pay even though the ox wanted the ashes, whereas a man is exempt from payment when he burned the grain on Shabbos in order to obtain the ashes (because of the rule, "Kam Lei bid'Rabah Minei" -- one who is Chayav Misah is exempt from Tashlumin, monetary payments).
Why would one have thought that the ox's owner is exempt from liability when the ox needed the ashes? What difference does it make whether the ox burned the grain in order to obtain the ashes or not?
(a) RASHI (DH Af Shoro) explains that the Mishnah indeed does not mean to teach that the ox's intention matters. Rather, the Mishnah compares the two cases (an ox that burns grain on Shabbos and a man who burns grain on Shabbos) merely to teach that the circumstances are the same in both cases (as the Gemara explains, in both cases the grain is burned in order to obtain the ashes), and although the owner of the ox is obligated to pay the same amount whether or not the ox needed the ashes, the man who burned the grain is exempt only if he needed the ashes.
(b) The BA'AL HA'ME'OR understands that the Gemara's interpretation of the Mishnah is literal: if the ox would have burned the grain with no specific intent to obtain the ashes, it would have been considered an act of Keren and the owner would have been liable for only half of the damages. Since the ox intended to damage (to obtain the ashes), its act is considered an act of Shen. The Mishnah teaches that only in such a case is the owner obligated to pay the full amount of the damages. (Mordechai Zvi Dicker)
2) AN OX THAT CHASED ANOTHER
QUESTION: The Mishnah discusses a case in which one ox chased another ox which then suffered damage. The owner of the damaged ox claims that the pursuing ox caused the damage, while the owner of the pursuing ox claims that the ox was damaged by a rock. The Mishnah states that the owner of the damaged ox must prove his claim if he wants to receive compensation, because of the principle, "ha'Motzi me'Chaveiro Alav ha'Re'ayah."
Why does the Mishnah need to teach this ruling? This ruling is obvious, even without the Mishnah, because of the principle of "ha'Motzi me'Chaveiro Alav ha'Re'ayah," which applies in all cases in which one person makes a monetary claim against another person!
ANSWER: The NIMUKEI YOSEF writes in the name of the RAMAH that the Mishnah is teaching two novel points.
The first point is that although there is circumstantial evidence that the damage was caused by the pursing ox, the Halachah is not decided based on assumptions, regardless of how convincing they may be.
The second point is that even if the owner of the pursuing ox agrees that the damage happened because of his ox, he is exempt. The owner of the pursuing ox agrees that because his ox chased the other ox, the ox being chased stumbled on a rock and was harmed. The Mishnah teaches that even though the pursuing ox indirectly caused the damage, the owner is exempt from payment. He is exempt because of the rule that "Gerama b'Nizakin Patur" -- "indirect cause of damage is exempt."
The RASHASH points out that RASHI apparently does not agree that the Mishnah intends to teach this second point. Rashi (DH b'Sela) writes that the owner of the pursuing ox claims that the damaged ox intentionally scratched itself on the rock and thereby damaged himself. Rashi implies that only in such a case is the owner of the pursuing ox exempt from payment; if, however, the ox was damaged as a result of fleeing from the pursuing ox, its owner would be obligated to pay for the damages. (Mordechai Zvi Dicker)
3) CLAIMING WHEAT AND ADMITTING BARLEY (AS IT APPLIES TO OXEN)
OPINIONS: The Mishnah discusses a case in which the owner of an ox admits that his goring oxen damaged someone else's oxen, but he claims that it was his small Tam ox that did the damage (and thus he agrees to pay only half of the value of the damage). The owner of the gored oxen claims that it was the large Mu'ad ox that did the damage (and thus he demands full compensation). The burden of proof rests on the one who was damaged. Without proof, the owner of the damaged oxen may collect only what the owner of the damaging ox admits that he owes.
The Gemara asks why the owner of the damaged oxen may collect anything. Rabah bar Nasan teaches, "Ta'ano Chitim v'Hodah Lo b'Se'orim Patur." When one person claims that the other person owes him wheat, and the defendant admits that he owes barley but not wheat, he is exempt from payment. Similarly, in the case of the Mishnah in which the owner of the damaged ox claims payment from one ox (the Mu'ad) and the owner admits that he owes payment from a different ox (the Tam), the owner should be exempt from payment altogether!
The Gemara answers that the Mishnah refers to a case in which the owner of the damaged ox claims only that it might have been the Mu'ad ox that did the damage. His intention is to claim payment from one of the two oxen, and thus this case is not similar to the case of "Ta'ano Chitim v'Hodah Lo b'Se'orim."
What is the logic behind Rabah bar Nasan's ruling of "Ta'ano Chitim v'Hodah Lo b'Se'orim Patur"? Also, why does the Gemara initially assume that the case of the Mishnah is similar to that case?
(a) RASHI (DH Af) explains that by not claiming barley, the claimant releases any claim to barley. He therefore has no right to collect it.
(b) The ROSH disagrees with Rashi's explanation. He asserts that a person does not always state all of his claims. Moreover, the logic that the claimant shows that he relinquishes his claim to one object by claiming another does not apply to the case in the Mishnah. In the case of the Mishnah, it is clear that the claimant's motive for asserting that it was the large Mu'ad ox that did the damage and not the small Tam ox is to ensure that he receives the full value of the damages. He clearly has no intention to relinquish any claims for damages caused by the small ox.
The Rosh therefore understands that the logic for Rabah bar Nasan's ruling is that the claimant's claim of wheat implies that he admits that the defendant does not owe him barley. How does his claim of wheat imply that he admits that he is not owed barley? Perhaps he is making only one of several claims (as the Rosh himself asks on Rashi)!
The Rosh explains that the case of "Ta'ano Chitim v'Hodah Lo b'Se'orim" indeed is similar to the case of the Mishnah. In the case of "Ta'ano Chitim," the two disputants argue about a specific loan that transpired at a specific time. The lender claims that he lent wheat, and the borrower claims that he borrowed barley.
The reason why the borrower is exempt from payment entirely is that the lender clearly admits that he did not lend barley; both agree that there was only one loan. In the case of the Mishnah as well, the owner of the damaged ox admits that the small Tam ox did not do damage. He therefore should not be able to collect from the small ox.
(c) The NIMUKEI YOSEF explains that the reason why the defendant is not obligated to pay barley (even though he admits that he owes barley) is that the admission of the borrower that he owes barley is not a valid admission. Since this admission was made without a prior claim that barley was owed, the borrower may change his mind and say, "Meshateh Ani Bach" -- "I was joking with you." Only when he is confronted with a claim is his admission of that claim taken seriously. According to this explanation, if witnesses testify that the borrower indeed borrowed barley, the borrower is obligated to pay back the barley (since there was no admission by the lender that the borrower does not owe him barley).
The Rosh asks that this explanation does not seem consistent with the Mishnah. In the case of the Mishnah, there must have been witnesses who saw the goring (but are unable to identify which ox gored), because if no witnesses saw the goring the owner of the ox that damaged would be exempt because of the rule of "Modeh b'Kenas Patur" -- one who admits to a penalty is exempt from paying it, since "Palga Nizka Kenasa" -- the obligation of Chatzi Nezek for damages done by a Tam has the status of a penalty and not actual compensation for damages.
Whenever witnesses are present, one cannot claim "Meshateh Ani Bach." How, then, does the Nimukei Yosef understand the Gemara's comparison of the case of the Mishnah (in which there are witnesses and thus one cannot claim "Meshateh Ani Bach") with the case of "Ta'ano Chitim"?
The Nimukei Yosef is not bothered by this question because he maintains that the Gemara here follows the view that "Palga Nizka Mamona" -- the obligation of Chatzi Nezek for damages done by a Tam has the status of a monetary compensation (and is not a fine). Therefore, the case of the Mishnah does not need to be a case in which there are witnesses. Accordingly, the admission of the owner of the damaging ox was in response to no claim from the claimant; he could have denied the entire incident, and therefore he can claim "Meshateh Ani Bach." (Mordechai Zvi Dicker)