1) THE LIST OF THE FOUR "AVOS NEZIKIN"
QUESTION: The Mishnah teaches that there are four "Avos Nezikin." TOSFOS and the Rishonim point out that the Mishnah does not use the term "Hen" ("it says "Arba'ah Avos Nezikin" and not "Arba'ah Avos Nezikin Hen -- "four Avos Nezikin they are"), as it normally does when it lists a number of items and introduces the list with a number, and gives no descriptive terms for the items in the list. Similarly, the Gemara later (4b) cites a Beraisa of Rebbi Oshiya that lists thirteen Avos Nezikin, and a Beraisa of Rebbi Chiya that lists twenty-four Avos Nezikin, and both of those Beraisos omit the word "Hen." The Rishonim mention that the only other place where the Mishnah presents a numbered list without the word "Hen" is in Kerisus (8b), where the Mishnah says that there are "Arba'ah Mechusrei Kaparah" and it does not say "Arba'ah Mechusrei Kaparah Hen."
Why does the Mishnah here leave out the word "Hen"?
ANSWERS: The Rishonim suggest a number of answers which complement each other.
(a) The RASHBA suggests that the Mishnah does not say "Hen" to allude to the fact that these are not the only Avos Nezikin. There actually are more Avos Nezikin, as Rebbi Oshiya and Rebbi Chiya list. The Mishnah does not count the other Nezikin because it chooses to present a limited list (see reasons on 4b). The same is true for Rebbi Oshiya's Beraisa which omits the Avos Nezikin counted in Rebbi Chiya's Beraisa. The Gemara asks, about Rebbi Chiya's Beraisa as well, what is it that he omitted, and it explains that he also chose to limit his list by omitting two items from it.
The Rashba explains that the way that the Gemara knew that Rebbi Chiya omitted something from his list is because he did not say the word "Hen."
The Rashba, however, leaves unanswered the question of why the Mishnah in Kerisus does not say "Hen."
The GILYON cited by the Shitah Mekubetzes points out that the same answer might be applied to the Mishnah in Kerisus, according to TOSFOS in Kerisus (2b, DH la'Afukei). Tosfos there explains that the Mishnah in Kerisus chooses to limit its list and not enumerate all of the cases of Mechusrei Kaparah just as the Mishnah here limits its list.
(b) The MAHARI KOHEN TZEDEK cited by the Shitah Mekubetzes answers that the word "Hen" is written to emphasize the differences between the items listed. He apparently means that the word "Hen" is used when one might think that some of the items in the list are identical and should not be counted independently. The Mishnah adds the word "Hen" to emphasize that this indeed is the number of different items that must be enumerated, and not less.
In contrast, in the Mishnah here (and in the Mishnah in Kerisus) it is obvious that the different Avos (and, in Kerisus, the Mechusrei Kaparah) should be listed separately because of their distinct qualities. The Mishnah writes "four" to exclude more than four and not less than four, and therefore it does not need to use the word "Hen."
This is also the answer of the TOSFOS RID cited by the Shitah Mekubetzes, and the answer of the NACHALAS DAVID.
(Although the Mishnah continues and says "Lo Harei...," its intention is not to point out that the Avos are different, but rather that each Av has a Kula and therefore it cannot be derived from a combination of the others.)
A similar concept is expressed by TOSFOS in Kerisus (2b, DH l'Me'utei), who says that when the Mishnah emphasizes the differences between the items in its list, it is not necessarily excluding other items from the list. That is, some Mishnayos teach the minimum number of items, and other Mishnayos teach the maximum number of items.
(c) Perhaps the Mishnah uses the word "Hen" when the list includes items that are not discussed explicitly in the Torah. "Hen" means that besides the ones in the list that are already known, there is another, specific number of items that should be included in this list. For example, the Mishnah in Shevuos (49a) says, "Arba Shomrim Hen," because one of them, the Socher, is not mentioned anywhere in the Torah explicitly (see Rashi 5a, DH Tachas Nesinah). The Mishnah in Rosh Hashanah (2a) says, "Arba Roshei Shanim Hen," because those days are not described by the Torah as Roshei Shanim. The items -- the Avos Nezikin-- in the list of the Mishnah here, and in the lists of the Beraisos of Rebbi Oshiya and Rebbi Chiya, are written explicitly in the Torah, as are the Mechusrei Kaparah listed in Kerisus. They are mentioned in the Mishnah only to teach that they pay from "Meitav." (Although Rebbi Oshiya and Rebbi Chiya mention "Socher," they do not mean to teach anything new by that, since Socher is already listed in the Mishnah of the four Shomrim.)
(This answer is similar to the previous answer.)
2) DERIVING THE OBLIGATION TO PAY FOR DAMAGES THROUGH A "KAL VA'CHOMER"
QUESTIONS: The Mishnah teaches that had the Torah not mentioned each one of the Avos Nezikin, the ones not mentioned could not have been derived from those that are mentioned through a Binyan Av. (See Chart to 5b. The Rishonim point out that according to the Gemara's conclusion on 5b, this part of the Mishnah was written only "l'Hagdil Torah ul'Ha'adirah"; see also Tosfos here, DH v'Lo.) It seems clear from the Mishnah and Gemara that had one of the Avos been more lenient than all of the others, the rest could have been derived from it through a Kal va'Chomer or Binyan Av. TOSFOS (DH v'Lo) explains that although the normal rule is "Ein Onshin Min ha'Din," a punishment cannot be derived through an exegetical process such as a Kal va'Chomer or Binyan Av (rather, it must be written in the Torah explicitly or learned from a Hekesh), nevertheless a punishment may be given to the Mazik based on a Kal va'Chomer and he may be forced him to pay for the damage he caused, because monetary punishment may be learned from a Kal va'Chomer. It is only physical punishment that may not be learned from a Kal va'Chomer. This is clear from many Gemaras and Mishnayos that derive a monetary punishment through a Kal va'Chomer (see, for example, the Mishnah later on 24b; see also RASHI to Chagigah 11b, DH l'Vito).
There are a number of questions on this principle.
(a) This rule seems to contradict the Mechilta (cited by Tosfos) which teaches that the reason why the Torah writes that a person who "opens a ditch or who digs a ditch" (Shemos 21:33, "v'Chi Yiftach... O Ki Yichreh") is liable is to teach that had it not written explicitly that the digger is liable, he would have been exempt because of "Ein Onshin Min ha'Din" (TOSFOS DH v'Lo)!
(b) The basis (see HALICHOS OLAM 4:12) for the principle of "Ein Onshin Min ha'Din" is that a Kal va'Chomer is based only on logic, and thus it can be refuted by a logical disproof (Pircha). Since a logical disproof can counter the Kal va'Chomer, we can never be absolutely certain that the Kal va'Chomer is correct; perhaps someone later will come and find a logical disproof to the Kal va'Chomer. Therefore, we cannot rely on a Kal va'Chomer to administer a physical punishment but only to derive a prohibition against performing a certain act l'Chatchilah.
According to this logic, a Kol v'Chomer also should not be able to teach a monetary punishment. As long as there is a possibility that the defendant is not liable , he should be exempt from paying based on the claim of "ha'Motzi me'Chaveiro Alav ha'Re'ayah." (SEFER KOVETZ AL HA'RAMBAM, Hilchos Avodas Kochavim 6:4)
ANSWERS:
(a) TOSFOS implies that the Mechilta perhaps disagrees with the Mishnah.
Other Rishonim find this suggestion difficult to accept, since so many Mishnayos seem to take it for granted that a monetary punishment may be administered based on a Kal va'Chomer.
The RASHBA explains that the Mechilta means to say that with regard to Bor, a monetary punishment could not have been derived through a Kal va'Chomer had the verse not stated the punishment. The reason Bor is unique is that the law that a person is liable to pay for the damages caused by his Bor is a Chidush, since the damaged item (such as an ox) brought itself into the Bor, and the Bor did not approach the item and damage it. Also, the Torah teaches that although the Mazik does not own the Bor (for example, the Bor is in Reshus ha'Rabim), he still must pay as though it was his property that did the damage (see later, 29b). Since the law of Bor is a Chidush, one would have thought that a person can be obligated only for what the Torah itself obligates him and no additional obligation may be derived through a Kal va'Chomer; a Chidush of the Torah might not follow the dictates of human logic. (See Moed Katan 7a, Nazir 37a, Chulin 34a.)
The Rashba's point is not clear. It still seems that the Gemara does not agree with the Mechilta, since the Gemara (5b) proposes that the other Nezikin be derived from Bor through a Kal va'Chomer or Binyan Av. Moreover, if the rule of the Rashba is correct, why does the Mishnah and Gemara in Makos (5b) ask that Edim Zomemim should be liable for killing a person because of a Kal va'Chomer (the Gemara cites verses to prove that "Ein Onshin Min ha'Din")? Halachos of Edim Zomemim should be not able to be learned from a Kal va'Chomer because the law of Edim Zomemim is a Chidush (Bava Kama 72a)!
Perhaps the Rashba means that the Mechilta learns from this verse that Bor would have been viewed as a Chidush and no Halachos would have been learned from Bor through a Kal va'Chomer had the Torah not said "Ki Yichreh." Now, however, that the Torah says "Ki Yichreh," it teaches that Bor is to be viewed as the same as other Avos Nezikin (and other Avos Nezikin may be derived from it).
Why, though, does the Mechilta teach what would have been the Halachah in a case of Bor had it been a Chidush, if it is not a Chidush?
The answer is that the Mechilta wants to teach the way the logic of Kal va'Chomer is applied in other cases where a Halachah is indeed a Chidush. Perhaps such a case would be a case of Edim Zomemim who testified about a monetary obligation. The Mechilta would rule that in such a case no punishment may be derived through a Kal va'Chomer, unlike the view of Tosfos (4b, DH v'Edim) whom the Rashba himself cites (5a).
With regard to the Gemara in Makos which says that the rule of "Ein Onshin Min ha'Din" dictates that no punishment may be administered, based on a Kal va'Chomer, to Edim Zomemim who caused a person to be killed, the RITVA there writes that this is not the real reason why no punishment is administered to Edim Zomemim who cause someone to be killed. Rather, the real reason is that Edim Zomemim is a Chidush, and a Kal va'Chomer cannot be derived from a Chidush. The Gemara mentions the rule of "Ein Onshin Min ha'Din" only because its discussion there revolves around Edim Zomemim who caused a person to be killed, in which case it does not need to point out that the law of Edim Zomemim is a Chidush; even if the law of Edim Zomemim would not be a Chidush, no punishment could be given to them because of the rule of "Ein Onshin Min ha'Din." However, even if it is not a matter of corporal punishment but of a monetary obligation, the obligation could not be derived from a Kal va'Chomer because Edim Zomemim is a Chidush.
(b) The SEFER KERISUS (1:17) suggests that the words "Ein Onshin Min ha'Din" as used by the Mechilta mean something completely different from what they normally mean. (This is a common occurrence in the Gemara; see RASHBA to Yevamos 108a, and Nidah 21b.)
The Mechilta means as follows. The Gemara (50a) asks the question of the Mechilta: why does the Torah need to teach that one must pay for damages if he digs a Bor, if the Torah has already taught that one is obligated to pay even if he merely opens a pre-existing Bor? Rebbi Akiva answers that had the Torah taught only that one is obligated for opening a Bor, one might have thought that if one digs a Bor he is obligated to pay for damages even if he covers it with a strong covering. One might have thought that one is exempt from damages caused by his Bor only when he fills up the Bor entirely. The Gemara later (55b) cites a Beraisa that teaches that based on this point, Bor is one of the four things for which the Torah does not require a strong Shemirah, and it lessened the degree of the Shemirah required (one is not required to fill in the ditch but merely to cover it).
This is what the Mechilta means to say. One would have thought that, logically, one who digs a ditch must fill it in and it is not enough to cover it. The Torah says "Ki Yichreh" to teach that "Ein Onshin Min ha'Din" -- a person is not punished in the way that is befitting, according to what he deserves; rather, it suffices for him to cover the pit without filling it in.
(c) The MAHARI KOHEN TZEDEK cited by the Shitah Mekubetzes explains that the Mechilta means to say that a punishment "b'Yedei Shamayim" is not derived through a Kal va'Chomer.
Anyone who harms another person due to negligence, through one of the Avos Nezikin, may also be liable b'Dinei Shamayim (see Rashi to Shemos 21:29). This is why the Torah needs to state explicitly that a person is liable for digging a Bor. Without the verse, however, one would have known the monetary obligation (because of the Kal va'Chomer). (See also TOSFOS to Chulin 115b, DH Mah, who proves that the punishment of Kares cannot be derived from a Kal va'Chomer.)

2b----------------------------------------2b

3) THE "TOLDOS" OF "NEZIKIN"
OPINIONS: The Mishnah (2a) states that there are four "Avos Nezikin," implying that there are also Nezikin which are "Toldos." The Gemara shows that the Toldos of Melachos of Shabbos are "k'Yotzei ba'Hem"; the Toldos are similar to the Avos Melachos. It also shows that the Toldos of Tum'ah are not "k'Yotzei ba'Hem"; the Toldos do not have the same Halachos as the Avos ha'Tum'ah. The Gemara inquires whether the Toldos of Nezikin are similar to the Avos, "k'Yotzei ba'Hem," or not.
If the Toldah is like the Av, then the Halachos of the Toldah are learned from the Av. However, if the Toldah is not like the Av, then what determines its Halachos?
(a) RASHI (DH Hacha Mai; DH Mai Shena Keren; and 3a, DH Mai Shena Regel) explains that the Gemara's question is whether one is obligated to pay for damage when he inflicts it through a Toldah of one of the Nezikin, or whether one is completely exempt from compensating for the damage caused by a Toldah. If Toldos of Nezikin are similar to the Toldos of Tum'ah, then just as the Toldos of Tum'ah are not strong enough to be Metamei the same way as an Av, the Toldos of Nezikin are not strong enough to create an obligation for a person to pay.
If one is not obligated to pay for a Toldah of Nezikin, then in what sense is it a "Toldah"? It is not considered to be a Nezek altogether if one is not obligated to pay for it!
It seems that Rashi means that it is considered a Toldah insofar that one is obligated to prevent such damage from occurring. However, if one does not fulfill his obligation to prevent such damage from occurring and transgresses and causes damage to another person's property, he does not have to pay for it.
It is clear from Rashi that whenever a person damages someone else, or someone else's property, he also transgresses a prohibition, even if he fulfills his monetary obligation to compensate for the damage (or even if he is exempt from monetary obligation). What is the source for this prohibition?
1. RASHI in Gitin (21b) writes that the prohibition to cause damage may be derived from the law that the owner of an Eved is obligated to free his Eved if he damages any of the Eved's Roshei Evarim. This obligation implies that the owner is prohibited from damaging the Eved in the first place. Rashi seems to understands that in any case in which the Torah teaches a monetary obligation, the Torah also prohibits doing the act which causes such an obligation. (The BIRKAS SHMUEL cites RAV CHAIM SOLOVECHIK who suggests that since the Torah says "v'Lo Yishmerenu Be'alav" (Shemos 21:36), teaching that the owner of the ox must pay because he did not guard the ox properly, one may infer that the Torah expects a person to guard his ox properly.)
The KEHILOS YAKOV questions this logic. In the case of Regel, one's animal is simply walking in its normal manner through the marketplace when it causes damage (as the Gemara asks on 19b, "is the owner of the ox obligated to hold on to its tail [so that it does not wag it while walking]?"). One certainly is permitted to allow his ox to walk in its normal manner, and yet the Torah obligates him to pay if his ox does damage while walking.
Others point out that this is exactly why one is exempt from damages caused by Shen and Regel in Reshus ha'Rabim (see ROSH 1:1). When a person walks his ox through a neighbor's field, he indeed must be careful that it not cause damage even in the normal manner of walking.
2. RABEINU YONAH (beginning of Avos) writes that the prohibition to damage another person's property is derived from the Isur of "Lo Sigzol." This is also the implication of the TUR (beginning of CM 378).
It is not clear how the prohibition to cause damage is learned from the prohibition against stealing, since that prohibition is transgressed only when the thief does an act of Kinyan on the other person's property (see Bava Metzia 26b). Perhaps he means that it is learned from a "Mah ha'Tzad" from Lo Sigzol and from the prohibitions of Ona'ah and Rivis (see 61a).
Similarly, the RASHASH in Kesuvos (18a) and the KEHILOS YAKOV (Bava Kama #1) suggest that the prohibition to cause damage is learned from the Mitzvah of Hashavas Aveidah. If one is obligated to return another's property, then one certainly is not allowed to harm another's property.
3. The YAD RAMAH (Bava Basra 26a, #107) writes that the prohibition to damage another's property is learned from "Lifnei Iver Lo Siten Michshol" (Vayikra 19:14) and from "v'Ahavta l'Re'acha Kamocha" (Vayikra 19:18), Mitzvos that teach moral obligations.
(b) The RIF explains that there are some Avos Nezikin for which one must pay Nezek Shalem "Min ha'Aliyah" (Regel, Shen, and Keren Mu'edes), and there are some Avos for which one must pay Chatzi Nezek "m'Gufo" (Keren Tamah). Therefore, the Gemara is asking whether the Toldos of the Avos have the same Halachah as the Av, or whether they have the leniencies found in other Avos.
As the BRISKER RAV (beginning of Hilchos Nizkei Mamon) explains, the Rif was not satisfied with Rashi's explanation, because if a Toldah is completely exempt from liability, then it should not be called a Toldah altogether. Therefore, he preferred to explain that the Gemara's question is whether the Toldah has certain leniencies that the Av does not have.
Why did the Rif need to point out that the Av of Keren Tamah pays Chatzi Nezek? Even if there would be no Av that pays Chatzi Nezek, one still should question whether the Toldos are dealt with more leniently than the Avos and one only needs to pay Chatzi Nezek instead of Nezek Shalem for them?
The ROSH answers that had there been no Av that has these leniencies, one would not have questioned whether the Toldah has original leniencies of its own. Once the possibility that a Mazik must pay in such a manner is found, one may consider the possibility that a Toldah pays in such a manner. (The NACHALAS DAVID offers a similar explanation, although he does not understand this to be the intent of the Rosh.)
(c) The BRISKER RAV interprets the Rif's words differently. He points out from a number of Gemaras and Rishonim that there are times when it seems that a Mazik which is learned from a Binyan Av could be more severe than the Avos from which it was derived. To explain this, he suggests (as the Gemara concludes on 5b) that the Torah did not write the various Avos in order to teach their basic obligation since it is possible to derive the basic obligation for all of them through a Meh Matzinu from Keren and Bor. Rather, the Torah writes the Avos in order to teach the specific leniencies that apply to each one (for example, that one pays Chatzi Nezek for Keren when it is a Tam, that one is exempt for Shen and Regel in Reshus ha'Rabim, that there is no liability for a Bor that damages Adam or Kelim, and that there is no liability for an Esh that damages items that are hidden, "Tamun").
The Brisker Rav suggests that according to this understanding, the specific exemptions and leniencies should apply only to a Mazik that bears the "Shem Av" of the Av for which the leniency was originally given. Therefore, if a Mazik is derived through a Meh Matzinu between Keren and Bor, since it is does not have the title, or "Shem Av," of Keren nor the title of Bor, its laws will be more strict than the laws of both Keren and Bor and it will be liable in all situations.
This, he suggests, is the intention of the Rif. According to the Rif, the Gemara is asking whether the Toldos have the "Shem Av" of their respective Av, and therefore a Toldah of Keren, for example, pays Chatzi Nezek, or whether they do not retain the "Shem Av" and therefore a Toldah of Keren pays Nezek Shalem.