Bava Kamma, Chapter 2, Mishnah 5. Many people struggle with this Mishnah, even though in truth it is not a difficult Mishnah at all; and if people do struggle with it, the fault lies with the teacher. As Rabbi Noach Orlowek used to say: "A genius is someone who thinks slowly, fast." There is no need to be a genius - it is enough to think slowly and methodically throughout the Mishnah, and things will become properly clear. It is highly recommended to get a piece of paper and a pencil and draw a simple diagram to illustrate the concepts (exactly what to write down will be detailed later), and therefore it is proper to study this Mishnah with a settled mind, sitting at a table.
The Thirteen Principles by Which the Torah is Expounded:
The central topic of the Mishnah is the kal vachomer and its rules. We have a tradition that the Torah was written in a way that it can be expounded upon, meaning that new halachos can be derived from it using thirteen tools. There are varying opinions among the Sages regarding the exact count of these principles, but we hold that there are thirteen. The thirteen principles by which the Torah is expounded are an inseparable part of the tradition, and therefore a tradition is required in order to use these tools.
For this reason, already from the period of the Mishnah and the Talmud, drashos are no longer made using the thirteen principles. For example, in the book of Bamidbar 30:2, it appears that Rashi makes a drashah, and the Mizrachi wonders about this, stating explicitly that even the Geonim no longer made drashos. The matter remains, therefore, within the exclusive domain of the Tannaim.
Kal Vachomer: A Rule, Not Logic:
"Kal" means light, less severe and less strict, and "chomer" means heavy and more strict. One should not think that a kal vachomer is pure logic. This is not to say that it lacks logic - it does not contradict the rules of logic - but it is not dictated by strict logic. Rather, it is an independent set of rules, like a decoder ring that Hashem gave us to decipher halachos from the Torah.
When the Sages speak of logic in contrast to the principle of kal vachomer, they are referring to a 'kal shechen' (all the more so). For example: if one can lift a hundred-pound goat, kal shechen that they can lift a fifty-pound goat, since it weighs less. The 'kal shechen' can work in both directions: if a fifty-pound goat stepping on one's toe will break it, kal shechen that a hundred-pound goat will break it. However, this is logic, and this is not what is discussed in our Mishnah. The kal vachomer that we are dealing with is guided by a set of principles handed down to us through tradition.
How Kal Vachomer Works:
A kal vachomer comes to teach a new halachah that is not explicitly stated in the Torah. We have two halachic phenomena, A and B. If it can be shown that A is always lenient, or at least always lenient in matters relevant to the question at hand, while B is always strict relative to A, or at least strict in matters relevant to the discussion, then if a certain stringency applies to A - kal vachomer that it will apply to B. In this way, we derive a new halachah from the Torah, that B is also as strict as A. This also works in the opposite direction: if we found a leniency in B, we can say that kal vachomer it will also apply to A. And again it must be emphasized: a tradition is required in order to expound this drashah.
It is worth noting that even though these drashos have the validity of a drashah, punishments are not administered based on laws learned through a kal vachomer and the like, the way punishments are administered based on an explicit verse. Regardless, we have sources showing that a kal vachomer is a valid tool in the Torah, and the Baraisa lists ten different times where it appears in Tanach. We will bring one of them, which relates directly to our discussion.
In the book of Bamidbar, Chapter 12, Miriam was struck with tzaraas for speaking lashon hara about Moshe, and she was told to leave the camp for seven days, and the nation waited for her. The Holy One, Blessed be He, says to Moshe Rabbeinu explicitly: "Ve'aviha yarok yarak bepaneha halo tikalem shivas yamim" - if her father had spit in her face, she would surely be shamed for seven days, and therefore "Tisager shivas yamim michutz lamachaneh" - she shall be shut out of the camp for seven days, and afterward she shall be brought in.
Here we have a kal vachomer in a situation where the halachah is unknown: what is the law for someone in whose face the Holy One, Blessed be He, spits, as it were, by bringing tzaraas upon them, as He did to Miriam? To this we say: since if a flesh-and-blood father had spit in her face she would have had to be shamed for seven days, all the more so should she be shamed for seven days, meaning she should be shut out of the camp, when the Holy One, Blessed be He, spits in her face.
The Principle of 'Dayo':
One of the rules that applies to a kal vachomer is the principle of 'dayo'. The literal meaning of the word "dayo" is 'enough' or 'sufficient', and the name 'dayo' is simply an abbreviation for the full expression that appears explicitly in our Mishnah: "Dayo lavo min hadin lihyot kanadon" - it is sufficient for the newly derived law to be like the source from which it is derived. "Din" is the newly derived rule, and "nadon" is the subject from which we learn (in the passive nifal form, similar to mashal and nimshal).
The meaning of the rule: One who derives a law from a known given to an unknown case cannot receive more in the new law than what was in the source. He is quantitatively limited by the source itself. An example of this is the story of Miriam, which is the source in the Torah for the principle of 'dayo'. After all, being disgraced by the Holy One, blessed be He, is more humiliating than being disgraced by a mortal father, and there was room to say: If seven days are required to recover from the humiliation of a father spitting in public, fourteen days should be required to recover from the spitting of one's Father in Heaven, as it were. Nevertheless, the verse says: Just as with her father's spitting it is seven days, so too with My spitting it is seven days. Even though the severity is greater, we do not add to the seven, since the foundation upon which the rule is built is quantitatively limited to a period of seven days. This is 'dayo': We do not deviate beyond the given from which we learn, and we do not increase the quantity.
The Dispute at the Foundation of the Mishnah:
Everyone agrees that there is a principle of kal vachomer, and everyone agrees that there is a rule of 'dayo'. However, they dispute a case where applying the rule of 'dayo' completely nullifies the kal vachomer, to the point that it is left with no application at all:
According to Rabbi Tarfon: In a place where 'dayo' would completely nullify the kal vachomer, we do not apply the rule of 'dayo'. That is to say, 'dayo' can limit, but it cannot empty the kal vachomer of its content.
According to the Sages: We apply 'dayo' in every case, and if this means that no kal vachomer remains at all - so it shall be determined.
The Halachic Background to the Mishnah:
The Mishnah deals with the payments required when a person's animal causes damage through the category of keren (goring), about which the verse states that one pays half damages. The verse does not specify whether this means half damages in the public domain or in the injured party's domain; due to its complexity we will not enter into the wording of the verse itself, but it is clear that it does not specify the location.
In contrast, with shen (eating) and regel (trampling) we distinguish between the domains: If the damage occurred in the public domain, a place where the animal's owner is permitted to be, he is exempt; whereas if it occurred in the injured party's domain, on his private property, the one responsible for the animal is obligated to pay for all damages of shen and regel. Here we have two different domains with two different laws.
What is the law of keren in the injured party's domain? We know that there is a payment of half damages for keren, but we do not know if the law is identical in both domains, or whether in the basic case of the public domain it is half damages and in the injured party's domain it is more than that. And as you may recall, in Chapter 1, Mishnah 4, the five ways in which there can be a mu'ad (forewarned) liability for an animal were listed, and the fourth of them is "an ox that damages in the injured party's domain" - meaning that if a person's ox caused damage on the private property of the injured party, even through keren, he pays full damages. As was noted there, this is the view of Rabbi Tarfon, which is subject to dispute and the halachah does not follow him, and here before us is the dispute itself.
The Text of the Mishnah:
"Shor hamazik birshut hanizak keitzad" - how does this case work, that if a person's ox caused damage in the private domain of the injured party, the damager, who is responsible for the animal, is obligated to pay full damages. "Nagach, nagaf, nashach, ravatz, ba'at" - five ways:
"Nagach" - gored with its horns.
"Nagaf" - shoved with its body.
"Nashach" - bit with its teeth.
"Ravatz" - lay down upon it to break it.
"Ba'at" - kicked with its legs.
"Bereshus harabbim - meshalem chatzi nezek" - in the public domain, it pays half damages. As the verse states, the damager pays half of the damage caused. "Uvereshus hanizak - Rabbi Tarfon omer: nezek shalem" - and in the domain of the injured party, Rabbi Tarfon says: full damages. Rabbi Tarfon holds that in the private domain of the injured party, the payment is full, as he stated in Chapter 1, Mishnah 4. "Vachachamim omrim: chatzi nezek" - and the Sages say: half damages. The Sages disagree and hold that there is no difference between the public domain and the domain of the injured party; in both cases, the liability for horn damages, since it is not the animal's normal behavior to cause damage and it is a docile ox, is only half damages.
The Chart:
To understand the rest of the Mishnah, it is highly recommended to draw a two-by-two chart (actually three-by-three, to include the row and column headers):
The Rows: the public domain, and the domain of the injured party.
The Columns: foot and tooth, and horn.
Above the columns, we can write: foot and tooth are the lenient case (the "kal" in the kal vachomer equation), and horn is the strict case (the "chomer"), the more severe scenario. Now, let us fill in the four boxes:
The public domain - tooth and foot: zero percent, since one is exempt for tooth and foot damages caused by his animal in the public domain.
The public domain - horn: fifty percent, since everyone agrees that for horn, one pays half damages in the public domain.
The domain of the injured party - tooth and foot: one hundred percent, full damages.
The domain of the injured party - horn: the empty box. The verse is not explicit on this matter, as it merely states half damages and does not differentiate between domains.
From here we see that horn is the strict case: in the public domain, one pays half damages for it, whereas for tooth and foot, one pays nothing at all. Indeed, this is the general rule everywhere - horn is more severe in this respect.
Rabbi Tarfon argues that it makes sense for there to be two different laws, one in the public domain and one in the domain of the injured party, since this concept is already established for tooth and foot, which have two domains and two payment arrangements, with the domain of the injured party being far more severe. The reason is understandable: my animal has the right to walk in the street, and if it overturns a potato cart there, it is the public domain and I am permitted to be there; however, if my animal enters your courtyard and tramples your cart there, you can rightly argue: what is your animal doing in my courtyard? Therefore, it is logical that the liability in the private domain of the injured party, a place where you have no right whatsoever to let your animal roam, is more severe.
Rabbi Tarfon's Kal Vachomer:
The question, therefore, is what the law is regarding horn in the domain of the injured party. If my cow entered your courtyard and began goring your animals, is the payment half damages or more than that? Rabbi Tarfon argues that it is more than that, based on a simple kal vachomer (a fortiori inference): if tooth and foot are more lenient than horn - as we see in the row for the public domain, zero percent for tooth and foot compared to fifty percent for horn - and yet in the domain of the injured party one is liable for one hundred percent for tooth and foot, certainly for horn it should also be one hundred percent, since its law cannot possibly be more lenient than theirs.
As the Mishnah states: "Amar lahem Rabbi Tarfon: umah makom sheheikal al hashen veal haregel bereshus harabbim - shehu patur" - Rabbi Tarfon said to them: if in a place where it is lenient regarding tooth and foot in the public domain - that he is exempt. In the row for the public domain, in the column for tooth and foot, the liability is zero. "Hechmir alav bereshus hanizak leshalem nezek shalem" - it was strict upon him in the domain of the injured party to pay full damages. And in the row below it, for the domain of the injured party, the Torah was strict to the point of requiring the payment of full damages. "Makom shehechmir al hakeren bereshus harabbim" - in a place where it was strict regarding the horn in the public domain. And in the column for horn in the public domain, we already have fifty percent. "Eino din shenachmir alav bereshus hanizak leshalem nezek shalem" - is it not logical that we should be strict upon him in the domain of the injured party to pay full damages? Is it not logical that we should be strict regarding horn in the domain of the injured party to pay full damages as well? According to this reasoning, we must write one hundred percent in the empty box at the intersection of the domain of the injured party and horn.
The Sages' Response - The Principle of Dayo:
The Sages reject this. Draw a pencil arrow going down from the fifty percent in the box for Horn in the public domain to the new box below it. The Sages say: You want to apply the fifty from Horn in the public domain to Horn in the injured party's domain, but we have the principle of Dayo that limits you. It is impossible to go up from fifty to a hundred. Indeed, it makes sense to be more stringent in the injured party's domain, but up to what point? Not beyond fifty, which is the foundation from which you are learning. Just as when Hashem spat in Miriam's face, as it were, we limit it to only one week, even though the severity is greater than her father spitting - so too here.
And in the words of the Mishnah: "Amru lo: dayo lavo min hadin lihyos kanidon" - it is sufficient for the derived law, which is the empty box of Horn in the injured party's domain, to be quantitatively equal to the source from which you are learning. And since Horn in the public domain pays half damages, it is impossible to increase it through a kal vachomer beyond half damages in the injured party's domain; the arrow going down from the fifty is limited to fifty. "Mah birshus harabim chatzi nezek - af birshus hanizak chatzi nezek" - just as in the public domain it is half damages, so too in the injured party's domain it is half damages.
Rabbi Tarfon's Rejection:
Rabbi Tarfon rejects this, because in his view Dayo limits the kal vachomer only in a case where it does not completely nullify it. And here, argues Rabbi Tarfon, we already know from the verse that there is half damages for Horn, and even though the verse does not explicitly state where this applies, even without any additional derivation - without a kal vachomer and without any other exegesis - we would know that in the injured party's domain he is liable for fifty percent, half damages, because that is what the verse says. The entire intent of the kal vachomer is that there are two different domains here that warrant different laws, and if we apply Dayo and limit it to fifty - no substance is left to the kal vachomer, since the fifty was already known beforehand. Therefore, Rabbi Tarfon holds, we do not apply Dayo in such a case, and we are not limited, and we learn the full one hundred percent. The Sages, on the other hand, disagree and hold that Dayo is valid at all times, and if this means that there is no kal vachomer here at all - we will not learn the law of Horn in the injured party's domain, and so it shall be established.
Rabbi Tarfon's Second Attempt:
Rabbi Tarfon is not satisfied with this. According to his approach, it was indeed difficult, because in his opinion Dayo does not belong here at all, but now he wants to convince the Sages that even according to their approach Dayo does not limit the kal vachomer. His claim: The diagram was drawn incorrectly. We are not talking about an arrow going down from the fifty to the box of Horn in the injured party's domain, but rather an arrow stretched horizontally - from the one hundred percent of Tooth and Foot in the injured party's domain to Horn in the injured party's domain. When the arrow comes from the hundred and does not go down from the fifty, we learn from a hundred to a hundred: I do not seek to decrease and I do not seek to increase. Tooth and Foot in the injured party's domain are full damages, and Horn is more severe than them, and if so, it is impossible for Horn in the injured party's domain to be less than one hundred percent.
And in the words of the Mishnah: "Amar lahem: lo, im amartem bekeren birshus harabim... ani adun keren meregel" - I am not deriving Horn from Horn, meaning I am not learning Horn in the injured party's domain from Horn in the public domain and I am not stretching the arrow downward from the fifty to make it a hundred, but rather I am deriving Horn from Foot, and stretching the arrow horizontally, to learn Horn from Tooth and Foot. "Umah makom sheheikal al hashen veal haregel birshus harabim" - for we have established that in the public domain the Torah was stringent regarding Horn and lenient regarding Tooth and Foot, since they are exempt and Horn pays half damages. "Makom shehichmir al hashen veal haregel" - in the injured party's domain, where one pays one hundred percent for Tooth and Foot, "eino din shenachmir bekeren" - is it not logical that we should be stringent regarding Horn, that at the very least the same liability of one hundred percent, full damages, which applied there to Tooth and Foot, should also apply to Horn? Thus, Dayo does not hinder us, because I am not seeking to go beyond a hundred, and quantitatively we remain where we were: the lenient one, Foot and Tooth in the injured party's domain, is a hundred - and the severe one too, Horn in the injured party's domain, is a hundred.
The Sages' Second Response:
The Sages reply that the principle of Dayo does not only limit the final result, ensuring that the derived law is not quantitatively greater than its source, but it also limits the foundations upon which the kal vachomer is built and the assumptions you make within it. For how do you know that Horn is more severe than Tooth and Foot? From the fact that in the public domain there is half damages for Horn while Tooth and Foot are exempt. If so, all you know is that the concept of half damages exists for Horn, and you have no basis for knowing about full damages. And since the starting point that you introduced into the proof that Horn is more severe is nothing but half damages, it is impossible to extract a full payment from it now. It turns out that Dayo limits not only the result from increasing quantitatively, but even the data entered as the basis of the proof and as the principles from which the kal vachomer is constructed.
And this is what they said: "Dayo lavo min hadin lihyos kanidon" - you are limited. Since you want to learn Horn in the injured party's domain, and the only starting point we have is that Horn is more severe than Tooth and Foot because of the half damages payment in the public domain, you are limited to half damages. "Mah birshus harabim chatzi nezek - af birshus hanizak chatzi nezek" - just as all we know is a payment of half damages in the public domain, so too you cannot say anything in the injured party's domain other than half damages.
In summary: In this Mishnah we have focused on the method of kal vachomer, which is not merely logic but one of the principles of exegesis handed down in the tradition, and on the principle of Dayo - "Dayo lavo min hadin lihyos kanidon" - which is learned from the episode of Miriam. From here Rabbi Tarfon and the Sages debated whether we apply Dayo when it completely nullifies the kal vachomer, and regarding the specific case of Horn in the injured party's domain. The halachah follows the Sages: for Horn one pays half damages, whether in the public domain or in the injured party's domain, as long as the ox is a tam; and if it was made a mu'ad - full damages. Therefore, the halachah does not follow the list of five in Chapter 1, Mishnah 4, because only four of the five are mu'ad, and in the fourth case among them - Horn in the injured party's domain - the halachah is not like Rabbi Tarfon but like the Sages, and it is only half damages.