Tractate Kerisos, chapter 4, Mishnah 2. The Mishnah comes to answer the question: if a person committed several transgressions, how many Asham Taluy sacrifices is he obligated to bring? The answer is fundamentally simple - the Asham Taluy takes the place of a regular chatas when a person is uncertain if he became obligated in one. Therefore, if the scenario would have obligated him in one chatas had he definitely sinned, he brings one Asham Taluy; and if it would have obligated him in two chatas offerings, he brings two Asham Taluy offerings, and so on.
The wording of the Mishnah:
"Keshem she'im achal chelev vechelev behe'elem echad eino chayav ela chatas achas, kach al lo hoda shelahen eino mevi ela asham echad" - a person who ate chelev (forbidden fat) twice in one lapse of awareness, unintentionally, brings only one chatas for both eatings, since there was only a single lapse of awareness. The same applies when he ate twice and then it became clear that it was doubtful whether it was chelev or not: just as if he had known with certainty he would bring one chatas for both, so too he now brings one Asham Taluy for both.
"Im haysah yediah beintayim... keshem shehu mevi chatas al kol achas ve'achas, kach hu mevi Asham Taluy al kol achas ve'achas" - if between the two eatings he became aware of the matter (for example, he was warned that there is chelev in the refrigerator), this is not one lapse of awareness but two lapses of awareness. Therefore, just as he would certainly bring a chatas for each individual eating, so too in a case of doubt: he ate one of two pieces where one of them is chelev and he does not know which he ate, he was warned in between, and then again ate one of two pieces and he does not know which he ate - he brings two Asham Taluy offerings, one for each and every one.
"Keshem she'im achal chelev vadam venosar upigul behe'elem echad chayav al kol achas ve'achas, kach al lo hoda shelahen mevi Asham Taluy al kol achas ve'achas" - a person who ate food containing four k'zeisim (olive-sized portions) of four different prohibitions: chelev, blood, nosar (sacrificial meat left over past its time), and pigul, where eating a k'zayis of each carries a penalty of kares, and if done unintentionally requires a chatas. Even though he ate them in one lapse of awareness, he brings four chatas offerings, one for each prohibition. And the same applies in a case of doubt: he had two foods before him, one kosher and one including all these four prohibitions, and he does not know which of them he ate - he brings four Asham Taluy offerings, one corresponding to each chatas he would have been obligated in.
From here the Mishnah moves on to a new topic: a person who knows with certainty that he committed a transgression that obligates him in a chatas, but he does not know which transgression it was. May he, or must he, bring a chatas? Three examples are given for this.
The three examples:
Chelev and nosar: He had two foods before him, one containing chelev and the other nosar, for either of which he would be obligated in a chatas if he ate it unintentionally thinking it was kosher. He ate one of them and does not know if he ate the chelev or the nosar. He knows with certainty that he committed a transgression obligating him in a chatas, but he does not know for which sin he must atone.
His wife who is a niddah and his sister: There were two women with him in the house - his wife who is a niddah and his sister, both of which carry the penalty of kares and, if done unintentionally, a chatas. He "unintentionally sinned with one of them" and does not know with which one. Here the meaning of the term "unintentionally" (shagag) is exact: he thought the woman was permitted to him and did not know she was forbidden. It is worth noting that in the previous Mishnah we addressed the puzzling use of the word "shagag" - and the explanation is that the Mishnah there copied the phrasing from here, as here it is used in its proper context.
Shabbos and Yom Kippur: They fell on consecutive days, such as Yom Kippur falling on Sunday, and a person performed melachah (forbidden labor) during the transition time between them. There are different views regarding the definition of bein hashemashos (twilight), and in fact they can all be reconciled here, but for now we will simply say that bein hashemashos is like the blink of an eye. It turns out that he performed melachah and does not know whether he did it on one side of bein hashemashos or on the other side - meaning whether he desecrated Shabbos or Yom Kippur.
The dispute between Rabbi Eliezer and Rabbi Yehoshua:
Rabbi Eliezer obligates him in a chatas: Since he certainly committed a transgression for which one is obligated in a chatas, he is therefore obligated to bring it.
Rabbi Yehoshua exempts him: He does not bring anything. The source for his view is in the verse "Chataso asher chata bah" - the word "bah" (in it) is extra, and comes to teach us that he must know which sin he committed. And since he does not know which sin he committed, he does not bring a chatas.
And Rabbi Eliezer interprets the words "asher chata bah" for a different matter: that a misasek (one who acts unawares) is exempt. To understand this, we must clarify the distinction:
Shogeg: He performs the action intentionally, but does not intend to violate the halachah.
Misasek: He does one thing, and the forbidden thing happens by itself, and he had no intention whatsoever for the forbidden action itself. For example, one who reaches out his hand to take a book from the shelf, and his elbow bumps into the light switch on the way - there is no intention here to turn on the light.
According to Rabbi Eliezer, everyone agrees that one does not bring a chatas for acting as a misasek, and he learns this halachah from this verse. Because of this, his view remains that one brings a chatas even when a person does not know in which of the two transgressions he stumbled, since the very knowledge that he committed a transgression is what obligates him in a chatas.
The words of Rabbi Yosi:
"Lo nechlaku al ha'oseh melachah bein hashemashos shepatur" - they did not argue about one who performs a labor at twilight, that he is exempt. The third example, of the transition between Shabbos and Yom Kippur, is not included in their dispute at all. The reason: "She'ani omer miktzas melachah asah mehayom umiktzasah lemachar" - for I say that he performed part of the labor today and part of it tomorrow. It makes no difference between the opinions regarding the definition of twilight - whether it belongs to one of the days, to both of them, or to neither of them, and whether it lasts for a while or passes in the blink of an eye. Let us assume that performing the labor takes three seconds: if it began in the last second of Shabbos and continued into the first second of Yom Kippur - such as lifting the object on Shabbos and placing it down the next day on Yom Kippur - it turns out that he did not perform a complete labor either on Shabbos or on Yom Kippur, and he is completely exempt. Therefore, this case does not fit the previous pattern, which entirely deals with scenarios where it is known with certainty that he became obligated in a sin-offering and it is unknown for what he became obligated; here, it is possible that he is not obligated in a sin-offering at all.
"V'al mah nechlaku?" - And about what did they argue?
"Al ha'oseh besoch hayom ve'ein yadua im beShabbos asah im b'Yom HaKippurim asah" - about one who performs a labor during the day, and it is unknown whether he performed it on Shabbos or if he performed it on Yom Kippur. He performed a labor in the middle of the day, and he does not remember on which of the days he performed it. It turns out that he does not know for which of the two days he must bring a sin-offering.
"Al ha'oseh ve'eino yodea me'ein eizo melachah asah" - about one who performs a labor and does not know what type of labor he performed. He knows that he performed a labor and knows that he performed it on Shabbos, but he does not remember whether he planted or harvested. And as we saw earlier, the different labors on Shabbos are considered separate categories of different sins.
In these two cases, "Rabbi Eliezer mechayev v'Rabbi Yehoshua poter" - Rabbi Eliezer obligates and Rabbi Yehoshua exempts. Rabbi Eliezer holds that he brings a sin-offering, since he knows that he became obligated in one, and it makes no difference that he does not know for what he is bringing it; and Rabbi Yehoshua holds that whenever someone does not know for which specific sin he is bringing it, he does not bring a sin-offering at all.
Amar Rabbi Yehudah: "Pater Rabbi Yehoshua af me'asham talui" - Rabbi Yehudah said: Rabbi Yehoshua exempted him even from a conditional guilt-offering. For one might have thought that even though according to Rabbi Yehoshua there is no sin-offering here, since he does not know exactly which sin he committed, he should bring a conditional guilt-offering in its place. Rabbi Yehudah teaches us that this is not the case: the conditional guilt-offering is intended for a case where there is a doubt whether he sinned at all or not, whereas here he certainly sinned, but he just does not know whether it was on Shabbos or on Yom Kippur, and similarly in the other cases we mentioned. Therefore, there is neither a sin-offering here, nor even a conditional guilt-offering.
To summarize: In the first part of the Mishnah, we learned the rule that the number of conditional guilt-offerings follows the number of sin-offerings he would certainly have been obligated in - one lapse of awareness corresponds to one guilt-offering, and awareness in the interim or a multiplicity of prohibitions corresponds to a multiplicity of guilt-offerings. In the second part, we discussed the three cases where he certainly sinned but it is unknown what he sinned with: chelev and nosar, his wife who is a niddah and his sister, and Shabbos and Yom Kippur. Rabbi Eliezer obligates a sin-offering and expounds "asher chata bah" (in which he sinned) to exempt one who acts unawares (mis'asek), and Rabbi Yehoshua exempts and expounds "bah" - that he must know in what he sinned. Rabbi Yosi removed from the dispute the case of one who performs a labor at twilight, who is exempt for the reason that "he performed part of the labor today and part of it tomorrow," and he established the dispute in the case of one who performs it during the day and does not know on which day or which labor. And Rabbi Yehudah added that Rabbi Yehoshua exempts in these cases even from a conditional guilt-offering.