We now come to chapter 1, mishnah 3. The Mishnah seeks to define which types of rulings of the Sanhedrin fall into the category of cases that obligate a par he'elem davar shel tzibbur, and which rulings - even though they are mistaken - carry no obligation at all.
The basic principle:
In principle the Mishnah establishes that an error concerning the plain reading of a verse does not fall into this category. We are speaking of the kind of mistake that any schoolchild, or any Sadducee who opens the Tanach and reads the verses at face value, would immediately spot and say: "It doesn't say that, it says this, in black and white." Such an error does not count. It is essential that the error be in part and not in the whole, and therefore it must be an interpretation that is not spelled out in the verse, to the point that even a Sadducee reading the verses as they are, without the tradition, would not know that this is a mistaken reading. This is the Mishnah's understanding, even though its wording does not state it explicitly.
The exempt cases - uprooting an entire parashah:
If the Sanhedrin issued a ruling that does not recognize an entire parashah and an entire mitzvah of the Torah, saying "this is no mitzvah at all, there is no problem here":
"Ein niddah baTorah" - there is no such thing as the prohibitions of niddah, and there is no need to be concerned with the menstrual cycle.
"Ein Shabbos baTorah" - there is no prohibition of melachah on Shabbos at all.
"Ein avodah zarah baTorah" - the Torah contains no prohibition against idol worship.
Concerning all of these the Mishnah says: "Harei eilu peturin" - these are exempt. It is indeed possible that they issued such a preposterous ruling, but the beis din is exempt from bringing a par he'elem davar, and even if most of the Jewish people acted according to that ruling. The basis of the exemption rests on the verse: "V'ne'elam davar" - a matter, meaning that something was hidden from them, but not everything, not the entire package of a given mitzvah.
The cases that obligate - an error in part:
If they ruled that part of the mitzvah must be kept and part of it may be disregarded, and afterwards they retracted and said: "We erred, that part may not be disregarded," and in the meantime the community transgressed a sin that carries the punishment of kareis - they bring a par he'elem davar. How so?
Niddah: They said that there are indeed restrictions in the laws of niddah, but that a woman who is a shomeres yom keneged yom is not included in them.
To understand this: a woman who sees blood begins a new cycle, and for the following seven days she is a niddah by Torah law, whether she is bleeding or not. After seven days, as long as the bleeding has stopped and she immerses in a mikvah, she is tahor and there is no need to wait any longer. But between the eighth day and the eighteenth, if new blood appears, she must be concerned that she has become a zavah: if she saw blood for one day or two, she needs one full clean day without seeing blood - this is the law of shomeres yom keneged yom; and if she saw three consecutive days of blood, she becomes a zavah gedolah. Seeing blood on the nineteenth day is the beginning of a new niddah period.
It emerges that if they ruled that there is no concept at all of shomeres yom keneged yom - this is a classic case of an error that obligates a par he'elem davar.
Shabbos: They said "Yesh Shabbos baTorah" - there is such a thing as Shabbos, but "hamotzi mereshus hayachid lireshus harabbim patur" - carrying an object from a private domain to a public domain is permitted. This is only part of the mitzvah, and therefore they would be obligated in a par he'elem davar shel tzibbur if most of the people acted on that mistaken ruling.
Avodah zarah: They said "Yesh avodah zarah baTorah" - there is a prohibition and one may not worship idols, but "hamishtachaveh patur" - bowing down to an idol is permitted.
It should be emphasized that in all of these cases, when it says "patur," the intention is exempt and permitted, that one is allowed to do so. Concerning all of these the Mishnah says: "Harei eilu chayavin" - these are obligated, as it says "V'ne'elam davar" - a matter and not the entire body of the mitzvah, something and part of it, but not the whole thing.
The Gemara's precision in the three cases:
As stated, the criterion the Gemara established is that the mistake must be of a type that a Sadducee would not necessarily dispute, meaning something that is not spelled out in black and white in the verses. Now, in each of these cases there are hints in the verses that the Beis Din certainly knows, and therefore we must pinpoint exactly what their mistake was:
Regarding niddah: The law of shomeres yom k'neged yom is hinted at in the verse "V'safrah lah" - that she must count a day, and there is an explicit reference here to counting. However, the verse says "kol y'mei zovah" - all the days of her flow, and therefore they might have ruled that blood during the day is a problem while blood at night is not. A Sadducee would have no objection to this, since it says "y'mei" - the days and not the nights. If the Beis Din ruled that blood at night is not a problem, and the people acted according to this ruling, this is a case of par he'elem davar.
Regarding Shabbos: There is a verse that says "Al yeitzei ish mimkomo" - let no man leave his place, and although it truly speaks about the Shabbos boundary and restrictions on walking, it also includes carrying objects along with the person. Therefore, had they ruled that it is permitted to transfer from a private domain to a public domain, the Sadducee would respond: "No, there is a law here of let no man leave his place." You are forced to say that the case involves a person who does not leave his place, such as one who threw an object from a private domain, or who extended his hand and transferred it - moshit - from a private domain to a public domain. If they ruled that this is permitted when in fact it is not, and the people acted accordingly, this is a par he'elem davar.
Regarding avodah zarah: At first glance this is puzzling, since bowing to idols is explicitly forbidden in the verses: "Lo sishtachaveh l'el acher" - you shall not bow to another god. The answer is that the bowing spoken of in the verse refers to what is called spreading out one's hands and feet, where the person is stretched out entirely on the ground with his hands and feet spread out on the floor - and that no one could permit. But if they ruled that bending from the waist alone, or bowing without spreading out the feet but only the hands, is permitted - it is not permitted, and if the people acted according to their ruling, this is the case in which they would be liable to bring a communal par he'elem davar.
In summary: In this Mishnah we learned that a ruling which uproots an entire mitzvah of the Torah exempts from par he'elem davar, as it says "V'ne'lam davar" - a matter, and not the entire body of the mitzvah; whereas a ruling that uproots only part of a mitzvah obligates. We examined the three examples - niddah, Shabbos and avodah zarah - and the Gemara's precision, that the mistake must be in something not spelled out in the verses, to the point that even a Sadducee who reads the text at face value would not detect an error in it.