(8) Incidental to the Festival peace-offering, the mishna describes the nature of various areas of Torah study. The halakhot of the dissolution of vows, when one requests from a Sage to dissolve them, fly in the air and have nothing to support them, as these halakhot are not mentioned explicitly in the Torah. There is only a slight allusion to the dissolution of vows in the Torah, which is taught by the Sages as part of the oral tradition. The halakhot of Shabbat, Festival peace-offerings, and misuse of consecrated property are like mountains suspended by a hair, as they have little written about them in the Torah, and yet the details of their halakhot are numerous. The details of monetary law, sacrificial rites, ritual purity and impurity, and the halakhot of those with whom relations are forbidden all have something to support them, i.e., there is ample basis in the Torah for these halakhot, and these are the essential parts of Torah.

All the commandments of the Torah, whether they be operational precepts or prohibitory precepts; they are not revealed, and known, and explicated, except through the Oral Torah. For instance, the prohibitory precept that was said with respect to Shabbat—“You shall do no work”: it does not explain what is regarded as work. In the Oral Torah, however, it is explicated to refer to the well known 39 forms of work and not to the carrying of stones or heavy beams. And as it is with these, so it is with all the commandments, whether they be operational precepts or prohibitory precepts: they are indistinct and are explicated, revealed, and known only through the Oral Torah. That is why Scripture says of the Oral Torah: “And you shall not cast off the teaching of your mother,” as stated in the Zohar. Metaphorically speaking, just as all the limbs of the child are included, in great concealment, in the sperm of the father, and the mother brings this out into a state of manifestation [when giving birth to a child that is whole, with 248 limbs and 365 sinews], so, in precisely like fashion, the 248 operational precepts and the 365 prohibitory precepts emerge from concealment to manifestation through the Oral Torah.

Why do I need a verse to derive this? It is based on logical reasoning

(7) Rabbi Joshua said: I have received a tradition from Rabban Yohanan ben Zakkai, who heard it from his teacher, and his teacher [heard it] from his teacher, as a halakhah [given] to Moses from Sinai

As it is taught in a mishna (Sanhedrin 21a) concerning the mitzvot of a king: “And he should not multiply wives for himself, that his heart not turn away” (Deuteronomy 17:17). Rabbi Yehuda says: He may accumulate many wives for himself, provided that they are not like those who turn his heart from reverence for God. Rabbi Shimon says: Even one who turns his heart away, he should not marry her. If so, why is it stated: “He shall not multiply wives for himself”? This teaches that even with regard to wives like Abigail, who was righteous and prevented David from sin (see I Samuel chapter 25), he is forbidden to have many. In this case, Rabbi Shimon does not interpret the rationale of the verse, while Rabbi Yehuda does interpret its rationale. The Gemara answers: Actually, Rabbi Yehuda does not generally interpret the rationale of the verse, and it is different here, with regard to a king, as the verse itself specifies the reason: “And he should not multiply wives for himself, that his heart not turn away.”

(4) You shall not muzzle an ox while it is threshing.

The Sages raised a dilemma before Rav Sheshet: If the animal was eating from the produce it was threshing, and it was excreting diarrhea [matrezet], what is the halakha? The Gemara explains the sides of the dilemma: Is the reason that one must let the animal eat because the food is good for it, and this produce is evidently not good for it, and therefore the animal should be muzzled to prevent it from harm? Or perhaps the reason for the prohibition against muzzling is that it sees food and suffers when it cannot eat, and this one also sees food and suffers when it cannot eat.

Hillel expounded seven rules before the elders of Beteira: (1) kal va-chomer [a fortiori reasoning; i.e., drawing an inference from a more lenient case to a stricter one] (2) and gezeira shava [deriving a law from one case to another due to the same word root being used in both verses] (3) and binyan av ve-katuv echad [inferring a global principle from one verse] (4) and binyan av u-shnei ketuvim [inferring a global principle from two verses] (5) and kelal u-frat u-chlal: [a general statement followed by a particular case and then by another general statement] (6) and kayotzei bo mi-makom acher [something similar in a different place] (7) and davar ha-lameid me-inyano [something learned from its context]. These are the seven rules that Hillel the Elder expounded before the elders of Beteira.

(14) But GOD said to Moses, “If her father spat in her face, would she not bear her shame for seven days? Let her be shut out of camp for seven days, and then let her be readmitted.”

Rabbi Yoḥanan said in the name of Rabbi Shimon ben Yehotzadak: There is a verbal analogy between the festivals of Passover and Sukkot. It is stated here, with regard to Sukkot: “On the fifteenth day of this seventh month is the festival of Sukkot for seven days unto the Lord” (Leviticus 23:34). And it is stated: “And on the fifteenth day of the same month is the festival of matzot unto the Lord” (Leviticus 23:6) with regard to the festival of Passover. Just as there, with regard to Passover, on the first night there is an obligation to eat matzaand from that point onward it is optional, as from that point onward the only obligation is to refrain from eating leaven, so too here, with regard to Sukkot, on the first night there is an obligation to eat in the sukkaand from that point onward it is optional.

An item for lying down (mishkav) differs from an item for sitting (moshav), and an item for sitting differs from an item for lying down. The common denominator between them: that they are implements made only for a person’s comfort …so too, [only] implements that are made only for a person’s comfort are rendered impure should a zav [use the implement to support] most of his [weight]…this excludes a tarkav [a large measuring instrument], which is made for carrying something else [for measuring, rather than for carrying a person in comfort].

(2) Command the Israelite people to bring you clear oil of beaten olives for lighting, for kindling lamps regularly. (3) Aaron shall set them up in the Tent of Meeting outside the curtain of the Pact [to burn] from evening to morning before GOD regularly; it is a law for all time throughout the ages.

(2) Instruct the Israelites to remove from camp anyone with an eruption or a discharge and anyone defiled by a corpse. (3) Remove male and female alike; put them outside the camp so that they do not defile the camp of those in whose midst I dwell.

(20) If anyone who has become impure fails to undergo cleansing, that person shall be cut off from the congregation for having defiled GOD’s sanctuary. The water of lustration was not dashed on them—they are impure. (21) That shall be for them a law for all time. Further, whoever sprinkled the water of lustration shall wash their clothes; and whoever touches the water of lustration shall be impure until evening.

3b) binyan av mishnei kethuvim (a general rule derived from two verses). viz.: The topic of the lamps (on the menorah) is not like that of sending the unclean outside (of the encampment), and the latter is not like the former. What is common to them is that they are introduced by "Tzav" ("Command") — [the lamps, (Vayikra 24:2); sending, etc., (Bamidbar 5:2)] — and apply both immediately and for future generations. [The lamps: immediately — (Bamidbar 8:3): "And Aaron did so. He kindled its lamps towards the face of the menorah, etc."; for future generations — (Vayikra 24:3): "… an eternal statute throughout your generations." Sending the unclean outside: immediately — (Bamidbar 5:4): "And the children of Israel did so, and they sent them outside the camp"; for future generations — (Bamidbar 19:21): "And it shall be for them an everlasting statute."] So, all commandments introduced by "Tzav" apply both immediately and for future generations.

(26) and spend the money on anything you want—cattle, sheep, wine, or other intoxicant, or anything you may desire. And you shall feast there, in the presence of the ETERNAL your God, and rejoice with your household.

"And you shall give the money for all that your soul desires" — general; "of herd, flock, wine, and strong drink" — specific; "and for all that your souls asks" — reversion to the general: general-specific-general — ē ata dan ela ke'ein haprat (the rule is in accordance with the specific), viz.: Just as the specific is: one fruit from another, (e.g., wine from grapes), originating from the earth, so, everything of this nature is purchasable with ma'aser money) — to exclude mushrooms and truffles (which, although they are fruit, do not come from another fruit).

A certain heretic said to Berurya: It is written: “Sing, barren woman who has not given birth, open forth in song and cry, you did not travail, for more are the children of the desolate than the children of the married wife, said the Lord” (Isaiah 54:1). Because she has not given birth, she should sing and rejoice? Berurya responded to this heretic’s mockery and said: Fool! Go to the end of the verse, where it is written: “For the children of the desolate shall be more numerous than the children of the married wife, said the Lord.”Rather, what is the meaning of: “Sing, barren woman who has not given birth”? It means: Sing congregation of Israel, which is like a barren woman who did not give birth to children who are destined for Gehenna like you.

a person may derive an a fortiori inference on his own, i.e., even though he was not taught that particular logical argument by his teachers, a person may not derive a verbal analogy on his own

...One is not allowed to interpret on one’s own using any of the thirteen middot by which the Torah is expounded except for kal va-chomer.

...It is explained in Rashi… One is not allowed to interpret on one’s own using any of the thirteen middot by which the Torah is expounded except for kal va-chomer, and this is very puzzling…rather, a person may apply all of the middot on his own aside from gezeira shava, which a person may not apply except if he learned it from his teacher.

The first division are explanations transmitted from the mouth of Moshe and they have a hint in Scripture and it it possible to extrapolate them by way of reasoning...

The third division are the laws that they extrapolated by the ways of reasoning...

Rabbi Ḥiyya bar Ashi said that Rav said: The measures relating to mitzvot in the Torah, and the halakhot governing interpositions that invalidate ritual immersions, and the halakhot of partitions are all halakhot transmitted to Moses from Sinai. These halakhot have no basis in the Written Torah, but according to tradition they were orally transmitted by God to Moses together with the Written Torah. The Gemara questions this assertion: Are measures a halakha transmitted to Moses from Sinai? They are written in the Torah, as it is written: “A land of wheat, and barley, and vines, and figs, and pomegranates, a land of olive oil and honey” (Deuteronomy 8:8), and Rav Ḥanan said: This entire verse was stated for the purpose of teaching measures with regard to different halakhot in the Torah. Wheat was mentioned as the basis for calculating the time required for one to become ritually impure when entering a house afflicted with leprosy, as that which we learned in a mishna: One who enters a house afflicted with leprosy of the house (see Leviticus 14), and his clothes are draped over his shoulders, and his sandals and his rings are in his hands, both he and they, the clothes, sandals, and rings, immediately become ritually impure. However, if he was dressed in his clothes, and his sandals were on his feet, and his rings were on his fingers, he immediately becomes ritually impure, but they, the clothes, sandals, and rings, remain pure until he stays in the house long enough to eat half a loaf of bread. This calculation is based on wheat bread, which takes less time to eat, and not on barley bread, and it relates to one who is reclining and eating it together with relish, which hastens the eating. This is a Torah measurement connected specifically to wheat. Barley is also used as a basis for measurements, as we learned in a mishna: A bone from a corpse the size of a grain of barley imparts ritual impurity through contact and by being carried, but it does not impart impurity by means of a tent...Rather, they are halakhot that were transmitted to Moses from Sinai, and the Sages based them on verses in the Torah.

Rav Yehuda says that Rav says: When Moses ascended on High, he found the Holy One, Blessed be He, sitting and tying crowns on the letters of the Torah. Moses said before God: Master of the Universe, who is preventing You from giving the Torah without these additions? God said to him: There is a man who is destined to be born after several generations, and Akiva ben Yosef is his name; he is destined to derive from each and every thorn of these crowns mounds upon mounds of halakhot. It is for his sake that the crowns must be added to the letters of the Torah. Moses said before God: Master of the Universe, show him to me. God said to him: Return behind you. Moses went and sat at the end of the eighth row in Rabbi Akiva’s study hall and did not understand what they were saying. Moses’ strength waned, as he thought his Torah knowledge was deficient. When Rabbi Akiva arrived at the discussion of one matter, his students said to him: My teacher, from where do you derive this? Rabbi Akiva said to them: It is a halakha transmitted to Moses from Sinai. When Moses heard this, his mind was put at ease, as this too was part of the Torah that he was to receive.

The second luchot were more esteemed than the first…and the intent in all of this is that with the first luchot, the power of innovation was not given. Rather, Moshe received the meaning of the details in the verses and halachot and the like, but not [the power] to innovate halachot through the thirteen middot, and similarly Talmudic discourse…but with the second luchot, the power was given to every distinguished scholar to innovate halachot through the middot and learning…And for this very reason the Holy One, blessed be He, commanded that the second luchot be carved by Moshe, not because they did not merit to have it made by God [as the first luchot were], but rather to teach as that the halacha created with the power of these luchot is a partnership between human toil and Divine assistance—just as the luchot themselves were carved by Moshe and engraved by the Holy One, blessed be He…And this is what the Sages said, that whatever a distinguished scholar is destined innovate in the future was in the luchot; the intent is that with the power of the second luchot everything was included.

The Sages taught: The daughters of Zelophehad are wise, they are interpreters of verses, and they are righteous.

Berurya, wife of Rabbi Meir and daughter of Rabbi Ḥananya ben Teradyon, was so sharp and had such a good memory that she learned three hundred halakhot in one day from three hundred Sages...

Regarding a "klustra" (door bolt): Rabbi Tarfon declares it impure, but the Sages declare it pure. Beruriah says, "[One may] remove it from this doorway and hang it on the neighboring doorway on Shabbat." When these words were spoken before Rabbi Joshua, he said, "Beruriah has spoken well (i.e., correctly)."

...Rabban Simeon ben Gamaliel says in the name of Rabbi Sheila: If they plastered it in purity and it [subsequently] becomes impure, from what time does it become pure? Rabbi Halafta of Kefar Hanania said: I asked Rabbi Simeon ben Hanania, who asked the son of Rabbi Hanania ben Teradion, who said: From the time one removes it from its place. His daughter [however] says: From when one removes its coating (literally, "strips off its garment"). When these words were reported to Rabbi Yehuda ben Bava, he said: His daughter spoke better than his son!

“These and these [all differing halachic opinions] are the words of the living God.” The rabbis in France asked: “How is it possible that these and these are the words of the living God while one prohibits and the other permits? And they answered, that when Moshe ascended above to receive the Torah, they showed him regarding every single [halachic matter] forty-nine perspectives [that would lead] to prohibition and forty-nine perspectives [that would lead to] permission. And he asked the Holy One, Blessed be He, about this. And He said: this will be given over to the sages in every generation, and the decision will be according to them.