Kal Vachomer / Gezera Shava

Rabbi Yishmael says: The Torah is expounded by thirteen hermeneutical principles:

1) kal vachomer (a fortiori). 2) gezeirah shavah (Identity). 3a) Binyan av mekathuv echad (a general rule implicit in one verse). 3b) binyan av mishnei kethuvim (a general rule derived from two verses). 4) kllal ufrat (general-specific). 5) prat ukllal (specific-general). 6) kllal ufrat ukllal (general-specific-general). 7) kllal shehu tzarich lifrat ufrat shehu tzarich lichllal (general requiring specific and specific requiring general). 8) kol davar shehaya bichllal veyatza min hakllal lelamed, lo lelamed al atzmo yatza ela lelamed al hakllal kulo yatza. (Anything which was subsumed in a general category, and departed from that category to teach (something) — not in order to teach about itself did it depart, but in order to teach about the entire category did it depart). 9) kol davar shehaya bichllal veyatza min hakllal lit'on to'an acher shehu ke'inyano, yatza lehakel velo lehachmir. (Anything which was subsumed in a general category, and departed from that category for a particular requirement thereof, departed for leniency and not for stringency). 10) kol davar shehaya bichllal veyatza min hakllal lit'on to'an acher shelo ke'inyano, yatza lehakel ulehachmir. (Anything which was subsumed in a general category, and departed from that category for a particular requirement foreign to it, departed both for leniency and for stringency). 11) kol davar shehaya bichllal veyatza min hakllal lidon badavar hechadash, ē ata yachol lehachziro lichllalo ad sheyachzirenu hakathuv lichlallo befeirush. (Anything which was subsumed in a general category, and departed from that category for a new learning, cannot be restored to that category unless Scripture restores it explicitly). 12a) davar halamed me'inyano (something learned from context). 12b) davar halamed misofo (something learned from its end). 13) shnei kethuvim hamakchishim zeh eth zeh ad sheyavo hakathuv hashlishi veyachriya beneihem (two verses that contradict each other until a third verse comes and resolves the contradiction).

It has been taught: 1,700 Kal Vachomers and Gezerot Shavot and scribal teachings were forgotten during the mourning period for Moses. Yet Rabbi Abahau said: Be that as it may, Otniel ben Kenaz deduced them all through his reasoning, as it says (Joshua 15:17) "Otniel ben Kenaz, kinsman of Caleb, captured the city of Kiryat Sefer."

(12) But Moses appealed to the LORD, saying, “The Israelites would not listen to me; how then should Pharaoh heed me, a man of impeded speech!”

When you see the donkey of your enemy lying under its burden and would refrain from raising it, you must nevertheless raise it with him.

"Help shall you help with him": ... R. Yoshiyah says: This tells me only of unloading. Whence do I derive (the same for) loading. It follows qal vachomer: If unloading, which the owner of the animal can do by himself, the other is commanded to assist him with, how much more so loading, which he cannot do by himself! Scripture speaks of the less obvious instance to derive therefrom the more obvious — whence R. Yishmael says: Just as unloading is commanded by the Torah, so, loading.

In the name of Saadia [or Rashi] it was said: why did the verse talk about the enemy, and not the friend? The verse did not want to waste words, and spoke about the enemy in order to also include the case of the friend.

Case A (explicit) = your enemy's donkey

Case B (sometimes implicit) = your friend's donkey

Case B is stronger than A because = goodwill, love

Case A has feature x = YOU HAVE TO HELP

therefore, Case B also has feature x = YOU HAVE TO HELP

Nonetheless, we are not allowed to give priority to our friend before our enemy [if both of their donkeys need help at the same time,] because of the principle of dayo, anything that is learned by kal vachomer is equal in both cases.

The fourteenth of Nisan once occurred on Shabbat, and they forgot and did not know whether the Paschal lamb overrides Shabbat or not. They said: Is there any person who knows whether the Paschal lamb overrides Shabbat or not? They said to them: There is a certain man who came up from Babylonia, and Hillel the Babylonian is his name. He served the two most eminent scholars of the generation, Shemaya and Avtalyon, and he knows whether the Paschal lamb overrides Shabbat or not.

They sent messengers and called for him. They said to him: Do you know whether the Paschal lamb overrides Shabbat or not? He said to them: Have we but one Paschal lamb during the year that overrides Shabbat? Do we not have many more than two hundred Paschal lambs, i.e., sacrifices, during the year that override Shabbat? They said to him: From where do you know this? He said to them: “Its appointed time” is stated with regard to the Paschal lamb and “its appointed time” is also stated with regard to the daily offering. Just as the expression “its appointed time,” which is stated with regard to the daily offering, indicates that it overrides Shabbat, so too “its appointed time,” which is stated with regard to the Paschal lamb, indicates that it overrides Shabbat!

And furthermore, it is kal vachomer : If the daily offering, which is not punishable by karet, overrides Shabbat, is it not right that the Paschal lamb, the neglect of which is punishable by karet, should override Shabbat?

After Hillel brought these proofs, they immediately seated him at the head and appointed him Nasi over them, and he expounded the laws of Passover that entire day. He began rebuking them [mekanteran] them with words. He said to them: What caused this to happen to you, that I should come up from Babylonia and become Nasi over you? It was your laziness... They said to Hillel: Our teacher, if one forgot and did not bring a knife on the eve of Shabbat, what is the law? He said to them: I once heard this halakha from my teachers but I have forgotten it. But leave it to the Jewish people; if they are not prophets, they are the sons of prophets, and will certainly do the right thing. The next day one whose Paschal offering was a lamb took the knife and stuck it in its wool; and one whose Paschal offering was a goat stuck it between its horns. Hillel saw the incident and remembered the halakha and said: This is the tradition I received from the mouths of Shemaya and Avtalyon!

(2) Command the Israelite people and say to them: Be punctilious in presenting to Me at set times the offerings of food due Me,^-a as offerings by fire of pleasing odor to Me. (3) Say to them: These are the offerings by fire that you are to present to the LORD:
As a regular burnt offering every day, two yearling lambs without blemish.

(2) Let the Israelite people offer the passover sacrifice at its set time:

Issi ben Guria taught: How do we know that [eating] meat and milk together is forbidden? Here (Deut. 14:21), it says "For you are a holy people," and there (Exodus 22:30) it says "You shall be holy people to Me: you must not eat flesh torn by beasts in the field." Just as there eating is forbidden, here too it's forbidden!

This is only for eating, what about benefit? Learn it from kal vachomer! Just as in the case of Orlah, which doesn't involve a transgression, benefit is forbidden - how much more so in the case of meat and milk!

For you are a people holy to the LORD your God. You shall not boil a kid in its mother’s milk.

(30) You shall be holy people to Me: you must not eat flesh torn by beasts in the field; you shall cast it to the dogs.

From where [do we learn the requirement of a minyan]? R. Ḥiyya bar Abba said that Rabbi Yoḥanan said: It is as the verse states: “And I shall be sanctified among the children of Israel” (Leviticus 22:32), meaning that any expression of sanctity may not be performed with fewer than ten. How so? Rabbi Ḥiyya taught: It come from “among,” “among”... and from “congregation” “congregation”...

Rav Ḥisda said: We derive it by the hermeneutic principles of verbal analogy and juxtaposition: The term finding in one context is derived from finding in another context, and finding is derived from the word searching, and this searching is derived from searching elsewhere, and searching there is derived from the word lamps, and lamps is derived from lamp.

And whence is it derived that if it remained as it was at the end of the first week and it spread in the second week, he removes and scrapes and plasters, and he is given another week? .... It is, therefore, written of the end of the first week, (14:39) "And the Cohen shall return," and of the end of the second week, (14:44) "And the Cohen shall come." Returning and coming are one and the same. Just as with "returning," he removes, scrapes, and plasters, and is given an additional week, so, with "coming."