Question: Does R. Tarfon not apply Dayo? Dayo is mid'Oraisa!
(Beraisa): "If (Miryam's) father would spit at her, she should be shut up for seven days" - all the more so, she should be shut up for 14 days when the Divine Presence is angry at her!
However, due to Dayo, she will be shut up for seven days.
Answer: He agrees to Dayo when it still allows something to be learned from the Kal va'Chomer;
No verse teaches that she should be shut up seven days due to the Divine Presence. A Kal va'Chomer teaches 14, and Dayo says that we may only learn seven.
Regarding Keren, the verse that teaches half- damage also applies to the victim's premises. If we apply Dayo, the Kal va'Chomer will not teach anything!
Chachamim say, "She will be shut up seven days" already teaches seven days due to the Divine Presence (and even so, we say Dayo)!
R. Tarfon says, that verse teaches Dayo. Without it, we would have said that she will be shut up 14 days!
Chachamim: Another verse teaches that - "Miryam was shut up (...seven days)"!
R. Tarfon says, that teaches that we generally say Dayo (if there is no other Chidush of the Kal va'Chomer). One might have thought that Dayo applied only to Miryam, due to Moshe's honor.
TANA'IM WHO ARGUE ABOUT DAYO
Question (Rav Papa): The following Tana who does not apply Dayo even when it would not cause that nothing is learned from the Kal va'Chomer!
(Beraisa): What is the source that semen of a Zav is Tamei? We learn from a Kal va'Chomer.
Tahor emissions of a Tahor person (e.g. his spit), such emissions of a Tamei person (e.g. a Zav) are Tamei. Emissions of a Tahor person that are Tamei (e.g. his semen), all the more so from a Tamei person they are Tamei!
Summation of question: He learns (that a Zav's semen has all the Tum'ah of his spit, i.e.) Maga (through touching) and Masa (through moving). He should learn only Tum'as Maga. Dayo should prevent him from learning Tum'as Masa!
Suggestion: We do not need a Kal va'Chomer for Maga. The verse that teaches Tum'ah (of Maga) of semen applies also to a Zav!
Rejection: That verse says "a chance happening of the night." One might have thought that this does not apply to a Zav, for his semen has a cause (his malady)! We need the Kal va'Chomer to teach that this is not so.
Answer (Abaye): The verse does not say that the semen has no cause (we do not need the Kal va'Chomer for Tum'as Maga).
Question: Which Tana holds that semen of a Zav has Tum'as Masa? This is unlike R. Eliezer and unlike R. Yehoshua!
(Beraisa - R. Eliezer): The semen of a Zav has Tum'as Maga, but not Masa;
R. Yehoshua says, it has even Masa, for it surely has drops of Zivah.
R. Yehoshua says that it has Tum'as Masa only because it has drops of Zivah, but semen itself lacks Tum'as Masa!
Answer: It is the following Tana:
(Mishnah): Stricter Tum'os, i.e. the Zivah, spit, semen and urine of a Zav, and the blood of a Nidah, Tum'as Maga and Masa.
Question: Perhaps the Tana only says so because semen has drops of Zivah in it!
Answer: If so, he would have taught semen next to Zivah. Rather, it was taught next to spit, for he learned it from a Kal va'Chomer from a Zav's spit.
THE TUM'AH OF A MAT
Question (R. Acha mi'Difti): The Tana of the following Beraisa does not apply Dayo even when it would not cause that nothing is learned from the Kal va'Chomer!
(Beraisa): A Kal va'Chomer teaches that a mat can receive Tum'as Mes (i.e. of a corpse). Small flasks do not receive Tum'ah from a Zav (the opening is too small to stick his finger inside), but they receive Tum'as Mes;
A mat receives Tum'ah from a Zav, all the more so it receives Tum'as Mes!
Summation of question: The Tana learns both Tum'as Erev (for which it suffices to immerse it in a Mikvah, and it is fully Tahor at nightfall), and seven-day Tum'ah (which requires sprinkling with water with ashes of the red heifer)!
He should say learn Tum'as Erev from the Kal va'Chomer, and Dayo should prevent learning seven-day Tum'ah!
Answer (Abaye): Really, the Tana learns that a mat receives Tum'as Erev from Sheratzim (rodents) from the Kal va'Chomer:
Small flasks do not receive Tum'ah from a Zav, but they receive Tum'as Sheratzim (since very small rodents can enter them);
A mat receives Tum'ah from a Zav, all the more so it receives Tum'as Sheratzim!
Question: From where does he learn Tum'as Mes of a mat?
Answer: It says "a garment or leather" regarding Tum'as Sheratzim and also regarding Tum'as Mes. Just like a mat receives Tum'as Sheratzim, it receives Tum'as Mes.
Assertion: We must say that the words "a garment or leather" are extra only to teach the Gezeirah Shavah. If not, we could refute the teaching!
A lentil's volume of a Sheretz is Metamei, but an olive's volume of a Mes is needed to be Metamei (this shows that Tum'as Sheratzim is broader. Perhaps mats only receive Tum'as Sheratzim, but Tum'as Mes.)
Confirmation: Indeed, the words are extra.
Sheratzim are equated to semen "a man who will have a seminal emission... a man who will touch a Sheretz."
Question: It says about semen "any garment and any leather that semen it will be on (will be Tamei)." Why did the Torah write "a garment or leather" regarding Sheratzim? (We could have learned from semen!)
Answer: The words "a garment or leather" written regarding Sheratzim are free for the Gezeirah Shavah.
Question: We showed that "a garment or leather" written regarding Sheratzim is extra. This suffices for the opinion that does not challenge a Gezeirah Shavah if (the word(s) of) one side is extra;
According to the opinion that challenges it unless both sides are extra, how can we answer?
Answer: The words "a garment or leather" written regarding Tum'as Mes are also free.
Tum'as Mes is equated to semen - "anyone who will touch someone who is Tamei Mes, or a man who will have a seminal emission";
Question: It says about semen "any garment and any leather that semen will be on it (will be Tamei)." Why did the Torah write "a garment or leather" regarding Tum'as Mes?
Answer: The words are free for the Gezeirah Shavah.
Question: This is like the opinion that when we learn a law from another topic, the law is governed by rules of its own realm. (I.e. when we learn from semen (Rashi, according to Maharsha; Maharshal - from Sheratzim) that Tum'as Mes applies to a mat, we say that it is like all things that receive Tum'as Mes, it can receive seven-day Tum'ah);
According to the opinion that when we learn a law from another topic, we totally learn from that topic (i.e. when we learn from semen or Sheratzim that Tum'as Mes applies to a mat, we learn only Tum'as Erev, which applies to Sheratzim), how do we learn seven-day Tum'ah?
Answer (Rava): "You will wash your clothing on the seventh day" - no Tum'ah of Mes is less than seven days.
SHEN AND REGEL ARE EXEMPT IN A RESHUS HA'RABIM
Suggestion: A Kal va'Chomer should obligate Shen and Regel in a Reshus ha'Rabim!
Keren only pays half-damage in the victim's premises, and it is liable in a Reshus ha'Rabim. Shen and Regel pay full damage in the victim's premises. All the more so they should be liable in a Reshus ha'Rabim!
Rejection: "It will consume in another's field" - not in a Reshus ha'Rabim.