(Beraisa - Beis Shamai): A Sadin (linen garment) is exempt from Tzitzis;
Beis Hillel obligate it.
R. Eliezer bar Tzadok: Anyone who puts Techeles on a Sadin in Yerushalayim is Masmiha (astounds all who see him)! (He argues with the first Tana, who says that Beis Hillel obligate. Alternatively, he disagrees about Beis Shamai's opinion. The first Tana says that a Sadin is exempt, and one who puts Techeles on it transgresses Kilayim. R. Eliezer disagrees; such a person merely astounds.)
Rebbi: (If it really is obligated), why did Chachamim forbid putting Tzitzis (some say - Techeles) on it?
R. Eliezer bar Tzadok: This is because (some) people are ignorant (they do not know that the Mitzvah overrides the Lav, they will think that Kilayim is always permitted).
Question (Rabah bar bar Chana): Why didn't Chachamim tell 10 people to publicly wear it (to publicize the law that Kilayim in Tzitzis is permitted)?
Answer (Rava): All the more so, this will make ignoramuses think that Kilayim is always permitted!
Question: Why didn't Chachamim publicly teach that Kilayim is permitted only for the Mitzvah of Techeles?
Answer #1: People will wear (wool) Tzitzis dyed with Kala Ilan (a sap. Its color resembles Techeles.)
Question: What is wrong if they do? Even though they do not fulfill the Mitzvah of Techeles, they fulfill the Mitzvah of Lavan!
Answer: Since the Mitzvah of Lavan can be fulfilled with linen strings (without transgressing Kilayim), the Mitzvah does not override Kilayim.
(Reish Lakish): If one can fulfill an Aseh without transgressing a Lav, he must. If not, the Aseh overrides the Lav.
Version #1 - Question: Chachamim should have enacted that people must check Techeles in the pots in which it is cooked, by inserting a sample cloth!
Answer: They did not, for once Techeles in the pot is used to dye a sample (Tosfos (42b Mishum) - not for the sake of the Mitzvah), it is invalid for the Mitzvah!
Question: Letters should be sent out (instructing to put a little Techeles in an eggshell and test it, to avoid disqualifying the entire pot)!
Version #2 - Question: Chachamim should have enacted that people who buy Techeles strings must check them (with alum and sourdough, Daf 42b)!
Answer: This would not help. Perhaps the strings were made from test cloths (to see if the Techeles was cooked properly. They were not dyed Lishmah).
Question: Letters should be sent out informing people that the strings must be dyed Lishmah (so the dyers will discard test cloths)! (end of Version #2)
Answer: People do not heed such letters (Rashi; R. Gershom - perhaps someone will not see the letter).
Objection (Rava): When Chachamim are Me'aber (Rashi - add a month to the year; R. Gershom - add a day to Elul or Adar), we rely on letters to inform people. One who ignores them might eat on (the true) Yom Kipur or eat Chametz on Pesach, which are Chayavei Kerisus. All the more so, we can rely on them regarding the Aseh of Techeles!
Answer #2 (Rava, and R. Zeira): Chachamim forbade a Sadin, lest it tear within three fingers of the corner. (Rashi - perhaps it will be fixed with linen strings, and two such strings will be left hanging on the corner, for the sake of Lavan, but they are invalid, for they were not attached l'Shem Tzitzis. Tosfos - perhaps it will tear after the Tzitzis were attached, which disqualifies them, and the garment will be fixed);
Since the strings were there before the corner was fixed, they are invalid due to "Ta'aseh", v'Lo Min ha'Asuy (we must fulfill the Mitzvah when attaching Tzitzis. Here, the Tzitzis were attached before the corner was finished).
R. Zeira took the Tzitzis off his Sadin (due to this decree).
Answer #3 (Rav Zeira): Chachamim decreed against a Sadin due to a night garment;
Version #1 (Rashi, Tosfos): Since there is no Mitzvah to put (Tzitzis or) Techeles on a night garment, one who wears it transgresses Kilayim.
Version #2 (Rambam): Since the Mitzvah does not apply at night, one who wears it at night transgresses Kilayim.
(Tosfos - Rav Zeira is not R. Zeira; Rashba - R. Zeira gave this answer when he was in Bavel, before he got (Semichah in Eretz Yisrael and) the title 'Rebbi'.)
CONDITIONS OF ATTACHING THE TZITZIS
(Rava, and R. Zeira): If a garment is made of cloth and the corners are of skin, one must put Tzitzis on the corners;
Question: What is the reason?
Answer: The essence of the garment must be considered a 'Beged'.
(Rav Achai): It only depends on the corners. If they are made of cloth, one must put Tzitzis on them.
(Rava): If one put Tzitzis on the three corners of an unfinished garment, then finished the garment, the Tzitzis are invalid due to Ta'aseh v'Lo Min ha'Asuy.
Question (Beraisa): Tzadikim of old would put Tzitzis (on two corners) once they had woven the three fingers (width or length) of the garment. (According to Rava, this is invalid, for the garment is not yet large enough to require Tzitzis, and it lacks two corners of the final garment!)
Answer: It should say 'they would put Tzitzis (on all four corners) once they were within three fingers of finishing the garment.' (The corners of the outer edge will be considered part of the (final) corners. The last material will merely add on to the existing corners. Chazon Ish - even though the Tzitzis were inserted less than one finger from the end, Ta'aseh v'Lo Min ha'Asuy does not apply, since the essence of the Mitzvah is already here. We just need to fix (add to) the garment.)
Question: Are we really concerned for Ta'aseh v'Lo Min ha'Asuy?!
(R. Zeira): If one attached Tzitzis to a garment that already had Kosher Tzitzis, the latter are valid (Rashi. Rosh - even though the first three (of the second set) were not valid when attached, for the first set is not Batel until all four of the new set are attached).
Answer (Rava): Since he transgresses Bal Tosif (the prohibition to add to Mitzvos), attaching the second set is not considered an action. (When he later cuts the first set, it is as if he then attaches the second set. He fulfills the Mitzvah through this action!)
Objection (Rav Papa): If he does not intend to add to the Mitzvah, rather, to use the new Tzitzis and annul the first ones, he does not transgress Bal Tosif, so attaching the second set is an action (but it does not fulfill the Mitzvah. When he cuts the first, the latter become Tzitzis automatically.) Ta'aseh v'Lo Min ha'Asuy should apply!