1) "IGLA TILSA"
OPINIONS: The Gemara tells the story of two Amora'im who refused to eat from the "Igla Tilsa" (a type of choice calf) that Rav Idi bar Avin prepared for them, since it was slaughtered on the seventh day of its life. "Had you merely waited to slaughter it until this evening," the Amora'im complained, "we would have eaten it" -- since it would been clear that it was not a Nefel but a viable fetus. (These Amora'im maintained that only after an animal lives for eight days are we certain that it is viable.)
What exactly is an "Igla Tilsa"?
(a) Earlier in Shabbos (11a) and in Pesachim (68b) RASHI explains that an "Igla Tilsa" is a cow's third offspring. Such a calf is well developed, fat, and tasty.
TOSFOS in Bechoros (19a, DH d'Hach) questions the assertion that the third born animal is healthier than the first born. The Gemara in Bechoros states that a firstborn sheep is usually stronger and healthier-looking.
Rashi (Shabbos 11a) avoids this apparent contradiction by explaining that a cow normally bears its first young when it is still weak and relatively immature. By the time it bears its third calf, it is mature enough to bear strong offspring. (The Gemara in Bechoros discusses a mature sheep that has not yet given birth.)
However, Rashi himself in Eruvin (63a) rejects this explanation based on the Gemara in Sanhedrin (65b) that says that every Erev Shabbos, Rebbi Yochanan and Reish Lakish would use the Sefer Yetzirah to create an "Igla Tilsa." How can one "create" a calf that is the third to it mother? (Rashi in Sanhedrin suggests that it just "tasted like" a healthy, third-born calf.)
(b) RASHI in Eruvin (63a) explains that "Igla Tilsa" is a third-grown calf (one that has reached one-third of its full growth), which is particularly tasty. (See also Rashi to Bava Metzia 68a, DH l'ch'she'Yiheyu Meshulashim.)
However, as TOSFOS in Gitin (56a) points out, this clearly does not seem to be the case with the "Igla Tilsa" mentioned here, which was only seven days old. A calf certainly does not reach one-third of its full size after only seven days!
(c) In a similar explanation, RASHI in Sanhedrin (65b) explains that an "Igla Tilsa" is a calf that has reached one-third of its expected lifespan, at which time it has reached its full growth. This explanation is also problematic in the context of the Gemara here, for how can a seven-day old calf have reached one-third of its expected lifespan?
(d) TOSFOS in Gitin (56a) and Bechoros (19a) therefore concludes that "Igla Tilsa" refers to a calf that is healthy and tasty. The word "Tilsa" is not related to the root "Telasa," meaning "three," but to the root "Shalish," which means "an appointee" (i.e., one who is worthy of being appointed over others due to his competence). Tosfos cites examples of this usage from the verse, "v'Shalishim Al Kulo" (Shemos 14:7, see Targum Onkeles there), and "Eglah Meshuleshes" (Bereishis 15:9; Tosfos' understanding is an original interpretation of that verse; see also Chizkuni there).