Gemara

(Rav): To be liable for eating Ever Min ha'Chai, one must eat a k'Zayis.

This is because the Torah forbids 'eating' it. This always connotes a k'Zayis.

98a: A half-k'Zayis of Chelev fell into a pan of meat. Mar bar Rav Ashi thought that if there was 30 times as much Heter, it would be Mevatel the Chelev.

Rav Ashi: Do not be lenient about the quantities that Chachamim fixed (i.e. 60 times);

Also, you must be stringent because R. Yochanan forbids mid'Oraisa even Chetzi Shi'ur (less than the quantity for which one gets lashes or Kares, i.e. k'Zayis).

108b (Rav): If Reuven cooked half a k'Zayis of meat with half a k'Zayis of milk, he is not lashed for cooking it, but one who eats (all of) it is lashed.

Question: In any case, this is difficult!

If the meat and milk join up, Reuven should be lashed for cooking it!

If they do not join up, one who eats it should be not be lashed!

Answer: Really, they don't join up. One is lashed for eating it when half a k'Zayis of meat and half a k'Zayis of milk were taken from a pot in which a k'Zayis of meat was cooked with a k'Zayis of milk.

(Levi): One is lashed even for cooking together half a k'Zayis of each.

(Levi - Beraisa): Just like one is lashed for eating half a k'Zayis of each, one is lashed for cooking them together;

Berachos 14a - Question (Ashi'an): If one is fasting, may one taste (food, to see if it needs seasoning)?

Perhaps he only accepted not to eat or drink. Tasting is not considered eating;

Or, perhaps he forbade himself to benefit from food. Tasting is benefit!

Answer (R. Ami): He may taste. This is not a problem.

Yoma 74a (R. Yochanan): The Torah forbids Chetzi Shi'ur.

Since it can join to a Shi'ur, it is forbidden.

(Reish Lakish): The Torah permits it.

The Torah forbids Achilah (which connotes a k'Zayis). This is not Achilah.

(Beraisa): "Kol Chelev" forbids Chetzi Shi'ur, and Chelev of a Kvi (a Safek Chayah).

Answer: This is an Asmachta. Surely, a verse would not include a Safek!

Rishonim

Tosfos (14a DH To'em): R. Chananel says that he must spit out what he tastes, lest he benefit from tasting. He may not swallow, even on other fast days. One who spits out need not bless, for he does not benefit.

Rivash (287): We hold like R. Yochanan, that the Torah forbids Chetzi Shi'ur, for it can join (to a full Shi'ur - Yoma 74a). Likewise, one may not intentionally eat a Chetzi Shi'ur of an Isur mid'Rabanan. Chachamim enacted everything like Torah law.

Poskim

Shulchan Aruch (YD 238:10): If one swore 'I will not eat this loaf', he is lashed for each k'Zayis that he eats. He may not eat any amount. If one swore 'I will not eat it, he is lashed only if he ate (almost) all of it, and left over less than a k'Zayis. He may not eat any amount. If one swore 'I will not eat it. I will not eat this loaf', also the latter oath takes effect, for the first oath forbids only the entire loaf, but permits half.

Shach (YD 238:12): Also the Tur says so. I do not understand their source. Also, in Sa'if 15, if one swore 'I will eat this loaf', and half of it burned, he need not eat what remains. The Bach compares this to Chetzi Shi'ur, which the Torah forbids. We must say that this applies only to an oath not to eat it, but not to an oath to eat it. What is the source to distinguish? This is unlike Chetzi Shi'ur. When the Torah forbids Stam, even though one is lashed only for a k'Zayis, the Torah forbids even Chetzi Shi'ur. Here, he swore only about the entire loaf! If one swore not to eat a k'Zayis, surely Chetzi Shi'ur is permitted! Rashi and the Ran say that an oath 'not to eat it' connotes all of it. He did not forbid only part. The Tur holds that even if one swore not to eat less than a k'Zayis of Neveilah, it does not take effect, for Chetzi Shi'ur is already forbidden. If so, if an oath 'I will not eat it' forbids part, when he later swears 'I will not eat this loaf', why does it take effect? This requires investigation.

Shulchan Aruch (239:10): If one swore about a Mitzvah mid'Rabanan, or something that Chachamim expounded that is not explicit in the Torah, an oath takes effect on it. However, an oath to transgress a Lav, even mid'Rabanan, does not take effect.

Question (Shach 20): Above (238:4), the Shulchan Aruch rules like the Rambam, who says that an oath to eat less than a k'Zayis of Neveilah takes effect, even though the Torah forbids Chetzi Shi'ur, since mid'Oraisa one is not lashed for it. Here he says that an oath does not take effect even on an Isur mid'Rabanan! Perhaps he means that it does not take effect that he will transgress it, rather, he should permit it (through regret). Also in Siman 238, 'he is liable' means that he must permit it. Alternatively, we can say like Teshuvas Maharal ben Chaviv (103), that the Ran holds that mid'Rabanan laws are more stringent than Chetzi Shi'ur mid'Oraisa. The latter is forbidden due to "Kol (Chelev)." There is no special Lav for Chetzi Shi'ur (of different Isurim). When there is no specific Lav, an oath takes effect. "Lo Sasur" applies to every Lav mid'Rabanan. Also, we can say that Chachamim authorized their words like Torah law.

Beis Yosef (YD 68 DH v'Chasav Od): The Mordechai (Chulin 664) says that a case occurred in which the head of a goose was cooked whole, without cutting it. R. Klonimus permitted, because there is not a k'Zayis of blood to forbid. A Talmid mistakenly wrote this, and attributed it to a Gadol. The Gemara says that a half-k'Zayis of Chelev fell into a pan of meat, and we required 60 times as much meat to permit!

Mahari Mintz (15): Why was R. Klonimus lenient? The Torah forbids Chetzi Shi'ur! If blood was cooked or salted, it is forbidden only mid'Rabanan. In Chulin, Rav Ashi was stringent when half a k'Zayis of Chelev fell in. A bird's head is different, for the blood in it will never lead to lashes or Kares. Therefore, we need not be stringent, like the Hava Amina of Mar bar Rav Ashi, and it is mid'Rabanan for two reasons (it was salted and cooked).

Pri Chodosh (YD 68:7): This does not suffice to be lenient. Not all exempt for cooked blood. Also, the Gemara said 'do not disgrace Shi'urim of Chachamim.' Even Chetzi Shi'ur of an Isur mid'Rabanan requires 60 parts for Bitul. Do not exempt because it will not lead to lashes. It can join to a Shi'ur, like it says in Yoma! Chachamim enacted like Torah law! Surely, one should not be lenient, like the Beis Yosef says. The Rema (Torah Chatas 91) and Be'er Sheva (82) agreed.

Chavos Ya'ir (15): L'Chatchilah, Chetzi Shi'ur is forbidden. However, surely one may leave the city (within the permitted 2000 Amos) on Shabbos. If one swore not to eat a k'Zayis of a loaf, we do not forbid half a k'Zayis. If one swore not to eat an entire loaf, we do not forbid eating half. The same applies to matters other than food, e.g. Hotza'ah and all Melachos of Shabbos. Everything exempt on Shabbos is forbidden, with only three exceptions. I say that we do not forbid Chetzi Shi'ur when the Torah gave the Shi'ur, e.g. carrying four Amos in Reshus ha'Rabim, which we expounded (Eruvin 51a), or a Mil (2000 Amos) Techum, which we learn from the vacant area left around the cities of the Leviyim. (Another opinion says that the Torah forbids going past 12 Mil; we learn from Machaneh Yisrael in the Midbar. Chachamim saw a need to decree against going past a Mil, and found a support for this. To, when the Torah explicitly permitted, Chachamim did not forbid due to Chetzi Shi'ur. I bring a proof from the Taz (YD 117:1), who says that Chachamim have no authority to forbid what the Torah explicitly permits. Also, Chetzi Shi'ur does not apply to something without a source in Torah for a Lav, e.g. Tum'ah of food and drink, Mes, Neveilah, and Sheretz. There is a tradition for the Shi'urim. Less than this is not Tamei at all, even though a Shi'ur of Tum'ah leads to lashes and Korban. R. Yochanan learns from "Kol Chelev" that Chetzi Shi'ur is always forbidden, i.e. when the Torah forbade and Chachamim fixed the Shi'ur, even though there is an Asmachta (for Shi'urim) from a verse (Berachos 41b). In Yoma 79a, we say that the Shi'urim are a tradition from Sinai. The Shi'ur is only for lashes or Korban, but the Torah forbids even Chetzi Shi'ur. Reish Lakish agrees that Chetzi Shi'ur is Asur, but it is mid'Rabanan.

Chavos Ya'ir: If one vowed about a Shi'ur, this is like when the Torah fixed a Shi'ur, and Chetzi Shi'ur is permitted. Based on this, one who vowed 'I will not eat this bread' is forbidden Chetzi Shi'ur. Most Poskim permit to taste food on a fast day, if he will spit it out. Perhaps R. Chananel obligates spitting it out due to Chetzi Shi'ur! The Rif and Rambam did not say that he must spit it out. Chazal say 'taste' to refers to swallowing. Why did R. Chananel say that he must spit out, lest he benefit? He should have said that it is not called eating, for the question was whether he accepted not to eat, or not to benefit. Presumably, R. Ami resolved that it is permitted because he accepted only not to eat! R. Chananel rejected this, for the Gemara did not answer merely 'he tastes.' It added 'and there is no problem.' Also, he should have said 'it is permitted.' Why did he say 'he tastes'? Rather, it is to teach that it is permitted in any case, even if he accepted not to benefit. We must say that this is because he spits out. Surely, the questioner asked only about this. He forbids swallowing for some reason.

Yehudah Ya'aleh (OC 161): How do we learn that Ta'am k'Ikar from absorbed tastes in Nochri Kelim? Perhaps they needed to be Kashered due to Basar v'Chalav. All agree that Ta'am k'Ikar regarding Basar v'Chalav! R. Shlomo Siriliyo (Yerushalmi Terumos 6) says that regarding Isurei Hana'ah, all agree that the Torah forbids Chetzi Shi'ur. If so, we need no source for Basar v'Chalav. I do not understand this. Still, perhaps the Torah commanded to Kasher the Kelim from Midyan due to Basar v'Chalav, but not due to Ta'am k'Ikar, rather, due to Hana'ah!

Yehudah Ya'aleh: Does Chetzi Shi'ur apply to "v'Lifnei Iver Lo Siten Michshol"? "Nesinah" connotes a k'Zayis. Surely, Lifnei Iver applies mid'Rabanan (Tosfos Avodah Zarah 22a DH Teipuk). A Tosefta in Demai proves this. Here Nesinah does not connote a Shi'ur, just like "Nerdi Nasan Reicho" and "v'Lo Nasno Elokim Lehara." It connotes a Shi'ur when something is given from hand to hand.