Mishnah 11 is a direct continuation of the previous mishnah. There we learned that when vegetables are pickled together we are not concerned that they will transmit taste to one another, except for vegetables with a sharp taste, such as onions and the like. Our mishnah presents four Tannaim who disagree with that mishnah.
What is the point of dispute?
The previous mishnah, which ruled that pickling vegetables does not transmit taste, implies that cooking them together does transmit taste, since cooking is a more intensive process than pickling in terms of drawing out taste and transferring it. The four Tannaim in our mishnah are more lenient, holding that even cooking vegetables together does not transmit taste, apart from a few exceptions that will be detailed below.
It is worth stating at the outset that the halachah does not follow any of these opinions, but rather the previous mishnah: pickling ordinary vegetables creates no problem, but cooking them together does transmit taste. Therefore, if one of the vegetables in the pot is Terumah, second tithe, consecrated produce or seventh year produce, it causes the rest of the vegetables cooked with it to become subject to those same restrictions.
Rabbi Yosi - the beets:
Rabbi Yosi deals with vegetables that are cooked more than usual, such as those soft, mashed vegetables that remain at the bottom of the pot after prolonged boiling. In his view, even with such extended cooking the vegetables do not transmit taste to one another, except when it is done with "terradin" - beets (in modern Hebrew 'terradin' means spinach, but here it apparently refers to beets). Beets have a strong taste when cooked, and therefore if the beet is the source of the prohibition, it prohibits anything else cooked with it in the pot. The other vegetables, by contrast, do not transmit taste.
Rabbi Shimon - cabbage of an irrigated field and cabbage of a rain fed field:
Rabbi Shimon agrees with the principle, but focuses on a different type of vegetable - cabbage, and distinguishes between two kinds of cabbage according to the way the field in which they grew was watered: a beis habaal field, watered naturally by rainwater, as opposed to a beis hashelachin field, which requires manual irrigation. Although this may seem surprising to us, an irrigated field produces less juicy vegetables, since in the absence of irrigation systems a person had to draw water from the well and bring it to the vegetables, and consequently the vegetables received relatively little water.
Therefore, cabbage that grew in an irrigated field is relatively dry, and it draws in and absorbs moisture from the moist cabbage that grew in a rain fed field. If the moist cabbage is the source of the untithed produce, the prohibition is absorbed into the dry cabbage. This is the language of the mishnah: "keruv shel shikya" - cabbage from a field watered by hand, cooked together with "keruv shel baal" - cabbage from a field that relies on rainwater (named for beis habaal), is "asur, mipnei shehu bolea" - forbidden, because it absorbs: the cabbage that had been permitted becomes forbidden, because it absorbs the taste from the other cabbage.
Rabbi Yehudah (and in the Bartenura's version: Rabbi Akiva):
The language of the mishnah: "kol hamisbashlim zeh im zeh" - all things cooked with one another are permitted. The Bartenura explains that this refers to items that are of precisely the same species, such as two cabbages and the like. In such a case we are not concerned about transfer of taste, since the taste is identical in both and is of no significance. Therefore, if two items of the same species are cooked together in a pot (and not pickled), and one of them is subject to restrictions - Terumah, wine used for idolatry and the like - the item that had been permitted remains permitted.
The exception is meat. When two pieces of meat are cooked together in a pot, one kosher and one a tereifah, meat emits and absorbs taste. Therefore, even when it is the same type of meat, and the only difference is that one was properly slaughtered and the other was not, everything in the pot becomes forbidden, and sixty times its volume is required to nullify it. But as stated, the halachah does not follow these opinions, but rather that whatever is cooked together transmits taste, and that is a problem.
Rabbi Yochanan ben Nuri - the Liver:
The final opinion is more lenient still. According to the understanding of Chazal, the liver is saturated with blood through and through, and therefore it releases blood constantly and without letup. Since it is always releasing, it is never free to absorb anything back. Hence the ruling in the Mishnah: the liver "oser" - if it was cooked in a pot with non-kosher meat, it releases its blood and renders the rest of the contents of the pot forbidden, but it itself "eino ne'esar" - it does not become forbidden, because it releases and does not absorb, and so it takes in nothing.
Here too the halachah is not like this at all. In practice, when it comes to liver there is simply no way to cook it in a pot, since we are concerned that the blood it releases will be reabsorbed into it and become trapped inside, and blood is forbidden to eat. For this reason liver is never cooked, and the only way to eat it is by roasting it directly over an open flame - not by way of salting or the like, but by roasting alone, in which the blood that comes out of the liver drips down and away. Halachically, this is the only way to eat liver.
In summary: in this Mishnah four Tannaim disagree with the previous Mishnah and hold that even vegetables cooked together do not transfer taste: Rabbi Yosi makes an exception for beets; Rabbi Shimon deals with irrigated cabbage that absorbs from rain-fed cabbage; Rabbi Yehudah permits everything cooked together from the same species, and makes an exception for meat; and Rabbi Yochanan ben Nuri rules that liver renders other things forbidden but does not itself become forbidden, because it releases and does not absorb. The halachah does not follow any of these opinions; rather, anything cooked together transfers taste, and liver is not cooked at all but is roasted over the fire.