Gemara

111b (Rav Kahana, brother of Rav Yehudah): One may not put hot food in a basin in which meat was salted; a radish cut with a knife (used for meat) may be eaten with milk.

Question: Why is one forbidden and the other permitted?

Answer (Rava): The radish can be permitted if one tastes it (and does not taste meat in it); the basin cannot be permitted (one may not taste food put in it)!

Question (Rav Papa): A Nochri cook can taste it!

(Beraisa): One may not cook milk in a pot in which meat was cooked; if milk was cooked in it, if it absorbed the Ta'am of meat, it is forbidden;

One may not cook Chulin in a pot in which Terumah was cooked; if Chulin was cooked in it, if it absorbed the Ta'am of Terumah, it may only be eaten by a Kohen.

Question: Granted, a Kohen can taste whether the Terumah can be tasted in the Chulin. However, regarding meat and milk, how can we tell if the meat gave Ta'am? One may not taste the milk, lest it absorbed Ta'am of meat!

Answer (Rava): A Nochri cook may taste it.

Answer (Rava): The basin is forbidden when there is no Nochri cook to taste it.

97a (Rava): Sometimes, Chachamim say that we taste food. Sometimes, we rely on a Kefeila. Sometimes, we say that an Isur is Batel only if it was mixed with 60 times its own volume of Heter (permitted food):

An Isur is Batel in 60 times its own volume Min b'Mino (if identical foods were mixed), or Min b'Eino Mino (diverse foods were mixed), and a Kefeila is not available.

99a (Beraisa): If Terumah beans were cooked with Chulin lentils, and the beans didn't give taste, whether or not there is 101, the lentils are like Chulin.

Question: If there is not 101, what quantity is there for Bitul?

Answer #1: There is 60.

Answer #2 (Rav Dimi): No, there is 100.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 15:30): If meat and milk, Yayin Nesech, Orlah or Kil'ai ha'Kerem fell into honey, a Nochri tastes it and we rely on him. If there is no Nochri, we estimate if there is the Shi'ur for Bitul, i.e. 60 or 100 or 200.

Ran (34a DH u'Min): We rely on a Yisrael whether or not he is a chef. The Gemara said that a Kohen may taste. It did not stipulate that the Kohen is a chef!

Rashi (98a DH b'Samech): (We rely on 60) if we checked a mixture and there was no taste (of Isur), or in any case when the Isur could not be tasted, e.g. Min b'Mino. If it gives taste, this is never Batel. When there is no taste, we require 60 for Bitul. In a case when the Isur did not give taste, the Gemara asked 'if there is not 101, what quantity is there for Bitul', and answered that we require 60 or 100.

Ran (DH 34a DH u'Min): This is wrong. The Gemara says that we rely on a Kefeila. This implies that this is a leniency. According to Rashi, this is a stringency, for when there is 60 and there is no Kefeila, we permit.

Rosh (7:25): 'We rely on a Kefeila' connotes unlike Rashi. If there is 60, what is the Chidush that we rely on him? Rather, we rely on his tasting even when there is not 60. Throughout the Gemara, we say that Isurim are Batel in 60. One need not seek anything else to permit. Rava said 'Chachamim say that (sometimes Bitul depends on) taste, and sometimes it depends on 60.' This implies that 60 applies only when we cannot determine whether there is taste. Also Tosfos says so.

Ra'avan (cited in Mordechai 679): If one cooked milk in a pot used for meat; and the milk absorbed the taste of meat, it is forbidden. According to R. Yehudah (Min b'Mino forbids any amount), we should say that milk is absorbed in the pot and is forbidden due to the meat, and becomes (pure Isur,) like Neveilah, and it forbids everything in the pot! Rather, the milk absorbed and the permitted milk in the pot combine to be Mevatel the taste of meat absorbed in the pot.

Poskim

Shulchan Aruch (YD 98:1): If an Isur became mixed with Heter Min b'Eino Mino, e.g. Chelev with meat, a Nochri tastes it. If he says that he cannot taste the Chelev, or its taste is Pagum (detrimental), it is permitted.

Beis Yosef (DH u'Piresh): Rashi says that we rely on a Kefeila only when there are 60 times as much Heter as Isur. The Rosh connotes that when there is 60, we assume that there is no taste. If one tastes the Isur, even if there is 100 or more, it is forbidden, for the taste is not Batel. The Rashba and Ran agree.

Drishah (1): We forbid a Yisrael to taste it. This shows that if one bought meat, and it is a Safek whether it was salted, one may not taste it with his tongue.

Rebuttal (Taz 2): The Shulchan Aruch (42:3) permits tasting the gall bladder with one's tongue! This shows that one may taste a Safek with his tongue. Likewise, one may taste meat (to see if it was salted) if it is clean from blood. Here is different, for one must truly eat in order to know whether there is taste of the Isur. Therefore, we require a Nochri. Regarding a Ta'anis, (OC 567:1), there is no Isur to taste with the tongue. Regarding putting in the mouth, we distinguish a fast from Isurim.

Shulchan Aruch (ibid.): If there is no Nochri, we estimate if there is 60 (times as much Heter as Isur). The same applies to Min b'Mino, which cannot be tasted.

Shach (4): The Mechaber connotes that when there is a Nochri, we permit only through a Nochri. If he says that he tastes Isur, it is forbidden, even if there is more than 60 times as much Heter. We permit based on 60 only when there is no Nochri, or for Min b'Mino. This is how the Beis Yosef explained the Rambam.

Rema: Nowadays we do not rely in Nochrim. We require 60 in every case.

Gra (7): This is a stringency, like the Rosh and Ran, who say that when there is 60, presumably it does not give taste. The Mechaber merely cited the Gemara. His words do not show how he learns (whether one may rely on 60 where there is a Kefeila), unlike the Shach (4, who says that the Mechaber permits relying on 60 only when there is no Kefeila).

R. Akiva Eiger: I do not know why we do not rely on Nochrim nowadays. Perhaps we are stringent for all of the opinions about when we rely on a is not considered. Perhaps we require a Kefeila, and l'Fi Tumo (unaware of the consequences of what he says); he must be a chef, for we require an expert. We do not permit without l'Fi Tumo, and we do not permit l'Fi Tumo, for this helps only for Edus Ishah (to testify that a man died, to permit his widow to remarry - Bava Kama 114a). Perhaps we require a Kefeila, for he would not ruin his reputation, so we cannot rely on l'Fi Tumo. However, we rely on l'Fi Tumo for mid'Rabanan laws. If we will say that we are concerned for Rashi's opinion, that tasting helps only if there are 60 times as much Heter as Isur, we should not rely on a Yisrael, either!

Shach (5): The Rema did not say that nowadays we do not rely on taste, rather, nowadays we do not rely on Nochrim. This implies that we rely on a Yisrael for Min b'Eino Mino of Heter, e.g. Terumah that fell into Chulin. Even though nowadays we do not have Terumah, this is relevant to one who forbade a food through a vow. Alternatively, one may taste whether meat or milk can be tasted in a radish. The Bach says that for Min b'Eino Mino of Heter, one may rely on a Yisrael, even if he is not a professional, even nowadays. Surely he will not lie. The Rema said so also in a Teshuvah (54, 119:3). This is unlike the Levush (1), who says that nowadays we do not rely on a Kohen or Nochri to taste.

R. Akiva Eiger: Why can we rely on a Kohen to taste it? We hold that Chatichah Na'asis Neveilah (a food forbidden due to absorptions is considered like pure Isur). Chulin enters the Terumah, and leaves (and mixes with the rest of the Chulin). This is Min b'Mino. We should require 60 parts against the Chulin that left. This cannot be tasted! We must say that we rely on a Kohen to taste when Chulin was cooked in a pot used for Terumah. Chatichah Na'asis Neveilah does not apply to what enters the walls of the pot, for it is always connected to the food, and never separates from it, since the pot does not have its own taste. Ra'avan derived this from the Beraisa (97a). Alternatively, we rely on tasting when Chulin was cooked with Terumah, and the pot did not cease boiling. The Chulin absorbed in the Terumah is not emitted until it ceases boiling (92:1). This is even for meat and milk. (I.e. we may rely on a Nochri to taste in such a case.) The Pri Megadim (Mishbetzos Zahav 92:1) said that if Ploni vowed not to eat a food (A), another Yisrael cannot taste whether it was absorbed in another food (B). Perhaps A was absorbed, and B became like Neveilah (for Ploni), and forbids the entire pot, for this is Min b'Mino and we require 60, for we are not experts to know what is considered ceasing to boil. The same applies to Terumah. If so, the Shach refers only to a pot used for Terumah. However, since mid'Oraisa Min b'Mino is Batel in a majority, and Chatichah Na'asis Neveilah is mid'Rabanan for other Isurim (other than Basar v'Chalav), even if we are unsure whether it ceased boiling, it is a Safek whether the Isur emitted the Heter that it absorbed, so we may be lenient about a Safek mid'Rabanan. Perhaps the Pri Megadim discussed only Nedarim, which is Davar she'Yesh Lo Matirim (the Isur can be permitted), so we must be stringent about a Safek. Also, this is relevant to all Isurim, if b'Di'eved a Yisrael unknowingly tasted them. If he did not taste Isur, one may rely on this before it ceases boiling. We can join the Ra'avad's opinion, that Chatichah Na'asis Neveilah does not apply to mixtures of two wet things. If so, even if Isur was absorbed and emitted, it is like a standard mixture of wet things. This requires investigation.