1) "HETER MITZTAREF L'ISUR" AND "TA'AM K'IKAR"
QUESTION: Rebbi Eliezer states that a mixture that contains Chametz (such as the "Kutach ha'Bavli" dish) is forbidden as a Lav by the Torah and one who eats it on Pesach is punished with Malkus. The Gemara says that it is clear that Rebbi Eliezer applies the principle of "Heter Mitztaref l'Isur" to the Isur of Chametz. Since Rebbi Eliezer says that a mixture that contains Chametz is forbidden, it must be that the permissible part of the mixture combines with the small amount of Chametz to make a full Shi'ur, for which Malkus may be administered. Consequently, in order to be liable for Malkus, one does not have to eat a k'Zayis of the taste of Chametz itself, but merely a k'Zayis of the entire mixture.
Where in the words of Rebbi Eliezer is this implied? Perhaps Rebbi Eliezer does not mean that one is liable because of "Heter Mitztaref l'Isur." Rather, he means that Kutach ha'Bavli is forbidden because the entire mixture has the taste of Chametz in it ("Ta'am k'Ikar"). If one does not eat a k'Zayis of the Isur itself, he is not liable; it does not suffice to eat a k'Zayis of the Isur and the Heter together.
Moreover, why do the Rabanan argue with Rebbi Eliezer and say that one who eats a mixture that contains Chametz (such as Kutach ha'Bavli) on Pesach is exempt? The Kutach ha'Bavli is a classic case of "Ta'am k'Ikar" in which the taste of the Isur forbids the entire mixture. In such a case, even the Rabanan agree that one is liable! However, when the Gemara challenges the opinion of the Rabanan, it asks only that one should be liable because he ate a k'Zayis of Isur within the time span of "Kedei Achilas Peras." Why does the Gemara not ask that he should be liable even when he eats less than a k'Zayis of Isur within "Kedei Achilas Peras," because of the principle of "Ta'am k'Ikar"?
(a) The RA'AVAD explains that indeed there is no proof from the Mishnah that Rebbi Eliezer maintains "Heter Mitztaref l'Isur." Rather, the Gemara infers that Rebbi Eliezer maintains "Heter Mitztaref l'Isur" from the fact that he expounds the phrase "Kol Machmetzes" (Shemos 12:20) to teach that a mixture that contains Chametz is also Asur mid'Oraisa. It is logical to assume that he also derives from that verse that "Heter Mitztaref l'Isur" -- "Kol" means anything (even less than a k'Zayis of Isur). (The Ra'avad concludes, however, with a question on this approach. He asks that the verse says "Kol" with regard to many prohibitions, and yet the Gemara does not say that in all of those cases, Rebbi Eliezer maintains "Heter Mitztaref l'Isur.")
The Rabanan argue that one is not liable for eating such a mixture with Chametz, even though the Isur (Chametz) gives its taste to the Heter and the principle of "Ta'am k'Ikar" should apply. The Rabanan maintain that, in this case, Malkus is not administered to one who eats the taste of Isur, because he does not eat a k'Zayis of the taste of Isur within Kedei Achilas Peras (as the RAMBAN in Milchamos explains, this means that the taste of the Isur is not as strong as it is when there is a k'Zayis of Isur in the mixture).
Alternatively, the Rabanan maintain that the principle of "Ta'am k'Ikar" is derived from a Kal v'Chomer (from "Mishras," written with regard to a Nazir who eats bread dipped in wine). Although a prohibition may be derived through a Kal v'Chomer, its punishment may not ("Ein Onshin Min ha'Din"). Therefore, one is not liable for Malkus if he eats a mixture that contains Chametz. (RAMBAN, BA'AL HA'ME'OR)
A third way to understand the opinion of the Rabanan is that they maintain that "Ta'am k'Ikar" is only a Mitzvas Aseh (according to the opinion that derives it from Gi'ulei Midyan). Therefore, a mixture that is prohibited because of "Ta'am k'Ikar" is not punishable with Malkus. (See TOSFOS to Chulin 99a, in the name of RABEINU YOSEF of Orleans.)
(b) The BA'AL HA'ME'OR explains that this case is not considered a case of "Nosen Ta'am" (an Isur that gives its taste to a Heter). "Nosen Ta'am" applies only when the taste of the Isur is actually palpable in the mixture. Here, though, the taste of the Chametz is not discernible in the mixture. Rather, the Chametz chemically reacts with the Heter to produce an entirely new taste. Even though the Chametz was added to the mixture in order to contribute to the new taste, the taste of the Chametz itself is not discernible in the mixture and thus it is not called "Nosen Ta'am."
Why, then, does Rebbi Eliezer forbid the mixture? It must be that he forbids it because of the principle of "Heter Mitztaref l'Isur." (Even though the taste of the Chametz itself is not discernible, the taste of the Chametz is significant because it contributes to the formation of the new taste.)
The Rabanan argue and do not derive from the verse that "Heter Mitztaref l'Isur." Since there is no such principle, and the taste of the Chametz itself is not discernible in the mixture (i.e., there is no "Nosen Ta'am"), such a mixture is not forbidden mid'Oraisa.
(c) RASHI does not seem to follow either of the abovementioned approaches. Rashi writes later (45a, DH Rebbi Akiva) that Kutach ha'Bavli is forbidden because of "Ta'am k'Ikar," and that the reason why the Rabanan exempt a person who eats it is because they maintain that "Ta'am k'Ikar" is mid'Rabanan.
According to Rashi's words, the original question returns. How does the Gemara know that Rebbi Eliezer maintains "Heter Mitztaref l'Isur"? Perhaps his reason for ruling that one who eats Kutach ha'Bavli is liable is because he maintains that "Ta'am k'Ikar" is mid'Oraisa!
The NACHALAS DAVID suggests an answer based on an inference from the words of TOSFOS in Nazir (36a). He says that Rashi understands that at this point in the Gemara, Abaye did not know that there is a concept of "Ta'am k'Ikar" mid'Oraisa; he assumed that the prohibition of "Ta'am k'Ikar" is only mid'Rabanan. Therefore, his only possible explanation for why Rebbi Eliezer says that one is Chayav mid'Oraisa for eating a mixture that contains Chametz is that he maintains "Heter Mitztaref l'Isur." The Gemara concludes that the principle of "Ta'am k'Ikar" is mid'Oraisa.
However, according to the Gemara's conclusion, why do the Rabanan exempt one who eats Kutach ha'Bavli? Rashi (45a, DH v'Rebbi Akiva) explains that the Rabanan, even in the Gemara's conclusion, maintain that "Ta'am k'Ikar" is not mid'Oraisa but only mid'Rabanan.
Alternatively, it is possible that Rashi maintains that the inference that Rebbi Eliezer maintains "Heter Mitztaref l'Isur" is not from the fact that he says that one is liable for eating Kutach ha'Bavli, because the person's liability could be simply because of the law of "Ta'am k'Ikar." Rather, the Gemara's inference is from the fact that Rebbi Eliezer needs a new verse to teach that a mixture that contains Chametz is forbidden. Why does he need a new verse for this if "Ta'am k'Ikar" is derived from other verses? It must be that the new verse teaches a new principle -- "Heter Mitztaref l'Isur," and it teaches that even if one eats a mixture in which the taste of Isur is not dispersed throughout the entire mixture, one is still liable. (See Insights to Pesachim 43:2 and Nazir 37:1.)