While the principle of bitul may make more sense in the lach bi'lach case than in the case of yavesh bi'yavesh, it is one aspect that makes it harder for bitul to work - the presence and diffusion of taste. In the chicken soup scenario, it might be true that the chicken soup overwhelms the presence of the pork, but if I can still taste the pork in the soup, can I really say that there is no pork here? The halakhic significance of this reality is addressed in the sugyot in Pesachim, Avoda Zara, and Chullin (as well as others). These sugyot discuss the principle of taam ki 'ikkar, whether this taste is considered to be like the original food, and thus equally forbidden.
Rav Chaim (Psulei Hamukdashim 10:12) clearly articulates the two conceptual categories that can be used for thinking about ta'am ki 'ikkar. One is to say that the presence of taste prevents bitul from occurring - since the pork can be tasted, there is no way to say that it has lost its identity in the mixture. The other is to say that bitul occurs - the pork is no longer here - but that what is left is taste - ta'am. The question then is, what is the halakhic status of this taste? Ta'am ki 'ikkar says that the status is that it is forbidden as well, just like the pork itself is forbidden.
The first approach is probably the most logical of the two - we can understand why bitul would not occur in such a case. This would also be able to be expanded to other ways in which the food can continue to be felt -for example, what if it cannot be tasted, but it changes the color of the mixture? Or what if it causes the mixture to congeal, or to ferment (ma'amid or machmitz)? According to this approach, there is good reason to say that it would not be batel and the mixture would be forbidden.
The second approach - that there is a new prohibition of taste - is a bigger innovation (why should such a new prohibition exist?) but it is also the simple meaning of the phrase ta'am ki 'ikkar - the taste is considered like the thing itself -and it is consistent with the Gemara's need to derive this law from verses and through rabbinic hermeneutics. This approach, while not extendable to non-taste areas, could be extended to cases where there is none of the original prohibited food present. Consider a pot that was used to cook pork and now is being used to cook my chicken soup. In this case - if we assume that some pork taste comes out of the pot -it is not enough to say that the taste is not batel. We must actually say that taste of pork alone is forbidden, even if there is no pork present.
Rishonim debate how we rule regarding ta'am ki 'ikkar. Some Rishonim (Rashi Hullin (98b) s.v. Ta'am Ki 'ikkar, and elsewhere) states that we rule that this is not d'oraitta, Biblical, and the status of ta'am is only rabbinic. Rabbeinu Taam, Rosh and Ra'avad all rule that it is d'oraitta, whereas Rambam distinguishes between cases where there is a large proportion of the prohibited food (kezayit bi'khdei achilat prass, an olive's worth per half-a-loaf of bread - either 1/9 or 1/8 of the mixture), where the taste is forbidden d'oraitta as opposed to cases of a small proportion of the prohibited food where the taste is only rabbinically prohibited. Rashba weighs in favor of those who deem the prohibition to be d'oraitta, and this is the de facto ruling of the Shulkhan Arukh (there are poskim who believe that the position that it is rabbinic has not been totally rejected in halakha).
It should be noted that while Rashi is often understood as completely rejecting - on the d'oraitta level - the significance of taste, a close read of Rashi actually shows that he splits his vote between the two understandings of ta'am ki 'ikkar. Basing himself on the phrasing and distinctions of Rav Yochanan in Avoda Zara (67a), Rashi states that when all that is present is the taste, for example, when a piece of pork fell into the chicken soup, but is then removed, so only its taste remains - when it is ta'amo vi'lo mamasho - the taste but not the essence of the thing, then such taste has no halakhic significance. Ta'am ki'ikar is not d'oraitta - the Torah does not recognize the significance of taste alone. This is a halakhic rejection of the second understanding of ta'am ki'ikar. However, when the thing itself is present, but intermingled - when pork and beef were chopped and blended together, or when liquefied pork fat fell into the chicken soup - that is not ta'am, but mamash -ta'amo u'mamasho. In such a case, the presence of taste prevents the pork from being batel, and the mixture remains forbidden d'oraitta.
Rambam, it seems, makes the same conceptual distinction, but rather than defining taste versus essence based on the physical realities, he defines them based on their proportions. When the proportion is small, it is considered only the taste of the thing. When it is large, it is considered like the thing itself is present, and the taste prevents bitul from occurring. Ta'am alone has no Biblical status, but when we are dealing with mamash, the thing itself, but it is just intermingled, then its taste prevents bitul.
Finally, according to those who rule that the Torah treats ta'am as forbidden, even when it is physically only ta'am and even in small proportions, the question still remains what is the nature of this prohibition of the taste of forbidden foods? Is this a new, generic prohibition - one is not allowed to eat the taste of forbidden foods - or is it a derivative prohibition of the original food - don't eat pork, and that includes the taste of pork? This is debated between Rabbenu Tam and Rabbenu Yosef in Tosafot (Avoda Zara (67b) s.v. Amar Rebbe Yochanan). Rabbenu Yosef states that taste is a new prohibition, and it is only prohibited by an issur aseh, a prohibition derived from a positive mitzvah, whereas Rabbenu Tam states that after we learn that ta'am is forbidden, we understand that it is exactly the same as eating the original item, and one gets lashes for eating the taste of the pork, just like they would for eating pork itself. Presumably, according to Rabbenu Tam, if one ate the taste of blood, or the taste of chametz, one would get karet, divine excision, assuming that one had eaten a kezayit's -worth of it, and this seems to be the qualification of Rav Yochanan (Avoda Zara (67a), that one only gets lashes if she eats a kezayit, an olive-sized amount, of the prohibited food that is in the mixture.
The final issue is whether - in such a mixture - every bit of the mixture is now considered forbidden, or only the part of the mixture that is the pork or the taste of the pork. Almost all Rishonim state that it is only the part of the mixture that is pork that is forbidden, but Rashi (Pesachim 44b) and Rosh (Hullin 7:31) say that every part of the mixture now becomes forbidden. That is, that taste is reverse bitul. Whereas bitul makes the prohibited permitted, the presence of forbidden taste makes the permitted forbidden. Now, according to Rashi, this is exactly what is rejected when we rule (according to him) that ta'am ki 'ikkar is not d'oraitta. However, Rosh rules that it is d'oraitta and also that we rule that in such a mixture the Torah prohibits not just the pork or the pork taste, but the entire mixture. Thus, if one were to eat even 1 kezayit, and even if the mixture is only 3% pork, one would get lashes.
Rosh's position is largely ignored. It assumes, clearly, that ta'am ki 'ikkar is not just a prevention of bitul, but a new prohibition of taste, and that the scope of this prohibition is to say that as long as a mixture has some taste of pork in it, then every bit that has that taste is considered like a piece of pork itself. However, most poskim are not prepared to assign taam such transformative power. This idea is usually associated with the principle chatikha na'asit neveila -" the entire piece becomes like a piece of treif meat." However, the general consensus there is that we either do not hold of such a principle (outside of meat and milk) or we say that such a principle is only rabbinic.
So, in the end, while ignoring the Rosh, the Shulkhan Arukh rules that this principle of ta'am ki 'ikkar is d'oraitta even in small proportions and even when there is only the taste of thing present. This has relevance to cases of doubt, and means that we will be strict when we cannot determine if the taste is present, since the prohibition is Biblical. We will continue next week to see the practical application of these laws.