Last week was discussed the principle of ta'am lifgam - when the addition of a forbidden food to a mixture makes the mixture taste worse. In such a case, the mixture may be eaten, because while the forbidden food itself, even if it has an off-taste, is forbidden, when we are only dealing with the taste of such food, and not the food itself, this bad taste is not forbidden. As Rashba explains, this is because the taste - ta'am - is in a different category than the food itself. Although we normally say ta'am ki'ikar - the taste is like the thing itself - this is only an analogy and not stating a true equality. It is true that the taste is forbidden to eat, just like the food is forbidden to eat, but taste represents as an independent prohibition. Thus, for example, although it is more forbidden to eat blood than to eat pork (the former is prohibited by karet, excision, and the latter by a negative prohibition), to eat the taste of blood in a mixture would be no more prohibited than to eat the taste of pork in a mixture. They both share the same prohibition of eating the taste of forbidden foods. Because we are dealing with an independent prohibition of eating the taste of forbidden foods, such taste is defined on its own terms, and something with a bad taste is not considered real taste, and is not prohibited.
Now, the principle of ta'am lifgam has great relevance to the case of cooking utensils, a case which seems to derive from the principles of ta'am but, like ta'am itself, may actually be its on category. In the case of cooking utensils which were used to cook non-kosher foods, they cannot be used for kosher foods. Presumably, this is because the absorbed taste of, say, the pork in the walls of the vessel will go into the kosher food and make it forbidden. When the vessel is more than 1 day old, we assume that the absorbed taste has by now gone bad, is ta'am lifgam, and thus even were one to cook in it, it would not forbid the kosher food, because it would only impart bad taste. Such 1 day old vessels are called eino ben yomo (not of the same day), and while one cannot lichatchila cook in them, if one did so they do not make the food forbidden.
The same would apply to milk and meat vessels, and this is why when someone accidently cooks a fleishig food in a milkhig pot (or the opposite), the rabbi will ask when the last time the pot was used for cooking fleishig. If it is more than 24 hours before this milkhig dish was cooked, the food is permissible because the meat taste that goes into the milk dish is ta'am lifgam.
There are, however, reasons to think that these laws are more than just a straight application of the principles of ta'am (they will make the food forbidden because of the absorbed and transferred taste) and of ta'am lifgam (they won't make it forbidden after 24 hours because the taste is bad)? Let's start with the problem of using the vessels in the first place. This idea appears in the Torah in reference to the vessels that were capture from Midian (Bamidbar 31:21-24), and - as Ramban states (verse 23) - the context there is one of purifying the vessels, not of kashering them. This is underscored by the fact that Chazal learn from the same verses the concept of immersing vessels purchased from non-Jews - clearly a ritual not related to removing the bad taste from the vessel walls. Reflecting and reinforcing this is the Mishna in Avoda Zara (75b) which deals with kashering and toveling vessels all in the same discussion. All of this could suggest that kashering vessels is somewhat conceptually related to purifying them and immersing them, and not about the taste in the walls.
While the juxtaposition of these laws is suggestive, it would not, in itself, lead to a reformulation of the operative halakhic principle where there not more concrete evidence that we are dealing here with something besides ta'am. As it happens, there is such evidence, and it comes from the classic discussion in the Talmud regarding the prohibition of ta'am. In its search for the Biblical basis of this prohibition, the Talmud (Pesachim 44b) suggests that the vessels of Midian provide such a source - they are prohibited because of the absorbed taste. No, says the Talmud, perhaps that case is a chidush, an exception, because there - according to one opinion - the Torah prohibited the vessels even though they gave off a bad taste. Now, when the Talmud says that the case of vessels in an exception, it may be saying that it is based on ta'am but it does not follow those rules in all their specifics. However, it may be saying something else - that because this case does not follow the exact rules of ta'am, it is not based on ta'am at all, but it is a completely separate prohibition.
The possibility that we are dealing with a completely separate prohibition is taken up by Ra'ah (Chezkat HaBayit on Torat HaBayit 4:1, 11a), a student of Ramban. Ra'ah asks what he calls a "strong question." How is possible, he asks, that vessels should be forbidden? According to Chazal even the smallest amount of taste is forbidden, and this will usually be present in as little as 1.6% of the mixture. However, he rules that the only time the Torah prohibits taste is when it is a kizayit bi'khdei achilat pras, roughly 11-12% of the mixture. How, he asks, can vessels be a problem, since there is never that much taste absorbed in their walls? His answer - in Ramban's name no less! - is that the Torah's prohibition to use such vessels is not based on the principle of ta'am. Rather, the Torah did not want us to use vessels with an identity of treif vessels. To change this identity we have to kasher them and immerse them. This is why the laws of kashering are juxtaposed to and embedded in the laws of purification, because what we are doing is changing the identity of the vessel from treif to kosher.
While this approach is unconventional, there is something compelling about it (and, it should be noted, Rambam's framing of the law of vessels (Forbidden Foods 17:1-2) indicates a similar approach). First of all, it explains the context and juxtaposition noted above. Secondly, it helps us understand the whole issue of "treif vessels," since it is often hard to really believe that tastes are absorbed into or exuded from, the walls of our cooking vessels. According to Ra'ah, this would not matter, because at the end of the day, the vessel has an identity as kosher or treif. This also helps explain an interesting fact about kashering vessels. We rule, in accordance with Rabbenu Tam, that one need only kasher a vessel based on its standard use. Thus, if one usually cooks in a pot, but every now and then fries in it, and now it needs to be kashered, say for Pesach use, one can kasher it by putting it in a boiling pot, and there is no need to treat it like a frying pan and to kasher by direct heat. Now, if we were really concerned with the physics of absorption, the "majority use" should be irrelevant. Since it absorbed by direct heat - when it was used to fry - then it should need to be kashered by direct heat. However, if we are talking about a ritual that transforms its identity, and since it is primarily a cooking pot, we can understand that it will gain a new identity when it is kashered through a process of cooking.
This approach, as stated, emphasizes using a treif pot, and not the transfer of taste, as the problem. This raises two questions: (1) Why is the food that is cooked in the pot prohibited? and (2) Since the concept of tvilat kelim, to which kashering is linked,only applies to pots of non-Jews, would there be a requirement from the Torah to kasher the treif pots of Jews? Ra'ah addresses both of these questions, and states that (1) the Torah prohibited the food cooked in such a pot as a way to require us to kasher the pot and (2) that although the starting point is the pots of non-Jews, it is reasonable to assume that the Torah likewise prohibited the treif pots of Jews, and insisted that one only use a kosher pot. What, however, would Ra'ah state regarding kosher pots which were milkhig or fleishig and used for the opposite item. In such a case, the pot is not treif. Would the Torah prohibit it? It sounds from Ra'ah that the answer is no, and that the only problem would be a rabbinic one. Presumably building on this, Ra'ah states that there is no problem - not even Rabbinic! - to use a milk vessel for meat, or vice-versa - if the vessel is more than 24 hours old (see Ritva Pesachim 30a). We, clearly, do not rule this way. Whatever may be the case on a Biblical level, we rule that the use of the wrong vessel, even when more than 24 hours old is always prohibited mi'di'rabanan.
Keeping these two approaches to cooking vessels in mind - (1) that it is based on ta'am and (2) that it is an independent prohibition, let's look at the case of the day-old vessel. Why does such a vessel not make the food forbidden? We have been assuming that it is because the absorbed taste has turned bad. But how can we be so sure? Also, according to Rashi (Avoda Zara 76a, s.v. Bat Yoma), the principle is not 24 hours, but whether it is the same day that it was used or a different day. If I cooked treif at 4:30 PM, and then used it for kosher at 6:00 AM the next morning, it would not be a problem, since it is the next day. What sense does this make? How can the taste be a function of "same day/different day" and not a function of the passage of time? The answer, according to Ra'ah, is that if the issue is the status of the vessel and not the absorbed taste, that status is different tomorrow than it is today. Remember, according to Ra'ah, the taste absorbed in it is insignificant. The status of the vessel, then, is based on how it was used. Thus, today, on the same day it was used for treif, it is a treif vessel. Tomorrow, however, it is just a vessel that once was used for treif, but its identity is no longer that of a treif vessel. It is thus not surprising that Tosafot (ad. loc., s..v, Bat Yoma) compares this to the rule of sacrifices, which become invalid - that is, their status changes - the following morning. This is about status, not about taste.
One final application is the difference b'dieved between the food and the vessel. One the vessel is no longer a bat yoma, "of the day," it does not make the food forbidden, but it still may not be used. Why are we more strict regarding the vessel than the food? One cannot argue that it is a difference between lichatchila and b'dieved, since if the pot were ceramic, we would have to discard it, so the rabbinic prohibition to use the vessel would apply even in a b'dieved case. According to Rosh (Avodah Zara 5:36) the explanation is a practical one: we forbid using the vessel when it is not "of the day" so one should not come to use it in cases when it is "of the day." Once people don't use these vessels at all, there is no need to prohibit the food that was cooked in a day-old vessel due to a concern of eating food cooked in a vessel "of the day," since, thanks to the Rabbinic prohibition, it is highly unlikely that someone will come to cook in a vessel that is "of the day."
Tosafot, however, gives a more formal reason that resonates with the approach of Ra'ah. Tosafot (AZ 76a, s.v. mi'Kan) states that the vessel was used with forbidden food. Thus, even after it is a day old, it remains forbidden. However, food cooked in a day-old vessel never came in contact with forbidden food or forbidden taste, and thus remains permissible. In other words, the day old vessel still has a (Rabbinic) status of a "treif vessel" and can never be used whereas the food never gets such a status and can be eaten.
While halakha generally follow the non-Ra'ah approach, and 24 hours is the required time to change the status of the vessels, the Ra'ah's approach still appears in various forms, and it certainly is how we psychologically relate to our vessels. We consider vessels milkhig or fleishig, kosher or treif, and not in terms of their absorbed taste. Perhaps this is because of the difficulty in relating to the concept of absorbed taste, and perhaps because it is an easier way to categorize things. There thus exists and interesting tension between the psychologically attractive and formalistic approach of Ra'ah and the more "real-world" approach of absorbed taste, a tension that plays out in other areas of halakha as well.