I grew up thinking of "bagels, lox, and cream cheese" as a quintessential Jewish food. Imagine my shock when I learned that there are poskim who hold that eating fish with dairy is assur! I had some relief when subsequently learned that the prevailing opinion, led no less than the Taz, is to disregard that ruling in the Beis Yosef as a "ta'os sofrim"/scribal error. That's not today's topic. The Taz, by the way, says that it should have said, "fish with meat"; that is today's topic. (For the interested reader, the YU Torah website has a well researched article on eating fish with meat.)
Chazal (TB P'sachim 76b) say not to eat fish and meat together lest it lead to "davar acher"; which Rashi understands to mean "tzara'as" (not leprosy, but something really not good). In other words, eating fish with meat is forbidden -- by decree of the gemara and brought as halacha in the Shulchan Aruch (Yoreh Deah 116:2) -- because it is dangerous. We have a rule that "sakanta kasha mei'issura" -- we are more strict about physical poisons than spiritual ones (go figure, but that's the way halacha works); fish with meat thus presents a serious concern.
So how much fish with meat is a problem? That is to say, at what point is the amount of fish in your cholent so minuscule that is no longer dangerous? The rule regarding issur is "batel b'shishim"/nullified in 60 times its volume; one ounce of milk is nullified in 60 ounces of cholent. What about sakana; how much is too much? The answer to that is going to depend on how we arrive at the "1 in 60" rule. The Shulchan Aruch says that if some milk falls into meat, then ask an expert (a goy, who is allowed to eat milk/meat combinations) to taste the mixture. If he cannot taste it, then the food is permissible. The Rema says that we don't rely on an expert, but require a volume of sixty times meat to milk; or milk to meat, or kosher chicken soup to treif chicken soup. Why sixty? There are two explanations: (1) We don't have such great expert chefs anymore, but we know with certainty that no one could taste such a small addition, so we are stringent and and always require 60 times the volume to nullify. (2) Once something is less than one part in 60, the Torah considers it as essentially non-existent; hence, there is no taste.
If the reason for "1 in 60" is taste, then that doesn't help for poison; taste is irrelevant, the problem is the danger, not enjoying the experience. If, on the other hand, the reason is that it is halachically non-existent, then that same Torah that says fish with meat is dangerous would also say that such a small fraction of fish is not dangerous. That, together with the Magein Avraham who says that anyway fish with meat is no longer dangerous (nishtana ha'teva), leads most poskim to say that bitul works.
Now that we know bitul works, what happens if one ounce of fish falls into 30 ounces of cholent? Are you allowed to add another 30 ounces of cholent to m'vatel (nullify) the fishiness? The rule for issurei d'oraisa is that one is "ein l'vatel issur l'chatchila" -- if the issur gets nullified, it gets nullified, but one is not allowed to help the process along by adding more cholent. Why not? Because Chazal were afraid that you you wouldn't measure carefully and would end up not quite nullifying the issur. Here, though, when it comes to sakana there is much less reason for that concern; we are all very machmir (stringent) when it comes to our possible poisons. Hence there is good reason to believe that Chazal would permit one to m'vatel sakana l'chatchila; and that is the sense of most poskim.
With all that to rely on, I guess if some fish falls into your cholent, you have to ask yourself one question: "Do I feel lucky?"
Chazal (TB P'sachim 76b) say not to eat fish and meat together lest it lead to "davar acher"; which Rashi understands to mean "tzara'as" (not leprosy, but something really not good). In other words, eating fish with meat is forbidden -- by decree of the gemara and brought as halacha in the Shulchan Aruch (Yoreh Deah 116:2) -- because it is dangerous. We have a rule that "sakanta kasha mei'issura" -- we are more strict about physical poisons than spiritual ones (go figure, but that's the way halacha works); fish with meat thus presents a serious concern.
So how much fish with meat is a problem? That is to say, at what point is the amount of fish in your cholent so minuscule that is no longer dangerous? The rule regarding issur is "batel b'shishim"/nullified in 60 times its volume; one ounce of milk is nullified in 60 ounces of cholent. What about sakana; how much is too much? The answer to that is going to depend on how we arrive at the "1 in 60" rule. The Shulchan Aruch says that if some milk falls into meat, then ask an expert (a goy, who is allowed to eat milk/meat combinations) to taste the mixture. If he cannot taste it, then the food is permissible. The Rema says that we don't rely on an expert, but require a volume of sixty times meat to milk; or milk to meat, or kosher chicken soup to treif chicken soup. Why sixty? There are two explanations: (1) We don't have such great expert chefs anymore, but we know with certainty that no one could taste such a small addition, so we are stringent and and always require 60 times the volume to nullify. (2) Once something is less than one part in 60, the Torah considers it as essentially non-existent; hence, there is no taste.
If the reason for "1 in 60" is taste, then that doesn't help for poison; taste is irrelevant, the problem is the danger, not enjoying the experience. If, on the other hand, the reason is that it is halachically non-existent, then that same Torah that says fish with meat is dangerous would also say that such a small fraction of fish is not dangerous. That, together with the Magein Avraham who says that anyway fish with meat is no longer dangerous (nishtana ha'teva), leads most poskim to say that bitul works.
Now that we know bitul works, what happens if one ounce of fish falls into 30 ounces of cholent? Are you allowed to add another 30 ounces of cholent to m'vatel (nullify) the fishiness? The rule for issurei d'oraisa is that one is "ein l'vatel issur l'chatchila" -- if the issur gets nullified, it gets nullified, but one is not allowed to help the process along by adding more cholent. Why not? Because Chazal were afraid that you you wouldn't measure carefully and would end up not quite nullifying the issur. Here, though, when it comes to sakana there is much less reason for that concern; we are all very machmir (stringent) when it comes to our possible poisons. Hence there is good reason to believe that Chazal would permit one to m'vatel sakana l'chatchila; and that is the sense of most poskim.
With all that to rely on, I guess if some fish falls into your cholent, you have to ask yourself one question: "Do I feel lucky?"
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