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In Halachah there's a tremendously powerful concept of Bitul BeRov (nullification among the majority). It goes like this: If you have three identical pieces of meat, and you know for a fact that one is not Kosher but it's not known which one is the non-Kosher one, you can eat all of them because of Rov: You can eat the first because Rov dictates that one of the two you're leaving on the table is probably the non-Kosher one; you can eat the second because the one still on the table or the one you already ate is probably the non-Kosher one; and you can eat the third one because you probably already ate the non-Kosher one. It's generally accepted that you must eat them one at a time for this to work, but the Rosh (Hulin 7:37) is of the opinion that, in fact, you can eat them all together, because once Bitul takes effect, the Isur (prohibited item) becomes Heter (a permitted item).

How do we apply this today? Is it straight textbook? Are there caveats added today? If it's textbook, which opinion do we follow? Finally, how far do we carry this - does it carry to other areas of Halachah, or do we restrict it to the classic case?

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some opinions say you need to throw away one of the pieces. –  Menachem Apr 17 '12 at 5:56
    
@Menachem IIRC the Rosh. –  Baal Shemot Tovot Apr 17 '12 at 13:16
    
@ه ه I'm almost positive that that is impossible. Also, how would that help? –  Seth J Apr 17 '12 at 14:29
    
@ه ه How would it help to discard one of the pieces (from the perspective of whoever holds that you do)? –  Seth J Apr 17 '12 at 19:50
    
Are you only asking about min b'mino? Only about discrete objects? Are you asking about milk in a pot of chicken soup, for example? I'm not sure I understand your question ("How do we apply this today?" and "how far do we carry this"). –  msh210 Apr 18 '12 at 18:48
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The Shulchan Aruch (YD 109:1) rules in accordance with the Rashba who says you may only eat them one after another, but not at the same time. It should be understood, however, that we are only discussing things which do not fall into the category of חתיכה הראויה להתכבד. For specifics see YD 101.

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I liked the first paragraph, but I strongly disagree with your position in the second paragraph. Firstly, besides arguing with the Pri Megadim, you are arguing with the Taz himself as well as the Aruch quoted in the P"M. Secondly, I don't see why the Rashba's words indicate that it is min hatorah. If you are referring to the part "afilu issur shel divreihem ain cahn", that is referring to the issur of shishim as is apparent from the Rashba's words in Toras haBayis. –  YDK Jun 10 '12 at 22:33
    
Thirdly, despite that you have found a similarity between how the Rosh and Rashba pasken by taam keikar, the inyan of taam keikar and that of acharei rabim lehatos are not related and have independent laws. It is an understatement to say that I would be very wary of arguing with the Taz and the Pri Megadim based on a snippet from the Beis Yosef and a svara. –  YDK Jun 10 '12 at 22:34
    
Trust me, I don't argue on a Pri Megadim based on a snippet of from the BY and a svara. But I am going to delete it because clearly it is better for me not to put it there. –  Dov F Jun 10 '12 at 22:59
    
Just one point - that which you write "the inyan of taam keikar and that of acharei rabim lehatos are not related" is not completely true. In the link I had provided I dealt with this extensively, if you want to have a look here (beismedrash.blogspot.com/2011/07/blog-post.html) in the section on the Ra'avad, look at the paragraph beginning with עיין בדברי הראב"ד. –  Dov F Jun 11 '12 at 0:36
    
True, they intersect. I was questioning your assumption that they share a similar idea. –  YDK Jun 11 '12 at 4:04
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