I am trying to find a definition to the principle תרי משהו. I am totally confused by what I have read. Could someone explain this principle to me?
In the gemara chullin (108A), Rav says that if a משהו - a minimal piece of something forbidden to eat, falls into a pot with numerous whole pieces of food (חתיכות) that are the same type of food (מיו במינו), even though it just touched one piece, everything in the pot is forbidden. This is in accordance with Rebbi Yehuda who hold one item which is forbidden mixed with other items of the same type cannot be nullified and everything is forbidden.
The Shach and Taz argue about the next step in the same case, when a piece of food from the pot (explained above) which itself became forbidden from one piece that touched a piece within it, now a random piece from the pot, extracted from the pot and fell into another pot of the exact same scenario - i.e. it touched one piece in the pot when everything of the pot is the same type. This is תרי משהו, loosely translated as '2 somethings', meaning a double case of משהו.
The Taz is of the opinion that the 2nd pot is permitted, however this is on condition that the piece of food that was touched was removed from the pot, and that there is 60 times the amount of permissible food in the pot more than the forbidden, otherwise everything in the 2nd is forbidden. The Chazon Ish explains this that the piece which was touched only becomes חתיכה של נבילה with regards to itself, but not regards to the other pieces, and that's why 60 times permissible amount would permit the rest of the pieces in the pot.
The Shach is of the opinion in the scenario described, the rest of the pieces in the pot are permitted even without removing the infected piece as long as there is 60 times of permissible pieces more than forbidden which will in effect nullify the forbidden. The understanding is that the infected piece is not considered חתיכה של נבילה , rather as as an item that something else (כח אחר) was merely mixed into it, and when that piece is mixed with other pieces in the pot its considered of a different type than the other pieces (מין בשאינו מינו), and suffices with בטל בששים.
There is a case which exemplifies this argument very well regarding חמץ בפסח which is not nullified when mixed with its own type or a different type. According the Shach, in a scenario when there was a double משהו like described earlier, when that משהו was חמץ, since the infected piece is considered מין בשאינו מינו, nothing can permit the entire pot/mixture. But according to the Taz, the infected piece is considered חתיכה של נבילה and the reason why the other pieces are permitted has nothing to do with מין במינו or not, rather its a leniency in חתיכה של נבילה, therefor regarding חמץ it would also be permitted with ששים של היתר כנגדו.