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related: Does דבר שיש לו מתירין apply to כל דפריש‎?

Sh O, O Ch, 439 (1).

This is one of the places where we find the difference between כל הקבוע כמחצה על מחצה and כל דפריש מרובא פריש.

דין מי שבדק ולא מצא מספר ככרות שהניח. ובו ד' סעיפים: ט' ציבורין של מצה וא' של חמץ ובא עכבר ונטל ולא ידענו אם נטל חמץ או אם נטל מצה ונכנס לבית בדוק צריך לחזור ולבדקו (מיהו אם הככר קטן שיכול העכבר לאכול תלינן להקל שאכלו וא"צ לבדוק (טור) שכל הקבוע כמחצה על מחצה ואם פירש הככר ממקום קביעתו ונטלו העכבר משם א"צ לחזור ולבדוק דכל דפריש מרובא פריש:

Nine piles of matza, and one of chametz, and a mouse comes and takes [from the piles] and we do not know if the mouse took chametz or matza, and the mouse entered a checked house - you must return and check it (however, if the food is small enough that the mouse could have eaten it - we can rely on a leniency that the mouse did eat it, and you do not need to check) (Tur), as every established place is like a half of a half [i.e. each established location is treated as its own majority].

If the food was separated from its established place, and the mouse took it from there - you do not need to return and check it, as anything separated [is considered to be] separated from the majority.

What is the logic behind this distinction? Can it be explained in terms of probability or is it a halachic concept of Chazal which we must accept?

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    "They" say this is one of three Sugyot that R Chaim Brisker never understood – Double AA Jan 8 at 17:00
  • See sharei yosher. If I remember correctly, there is a difference in the question of the safek. If someone did take a meat piece from an unknown place, the question is what's the place he takes it from. We analyse the group of places. The group is "colored" by the colour of the rov. In kavua the question is what's the nature of this object. In this question the object is not colored by nothing. This is a binary question – kouty Jan 8 at 17:42
  • E.g. if you see a wheel that is running, you analyse the colour you're seen. But if you're examining a portion of the wheel, a static wheel, and your question is what's it's colour – kouty Jan 8 at 17:45
  • Are you asking why either of the principles is true, or is there one principle that makes sense to you and you're just asking why the other principle differs? E.g. perhaps you understand why we normally follow the majority and you're just wondering why we don't follow it when it's קבוע? – Alex Jan 8 at 18:49
  • @Alex I would really like a clear explanation of when the principles apply and why they are different. (But, yes, it seems more reasonable that we normally follow the majority and I wonder why we don't follow it when it's קבוע) – Avrohom Yitzchok Jan 8 at 19:21
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Dr Moshe Koppel presents a statistical/probabilistic explanation of the issue in this article.

In the case you bring, he would argue that if the loaf is parish we would ask the question,”What is the status of this individual loaf?” We can assign its status as matzah, by following the majority, and thus do not need to check the house again.

However, in a case of kavua, the rule is that we assign a hybrid chametz/matzah identity to the entire group of loaves. Thus, any loaf taken from this kavua set has a known, ‘mixed’ status, and so the house must be checked again.

  • There's been some interesting back-and-forth in the journals on this; Koppel argues that probability can't be used, not unlike quantum uncertainty; others suggest it's a moral hazard issue. (So no one benefits from having "oops, forgotten.") Koppel recently wrote that he still thinks his answer "wins on points, but it's not a knock-out." – Shalom Jan 9 at 10:14

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