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DAAT · LEVEL 2 — LAMDAN

Siman 109 — Lamdan level: a forbidden piece that can no longer be told apart

Dry mixed with dry — nullification by majority, and what cooking undoes — study and pilpul
סימן ק״ט
חד בתרי בטיל, ממה נפשך, מין במינו מול שלא במינו, ובישול התערובת
The sugya, chakiros, shitos of Rishonim and Acharonim, nafka minos
⚡ For lomdim and talmidei chachamim ⚡
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Pilpul and in-depth study

Sugyos, sources, the underlying chakira, machlokos of Rishonim and Acharonim,
nafka minos for halakha, and a look at the shitos

Subject:
שולחן ערוך יורה דעה סימן ק״ט (ב׳ סעיפים)
with the ש״ך (שפתי כהן), ט״ז (טורי זהב) and פתחי תשובה

Root of the sugya in Shas:
חולין ק׳. וק״ח. (מין במינו ושלא במינו) · גיטין נ״ד: (חד בתרי) · ביצה ג׳: (ביטול ברוב, דבר שיש לו מתירין) · זבחים ע״ג (ביטול ברוב)
and, as cited by the Shach ס״ק ג: תוספות זבחים ע״ג ע״א ומנחות כ״ב ע״ב (קמח בקמח)

Written by:
הרב יוסף חיים סממה · DAAT

📑 Table of contents

  1. Introduction to the sugya — dry mixed with dry, the piece not fit to be served, and חד בתרי בטיל (seif 1)
  2. The root of nullification by majority — אחרי רבים להטות, the Taz ס״ק א, and why sixty is not required
  3. The sevara of ממה נפשך — the Rashba as the Shach brings him in ס״ק ז, eating them one by one, and the ban on all three together
  4. מין במינו against שלא במינו — why the same kind needs no sixty, and why another kind needs it even dry (the Ran, the Taz ס״ק ב)
  5. Derabanan and deoraisa — the Beis Yosef draws no line; the Shach ס״ק ט–י and the Ran do, and the gloss of the Or Zarua
  6. The Shach’s finer points — קמח בקמח counts as liquid in liquid (ס״ק ג), and the issur stands on its own even cooked (ס״ק ד)
  7. The great chakira of seif 2 — cooking the mixture, the Taz ס״ק ב: how does the issur return min haTorah?
  8. Adding up to sixty without nullifying an issur (ט״ז ס״ק ג) · known beforehand — the name of heter, and the two pots (ש״ך ס״ק י״ב)
  9. Pischei Teshuva — majority of count and double (ס״ק א), the Noda biYehuda (ס״ק ב), Rabbi Akiva Eiger on the lost portion (ס״ק ג), salting (ס״ק ד)
  10. Chakira and nafka mina for practice
  11. Summary tables

📜 The text of the Shulchan Aruch — seif 1

↩ Detailed explanation (level 1)

דין יבש ביבש שנתערב. ובו ב׳ סעיפים

חתיכה שאינה ראויה להתכבד שנתערבה באחרות מין במינה יבש ביבש (דהיינו שאין נבלל והאיסור עומד בעצמו אלא שנתערב ואינו מכירו) (ב״י בשם תשובת הרשב״א והרמב״ן וסה״ת) חד בתרי בטיל ומותר לאכלן אדם אחד כל אחת בפני עצמה אבל לא יאכל שלשתם יחד ויש מי שאוסר לאכלם אדם אחד אפילו זה אחר זה

הגה וכן יש לנהוג לכתחילה ויש מחמירין להשליך אחד או ליתן לעובד כוכבים (הגהות ש״ד בשם מוהר״ם ורש״י בעבודת כוכבים דף ע״ד ע״א) ואינו אלא חומרא בעלמא וכל זה כשנתערב במינו אבל שלא במינו ואין מכירו אפילו יבש ביבש צריך ששים (טור בשם בעל התרומה ועוד הרבה פוסקים) ואין חלוק בכל זה בין אם האיסור מדרבנן או מדאורייתא (בית יוסף בשם הפוסקים דלא כהגהת ש״ד) וע״ל סימן קכ״ב אם נתערבו כלים ביחד

(שו״ע יו״ד ק״ט:א)

1. Introduction to the sugya — dry mixed with dry, and the piece not fit to be served

↩ Detailed explanation (level 1)

The foundation — what is “dry in dry”?

The siman opens on one precise situation. A dry piece of issur — one that has not dissolved and has not blended into the heter but, in the Mechaber’s own parenthesis, שאין נבלל והאיסור עומד בעצמו אלא שנתערב ואינו מכירו, “does not blend, the issur stands on its own, only that it has become mixed and can no longer be told apart” — has fallen among permitted pieces of its own kind, and nobody knows which of the three is the forbidden one. Such a mixture is not judged by taste, as liquid spread through liquid is, but by count. Hence חד בתרי בטיל — one is nullified in two, by plain majority, with no need of sixty. And all of this on one condition: that the piece not be fit to be served to guests; for an important piece is not nullified even in a thousand (see simanim 101 and 110).
« חתיכה שאינה ראויה להתכבד שנתערבה באחרות מין במינה יבש ביבש » (שו״ע יו״ד ק״ט:א)
Why dry and not liquid: in liquid mixed with liquid the body of the issur comes apart and spreads through the whole heter; only its taste is then judged, and the measure of that is sixty. In dry mixed with dry every piece stays whole, the body of the issur stands on its own and has given no taste to its neighbour; the entire deficiency is that we can no longer tell which piece is forbidden. That deficiency is not a matter of taste but of identification — and for identification a majority suffices, by the verse אחרי רבים להטות. The Shach makes the point already in ס״ק ג: קמח בקמח does not belong to the dry category at all — flour blends, and its din is that of liquid in liquid. He brings it in the name of the Bach, and then supports it from the Rashba and from Tosafos in Zevachim and Menachos.
« דקמח בקמח כיון דנבלל מיקרי לח בלח » (ש״ך יו״ד ק״ט ס״ק ג)
The Shach ס״ק א — “fit to be served”: the Shach sets the boundary of the whole siman. A piece fit to be served is not nullified, neither in its own kind nor outside it, even in a thousand, and he refers back to siman 101 and ahead to siman 110. Everything that follows is therefore said only of a piece that is not fit to be served; for if it is, even dry in dry and in its own kind it is not nullified by majority.
« ראויה להתכבד בין במינה בין שלא במינה לא בטלה אפילו באלף » (ש״ך יו״ד ק״ט ס״ק א)
The Shach ס״ק ב — the second boundary: the Shach’s lemma is the Mechaber’s words מין במינה, and it announces in advance what the Rama’s gloss will say below: outside its own kind, sixty are required. The two ס״ק that open the siman thus fix its exact field together — a piece not fit to be served, mixed within its own kind.
« אבל שלא במינה צריך ס׳ כדבסמוך בהג״ה » (ש״ך יו״ד ק״ט ס״ק ב)

2. The root of nullification by majority — אחרי רבים להטות

↩ Detailed explanation (level 1)

This is the root of the whole siman, and it is where the Taz puts the weight of his ס״ק א.

The chakira — why does dry in dry not require sixty? Wherever forbidden things mix by way of taste, sixty are needed. Why does a majority suffice here — two pieces only against one?
The Taz’s answer (ס״ק א) — this is the din of majority, from the Torah: the Taz explains that חד בתרי בטיל rests on the verse אחרי רבים להטות. The measure of sixty belongs only where a real taste spreads — in liquid, or outside the kind — and there the taste must be nullified. In dry within its own kind there is no taste at all: the issur stands on its own and has given nothing to the heter; the entire deficiency is not knowing which piece is forbidden, and the majority of permitted pieces settles that. The Taz adds two things that must be read together: the Sages did not require sixty because the piece is not fit to be served; and what they did require, as a stringency, is only that one not eat all three at once — for then, whichever way you turn it, he is eating the issur in that very mouthful.
« דכתיב אחרי רבים להטות ולא החמירו רבנן להצריך ס׳ כיון שאינה ראוייה להתכבד » (ט״ז יו״ד ק״ט ס״ק א)
« רק שהחמירו שלא יאכל שלשתן כא׳ דהא ממה נפשך אוכל האיסור באותה אכילה » (ט״ז יו״ד ק״ט ס״ק א)
A point of method not to be missed: in the Taz, the sevara of ממה נפשך serves to forbid — it shows that one who swallows all three at once certainly swallows the issur. In the Rashba, whom the Shach brings in ס״ק ז, the very same reasoning serves to permit — one who eats a single piece may say of each that it is the permitted one. This is no contradiction: it is the same reckoning read in both directions, and it is what allows one seif to permit one thing and forbid the other in the same sentence.
The Shach ס״ק ו — the majority is counted, not weighed: the Shach glosses the words בתרי בטיל: this means by majority, as the verse says; and even if the majority exists only in those two pieces while they are smaller than the issur, it is nullified. The Shach adds in parentheses the condition of the case: that it not be known which is forbidden, as he will explain in ס״ק ח.
« ברוב כדכתיב אחרי רבים להטות ואפילו ליכא רוב אלא בהנך תרי שהם קטנים מהאיסור » (ש״ך יו״ד ק״ט ס״ק ו)
The Shach ס״ק ה — what the Mechaber left out: the Shach notes that the Tur brought here a machlokes of the poskim about things from which no benefit may be taken, such as chametz on Pesach, and that the Mechaber omitted it in this place — because he relied on what he writes in Orach Chaim 447, that such a thing is not nullified even in a thousand, and that there are those who hold chametz is like other issurim. He further refers to his own ס״ק י״ב in siman 102.
« הטור הביא מחלוקת הפוסקים גבי אסורי הנאה כגון חמץ בפסח » (ש״ך יו״ד ק״ט ס״ק ה)

3. The sevara of ממה נפשך — the Rashba

↩ Detailed explanation (level 1)
The foundation — one by one is permitted, all three together is forbidden:
Since the nullification here is only an identification by majority, it is permitted to eat the pieces one by one. The Shach gives the Rashba’s words: when he eats the first he says “this one is the permitted piece”; and so of each; and even of the last he may say that what was eaten first was the issur, that it has already gone, and that this one is heter — which cannot be said of things that blend. But if he eats all three together, there is nothing left to say: he certainly swallows the issur. That is why the Mechaber forbids the mouthful of three and permits eating them separately.
« דכשאוכל הא׳ אני אומר זהו של היתר » (ש״ך יו״ד ק״ט ס״ק ז)
« חד בתרי בטיל ומותר לאכלן אדם אחד כל אחת בפני עצמה אבל לא יאכל שלשתם יחד » (שו״ע יו״ד ק״ט:א)
One person — one by one, or two at once?
ShitaWhat one person may eatSource
The Rashba, brought and held by the Shach Each separately; and the Shach deduces that it is likewise permitted to eat one and two, or two and one — there is always something left to say “the issur is that one” — to the exclusion of all three together. He supports the deduction from what he will explain in ס״ק י״ב, that they may be cooked in two pots. ש״ך ס״ק ז
The “there is one who forbids” (end of seif 1) One person shall not eat them, even one after another מחבר ס״א
« דה״ה דמותר לאכול א׳ וב׳ או ב׳ וא׳ לאפוקי שלשתן יחד דלא » (ש״ך יו״ד ק״ט ס״ק ז)
« ויש מי שאוסר לאכלם אדם אחד אפילו זה אחר זה » (שו״ע יו״ד ק״ט:א)
What the Shach holds, and what the Rama makes of it: for the Shach the prohibition falls only on the three together, because only there is nothing left to suppose. The Rama rules for practice: it is proper to conduct oneself lechatchila like the “there is one who forbids”, and one person shall not eat them even one after another. As for those who are stricter still and throw one piece away or give it to a non-Jew, the Rama writes in so many words that this is nothing but a stringency.
« וכן יש לנהוג לכתחילה ויש מחמירין להשליך אחד או ליתן לעובד כוכבים » (שו״ע יו״ד ק״ט:א)
« ואינו אלא חומרא בעלמא » (שו״ע יו״ד ק״ט:א)

4. מין במינו against שלא במינו — the fear of cooking

↩ Detailed explanation (level 1)

This is the sharpest distinction in seif 1, and the whole of seif 2 will depend on it.

The chakira — why sixty outside the kind, when it is still dry? If in dry within its own kind a majority suffices, why does the Rama require sixty when the forbidden piece has fallen among pieces of another kind and can no longer be told apart? There too the issur stands on its own and has given no taste.
« וכל זה כשנתערב במינו אבל שלא במינו ואין מכירו אפילו יבש ביבש צריך ששים » (שו״ע יו״ד ק״ט:א)
The answer — the measure of the dry is taken from what it would become if cooked (the Ran, in the Shach ס״ק ט; the Taz ס״ק ב): the distinction rests on the root of nullification in the Torah.
« דבמינו אפי׳ בלח בלח אין צריך ס׳ רק מדרבנן כמ״ש סי׳ צ״ח ס״ח ביבש אפי׳ מדרבנן לא החמירו » (ט״ז יו״ד ק״ט ס״ק ב)
« אבל באינו מינו שמן התורה צריך בלח בלח ששים כיון שיש נתינת טעם » (ט״ז יו״ד ק״ט ס״ק ב)
« ע״כ החמירו רבנן גם ביבש להצריך ס׳ שלא יבוא לידי איסור דאורייתא בבישול » (ט״ז יו״ד ק״ט ס״ק ב)
The root of the matter: the whole distinction is therefore taken from the liquid case. In the dry there is never any real taste; but the Sages set the din of the dry according to what it would be were it cooked. Within its kind — even cooked, a majority would suffice; so nothing was added. Outside the kind — cooked, sixty would be required from the Torah; so the stringency was imposed already while it is dry. And this is the foundation on which the whole of seif 2 is built: what is feared is the cooking, which will draw out the hidden taste. The Shach says the same in citing the Ran’s language, and his own parenthesis refers to siman 98 seif 2 — where the Taz, at the same place, refers to seif 8. The two references do not point at the same thing, and they are worth reading apart.
« מין בשאינו מינו דבלח בלח אזלינן בתר טעמא אפילו ביבש נמי בעינן ס׳ » (ש״ך יו״ד ק״ט ס״ק ט)
The Shach ס״ק ח — what is called “outside its kind”? The Shach gives two forms. The Tur’s: the issur has crumbled into fine pieces that can no longer be told from one another. And the one he adds himself: two or three kinds are present, one of them is known to be forbidden and it is not known which — for instance several animals slaughtered, one of them improperly. In all these, even dry in dry requires sixty. The Shach further discusses, and leaves on a צריך עיון, the formulation of other Acharonim who speak of kinds differing in their fat and alike in appearance: to his mind what matters is that they differ in taste, since it is taste that forbids, and he inclines to see a copyist’s error there.
« כגון שנפרך לחתיכות דקות שאין ניכר בין זה לזה » (ש״ך יו״ד ק״ט ס״ק ח)

5. Derabanan and deoraisa — the Rama draws no line, the Shach does

↩ Detailed explanation (level 1)

The Rama’s gloss (end of seif 1) — “no difference”

The Rama closes the seif with a sentence the Beis Yosef gave him: in all of this there is no difference between a rabbinic issur and a Torah issur. That is: in either case, within its kind, the dry is nullified by majority and not by sixty; and we do not say that a rabbinic issur would already be nullified one against one — a majority is always needed.
« ואין חלוק בכל זה בין אם האיסור מדרבנן או מדאורייתא » (שו״ע יו״ד ק״ט:א)
Outside its kind and rabbinic — are sixty required?
ShitaDry, outside the kind, rabbinic issurSource
The broad reading of the gloss (Beis Yosef) No difference — the rabbinic issur too requires sixty רמ״א ס״א; ב״י
The Shach, in the name of the Ran (ס״ק ט–י) Outside the kind, a rabbinic issur does not require sixty when dry — since the whole of that sixty is only so that one not come to a Torah prohibition, and here there is no Torah prohibition to come to. The Shach uses this to reconcile the two contradictory glosses of the Or Zarua brought in the Hagahos Sha’arei Dura. ש״ך ס״ק ט–י
« דדבר שאינו אסור אלא מדרבנן אף שלא במינו א״צ ס׳ ביבש » (ש״ך יו״ד ק״ט ס״ק ט)
« ועל פי זה נ״ל ליישב מה שנמצא בהגהת ש״ד סי׳ ל״ט שני הגהות מא״ז דסתרי אהדדי » (ש״ך יו״ד ק״ט ס״ק ט)
The root of the disagreement: everything turns on the reason for sixty outside the kind. If the sixty are there because the dry issur already “counts” as giving taste, then rabbinic and biblical are not to be told apart. But if the sixty are only a guard, so that one not arrive at a Torah prohibition, then a rabbinic issur has nothing to arrive at, and sixty are not required. The Shach holds the second branch, and establishes in ס״ק י that these sixty are only rabbinic and not from the Torah, against what might be inferred from Tosafos. One thing must be said plainly here, because the Shach says it of himself: on the Rama’s sentence “no difference” he raises a צריך עיון and asks where it is taken from; he then proposes that the Rama speaks only of the first half of the sentence — that a majority is needed and one against one does not suffice. The question stays open in the Shach, and we leave it open.
« וא״כ צריך עיון על מ״ש הרב ואין חילוק בכל זה בין אם האיסור מדרבנן » (ש״ך יו״ד ק״ט ס״ק ט)
« ולי נראה כדברי הרב כדמשמע בסה״ת וטור להדיא דלא הוי אלא מדרבנן » (ש״ך יו״ד ק״ט ס״ק י)
The Shach ס״ק ד — the issur stands on its own even cooked: even if the forbidden piece has been cooked in water or in other liquids, it keeps the name “dry”. But the Shach at once adds the consequence, and it is twofold: once cooked, sixty are required — the pieces and the water together — against the issur; and the pieces must still be in the majority, for if they are not, all the pieces are forbidden even though there are sixty.
« אע״פ שהוא מבושל במים או משקים אחרים מקרי יבש » (ש״ך יו״ד ק״ט ס״ק ד)
« ואם אין בחתיכות רוב כל החתיכות אסורות אע״פ שיש ס׳ » (ש״ך יו״ד ק״ט ס״ק ד)

📜 The text of the Shulchan Aruch — seif 2

↩ Detailed explanation (level 1)

יבש ביבש שנתבטל חד בתרי אם בשלן כולן כאחד ואפי׳ לאכול כל א׳ בפני עצמו אסור אם אין שם ששים מפני שהרוטב בנותן טעם ונבלע בחתיכות ואם רוצה לבשלן יחד ואין שם ס׳ מותר להרבות עליהם כדי שיעור ששים ולבשלן ואין בו משום מבטל איסור

הגה וי״א דאם נודע התערובת קודם שנתבשלו ביחד הכל שרי דאין חוזרין ונאסרים מאחר שנתבטל ביבש (טור בשם הרא״ש ור׳ ירוחם בשם התוספות וכתב שכן עיקר) ובמקום הפסד יש לסמוך אדברי המקילין ולהתיר

(שו״ע יו״ד ק״ט:ב)

6. The great chakira of seif 2 — cooking the mixture

↩ Detailed explanation (level 1)
The foundation — how does cooking forbid what was already nullified?
A mixture of dry in dry, already nullified one in two and permitted, if it is cooked all together becomes forbidden again where there are not sixty — and that even to eat the pieces one by one. The reason is in the Mechaber: the gravy gives taste and is absorbed into the pieces. By cooking, the taste of the issur goes out into the gravy and spreads through all the pieces; there is no longer an identification by majority here, but a prohibition of taste — and a prohibition of taste requires sixty.
« מפני שהרוטב בנותן טעם ונבלע בחתיכות » (שו״ע יו״ד ק״ט:ב)
The Taz’s question (ס״ק ב) — where would a Torah prohibition return from? The Taz raises the difficulty in his own name. Before the cooking the issur was nullified by majority; had he wished, he could have eaten it by Torah law, and the thing had become complete heter. Why then should it be forbidden afterwards, from the Torah, by cooking? And how does it differ from the case of siman 98 seif 2, where an issur fallen into its own kind and into another kind is said to be overtaken by its own kind, so that we do not worry about the taste it will later give to what is not its kind — since it has already become heter, and the Torah requires no sixty there?
« וקשה לי קודם הבישול נתבטל ברוב ואי בעי שרי למיכליה מדאורייתא ונעשה כהיתר גמור ולמה יאסר אח״כ מן התורה בבישול » (ט״ז יו״ד ק״ט ס״ק ב)
« ומ״ש מההיא דסי׳ צ״ח בסעיף ב׳ בנתערב במינו ואינו מינו דאמרינן מינו רבה עליו » (ט״ז יו״ד ק״ט ס״ק ב)
The Taz’s answer — the taste is felt on its own: the Taz draws a distinction, and it bears on taste, not on status. In siman 98 the issur may well give taste to what is not its kind, yet that taste is never felt on its own, because its own kind has already overtaken it. Here, in dry mixed with dry, the issur stands whole inside its piece; and when it is cooked, the taste of the issur is felt on its own. That is the difference, and that is what brings the prohibition back.
« דשם אע״פ שגם האיסור נ״ט לאינו מינו מ״מ אין הטעם נרגש בפני עצמו משא״כ בדין זה שטעם האיסור נרגש בפני עצמו » (ט״ז יו״ד ק״ט ס״ק ב)
The depth of the foundation: it emerges that nullification by majority in the dry case did not make the body of the issur disappear — it only lifted the prohibition of doubt, so long as the pieces lie dry side by side. The forbidden piece is still there, whole, in the heap; it is our ignorance that was dealt with, not its substance. Then comes the cooking, which draws out its taste: the issur truly spreads, and sixty are required. In this the case differs from the liquid in liquid of siman 98, where the body of the issur has come apart and has no standing of its own left. How far this reading goes — whether the nullification of the dry is a true ביטול or only a היתר ספק — the Taz does not settle in these terms, and we do not settle it for him.

7. Adding up to sixty · known before the cooking — the name of heter

↩ Detailed explanation (level 1)
Adding on top up to sixty — and this is not nullifying an issur:
The caseThe dinSource
He wants to cook them and there are not sixty He may add on top permitted pieces up to the measure of sixty, and then cook them מחבר ס״ב
The concern of nullifying an issur lechatchila There is no issur here at all — since every piece is already permitted on its own ט״ז ס״ק ג; ש״ך ס״ק י״ג בשם הר״ן
« מותר להרבות עליהם כדי שיעור ששים ולבשלן ואין בו משום מבטל איסור » (שו״ע יו״ד ק״ט:ב)
The Taz’s chiddush (ס״ק ג): at first glance one may not nullify an issur lechatchila. The Taz answers in one line, and the Shach says the same in the name of the Ran: since each piece is permitted on its own, there is no issur here. The one who adds therefore nullifies nothing — he adds heter to heter, so that the cooking should not draw the taste out. And it follows that the whole heter rests on the earlier nullification: had the mixture not already been nullified one in two, adding would have been forbidden.
« כיון שכל אחד בפני עצמו מותר אין כאן איסור » (ט״ז יו״ד ק״ט ס״ק ג)
« כיון שכל אחד מותר בפני עצמו ר״ן שם » (ש״ך יו״ד ק״ט ס״ק י״ג)
The Rama — known before the cooking, all is permitted (the Rosh and Tosafos): if the mixture was known before they were cooked together, all is permitted: they do not become forbidden again, since they were already nullified while dry. The Rama brings it from the Tur in the name of the Rosh, and from Rabbenu Yeruham in the name of Tosafos, writing that this is the main view. The Taz gives the reason in a single line: the name of heter had already been called upon it. And in a case of loss, one may rely on the words of those who are lenient and permit.
« דאם נודע התערובת קודם שנתבשלו ביחד הכל שרי דאין חוזרין ונאסרים מאחר שנתבטל ביבש » (שו״ע יו״ד ק״ט:ב)
« משום דכבר נקרא עליו שם היתר » (ט״ז יו״ד ק״ט ס״ק ד)
« ובמקום הפסד יש לסמוך אדברי המקילין ולהתיר » (שו״ע יו״ד ק״ט:ב)
The Shach ס״ק י״ב — the two pots, and the Torah doubt:
« מיהו לבשלן בב׳ קדרות שרי » (ש״ך יו״ד ק״ט ס״ק י״ב)
« ה״ל ספיקא דרבנן לקולא » (ש״ך יו״ד ק״ט ס״ק י״ב)
« ה״ל ספיקא דאורייתא ולחומרא ואסור לכ״ע » (ש״ך יו״ד ק״ט ס״ק י״ב)
« ודינו כדלקמן ס״ס קי״א דב׳ קדרות של אדם אחד מצטרפים לבטל בס » (ש״ך יו״ד ק״ט ס״ק י״ב)
Nafka mina — known or not known: the whole heter of “known beforehand” rests on the name of heter having fallen on the mixture before the cooking. Hence: (a) known, nullified while dry, then cooked → permitted, and whoever wishes to be strict adds up to sixty; (b) never known, then cooked → a Torah doubt, sixty are required, and two pots of one man join for the count. And for practice — ask your Rav.

8. Pischei Teshuva — majority of count, double, a lost portion, and salting

↩ Detailed explanation (level 1)
פ״ת ס״ק א — which majority, and the “double”: the Pischei Teshuva opens with the Pri Chadash, who concludes that anything at all more than half suffices. He then brings the Minchas Yaakov, who holds that rabbinically the double is required; then the Pri Megadim, who writes that in a rabbinic issur the Minchas Yaakov himself concedes, and that in a Torah issur one does not rebuke the one who is lenient like the Pri Chadash. He further refers to the Chasam Sofer, responsum 99.
Then comes the most instructive part of the ס״ק, and it must be read to the end. A certain scholar had read the Shach ס״ק ו as saying that a majority of count suffices — two parts against one — without a majority of bulk. The Chinuch Beis Yehuda refutes him and reads the Shach otherwise: the two pieces, in the Shach, are together larger than the issur, and what is not demanded is only the double. His practical conclusion follows his reading: we do not say that the forbidden piece is nullified in six, nor in sixty, once it is by itself greater in quantity than all sixty together. We do not decide between these two readings of the Shach; we note only that the second is the one the Pischei Teshuva brings last, and that the first is presented there as refuted.
« עיין פר״ח דמסיק דכל דהו טפי ממחצה סגי » (פת״ש יו״ד ק״ט ס״ק א)
« ועי׳ בספר מנ״י כלל ל״א וכלל ל״ט דעתו דמדרבנן בעינן דווקא כפל » (פת״ש יו״ד ק״ט ס״ק א)
« ופירש דר״ל דבהנך תרי יש גם רוב בנין שהב׳ יותר גדולים מן הא׳ אלא דא״צ כפל » (פת״ש יו״ד ק״ט ס״ק א)
« לא אמרינן שתתבטל בששה ולא בס׳ אם הגדולה גדולה בכמות מכל הס » (פת״ש יו״ד ק״ט ס״ק א)
פ״ת ס״ק ב — he threw one away, he eats the rest: the lemma is the Rama’s stringency, “to throw one away”. The Pischei Teshuva brings the Noda biYehuda (Tinyana, Yoreh De’ah 47): once one has been thrown away, even a single person may eat of the two that remain, and we do not say here that “the issur remained in the majority”. The reason is plain: since the nullification has already taken place through the majority, the issur does not fasten itself onto one of the remaining pieces.
« דשוב אפילו אדם אחד יכול לאכול משנים הנותרים ולא אמרינן בהא איסורא ברובא אישתייר » (פת״ש יו״ד ק״ט ס״ק ב)
פ״ת ס״ק ג — Rabbi Akiva Eiger, a lost portion outside the kind: the lemma is “sixty are required”. Rabbi Akiva Eiger (responsum 82) is asked about a dry mixture outside its kind, part of which has been lost without its being known whether there were sixty: does one assume leniently, as one does for a mixture within its kind that has been spilled? He answers in two stages. First the underlying difference: in liquid mixed with liquid, for want of sixty the heter itself becomes forbidden by what it has absorbed — so there is presumption against presumption, and the doubt is treated leniently; in the dry case the heter never turns into issur, it is merely withheld because the issur can no longer be recognised — so the heter is not removed from its state, and the presumption of issur stands to say it was not nullified. Then a second reason: since the reason for the sixty is the fear that they be cooked, that fear applies here too. And Rabbi Akiva Eiger closes by noting himself that the words of the Shach in siman 102 ס״ק י״ד do not appear to go that way — the question therefore stays open with him, and we leave it so.
« וקיימא חזקת האיסור לומר דלא נתבטל » (פת״ש יו״ד ק״ט ס״ק ג)
« ועוד כיון דטעמא שמא יבשלם ממילא גם בזה שייך הגזירה שמא יבשלם » (פת״ש יו״ד ק״ט ס״ק ג)
« אולם מדברי הש״ך סימן ק״ב ס״ק י״ד לא משמע כן » (פת״ש יו״ד ק״ט ס״ק ג)
פ״ת ס״ק ד — is salting like cooking? The lemma is “he may add”. The Pischei Teshuva first brings the Chinuch Beis Yehuda (responsum 41): just as salted counts as boiling, if the mixture became known only after the salting, the name of heter had not yet fallen upon it and this nullification is of no use — sixty are required. The Noda biYehuda writes the same. But the Pischei Teshuva goes on, and this must not be dropped: the same Chinuch Beis Yehuda, at the end of his responsum 97 and in the name of his grandfather, writes the opposite — for dry mixed with dry, salting does not count as cooking, since what makes the difference here is the melting of the fat. And the Pischei Teshuva adds on his own account that those words seem puzzling to him, and he discusses them in the light of the Shach ס״ק ד. There is therefore a machlokes here, and we do not decide it.
« דקיי״ל מליח כרותח אם לא נודע עד אחר מליחה דעדיין לא נקרא עליו שם היתר לא מהני ביטול זה אלא צריך ס׳ » (פת״ש יו״ד ק״ט ס״ק ד)
« אמנם בתשובת חב״י הנ״ל גופיה סוס״י צ״ז בשם זקינו מבואר דבמליחה לא אמרינן הכי » (פת״ש יו״ד ק״ט ס״ק ד)
« ולע״ד דבריו תמוהים » (פת״ש יו״ד ק״ט ס״ק ד)

9. Chakira and nafka mina for practice

↩ Detailed explanation (level 1)
The chakira that runs through the siman: of what nature is the nullification of חד בתרי — a completed nullification, or the lifting of a doubt — and what force does cooking have against it?
Nafka mina for practice, as the siman gives it:
  1. A forbidden piece not fit to be served, dry and within its kind → חד בתרי בטיל, and they may be eaten separately; lechatchila the Rama wants that one person not eat them even one after another, and he calls the throwing away of one piece a stringency.
  2. Outside the kind — or crumbled into fine pieces no longer distinguishable → sixty are required even when dry.
  3. As to the majority, no difference between rabbinic and biblical; as to sixty outside the kind in a rabbinic issur, the Shach ס״ק ט–י is lenient in the name of the Ran and raises a צריך עיון on the Rama’s wording. The question stays open.
  4. Cooked all together without sixty → forbidden (the gravy gives taste); and whoever wishes to cook them adds up to sixty, with no concern of nullifying an issur.
  5. Known before the cooking → all permitted (the name of heter); not known → a Torah doubt, and two pots join (siman 111).
And for practice — ask your Rav.

10. Summary tables

↩ Detailed explanation (level 1)

Table — the forms of the mixture and their din

Form of the mixture What follows Source
Dry within its kind, a piece not fit to be served חד בתרי בטיל by majority; one by one permitted, all three together forbidden מחבר ס״א; ט״ז ס״ק א
What one person may eat One by one, and per the Shach one and two or two and one; lechatchila the Rama does not want it even one after another רשב״א; ש״ך ס״ק ז; רמ״א ס״א
Outside the kind, or crumbled into fine pieces Sixty required even when dry — so that one not come to a Torah prohibition through cooking רמ״א ס״א בשם בעל התרומה; ט״ז ס״ק ב; ש״ך ס״ק ח–ט
Flour in flour Its din is that of liquid in liquid, not of the dry ש״ך ס״ק ג בשם הב״ח; רשב״א ותוספות
Cooked after being dry and nullified, without sixty Forbidden — the gravy gives taste and is absorbed מחבר ס״ב; ט״ז ס״ק ב
He wants to cook and there are not sixty He adds up to sixty; there is no issur here to nullify מחבר ס״ב; ט״ז ס״ק ג; ש״ך ס״ק י״ג
Known before the cooking All permitted — the name of heter had fallen; in a case of loss, one is lenient רמ״א ס״ב; ט״ז ס״ק ד; ש״ך ס״ק י״ב
Cooked in two pots Permitted if the mixture was known; if it was not, a Torah doubt and the two pots join (siman 111) ש״ך ס״ק י״ב
A portion lost, outside the kind Rabbi Akiva Eiger is stringent, noting that the Shach 102 ס״ק י״ד seems to say otherwise רעק״א סי׳ פ״ב; פ״ת ס״ק ג
Known only after the salting Two views: the nullification is of no use and sixty are required; or salting does not count here as cooking פ״ת ס״ק ד (חינוך ב״י סי׳ מ״א ונוב״י against חינוך ב״י סוס״י צ״ז)

Table — the central machlokos of the siman

Subject First shita Second shita
What one person may eat The Rashba — one by one, and one and two (ש״ך ס״ק ז) The “there is one who forbids” — even one after another; and the Rama wants this conduct lechatchila
Outside the kind, a rabbinic issur — are sixty required? The broad reading of the Rama’s gloss (ב״י) — no difference The Shach in the name of the Ran — the rabbinic issur needs no sixty, and he raises a צריך עיון on the Rama’s wording (ס״ק ט–י)
Cooking a mixture already nullified The Mechaber — it becomes forbidden again (the taste is felt on its own; unlike siman 98) The Rosh and Tosafos, in the Rama — known beforehand, it does not become forbidden again
Which majority is required The Pri Chadash — anything at all more than half (פ״ת ס״ק א) The Minchas Yaakov — the double, rabbinically; and the Chinuch Beis Yehuda reads in the Shach a majority of bulk without the double
A portion lost outside the kind, without sixty Rabbi Akiva Eiger — stringent (the presumption of issur stands) Liquid in liquid that was spilled — there one is lenient; and Rabbi Akiva Eiger notes that the Shach 102 ס״ק י״ד seems not to distinguish

Table — the sources of the sugya

Gemara: חולין ק׳. וק״ח. (מין במינו ושלא במינו) · גיטין נ״ד: (חד בתרי) · ביצה ג׳: (ביטול ברוב, דבר שיש לו מתירין) · זבחים ע״ג (ביטול ברוב) · and, as cited by the Shach ס״ק ג and ס״ק י: תוספות זבחים ע״ג ע״א, מנחות כ״ב ע״ב, פסחים מ״ד ע״א, חולין צ״ט
Rishonim: רש״י · רשב״א (חידושים ותורת הבית ותשובות) · רמב״ן · ר״ן · רא״ש · תוספות · רבנו ירוחם · טור · ספר התרומה · אור זרוע · איסור והיתר הארוך · הגהות שערי דורא
Acharonim: בית יוסף · רמ״א · ב״ח · ש״ך · ט״ז · מהרש״ל · פרי חדש · פרי מגדים · מנחת יעקב · פתחי תשובה · נודע ביהודה · רבי עקיבא איגר · חתם סופר · חינוך בית יהודה

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