Rav Miller zt'l - Pesachim 45

Published on August 31, 2026

אִם יִרְצֶה הַשֵּׁם

Taste is not combining. A chiddush never teaches. Kodshim cannot teach chulin. Two verses teaching one rule lock that rule in place. R. Akiva’s map is forced by his commitments Rabbanan’s map is clean: mishras = taste, chatas = combining. Kutach requires a third group.

A kezayis in one crack is food until a Tanna lets a real job take the name away.

Water at the bottom is the clean example of a real job. The rim is not.

R. Shimon: a new job can make even a kezayis into wood. Tanna Kama: a kezayis can still leaven, so it stays food.

A thread of dough joins two small pieces only if they come away as one. A house is stricter than a trough, because a broom gathers.

If Rav needs טִיט tit (clay) smeared on the stool, the name alone was never enough.

On 44b the Rabbanan spent מִשְׁרַת mishras on טַעַם כְּעִיקָר ta’am k’ikar. R. Akiva spent it on הֶיתֵּר מִצְטָרֵף לְאִסּוּר heter mitztaref l’issur and took ta’am k’ikar from גִּיעוּלֵי נָכְרִים giulei nochrim. This amud asks whether those vessels are a חִדּוּשׁ chiddush, then why two verses that look the same do not teach a third.

The amud in brief

R. Akiva: taste left in a non-Jewish pot is enough to forbid. That is his source that taste is treated as the substance.

The Rabbanan: the taste in those walls is already a bad taste. A bad taste is usually permitted. The Torah still forbade the pot. That is a chiddush. A chiddush does not teach the rest of the Torah. They therefore keep mishras for ta’am k’ikar.

R. Akiva answers: the Torah only forbade a קְדֵרָה בַּת יוֹמָא kedera bat yoma (a pot used within twenty-four hours). That taste is still a good taste. Not a chiddush.

The Rabbanan: even a same-day pot is a little spoiled. Still a chiddush.

Then the second fight. If R. Akiva uses mishras for combining, why is combining not a model for the whole Torah? Because nazir and חַטָּאת chatas are שְׁנֵי כְּתוּבִים הַבָּאִים כְּאֶחָד shnei kesuvim haba’im ke-echad (two verses that teach one thing). Two such verses do not teach a third.

The Rabbanan split the two verses, so they are not “the same thing twice.” Mishras can still travel. Chatas stays in kodshim.

A third set of Chachamim, says Rashi, spend both verses on combining and treat giulei nochrim as a chiddush. They have nowhere left to learn ta’am k’ikar. They do not hold it. That is why some Chachamim can exempt כּוּתָח הַבַּבְלִי kutach haBavli even though it tastes of chametz.

I. Recap the split of mishras

Kashya. Grapes soaked in water, then removed. The water tastes of wine. A nazir who drinks it is chayav. What did that verse buy?

Terutz. The beraisa uses mishras for ta’am k’ikar. No grapes remain. Only taste. From there the beraisa extends the rule to other prohibitions.

R. Yochanan uses the same word for heter mitztaref, following R. Akiva. Bread and wine together make a kezayis. The permitted half completes the shiur.

Sevara. Pieces stuck together, with no taste moving across, are combining. Taste that has actually entered the other food is ta’am k’ikar. Do not let those two wear one hat.

II. R. Akiva’s source for taste: giulei nochrim

Kashya. R. Akiva spent mishras on combining. Where does he get ta’am k’ikar?

Terutz. גִּיעוּלֵי נָכְרִים giulei nochrim (vessels of non-Jews). After they are washed, no forbidden fat is sitting there. Taste is in the pores. Food later cooked in that pot becomes forbidden. Taste without a visible piece of issur.

Sevara. If the Torah forbids food that only met the leftover taste in a wall, taste is being treated as the substance.

He already rejected בָּשָׂר בְּחָלָב basar b’chalav as a source. That law is a chiddush: cold soaking does not forbid, only cooking does. A chiddush does not build a general rule.

III. Why the Rabbanan will not learn taste from those vessels

Kashya. Why do the Rabbanan still need mishras for taste? Why not take giulei nochrim the way R. Akiva does?

Terutz. Giulei nochrim is a chiddush.

The taste absorbed in the walls is not a good taste. The ordinary rule is נוֹתֵן טַעַם לִפְגָם noten ta’am lifgam (it gives a spoiled taste) — permitted. That rule is learned from נְבֵילָה neveilah: only what is still fit for a ger to eat keeps the name neveilah. A spoiled neveilah has lost that name.

Here the Torah still said those pots are forbidden. So the Torah forbade a bad taste. That is exceptional. You cannot take an exception and apply it wherever issur falls into heter and the taste is already ugly.

R’ Miller’s kitchen:

Meat soaked a day in orange juice. The juice does not gain a favorable meat taste. Take the meat out. The juice is not forbidden as ta’am k’ikar.
A large insect falls into hot soup. Remove it. The soup did not become better. Noten ta’am lifgam. Permitted.

If giulei nochrim forbids even that kind of taste, it is a chiddush. A chiddush stays home.

Sevara. A general rule is built from a normal case. An abnormal case that the Torah singled out cannot be the teacher for every other kitchen.

IV. Kedera bat yoma — is the taste still good?

R. Akiva will not let the vessels stay a chiddush.

Kashya. If the taste in the walls is already spoiled, how can this be a model for ta’am k’ikar?

Terutz. לֹא אָסְרָה תּוֹרָה אֶלָּא בִּקְדֵרָה בַּת יוֹמָא lo asrah Torah ela bikedera bat yoma (the Torah forbade only a pot used that same day). Within twenty-four hours the absorbed taste has not yet gone bad. It is still נוֹתֵן טַעַם לְשֶׁבַח noten ta’am l’shevach (it gives a favorable taste). That is a normal case of taste. From there you may learn everywhere.

What everyone agrees, as a matter of later halachah in the kitchen:

Cook kosher meat in a treif pot that has sat unused for twenty-four hours: you should not have done it, but the meat is mutar. The old taste is lifgam.
Cook in a treif pot used within twenty-four hours: the meat is assur. The taste has not yet spoiled.

The fight is only whether that same-day pot can serve as a limud for the whole Torah.

Terutz of the Rabbanan. קְדֵרָה בַּת יוֹמָא נָמֵי לָא אֶפְשָׁר דְּלָא פָּגְמָה פּוּרְתָּא kedera bat yoma nami la efshar d’lo pagmah purta (even a same-day pot — it is not possible that it was not spoiled a little). Not spoiled enough that food cooked in it would be permitted. Still a little off. The Torah forbade that slightly-off taste. Still a chiddush. Still not a teacher.

Sevara. R. Akiva needs the taste in the wall to be a clean “taste is like the thing.” The Rabbanan say the wall-taste is never clean. The verse that forbids it is doing extra work. Extra work does not travel.

V. Why combining does not leave nazir — chatas

Kashya. The Rabbanan use mishras for taste and then say מִכָּאן אַתָּה דָּן לְכׇל הַתּוֹרָה כּוּלָּהּ mikan atah dan l’chol ha-Torah kulah (from here you judge the whole Torah). Why does R. Akiva not do the same with combining?

Terutz. מִשּׁוּם דְּהָוֵה נָזִיר וְחַטָּאת שְׁנֵי כְּתוּבִים הַבָּאִים כְּאֶחָד וְאֵין מְלַמְּדִין mishum de-haveh nazir ve-chatas shnei kesuvim haba’im ke-echad ve-ein melamdin (because nazir and chatas are two verses that come as one, and they do not teach).

If the Torah writes the same principle twice, and one of those two could have been learned from the other, the double writing is itself the lesson: do not take this principle anywhere else.

What is the chatas verse?

כֹּל אֲשֶׁר יִגַּע בִּבְשָׂרָהּ יִקְדָּשׁ kol asher yiga bivsarah yikdash (whatever touches its flesh shall become holy).

Hava amina. Even cold touching, with nothing absorbed, would join the two pieces. Heter mitztaref by contact alone.

Terutz. תַּלְמוּד לוֹמַר בִּבְשָׂרָהּ — עַד שֶׁיִּבָּלַע בִּבְשָׂר talmud lomar bivsarah — ad she-yibala bivsar (the verse said in its flesh — until it is absorbed in the flesh).

Not full ta’am k’ikar. The taste of the chatas does not have to fill the whole piece of chulin. It has to enter at least part way. That bond is enough. The two pieces now add up to a kezayis. Combining.

יִקְדָּשׁ yikdash (it shall become holy): the thing that absorbed becomes like the chatas. תֵּאָכֵל כֶּחָמוּר שֶׁבָּהּ te’achel ke-chamur shebah (it is eaten according to the stricter of the two).

R’ Miller’s picture: hot chatas meat touches shelamim, and some taste of the chatas enters part of the shelamim. The shelamim now carries the chumros of chatas: one day and its night, only inside the azarah, only kohanim.

Sevara. Combining here is not “the stew tastes of chatas all the way through.” It is “enough of the chatas entered to tie the two pieces into one shiur and one kedushah.”

VI. Are the two verses really the same thing twice?

Kashya. Then the Rabbanan also have nazir and chatas. Why are those two not shnei kesuvim for them too? Why may they still learn ta’am k’ikar from mishras to the whole Torah?

Terutz. הָנֵהוּ מִצְטָרִיךְ צְרִיכִי hanehu mitztarech tzerichi (those two are each needed). They do not teach one thing.

The Rabbanan’s budget:

Chatas buys heter mitztaref. You cannot take that out to chulin. חוּלִין מִקָּדָשִׁים לֹא גָּמְרִינַן chulin mi-kodshim lo gamrinan (we do not learn ordinary food from sacrificial food). Kodshim are stricter. Combining may live only there.
Mishras buys ta’am k’ikar. Nazir is chulin. From chulin you may learn the rest of the Torah.

Because each verse is doing a different job, they are not “the same principle written twice.” Mishras is free to travel.

Kashya on R. Akiva. Why does he call them the same thing twice? Could he not also split them?

Terutz. On his map both verses buy combining.

Granted: you cannot learn nazir from chatas. Chulin is not learned from kodshim. So nazir had to be written.

But you could learn chatas from nazir. Once combining is taught in chulin, kodshim — which are stricter — would follow. The Torah still wrote chatas. That second writing is extra. Extra writing of the same rule means: do not take combining anywhere else.

Sevara. Shnei kesuvim is not a count of verses. It is a test: could one have taught the other? If yes, the second verse is a fence, not a teacher.

The Rabbanan fail that test because the two verses are not buying the same product. R. Akiva passes the test: both buy combining, and chatas could have been learned from nazir.

R’ Miller reads Rashi in the middle of the amud the same way: mishras for R. Akiva is heter mitztaref; ta’am k’ikar he already has from giulei nochrim; therefore chatas is the extra combining-verse that locks combining inside those two rooms.

VII. Could the assignments flip?

Kashya. Why not give mishras to combining and chatas to taste? Or the reverse of the Rabbanan’s split?

Terutz. If chatas were the source for ta’am k’ikar, that source could not leave kodshim. You would have no model of taste for the whole Torah.

If mishras were combining and chatas were taste, combining might travel from nazir, and taste would be stuck in kodshim. That is not the Rabbanan’s result. They need taste to travel. So mishras — the chulin verse — must be the taste-verse.

R. Akiva does not need a traveling taste-verse. He already has giulei nochrim. He can afford to spend both nazir and chatas on combining, and then let shnei kesuvim keep combining from traveling.

Sevara. Who owns which verse is not taste. It is which result each Tanna still needs after his other sources are spent.

VIII. A third set of Chachamim and kutach

Kashya. Kutach haBavli has the taste of chametz in it. Both the Rabbanan of this sugya and R. Akiva hold ta’am k’ikar. Who then are the Chachamim who argue with R. Eliezer and exempt the dip?

Terutz of Rashi, as R’ Miller reads him. Another set of Chachamim.

They spend mishras on combining, like R. Akiva. They also read chatas as combining. So those two verses are shnei kesuvim and do not teach combining anywhere else — and they also do not teach taste.

They will not take taste from giulei nochrim, because they agree it is a chiddush (lifgam, even if only a little).

Nothing is left. They do not hold ta’am k’ikar at all. Taste of chametz in kutach is not enough. That is how the dip can be exempt.

Sevara. A Tanna is not only “the Rabbanan” or “R. Akiva.” The kutach dispute needs a third budget: both verses spent on combining, vessels treated as a chiddush, no leftover coin for taste.

Table

Din	Tzad	Rayah	Chal	Pivot
Taste in soaked grape-water	grapes removed	Rabbanan spend mishras	nazir is chayav; model for the Torah	not combining
Bread and wine adding to a kezayis	both named	R. Akiva spends mishras	combining	not taste
Taste in a non-Jewish pot	no visible issur	R. Akiva’s source for taste	food cooked there is assur	only if not a chiddush
Taste in the walls is ugly	noten ta’am lifgam	neveilah still fit for a ger	ordinarily mutar	giulei forbids it anyway
Same-day pot	taste not yet ruined	R. Akiva / kedera bat yoma	a normal good taste	can teach the Torah
Same-day pot, a little off	pagmah purta	Rabbanan	still a chiddush	cannot teach the Torah
Chatas absorbed in other meat	ad she-yibala bivsarah	kol asher yiga bivsarah	combining + the chumros of chatas	not full permeation
Combining everywhere	nazir would have taught chatas	R. Akiva	two verses, one job	ein melamdin
Taste everywhere, combining only in kodshim	each verse needed	Rabbanan	chulin mi-kodshim lo gamrinan	not shnei kesuvim
Kutach tastes of chametz but is exempt	no ta’am k’ikar at all	third Chachamim (Rashi)	both verses on combining; vessels a chiddush	no leftover source

Terms of art

מִשְׁרַת mishras (soaking) — the nazir’s word. Spent on taste or on combining, not both.
טַעַם כְּעִיקָר ta’am k’ikar (taste is treated as the substance)
הֶיתֵּר מִצְטָרֵף לְאִסּוּר heter mitztaref l’issur (permitted food completes the shiur of the prohibition)
גִּיעוּלֵי נָכְרִים giulei nochrim (vessels used by non-Jews; absorbed taste in the walls)
חִדּוּשׁ chiddush (an exceptional law; it does not teach a general rule)
נוֹתֵן טַעַם לִפְגָם / לְשֶׁבַח noten ta’am lifgam / l’shevach (gives a spoiled taste / a favorable taste)
נְבֵילָה neveilah (carcass) — only what a ger would still eat keeps that name
קְדֵרָה בַּת יוֹמָא kedera bat yoma (a pot used within twenty-four hours)
לָא אֶפְשָׁר דְּלָא פָּגְמָה פּוּרְתָּא la efshar d’lo pagmah purta (it is not possible that it was not spoiled a little)
חַטָּאת chatas (sin-offering)
כֹּל אֲשֶׁר יִגַּע בִּבְשָׂרָהּ יִקְדָּשׁ kol asher yiga bivsarah yikdash (whatever touches its flesh shall become holy)
עַד שֶׁיִּבָּלַע בִּבְשָׂר ad she-yibala bivsar (until it is absorbed in the flesh)
תֵּאָכֵל כֶּחָמוּר שֶׁבָּהּ te’achel ke-chamur shebah (eaten by the stricter of the two)
שְׁנֵי כְּתוּבִים הַבָּאִים כְּאֶחָד וְאֵין מְלַמְּדִין shnei kesuvim haba’im ke-echad ve-ein melamdin (two verses that come as one do not teach a third case)
חוּלִין מִקָּדָשִׁים לֹא גָּמְרִינַן chulin mi-kodshim lo gamrinan (ordinary food is not learned from sacrificial food)
מִצְטָרִיךְ צְרִיכִי mitztarech tzerichi (each verse is needed for its own job)
כּוּתָח הַבַּבְלִי kutach haBavli (Babylonian sour dip)

No new named middah is invoked on this amud beyond what 44b already flagged. The kal va-chomer from nazir to kil’ei ha-kerem and orlah was the beraisa on 44b. Today the work is chiddush and shnei kesuvim.

Main points

Giulei nochrim is R. Akiva’s source for ta’am k’ikar. The Rabbanan call it a chiddush because wall-taste is lifgam.
R. Akiva limits the verse to a kedera bat yoma, so the taste is still good. The Rabbanan say even that pot is a little spoiled.
Combining does not leave nazir for R. Akiva, because chatas teaches the same thing and one could have been learned from the other.
The chatas verse needs absorption, not mere touching. The absorbed piece takes the stricter kedushah.
The Rabbanan split the two verses: mishras for taste that travels, chatas for combining that stays in kodshim. That is why they are not shnei kesuvim.
A third budget (Rashi) spends both verses on combining and treats the vessels as a chiddush. Those Chachamim hold no ta’am k’ikar. That is a way to exempt kutach.

Open kashya

Tosafos on this amud points at Nazir 37b. There the Rabbanan look as if they need both nazir and chatas for ta’am k’ikar — chulin cannot learn from kodshim, and chatas cannot learn from nazir because a nazir is stringent in another direction (even the pits are forbidden). Our amud has the Rabbanan spending chatas on combining, not on taste. Can both pages be the same Rabbanan?

Rav Ashi then brings מִכֹּל אֲשֶׁר יֵעָשֶׂה מִגֶּפֶן הַיַּיִן mi-kol asher ye’aseh mi-gefen ha-yayin (from all that is made of the wine-grape): issur of a nazir combines with issur. If R. Akiva already lets heter complete an issur, why do we need a verse that issur completes issur? The Gemara starts to answer: combining heter with issur is in one eating; combining two issurim can be one after the other inside a p’ras. The shiur did not finish that line.

From 44a the parked stone is still on the table: a nikar clove of garlic and bitul. Nothing on 45a moved it.

And the mishnah already printed on this amud — dough in the cracks of a kneading trough — has not been opened.

אִם יִרְצֶה הַשֵּׁם

On 45a the Rabbanan and R. Akiva split מִשְׁרַת mishras and חַטָּאת chatas. Rav Ashi then asked why a nazir still needs a verse that pits and peels add to each other. This shiur answers that line, then opens the mishnah of dough in the cracks of an עֲרֵיבָה areivah (kneading trough).

The amud in brief

Rav Kahana: heter adding to issur is one swallow. Two issurim of a nazir add even one after the other. That is why מִכֹּל אֲשֶׁר יֵעָשֶׂה מִגֶּפֶן הַיַּיִן mi-kol asher ye’aseh mi-gefen ha-yayin is still needed.

Then the trough. A כְּזַיִת kezayis of dough in one crack: חַיָּיב לְבַעֵר chayav leva’er. Less than a kezayis: בָּטֵל בְּמִיעוּטוֹ batel bemi’uto. The same dough is also a חֲצִיצָה chatzitzah for tumah if he is מַקְפִּיד makpid to scrape it off, and it is like the trough itself if he wants it to stay.

Shmuel limits the mishnah by place: מָקוֹם הֶעָשׂוּי לְחַזֵּק makom he-asuy lechazek (a crack that mends the vessel) against מָקוֹם שֶׁאֵין עָשׂוּי לְחַזֵּק makom she-ein asuy lechazek. Two lishanos. Two beraisos. They fight.

Rav Huna wants the lenient beraisa erased. Rav Yosef says both are Tannaim. The witness is moldy bread versus a כּוֹפֶת שְׂאוֹר kofes se’or assigned as a footstool.

Abaye: that only settles a kezayis. For less than a kezayis both beraisos are R. Shimon b. Elazar, and lechazek is being used for two different heights of the trough.

Rav Nachman reports Rav’s psak, then asks whether assignment alone is enough or you must smear clay. The amud ends on two half-kezaysim tied by a thread, and whether a house is like a trough.

I. Recap, then why pits and peels need their own verse

Kashya. R. Akiva already holds הֶיתֵּר מִצְטָרֵף לְאִסּוּר heter mitztaref l’issur. A nazir who eats half a kezayis of bread with half a kezayis of wine is chayav. Why does the Torah still write מִכֹּל אֲשֶׁר יֵעָשֶׂה מִגֶּפֶן הַיַּיִן מֵחַרְצַנִּים וְעַד זָג mi-kol asher ye’aseh mi-gefen ha-yayin me-chartzanim ve-ad zag (from all that is made of the wine-grape, from pits to peel)? Issur plus issur should be obvious.

Terutz of Rav Kahana. אִסּוּר וְהֶיתֵּר בְּבַת אַחַת, אִסּוּר וְאִסּוּר בְּזֶה אַחַר זֶה issur ve-heter be-vas achas, issur ve-issur be-zeh achar zeh (heter with issur — at one time; issur with issur — one after the other).

R’ Miller’s picture. Half a kezayis of heter stuck to half a kezayis of issur, eaten as one mass: that is the combining R. Akiva took from mishras. Seeds first, then peels, not stuck, not one swallow: that still adds for a nazir. The vine-verse teaches the second case. You would not have known it from combining heter with issur.

Sevara. Adding a permitted half is a weaker claim. Adding two forbidden halves even when they are eaten apart is a stronger claim. The verse is doing the stronger work.

No new named middah is used here. The verse teaches the nazir’s own issurim combine. The shiur does not take it further.

II. The mishnah of the areivah

בָּצֵק שֶׁבְּסִדְקֵי עֲרֵיבָה batzek she-be-sidkei areivah (dough in the cracks of a kneading trough).

Kashya. The dough dried in the wood. Is it still chametz you must remove, or has it become like glue in the crack?

Terutz of the mishnah.

אִם יֵשׁ כְּזַיִת בְּמָקוֹם אֶחָד — חַיָּיב לְבַעֵר im yesh kezayis be-makom echad — chayav leva’er (if there is a kezayis in one place, he must remove it).
וְאִם לָאו — בָּטֵל בְּמִיעוּטוֹ ve-im lav — batel bemi’uto (if not, it is nullified by its smallness).

This is not ordinary bitul b’rov. The dough is small, hard, and sitting in a crack like paste. The mishnah treats that small paste as part of the trough.

Same dough, year-round, for tumah:

אִם מַקְפִּיד עָלָיו — חוֹצֵץ im makpid alav — chotzetz (if he minds it, it interposes). A sheretz that touches the dough has not touched the trough. The trough stays tahor. When he immerses the trough, that dough blocks the water.
אִם רוֹצֶה בְּקִיּוּמוֹ — הֲרֵי הוּא כָּעֲרֵיבָה im rotzeh be-kiyumo — harei hu ka-areivah (if he wants it to remain, it is like the trough). A sheretz on the dough is a sheretz on the vessel.

Sevara. “Part of the vessel” and “food I still own” are one question asked twice. If he is going to scrape it, it is a stranger sitting on the wood. If he is glad it stays, it is the wood.

R’ Miller’s first cut. Dough smeared on the side of the trough, not in a crack, is never the vessel. Sooner or later it is scraped. Dough packed in a crack can become the vessel — if it is small enough, or if the crack needs mending.

III. Two lishanos of Shmuel

Rav Yehudah in the name of Shmuel puts a second variable on the mishnah: where the crack sits.

Water always runs to the bottom. A crack at the bottom lets water out. Dry dough there mends the trough. That is makom he-asuy lechazek. A crack higher on the wall does not hold water. Mending it is less useful. That is makom she-ein asuy lechazek.

Lashon 1. The mishnah said a kezayis must be removed only where the crack does not mend. Where it does mend, even a kezayis may stay. From that we hear: less than a kezayis may stay even in a crack that does not mend.

Lashon 2. The mishnah said less than a kezayis is batel only where the crack does mend. Where it does not mend, even less than a kezayis must go. From that we hear: a kezayis must go even where the crack mends.

Kashya. One Tanna needs two disadvantages before you must remove: a kezayis, and a crack that does not mend. One advantage is enough to leave it. The other Tanna lets one disadvantage force removal. You may leave it only if you have both advantages: less than a kezayis, and a crack that mends.

Sevara. Size asks: is this still an eatable shiur of chametz? Place asks: is this dough doing a job for the wood? Lashon 1 lets either “small” or “useful to the vessel” save it. Lashon 2 wants both.

IV. The two beraisos, and what they do to tumah

Each lishon has a beraisa.

Beraisa 1, matching lashon 1. Where the crack mends: not a chatzitzah, and he does not transgress bal yera’eh. Where it does not mend: it is a chatzitzah, and he transgresses. That second line is said about a kezayis. Less than a kezayis is not a chatzitzah and he does not transgress, even where the crack does not mend.

Beraisa 2, matching lashon 2. The same two lines about mending and not mending. Then: that is said about less than a kezayis. A kezayis, even where the crack mends, is a chatzitzah and he transgresses.

R’ Miller’s in-between case, which the shiur spent time on. Less than a kezayis in a crack that does not mend, according to lashon 1:

For Pesach you may leave it. It is small.
For tumah it is not part of the trough. The crack is not doing a needed job. A sheretz on that dough does not make the trough tamei.

So “you may keep it on Pesach” and “it is the vessel” are not the same sentence. The shiur called that a temporary pshat until the beraisos are sorted.

Sevara. Pesach asks whether this is still chametz you own. Tumah asks whether this lump belongs to the wood. Smallness can answer the first without answering the second.

V. Rav Huna erases; Rav Yosef brings Tannaim

Kashya. The two beraisos contradict.

Terutz of Rav Huna. סְמִי קִילְּתָא מִקַּמֵּי חֲמִירְתָא semi kilta mikamei chamirta (erase the lenient one in front of the stringent one). Keep beraisa 2.

Terutz of Rav Yosef. תַּנָּאֵי שָׁקְלַתְּ מֵעָלְמָא? Tanna’ei shakalt me-alma? (have you taken the Tannaim out of the world?). Both beraisos stand. They are a machlokes Tannaim.

The witness beraisa:

הַפַּת שֶׁעִפְּשָׁה חַיָּיב לְבַעֵר, מִפְּנֵי שֶׁרְאוּיָה לְשׁוֹחֲקָהּ וּלְחַמֵּעַ בָּהּ כַּמָּה עִסּוֹת ha-pat she-ifshah chayav leva’er, mipnei she-re’uyah leshochkah u-lechame’a bah kamah isos (bread that grew moldy — he must remove it, because it is fit to grind and to leaven many doughs).

R. Shimon b. Elazar: that is only if it is being kept as food. אֲבָל כּוֹפֶת שְׂאוֹר שֶׁיִּיחֲדָהּ לִישִׁיבָה — בָּטְלָה aval kofes se’or she-yichadah le-yeshivah — batlah (but a lump of leaven that he assigned for sitting — it is nullified).

From R. Shimon saying batlah, we hear the Tanna Kama: it is not batel. A kezayis of chametz, even assigned as a chair, is still chametz. You can still grind a footstool of old dough into yeast.

Map that onto the trough:

Tanna Kama: a kezayis is never batel, even packed in a bottom crack as paste.
R. Shimon b. Elazar: once you assign it to a mechanical job — chair, or paste that mends the trough — even a kezayis is batel.

Sevara. The Tanna Kama looks at what the lump can still do as food. If it can still leaven, it is still chametz. R. Shimon looks at what you named it. A chair is not bread.

VI. Abaye: you settled the kezayis, not the small piece

Kashya of Abaye. תִּרַּצְתָּ בִּכְזַיִת, פָּחוֹת מִכְּזַיִת מִי תִּרַּצְתָּ? tiratzta bi-kezayis, pachos mi-kezayis mi tiratzta? (you settled the kezayis; did you settle less than a kezayis?).

The footstool beraisa is about a large lump assigned away from food. It explains why one beraisa lets a kezayis stay in a mending crack and the other does not. It does not explain why one beraisa lets a small piece stay in a crack that does not mend, and the other does not. Neither the Tanna Kama nor R. Shimon was talking about a crumb left in an unused crack with no new name given to it.

Terutz of Abaye. Both trough-beraisos are R. Shimon b. Elazar. They are not arguing. They are using makom he-asuy lechazek for two different heights.

Three heights on the same wooden trough:

The very bottom. Water sits there. A plugged crack is needed. Like assigning the dough as a real tool.
The wall, a little higher. No standing water. While you knead, dough can squeeze into a crack. Useful, not urgent.
The rim — שִׂפְתָא דְאַגָּנָא sifta de-agna (the lip of the vessel). Mending that crack does no work.

Beraisa 1 talks bottom versus wall.

Bottom = lechazek. Even a kezayis is batel. That is R. Shimon’s footstool.
Wall = ein lechazek. Only less than a kezayis is batel. A kezayis on the wall must go.

Beraisa 2 talks wall versus rim.

Wall = lechazek. Less than a kezayis is batel. A kezayis is not.
Rim = ein lechazek. Even less than a kezayis is not batel.

Rav Ashi: do not hear “rim” as only the back of the rim, outside, where nothing ever happens. Even the top of the lip itself is ein lechazek.

Kashya. That is obvious. Nobody kneads on the lip.

Terutz. מַהוּ דְּתֵימָא, זִמְנָא דְּאָטֵיף וּמָטֵי לְהָתָם mahu de-teima, zimna de-ateif u-mati le-hatam (you might say: sometimes it overflows and reaches there). Dough climbs the wall and lies on the lip. You might think a crack in the lip then does a small job. Rav Ashi: we do not count that. The lip is not a mending-place.

Sevara. R. Shimon only nullifies dough that is doing a real mechanical job. “Sometimes dough slops onto the rim” is not a job. The two beraisos are one Tanna walking the trough from the water-line up to the lip and changing what the same phrase means at each height.

VII. Does Rav follow R. Shimon — and is assignment enough?

Rav Nachman in the name of Rav: the halachah is like R. Shimon b. Elazar.

Kashya. Rav Yitzchak bar Ashi in the name of Rav: אִם טָח פָּנֶיהָ בְּטִיט — בָּטְלָה im tach paneha be-tit — batlah (if he smeared its face with clay, it is nullified). Smear, yes. No smear, no. So assignment as a footstool is not enough. How can Rav follow R. Shimon, who nullifies by assignment alone?

Terutz. Two lishanos about what Rav said.

One lishon: Rav does follow R. Shimon. The man who reported the clay-condition does not hold that Rav follows him.
Other lishon: Rav does not follow R. Shimon. That is why clay is required. A giant leftover challah kept as a souvenir is still chametz until you coat it.

On the second lishon, a kezayis packed in the bottom crack is not batel just because the crack needs paste. You would have to cover it.

Sevara. R. Shimon’s chiddush is that a new name can take food away from food. The clay-lishon says the new name is not enough until the lump no longer looks like food.

VIII. Two half-kezaysim and a thread — trough is not a house

Rav Nachman in the name of Shmuel. Two pieces, each less than a kezayis, in two cracks, with a thread of dry dough between them.

Kashya. Does the thread make them one kezayis?

Terutz. רוֹאִין ro’in (we look). Take hold of the thread.

Pull, and both pieces come out with it: they are one. Chayav leva’er.
Pull, and the thread snaps, the pieces stay: they are two. Each is less than a kezayis sitting in a crack of an areivah. Mutar to leave, on the lishon that a small piece in a crack may stay.

Kashya. Why only in an areivah? In a house, two crumbs less than a kezayis — even in floorboard cracks — you must remove.

Terutz. A house is swept. Sweeping can gather the two crumbs into one kezayis. An areivah is not swept that way. The pieces stay in their cracks.

The amud then asks, and does not answer:

Half a kezayis downstairs in the floor, half upstairs, and a hole in the ceiling with a ladder. Sweeping upstairs may drop dough through the hole.
Half in the house, half on the porch.
Two rooms, one reached only through the other.

Sevara. The trough-case is a piece that will stay where it was put. The house-case is a piece that lives in a room whose ordinary use is to gather dirt to one pile.

Table

Din	Tzad	Rayah	Chal	Pivot
Pits then peels, each a half	not one swallow	vine-verse	nazir is chayav	not heter plus issur
Bread plus wine, one mass	one swallow	R. Akiva / mishras	combining heter with issur	not sequential issurim
Kezayis in one crack	eatable shiur	mishnah	chayav leva’er	unless the crack mends, on lashon 1
Less than a kezayis in a crack	small, like paste	mishnah	batel bemi’uto	unless the crack does not mend, on lashon 2
He minds the dough	will scrape it	makpid	chatzitzah; trough not tamei from a sheretz on the dough	not “part of the wood”
He wants it to stay	mends, or he leaves it	rotzeh be-kiyumo	like the trough	sheretz on the dough is sheretz on the vessel
Bottom crack	water would leak	asuy lechazek	even a kezayis may stay — R. Shimon	real mechanical job
Wall crack	dough may squeeze in	less essential lechazek	only a small piece stays	same phrase, higher up
Rim	overflow only	ein asuy lechazek	even a small piece must go	not a job
Moldy bread / footstool	still can leaven	Tanna Kama	never batel	name does not help a kezayis
Footstool of se’or	assigned to sitting	R. Shimon b. Elazar	batel	new name takes it out of food
Two small pieces plus a thread	dry dough between them	ro’in if they come out as one	one kezayis or two	only in an areivah
Two small pieces in a house	sweeping gathers	Ula	chayav leva’er	house is not a trough

Terms of art

מִכֹּל אֲשֶׁר יֵעָשֶׂה מִגֶּפֶן הַיַּיִן מֵחַרְצַנִּים וְעַד זָג mi-kol asher ye’aseh mi-gefen ha-yayin me-chartzanim ve-ad zag (from all that is made of the wine-grape, from pits to peel)
אִסּוּר וְהֶיתֵּר בְּבַת אַחַת / אִסּוּר וְאִסּוּר בְּזֶה אַחַר זֶה issur ve-heter be-vas achas / issur ve-issur be-zeh achar zeh (heter with issur at one time / two issurim one after the other)
עֲרֵיבָה areivah (kneading trough)
סִדְקֵי עֲרֵיבָה sidkei areivah (cracks of the trough)
חַיָּיב לְבַעֵר chayav leva’er (he must remove it)
בָּטֵל בְּמִיעוּטוֹ batel bemi’uto (nullified by its smallness)
מַקְפִּיד makpid (he minds it / intends to remove it)
רוֹצֶה בְּקִיּוּמוֹ rotzeh be-kiyumo (he wants it to remain)
חֲצִיצָה / חוֹצֵץ chatzitzah / chotzetz (an interposition / it interposes)
מָקוֹם הֶעָשׂוּי לְחַזֵּק makom he-asuy lechazek (a place made to strengthen / a crack that mends)
מָקוֹם שֶׁאֵין עָשׂוּי לְחַזֵּק makom she-ein asuy lechazek (a place not made to strengthen)
בַּל יֵרָאֶה / בַּל יִמָּצֵא bal yera’eh / bal yimatzei (shall not be seen / shall not be found)
סְמִי קִילְּתָא מִקַּמֵּי חֲמִירְתָא semi kilta mikamei chamirta (erase the lenient before the stringent)
כּוֹפֶת שְׂאוֹר kofes se’or (a lump of hard leaven)
יִחֲדָהּ לִישִׁיבָה yichadah le-yeshivah (he assigned it for sitting)
מְקוּיֶּמֶת לַאֲכִילָה mekuyemes le-achilah (maintained for eating)
מְקוֹם לִישָׁה makom lishah (the place of kneading)
שִׂפְתָא דְאַגָּנָא sifta de-agna (the lip of the vessel)
טָח פָּנֶיהָ בְּטִיט tach paneha be-tit (he smeared its face with clay)
רוֹאִין ro’in (we look — pull the thread and see)
חַרְצַנִּים / זָג chartzanim / zag (pits / peel)

No kal va-chomer, binyan av, gezeira shava, heqqesh, kelal u-frat, or davar ha-lamed me-inyano is invoked on this amud by the sugya, by R’ Miller, or by Tosafos in the line the shiur walked. Yesterday’s shnei kesuvim is only the setup for the vine-verse.

Main points

The vine-verse is not extra on R. Akiva. Heter plus issur is one eating. Two issurim of a nazir add even in sequence.
A kezayis in one crack of the trough must be removed. Less than a kezayis can become part of the wood.
Tumah follows whether he minds the dough, not only whether Pesach would make him scrape it.
Two variables: size, and whether the crack mends the vessel. Lashon 1 needs two disadvantages to force removal. Lashon 2 needs only one.
Rav Huna keeps the stringent beraisa. Rav Yosef keeps both as Tannaim. The Tanna Kama will not let a kezayis lose the name chametz by assignment. R. Shimon will.
Abaye leaves both trough-beraisos with R. Shimon and splits lechazek into bottom, wall, and rim.
Whether Rav follows R. Shimon depends on whether clay must be smeared.
A thread of dough joins two small pieces only if they come away as one. A house is stricter than a trough, because a broom gathers.

Open kashya

The amud asked and did not answer: half a kezayis on this floor and half on the floor above, with a hole between them; half in the house and half on the porch; half in each of two rooms that open into each other. Is the fear of sweeping still alive once the rooms are not one floor?

Rav’s psak is also split. If clay is required, R. Shimon’s assignment-alone does not survive, and a kezayis in a bottom crack is not batel. Which lishon is the amud leaving us with?

From 44a the parked stone is still on the table: a nikar piece and bitul. The trough mishnah treats small hard dough in a crack as batel bemi’uto even though you can still point to it. That is a different bitul than a clove of garlic swimming in soup. The shiur did not put those two bituls next to each other.

Tosafos on Nazir 37b, left open on 45a, was not reopened today.