Mishnah Kelim 27:10-11

Sugya Map

The sugya of Mishnah Kelim 27:10 and Mishnah Kelim 27:11 lies at the absolute epicenter of the laws of tumah ve-taharah (ritual impurity and purity) as they relate to the transformation, disintegration, and physical reduction of vessels (kelim). At its core, the sugya grapples with a profound metaphysical question: When a vessel that currently carries a severe, primary status of impurity (av ha-tumah) undergoes physical partition or reduction, what is the status of the resulting fragments?

Specifically, the Mishnah focuses on a piece of cloth measuring three handbreadths by three handbreadths (shlosha al shlosha tefachim) that has contracted midras uncleanness (the severe uncleanness generated when a person with a discharge, a zav, sits, lies, or leans upon an object). If this cloth is split (nechlak) or has a single thread removed (nittol chot echad), it loses its susceptibility to midras—which requires a minimum size of three handbreadths square—but remains large enough (three fingerbreadths by three fingerbreadths, shlosha al shlosha etzba'ot) to be susceptible to other forms of uncleanness, such as contact with a corpse (tumat met) or general contact (maga).

[3x3 Tefachim Cloth (Impure with Midras - Av Ha-Tumah)]
                       |
                       | ---> SPLIT / PARTITIONED (Nechlak)
                       v
[Two Fragments (Each < 3x3 Tefachim, but >= 3x3 Etzba'ot)]
                       |
        +--------------+--------------+
        |                             |
[Tanna Kamma's View]          [Rabbi Yose's View]
- Pure from Midras            - Pure from Midras
- IMPURE via Maga Midras      - PURE from Maga Midras
(Due to Beit HaSetarim)       (No Maga without external touch)

Primary Nafka Minot (Halakhic Ramifications)

1. The Metaphysics of Separation (Sh'at Peirishah): Do we view the newly formed fragments as contracting impurity from their own parent vessel at the infinitesimal split-second of separation?
2. The Status of Hidden Areas (Tum'at Beit HaSetarim): Can ritual impurity be transmitted through contact in hidden, internal crevices (such as the inner fibers of a tearing cloth) that are not exposed to the outside?
3. The Limits of Precision (I Efshar Le-Tzamtzem): Is it physically possible to split an object without generating a transitional moment of contact between the newly separated parts?

Primary Sources

• Mishnah: Mishnah Kelim 27:10, Mishnah Kelim 27:11
• Gemara: Chulin 72b, Chulin 128a, Zevachim 95a
• Rishonim: Rashi on Chulin 72b; Rash mi-Shantz and Rosh on Mishnah Kelim 27:10
• Acharonim: Tosafot Yom Tov, Rashash, and Tiferet Yisrael (Yachin) on the Mishnah.

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Text Snapshot

To master the mechanics of this sugya, we must carefully parse the exact syntax of Mishnah Kelim 27:10:

"שלשה על שלשה שנחלק — טהור מן המדרס, אבל טמא מגע מדרס. אמר רבי יוסי: וכי באיזה מדרס נגע זה? אלא אם נגע בו הזב — טמא מגע זב..."

Linguistic and Grammatical Analysis

1. "שנחלק" (She-nechlak — "that was split")

The Mishnah uses the passive Nifal form. This implies that the partition occurred either by accident or through a simple act of tearing, without necessarily requiring a deliberate, constructive act of remodeling. This contrasts sharply with cases where a vessel is deliberately refashioned into a new functional item (such as "a sheet that was made into a curtain," sadin she-asao vilon).

2. "טהור מן המדרס אבל טמא מגע מדרס" (Tahor min ha-midras aval tamei maga midras)

The fragment is liberated from its status as an av ha-tumah of midras because it no longer meets the minimum dimensional threshold of three handbreadths square required for a seat or mat. However, it immediately becomes a rishon le-tumah (first-degree impurity) because it is deemed to have "touched" the midras impurity of the parent cloth.

The conceptual difficulty here is immense: how can a piece of cloth touch itself to become impure?

3. "وכי באיזה מדרס נגע זה" (Ve-khi be-eizeh midras naga zeh? — "But what midras did this touch?")

Rabbi Yose’s rhetorical question is a masterpiece of logical defiance. He argues that for "contact" (maga) to occur, there must be two distinct entities: a transmitter (metamei) and a receiver (mitamei). At the moment of splitting, the parent cloth ceases to exist as a 3x3 av ha-tumah, and the fragments are born. At no point did the independent fragment exist alongside the independent 3x3 av such that they could "touch" each other.

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Readings

The debate between the Tanna Kamma and Rabbi Yose, and the subsequent application of their dispute to different modes of physical separation, split the Rishonim and Acharonim into distinct conceptual camps.

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                       THEORIES OF FRAGMENT IMPURITY
================================================================================

1. THE BEIT HASETARIM THEORY (Rash mi-Shantz / Chulin 72b)
   - Mechanism: Internal fibers touch during the tear.
   - Core Premise: Tum'at Beit HaSetarim is metamei (Tanna Kamma).
   - Rabbi Yose's Counter: Hidden contact cannot transmit impurity.

2. THE "I EFSHAR LE-TZAMTZEM" THEORY (Tosafot Yom Tov)
   - Mechanism: Impossibility of perfect physical division.
   - Core Premise: Cutting from a larger sheet guarantees external contact.
   - Reconciliation: R' Yose agrees here because contact is open/exposed.

3. THE CONSTITUTIONAL INTEGRITY THEORY (Yachin / Tiferet Yisrael)
   - Mechanism: Flat fragments (Keli Pashut) retain structural identity.
   - Core Premise: No "shem keli" is destroyed; only size is reduced.
   - Contrast: Complex garments (Keli Gamur) are purified completely when torn.
================================================================================

1. The Rash mi-Shantz: Tum'at Beit HaSetarim and the Mechanics of Tearing

The Rash mi-Shantz[^1], drawing directly from the Gemara in Chulin 72b, explains that the Tanna Kamma’s ruling—that the split fragments are tamei maga midras—rests on the premise that "Tum'at Beit HaSetarim" (impurity of hidden or internal surfaces) is capable of transmitting uncleanness.

When a 3x3 handbreadth cloth is torn in half, the separation is not instantaneous across all molecular levels. As the fibers rip apart, the newly exposed inner surfaces of fragment $A$ physically rub against the newly exposed inner surfaces of fragment $B$. At that exact micro-second:

• The cloth is still technically connected at some points, meaning the av ha-tumah of the 3x3 handbreadth cloth is still halakhically present.
• The newly separated fibers are already considered independent "fragments" capable of receiving maga (contact) impurity.
• Because the contact occurs inside the tearing seam, it is classified as beit hasetarim (a hidden place).

The Tanna Kamma holds that tum'at beit hasetarim metamei—hidden contact is halakhically effective[^2]. Therefore, the newly emerging independent fragment contracts maga from the remaining portion of the parent cloth.

Rabbi Yose, conversely, holds that tum'at beit hasetarim lo metamei—hidden contact cannot transmit impurity. Since the contact between the fibers occurs inside the tear, it cannot transfer impurity, leaving the fragments completely pure.

2. The Tosafot Yom Tov: The Dichotomy of "Splitting" vs. "Cutting from a Large Sheet"

The Tosafot Yom Tov[^3] introduces a vital distinction to resolve a major contradiction in the rulings of Rabbi Yose. In our Mishnah, Rabbi Yose rules that the split fragments are completely pure. However, in Chulin 72b, Ulla states:

"לא שנו אלא שלשה על שלשה שנחלק, אבל שלש על שלש הבאות מבגד גדול — בשעת פרישתן מאביהן מקבלות טומאה מאביהן" "They only taught [that they are pure] in the case of a 3x3 that was split; but a 3x3 piece that comes from a larger garment—at the moment of its separation from its parent, it contracts impurity from its parent."

Rashi[^4] explains that even Rabbi Yose agrees to Ulla’s rule. Why?

The Tosafot Yom Tov explains that when a small 3x3 handbreadth piece is cut out of a massive, impure garment, we invoke the principle of "I efshar le-tzamtzem" (it is physically impossible to be perfectly precise). As the shears cut through the fabric, the newly cut 3x3 piece inevitably sways and touches the outer, exposed surface of the remaining parent garment (avihen).

This is not a case of beit hasetarim (hidden contact inside a tear). This is open, visible contact (maga b'galyah) between the newly independent 3x3 fragment and the remaining av ha-tumah parent garment. Since the contact is open, even Rabbi Yose—who rejects beit hasetarim—concedes that the fragment contracts maga midras from its "parent" at the exact moment of separation (sh'at peirishah).

3. The Rashash: The Metaphysical Paradox of Sheva Tumei'ah (Satiety of Uncleanness)

The Rashash[^5] raises a brilliant, devastating conceptual challenge to the entire mechanism of maga mi-avihen (contracting impurity from the parent vessel).

There is an established halakhic axiom that "Ein keli metamei et azmo" (a vessel cannot contaminate itself), and furthermore, a vessel cannot contract a lighter impurity (rishon le-tumah) while it is already saturated with a more severe, active state of impurity (av ha-tumah). This is known as the principle of Sheva Tumei'ah (satiated with uncleanness)[^6].

If so, asks the Rashash:

• At the moment of separation, as the thread or fragment is being pulled away, it is still physically connected to the parent garment.
• If it is connected, it is still halakhically part of the 3x3 av ha-tumah.
• How can it contract a lighter impurity (maga midras, which makes it a rishon) from the very vessel it is currently a part of? It is already an av!
• Conversely, if it is already completely detached, the parent garment (in the case of shlosha al shlosha she-nechlak) has already shrunk below the 3x3 threshold and is no longer an av! How can it transmit midras?

To resolve this, the Rashash cites the Tosafot in Chulin 72b (s.v. Ela)[^7]. He proposes that we do not apply the rule of "Sheva Tumei'ah" when the transition of impurity is "mi-gufo" (generated from its own physical body).

The physical fibers do not act as an external blocking agent. Rather, the transition from av ha-tumah to rishon le-tumah is a continuous, fluid degradation of the cloth's internal metaphysical state. The moment of separation (peirishah) acts as a dual-action mechanism: it simultaneously dissolves the av status of the whole and crystallizes the rishon status of the parts.

4. Tiferet Yisrael (Yachin): Form (Tzurat Keli) vs. Substance

The Yachin[^8] addresses a glaring contradiction between our Mishnah and the laws of torn garments in Mishnah Zevachim 11:5:

• In Zevachim, we learn that if an impure garment is torn across its majority, it becomes completely pure (tahor gamur). It does not retain any residual maga impurity.
• In our Mishnah, when the 3x3 handbreadth cloth is split, the fragments remain tamei maga midras. Why does the split cloth in Kelim remain impure, while the torn garment in Zevachim becomes completely pure?

The Yachin resolves this by distinguishing between "Keli Gamur" (a completed, complex vessel/garment) and "Keli Pashut / Chatichat Beged" (a simple, flat piece of cloth).

A complex garment (like a shirt or a coat) derives its halakhic status from its functional form (tzurat keli). When such a garment is torn across its majority, its functional form is utterly destroyed. The halakha views this not as a mere reduction in size, but as the complete death and dissolution of the vessel. Therefore, all prior states of impurity vanish entirely.

In contrast, a simple flat cloth (like the 3x3 handbreadth patch in our Mishnah) has no complex functional form; its utility is simply as a flat piece of material. When it is split, its "form" is not destroyed, because each resulting fragment is still a functional, flat piece of material (now susceptible to the smaller 3x3 fingerbreadth threshold). Because there was no destruction of tzurat keli, only a quantitative reduction in size, the residual impurity (maga midras) remains active in the fragments.

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Friction

The Ultimate Kushya: The Temporal-Causal Paradox of the Splitting Moment

Let us construct the strongest conceptual challenge to the Tanna Kamma’s position. This kushya exposes a severe temporal and logical paradox in the mechanics of maga mi-avihen (contracting impurity from the parent vessel at the moment of split).

Let $C$ represent the original 3x3 handbreadth cloth, which is currently an av ha-tumah of midras. Let $A$ and $B$ represent the two resulting halves (each 1.5x3 handbreadths) after the split.

================================================================================
                      THE TEMPORAL DILEMMA OF DIVISION
================================================================================

      T1 (Intact)                 T1.5 (Transition)             T2 (Split)
+-------------------+           +--------+ +--------+       +-----+     +-----+
|                   |           |        | |        |       |     |     |     |
|         C         |   ====>   |   A    | |   B    | ====> |  A  |     |  B  |
|   (Av Ha-Tumah)   |           |        | |        |       |     |     |     |
+-------------------+           +--------+ +--------+       +-----+     +-----+
                                 [Is C still an Av?]        [C is dead! No Av
                                                            exists to transmit.]
================================================================================

We must analyze the exact moment the impurity of maga midras is transferred. There are only three possibilities, each of which is logically untenable:

1. The contact occurred at $T_1$ (when the cloth was fully intact): At $T_1$, $A$ and $B$ do not exist as independent entities; they are merely spatial zones within the single entity $C$. A vessel cannot touch itself to contract impurity (ein keli metamei et azmo)[^9]. Therefore, no transfer of maga could have occurred at $T_1$.
2. The contact occurred at $T_2$ (when the split is fully complete and $A$ and $B$ are independent): At $T_2$, the parent cloth $C$ has already been reduced below 3x3 handbreadths. Therefore, $C$ has instantly lost its midras status. If $C$ is no longer an av ha-tumah, how can $A$ and $B$ contract maga midras from it? You cannot contract impurity from a source that no longer possesses it!
3. The contact occurred at the transitional state $T_{1.5}$ (during the tear): At any intermediate point during the tear, the remaining unsplit connection between $A$ and $B$ is either halakhically significant or it is not:
   • If the connection is still significant, then $A$ and $B$ are still part of the single vessel $C$. Therefore, they are still under the umbrella of the av ha-tumah itself and cannot contract maga from it due to Sheva Tumei'ah.
   • If the connection is no longer significant, then the 3x3 av ha-tumah has already dissolved, and there is no longer an av to transmit impurity.

In short: How can $A$ and $B$ contract maga midras when there is no single point in time where a separate, receptive fragment ($A$) coexists with a surviving, independent source of midras ($C$)?

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The Best Terutzim

Terutz A: The "Nitzutz" (Residual Exhalation) and the Liminality of Halakhic Time

This terutz, developed through the lens of the Rash and the Rambam, redefines how halakha views temporal transitions. We must abandon the assumption that halakhic transitions are binary, instantaneous shifts.

Instead, the process of division operates in a liminal state where both realities overlap. During the transitional micro-seconds of $T_{1.5}$ (the sh'at peirishah):

• The parent status is sustained b'di'avad: The halakha rules that the severe status of av ha-tumah does not instantly vanish the moment the integrity of the 3x3 dimensions is compromised. Rather, the av status is sustained as a "residual force" (nitzutz) during the active process of tearing.
• The fragments gain immediate independence: At the very same instant, the tearing fibers that have already parted are granted immediate, independent status as small fragments (susceptible to the 3x3 fingerbreadth threshold).

Therefore, at $T_{1.5}$, the newly independent fibers of fragment $A$ physically touch the still-active av status of the connected portion of fragment $B$. The transfer of maga occurs precisely within this liminal zone of physical separation.

Terutz B: The Brisker Analysis of Rav Velvel (The Soloveitchik Approach)

The Gry"d (Rav Yitzchok Ze'ev Soloveitchik)[^10] resolves the paradox by drawing a fundamental distinction between two entirely different dimensions of tumah:

1. Tumat Chafetz (Inherent Object Impurity): The physical substance of the cloth is saturated with the energy of midras.
2. Shem Keli (The Halakhic Status of the Vessel): The formal, external classification of the object as a "vessel" of specific dimensions.

When the Mishnah states that a 3x3 handbreadth cloth is an av ha-tumah, this is not merely an external label; the physical fibers themselves have become a localized source of midras energy.

When the cloth is split, the Shem Keli of the 3x3 handbreadths is indeed dissolved. However, the Tumat Chafetz (the inherent impurity residing in the physical fibers) does not simply evaporate into thin air. The act of splitting is not a purifying agent (mitaher); it is merely a resizing agent.

The inherent midras energy residing in the fibers must go somewhere. Because the physical substance of the cloth remains intact, the halakha channels this residual midras energy, converting it from an av ha-tumah (which requires a 3x3 handbreadth vessel) into a rishon le-tumah via the mechanism of maga (which only requires a 3x3 fingerbreadth piece of fabric).

The "contact" is not a physical event of one piece touching another; it is a metaphysical translation of the impurity status within the fabric itself, triggered by the act of partition (ma'aseh chaluqah).

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Intertext

To fully appreciate the conceptual depth of our sugya, we must analyze its parallels across the wider landscape of Shas and Halakha.

================================================================================
                         HALAKHIC PARALLELS MATRIX
================================================================================

   SUGYA SOURCE            CONCEPTUAL CORE               HALAKHIC OUTCOME
--------------------------------------------------------------------------------
Mishnah Kelim 27:10     Tum'at Beit HaSetarim    Tanna Kamma: Impure (Metamei)
                        in tearing fabric        R' Yose: Pure (Lo Metamei)

Chulin 72b /            Hidden contact with a    Sheretz inside a mouth is
Bava Kamma 4b           sheretz (reptile)        pure; must be Maga b'Galyah

Rambam, Hilkhot         Codification of splitting R' Yose is accepted regarding
Kelim 23:9              and cutting garments     Beit HaSetarim (pure in split)
================================================================================

1. The Classic Source of Beit HaSetarim: Chulin 72b and Bava Kamma 4b

The concept of Beit HaSetarim (hidden contact) is derived from the biblical verses governing contact with animal carcasses (nevelah) and creeping creatures (sheretz). The Torah states:

"וכל אשר יפל עליו מהם במתם יטמא" "And anything upon which any part of them falls when they are dead shall be unclean..." Leviticus 11:32

The Sages in Chulin 72b derive from the word "עליו" (alav — "upon it") that the contact must be external and exposed (maga b'galyah). This excludes contact inside the hidden parts of the body (such as a person swallowing a source of impurity, where the contact is inside the digestive tract, or contact inside deep, closed folds of skin).

Our sugya in Kelim represents the radical expansion of this concept from human anatomy to the structural anatomy of vessels. The Tanna Kamma of our Mishnah holds that the inner fibers of a tearing cloth are not classified as beit hasetarim, or that tum'at beit hasetarim is rabbinically decreed to transmit impurity in vessels. Rabbi Yose maintains the strict, unified definition: any contact that is not exposed to the open air cannot transmit impurity, whether in a human body or in the tearing seams of a piece of cloth.

2. The Halakhic Codification: Rambam, Hilkhot Kelim 23:9

How does this conceptual dispute land in the final halakhic codification? The Rambam writes:

"שלשה על שלשה שנחלק — טהור מן המדרס; ואם נחלק לשנים, אף על פי שאין בכל חלק מהן שלשה על שלשה — הרי שניהם טמאין מגע מדרס... במה דברים אמורים? בשנחלק. אבל אם נטל חוט אחד מן השלשה על שלשה... הרי זה טהור מן המדרס וטהור ממגע מדרס" "A 3x3 [handbreadth cloth] that was split is pure from midras; and if it was split in two, even though neither part has 3x3 handbreadths, they are both impure with the contact of midras... When does this apply? When it was split. But if one removed a single thread from the 3x3... it is pure from midras and pure from the contact of midras." [^11]

The Kessef Mishneh[^12] and the Tosafot Yom Tov wrestle with the Rambam's rulings:

• In Hilkhot Kelim 23:9, the Rambam rules like the Tanna Kamma that a split cloth is tamei maga midras.
• Yet, in Hilkhot Kelim 23:7, the Rambam rules like Rabbi Yose regarding other cases of beit hasetarim.

The resolution lies in a precise distinction between deliberate partition (nechlak) and accidental/minor disintegration (such as removing a single thread, nittol chot echad).

When a cloth is cleanly split into two substantial functional parts, we apply the rule of maga mi-avihen because the act of splitting is a significant physical transition that preserves the utility of the fragments. However, when a single thread is pulled out, the thread is ruined, and the remaining cloth is merely diminished. In such a case of disintegration, even the Tanna Kamma agrees that we do not apply the severe stringencies of maga midras, and the resulting pieces are entirely pure.

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Psak/Practice

While the laws of tumah ve-taharah are not fully active in our post-Temple era (with the exception of laws relating to family purity, niddah, and priesthood, tum'at kohanim), the conceptual engine of this sugya directly shapes modern halakhic decision-making. Specifically, the meta-heuristics of transitions of status and the limits of physical precision are highly active today.

================================================================================
                    MODERN HALAKHIC APPLICATIONS
================================================================================

1. THE PRINCIPLE OF "I EFSHAR LE-TZAMTZEM" (Impossibility of Precision)
   - Industrial Kashrut: Automated cutting blades in food processing.
   - Halakhic Assumption: Microscopic residue always transfers during a cut.
   - Action: Blades require koshering between dairy and meat runs.

2. LIMINAL TRANSITIONS OF VESSELS (Tzurat Keli)
   - Tevilat Kelim: Demolishing a vessel to exempt it from immersion.
   - Halakhic Standard: Must be damaged to the point of "bitul shem keli."
   - Action: Minor holes or removable parts do not destroy the vessel's identity.
================================================================================

1. Industrial Kashrut and I Efshar Le-Tzamtzem

The principle of i efshar le-tzamtzem—which Ulla and the Tosafot Yom Tov used to explain how cutting a cloth guarantees physical contact with the parent piece—is a cornerstone of modern industrial kashrut.

When food processing plants switch production lines from non-kosher to kosher, or from dairy to sharp meat products, they use high-speed automated cutting blades. Halakhic authorities (such as the Minchat Yitzchak and the Shevet HaLevi) discuss whether the physical impact of a blade cutting through food transfers flavor (b'de'avad) even without heat, via the pressure of the blade (duchka d'sakina)[^13].

Drawing from our sugya, we assume that physical separation is never clean. At the micro-level, there is always a transitional moment where the cut piece and the parent source rub against each other under intense pressure. Therefore, industrial blades must undergo rigorous cleaning and koshering (hag'alah or iruy) because we rule that i efshar le-tzamtzem—contact at the cutting edge is guaranteed.

2. Metaphysical Transitions: When is a Vessel "Destroyed"?

In the laws of koshering vessels (kashering kelim) and the immersion of new vessels (tevilat kelim), we often need to determine the exact moment a vessel loses its halakhic identity.

For example, if a Jewish person purchases a metal vessel from a non-Jew, it requires immersion in a Mikveh. If the vessel is highly complex or delicate and cannot be immersed, one common halakhic workaround is to have a professional craftsman damage the vessel to the point that it is no longer functional, and then repair it.

Based on the Yachin's distinction between a Keli Gamur (complex garment) and a Keli Pashut (simple cloth):

• To completely erase the vessel’s prior identity (and exempt it from the original obligation of immersion), the damage must destroy its form (tzurat keli), not just its size.
• A simple puncture or a removable part does not suffice; the damage must render the vessel completely unusable for its primary function[^14]. Only then does it undergo the transition of "death" and "rebirth" as a new, Jewish-made vessel.

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Takeaway

The split cloth of Kelim teaches us that halakhic boundaries are not static lines on a map, but dynamic transitions in time and space. Even when an object is physically reduced, the residual energy of its former status clings to its fragments at the moment of separation—proving that in the eyes of Halakha, physical division is never a clean break, but a profound transformation of identity.

[^1]: Rash mi-Shantz on Mishnah Kelim 27:10:1. [^2]: See the extensive discussion in Chulin 72b, where this is established as the core of the Tanna Kamma's position. [^3]: Tosafot Yom Tov on Mishnah Kelim 27:10:2. [^4]: Rashi on Chulin 72b, s.v. "בשעת פרישתן". [^5]: Rashash on Mishnah Kelim 27:10:1. [^6]: For the general rules of Sheva Tumei'ah, see Mishnah Menachot 3:4 and the Gemara in Menachot 24a. [^7]: Tosafot on Chulin 72b, s.v. "אלא שמע מינה". [^8]: Tiferet Yisrael (Yachin) on Mishnah Kelim 27:10 (commentary note 67). [^9]: This is a foundational rule in the laws of tumah. See Mishnah Kelim 1:1 and Bava Kamma 2b. [^10]: See Chiddushei Maran Riz"g on Hilkhot Kelim, Chapter 23, where this conceptual model of the transition of tumah is developed. [^11]: Rambam, Hilkhot Kelim 23:9. [^12]: Kessef Mishneh on Rambam, Hilkhot Kelim 23:9. [^13]: See Shulchan Aruch, Yoreh Deah 96:1, and the responsa of Minchat Yitzchak (Vol. 5, Ch. 28) regarding industrial cutting machinery. [^14]: See Shulchan Aruch, Yoreh Deah 120:14, and the commentaries of the Shach and Taz ad loc.