Rambam - 1 Chapter a Day

I.e., just as a large oven becomes susceptible to impurity when it is built to a height of four handbreadths (Chapter 15, Halachah 2), so too, it does not leave that category until it is destroyed to the extent that it is no longer of that height.

The rationale is that, at this size, it is still useful for its initial function.

Because once an oven is smashed, it is considered as if it no longer exists. Hence the impurity associated with it departs.

Since it is used for cooking, not for baking, it does not require as much heat as an oven and, hence, it remains useful even if it is much smaller.

As in Chapter 15, Halachah 2.

Cutting a space from its top to its bottom [see the Rambam’s Commentary to the Mishnah (Keilim 5:7)].

But is no longer attached to the earth with clay (ibid.).

If it is taken apart in this manner, it is no longer functional, and hence, regains purity.

Since it is the larger portion of the k’li, it retains the impurity originally associated with it.

This principle is cited in other halachic contexts as well; see Hilchot Rotzeiach 9:8.

Because neither constitutes the larger portion of the tabletop. In his commentary to Keilim 12:6, Tosafot Yom Tov questions why the ruling regarding the tabletop differs from that concerning an oven. He explains- admitting that the explanation is somewhat forced -that possibly one can be exact when dividing a tabletop. Tifferet Yisrael offers a different explanation, stating that since the tabletop is cut in half, it no longer has borders on all its sides. Hence, the impurity associated with it is only of Rabbinic origin. Accordingly, since it is impossible to determine which is the larger portion, each one is given the benefit of the doubt and considered as the smaller portion and therefore pure.

Because it constitutes half — or more — of the size of the original oven.

Instead of separating the oven by vertical cuts, thus divided its substance into rings.

The minimum height of a large oven, as stated in Halachah 1.

Since each ring is less than the minimum size of an oven, the impure oven is considered to have been disassembled entirely. Hence, its impurity departs; it does not attach itself to any of the rings.

As stated in Chapter 15, Halachah 1, this is the measure required for an oven to become susceptible to impurity.

The sand and/or pebbles create enough insulation for the clay coating to be supported and for the new oven to retain its heat.

Because the substance of the oven itself is separate from the coating. Thus, halachically, it is considered as if its different components are unconnected. Instead, they are considered as separate entities, each one too small to be susceptible to impurity. Compare to Halachah 5 below.

Keilim 5:8. That mishnah also uses the phrase “Concerning this [type of oven], it was said....”

I.e., it does not contract impurity as an oven does. The rationale for the Rambam’s ruling is that the majority of the rings are less than four handbreadths high. Hence, as a whole, the structure is not considered as an oven according to Scriptural Law. Accordingly, the law pertaining to an oven—that it contacts impurity because of presence of impurity within its inner space—does not apply to any of its components, even one that fulfills the minimum requirement for the size of an oven.

Since there is nothing to hold the oven together, it is considered as if it was disassembled. Hence its impurity departs [the Rambam’s Commentary to the Mishnah (Keilim 5:9); see Halachah 3].

Not only does the oven not return to its previous impurity, it is not susceptible to impurity in the future. It is not considered as if a new oven was constructed, for the supports cause it to be considered as a single entity only the first time, directly after it is brought from the craftsman’s workshop (ibid.).

As stated in Halachah 3.

As is usually required (Chapter 15, Halachah 1).

The bracketed additions are made on the basis of the Rambam’s Commentary to the Mishnah (op. cit.).

Each ring being less than four handbreadths.

With the intent of preventing the rings from being considered as joined.

The rationale is that even though the sand separates between the different rings, the external covering causes the entire oven to be considered as a single unified entity. As the Ma’aseh Rokeiach explains, this ruling cannot be compared to that in Halachah 3, for in that halachah, there is sand separating between the rings and the coating. Hence the coating is not considered to have joined all of the rings into a single entity. In this halachah, by contrast, since the coating is applied directly to the rings, they are considered to have been joined together.
This type of oven, referred to as “the oven of Achnai” is the subject of a classic, monumental debate that left its mark on the history of Talmudic study. As mentioned in Keilim 5:10, Rabbi Eliezer and the Sages differed on this issue. As related at length in Berachot 19a and Bava Metzia 59b, Rabban Gamliel followed the perspective of the Sages, ruling that such an oven is impure. Rabbi Eliezer argued vociferously in support of his position, citing different proofs, but they were not accepted by the other Sages.
[Rabbi Eliezer] declared: “If the halachah follows my position, let this carob tree serve as proof and the carob tree moved 100 cubits.... They told him: “Proof is not brought from a carob tree.” He said: “If the halachah follows my position, let this water canal serve as proof’ and the water canal moved behind them. They told him: “Proof is not brought from a water canal.” He pronounced: “If the halachah follows my position, let the walls of the House of study serve as proof’ and the walls of the House of Study leaned as if they would soon fall. Rabbi Yehoshua rebuked them saying: “If Torah scholars are contesting with each other in halachah, what is it your business?” Out of respect for Rabbi Yehoshua, they did not fall and out of respect for Rabban Eliezer, they did not stand straight and they are still standing tilted. [Rabbi Eliezer then] told them: “If the halachah follows my position, proof will come from heaven” and a heavenly voice proclaimed: “Why are you disputing with Rabbi Eliezer? The halachah follows his opinion in all instances.” Rabbi Yehoshua stood up... and said: “It is not in the heavens.” What does “It is not in the heavens” mean?... No attention should be paid to a heavenly voice, because it was written at Sinai in the Torah (Exodus 23:2): “veer after the majority.” Rabbi Nosson found Eliyahu. He asked him: “What did the Holy One, blessed be He, do then?” He told him: “He smiled and said: ‘You have vanquished Me, My children. You have vanquished Me.”’
That day, they brought all the sacrificial foods that Rabbi Eliezer had purified and they burnt them and they voted against him, placing him under a ban of ostracism.

Without being supported by the earth behind it.

For it is considered as an earthenware structure.

For then it is a mere pit in the ground.

The standard printed text of the Tosefta, Keilim 3:1 states “and coated either from the inside or from the outside.” The Rambam probably had a different version of that source and favored it, based on a parallel ruling in Chapter 15, Halachah 11.

As required by Chapter 15, Halachah 1.

See Chapter 18, Halachot 13-14.

Removing the base of the barrel causes it to lose its functionality and hence become insusceptible to impurity.

Here also the Rambam mentions coating the barrel both on the inside and the outside, even though his source, the Tosefta, Keilim 4:8, mentions only an external coating.

Because the oven is not considered as whole.

Because the patch is considered to have restored the oven’s integrity.

Our translation is taken from the Rambam’s Commentary to the Mishnah (Keilim 10:2). Note, however, (op. cit., Shabbat 8:4) where he interprets this term charsit as referring to a particularly thick type of mud. The commentaries note that the standard published text of the Tosefta, Keilim 4:7 includes charisit among the substances that can cause an oven to be considered impure. They explain that the Rambam had a different version of the Tosefta. It is possible to explain that the two versions are dependent on the two interpretations of the term charsit. According to the interpretation that it refers to a type of mud, it can serve as a patch, while according to the interpretation that it is a paste made from ground earthenware, it is not.

The Ma’aseh Rokeiach notes that in Chapter 14, Halachah 10, the Rambam rules that tar can be considered as an effective sealant for an earthenware container. Kin’at Eliyahu explains that there is no contradiction. An oven is heated and tar placed there will melt.

Attaching the oven to the wall of the home with the clay.

We are speaking about a situation where a shelf protrudes out from the oven. When the oven becomes very hot, it also becomes hot and will bake cakes placed upon it. Nevertheless, even though it is functional, it is not considered as an oven and is not susceptible to ritual impurity.

Since it comprises the major portion of the oven and it is functional, it is considered as part of the oven and susceptible to impurity.

For the portion covered with earth is considered as if it has been sealed closed.

E. g., the carcass of a crawling animal or the like [the Rambam's Commentary to the Mishnah (Keilim 5:6)].

The Rambam states the same concepts in Hilchot Shabbat 3:7.

I.e., it was split across its entire length. Thus neither of the places where the pots could be placed are useful.

Because it is not functional.

I.e., the crack runs between the places where the pots are placed down. Thus each of these places are functional.

For, regardless, the place on which the pot is placed down is no longer functional.

As mentioned previously, a range was often built without a floor. While at times, the ranges were placed on the ground itself, it was also common for homeowners to place their ranges on round bases. This halachah is speaking about an instance where there is a hole in the upper surface of the base and thus the kindling fuel used to heat the range falls into the base itself [see the Rambam's Commentary to the Mishnah (Keilim 7:1)]. Diagram

Although the stone is serving as part of the base for the range, since it is not permanently affixed to the structure, the range is still considered as unable to fulfill its function.

If, however, the range had previously been impure, that impurity is considered to have departed.