For an explanation of the methodology of this series, see the introduction.

"Whatever is used in fire you shall pass through fire and then it will be clean; it must, however, [also] be cleansed with sprinkling water, and whatever is not used in fire you shall pass through water." (Num. 31:23)

Peshat (basic meaning):

Rashi: "whatever is used in fire"
It is purged in the manner it is used. If it is used in hot water, it must be purged in hot water, and if it is used for roasting, such as a spit or grill, it must be made to glow in fire. (Avoda Zara 75b)

it must, however, [also] be cleansed with sprinkling water
According to its simple meaning, this sprinkling was to cleanse it from contamination by a corpse. He said to them, "The vessels require purging to cleanse them from the [absorption of] forbidden [food], and sprinkling to cleanse them of [spiritual] uncleanness [caused by a corpse]." Our Rabbis expounded from here that even to make them fit for use [after contamination] from forbidden food, ritual immersion was required for metal utensils. They expound "sprinkling water" written here to mean water fit for a menstruant to immerse herself in. How much is that? Forty 'seah.’ (Avoda Zara 75b)

"and whatever is not used in fire"
Anything which is not used in fire such as ewers, cups, and jugs, all of which are used for cold [food] and did not absorb forbidden food. (Avoda Zara 75b)

"shall be passed through water "
He immerses them and that is sufficient. This refers only to metal utensils. (Avoda Zara 75b, Sifrei Matot 50)

Remez (hinted meaning):

Because Moses entered the realm of anger, he entered the realm of error...

Baal HaTurim: "bimay/with the water of"
This word appears 5 times in Tanach: (1) here; (2) "But with the waters of sprinkling it must be purified" (3) at the waters of strife at Kadesh" (4) "in the waters of the Jordan" and (5) "though I would wash myself in the waters of melted snow". This similarity of expression alluded to the Sages' interpretation of the verse "Elazar the Kohen said to the men of the legion" (Num. 31:21) Because Moses entered the realm of anger, he entered the realm of error, for he forgot to inform the soldiers about the laws concerning the purging of cooking vessels that had been used by non-Jews, and that is the allusion of the phrase "at the waters of strife" because Moses entered the realm of strife, he erred about "the water of sprinkling."

But Moses addressed the leaders of thousands teaching them about the passage regarding purification of people, garments, and wooden utensils after contact with a corpse. But he did not teach them about koshering metal utensils because they did not have booty of metal utensils on the hands, only valuable garments. Elazar the Kohen , on the other hand, spoke to the warriors and he saw booty of household utensils in their hands. Therefore he instructed them in the laws regarding koshering utensils. (on 31:21)

Derash (interpretive meaning):

Rambam: The immersion of the dinnerware that is purchased from gentiles to allow it to be used for eating and drinking is not associated with ritual purity and impurity. Instead, it is a Rabbinic decree. (Laws of Prohibited Food, Halacha 5; Eliezer Touger's translation)

[As the Jerusalem Talmud (Avodah Zarah 5:15) states, this immersion was instituted to mark the article's transition from the impurity of the gentiles. However, others note that the Rambam occasionally employs the term he employs here - midivrei sofrim - to refer to obligations and laws that are of Scriptural origin. (Rashba, Vol. III, Responsum 255, 259)]

There is an allusion [to this] "Everything that can be passed through fire, you shall pass through fire and it will become pure." According to the Oral Tradition, we learned that the verse is speaking only about purifying [the utensils] from gentile cooking, not from ritual impurity, for there is no ritual impurity that is dispelled by fire. All those who are impure ascend from their impurity through immersion and the impurity stemming from [contact with] a human corpse is [dispelled] through the sprinkling [of water and the ashes of the red heifer].

There is no concept of fire [employed in this context], rather [it is employed] with regard to purification from gentile cooking. Since the verse states "and it will become pure," our Sages said: "Add to it another dimension of purity after passing it through fire to cause it to be permitted because [of its contact] with gentile cooking."

Ramban: The laws of purging were given here because in the earlier wars with Sichon and Og, the Jewish people had also taken plunder. Nevertheless these wars were part of the conquest of the Land of Israel, and the Talmud states that during the conquest they were allowed to eat non-kosher food from non-kosher vessels. The war with Midian, however, was not part of the conquest of the Land of Israel, so the Jewish people were faced with purging non kosher vessels, which is why the laws were given over here. is inappropriate to ask why a mitzvah was given at a particular time...

Har Tzvi (on Ramban): Ramban does not explain why the requirement to immerse vessels in a mikvah was only given here. In truth, however, it is inappropriate to ask why a mitzvah was given at a particular time, when the Torah deemed it fit to introduce it. The case of purging vessels, though, seems to be an exception, since it is a logical extension of the prohibition against eating non-kosher food that was already in force. That is why Ramban was troubled by this question.

Sod (esoteric, mystical meaning):

Zohar Exodus 20:
Rabbi Yitzhak said: From here and further it is written, "Everything that passes through the fire, you shall make it go through fire, and it shall be clean." (Num. 31:23) Rabbi Yosi said: When the Temple was in existence, a person would offer his sacrifices in this manner. And he is granted atonement. Now, the prayer of a person atones for him in place of the offering in that way.

BeRahamim LeHayyim:
We have no Temple, "down here." But you'd better believe that there is still one "up there." For the sacrifices have never stopped, and G‑d willing soon in our time the Temple will be rebuilt and the sacrifices rededicated "down here."

There is no service "down here" but we are promised that our prayers take the place of the offerings. We have no altar, but we are told that our dining tables grant us atonement in their stead. What an awesome responsibility!

We achieve wonders with our words and the way we comport ourselves at our tables!
At-one-ment is possible in the regular day to day structure of our lives.

If only we could live like this for just a portion of our consciousness!

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