Why Were Nadav and Avihu Killed/2

Why Were Nadav and Avihu Killed?

Exegetical Approaches

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Punished for Sin

Nadav and Avihu were killed as a punishment for sin.

Problematic Procedure

Nadav and Avihu did not abide by the proper protocol when bringing the incense offering.

Sources:Various opinions in Sifra Vayikra10:1About the Sifra Vayikra, BavliEiruvin 63aYoma 53aAbout the Bavli, Vayikra Rabbah12:520:8-10About Vayikra Rabbah, Pesikta DeRav Kahana, Targum Pseudo-JonathanVayikra 10:1Vayikra 10:9About Targum Pseudo-Jonathan, R. Saadia GaonVayikra 10:1About R. Saadia Gaon, RashiVayikra 10:1-3About R. Shelomo Yitzchaki, Lekach TovVayikra 10:1About R. Toviah b. Eliezer, RashbamVayikra 9:23-24Vayikra 10:1-3About R. Shemuel b. Meir, Ibn EzraVayikra 10:1-3About R. Avraham ibn Ezra, R. Yosef Bekhor ShorVayikra 10:1-3About R. Yosef Bekhor Shor, R. BachyaVayikra 10:1About R. Bachya b. Asher, RalbagVayikra 10:1-3About R. Levi b. Gershom

What protocol was done incorrectly? These sources bring an array of possible wrongdoings, including bringing the wrong fire,¹ not wearing the proper clothing, failing to wash before service,  or entering the Mishkan while intoxicated.²  Though there is a clear mention of the first wrongdoing, "וַיַּקְרִיבוּ לִפְנֵי י"י אֵשׁ זָרָה", there is no explicit mention of any of the other three.  Nonetheless, the fact that the prohibition to drink wine immediately follows the story might be brought as support that the crime involved drinking.

"אֵשׁ זָרָה"

• Wrong fire - According to most of these commentators, this phrase describes Nadav and Avihu's main sin, bringing fire from a foreign source.  According to R. Yosef Bekhor Shor, although a priest is normally allowed to bring fire of his own ("מן ההדיוט"),‎³‎‎ on this day Hashem had wanted the sacrifices to be consumed only via His fire⁴ so as to glorify His name.⁵  Others might maintain, instead, that the incense offering must always be brought from the Outside Altar (as per Vayikra 16:12),⁶ but Nadav and Avihu brought it from a regular oven.⁷
• Problematic offering –The sources who see other procedural mistakes as the problem might suggest that any sacrifice not brought according to proper protocol is in essence a "foreign fire".

"אֲשֶׁר לֹא צִוָּה אֹתָם" – These commentators can explain this verse in one of two ways, depending on the sin attributed to Nadav and Avihu:

• Lack of command – Ibn Ezra explains that the verse teaches that the brothers acted according to their own understanding, rather than on Hashem's command. Though Hashem had never prohibited Nadav and Avihu from bringing their own fire on the eighth day, He had not authorized it either.  Accordingly, the sources which view this as the sin will have to explain why the brothers received such a severe punishment.
• Prohibition – Those commentators who posit that the sin related to clothing, washing or drunkenness might instead explain the verse as if written,"אשר צוה אותם לא"‎⁸ ("that he commanded not to").  For each of these actions there is an explicit warning in Torah, and as such Nadav and Avihu should have known better.⁹ 

" לִפְנֵי י"י" – Most of these sources would likely explain that " לִפְנֵי י"י" refers to the Outer Sanctum where the brothers brought the incense on the altar.¹⁰

What motivated the brothers?

• Positive intentions – One opinion in the Sifra¹¹ states that when the brothers saw that Aharon had finished his service but Hashem's presence had not descended, they worried and decided to bring fire of their own to help it along.¹²  Though their intentions were positive, their actions suggested a lack of faith and led to a lessening of God's glory.¹³
• Mistake –  According to R"Y Bekhor Shor, Nadav and Avihu simply made a mistake, not realizing that Hashem did not want them to bring of their own fire on this day.¹⁴  Other procedural sins might similarly be explained as errors; the brothers were still new to service and not as aware as they should have been. 
• Negative –  It is also possible that the brothers were simply careless, not giving Hashem's service the attention to detail it deserved.  Alternatively, they might have been influenced by surrounding modes of worship.  Thus, for example, if others worshiped their gods while in a drunken frenzy, Nadav and Avihu might have thought to worship Hashem similarly.  This, though, brings worship of Hashem close to idolatry.¹⁵

"בִּקְרֹבַי אֶקָּדֵשׁ "

• R. Yosef Bekhor Shor asserts that the term refers to Nadav and Avihu, who, despite their error, were still considered close to Hashem.  This would work with all the sources who attribute positive or neutral intentions to the brothers, but makes it difficult to explain the severity of the punishment. 
• The others might explain, as does Rashbam, that the term refers not to Nadav and Avihu, but to Aharon, who was to sanctify Hashem's name by continuing with Hashem's service and not mourning.

Severity of Punishment

• Capital crimes – Those who maintain that the sin related to drinking, clothing or washing, can easily explain the severity of the punishment since all these sins are punishable by death.  Even if the brothers motives were not negative, they nonetheless committed capital crimes.
• Lesson to others –  Those who assert that the sin was bringing a foreign fire that was simply "not commanded" have a harder time explaining the punishment.  R"Y Bekhor Shor and Ralbag maintains that it needed to be severe to teach the nation the importance of being exacting in observing the laws of sacrifices. Seeing how Hashem punished even those who were close to him, taught laymen how much more they needed to fear God.

Context  - prohibition to drink wine – According to this approach, the prohibition to drink wine might follow this story either because the brothers sinned in this regard, or simply as another warning of the need to be exacting and careful (and thus unimpaired by drink) when serving in the Mikdash.

Breaching of Boundaries

The brothers were killed for reaching beyond what was permitted them in approaching God.

Sources:Sifra Vayikra10:1About the Sifra Vayikra, Vayikra Rabbah20:8-10About Vayikra Rabbah, TanchumaBehaalotekha 16About the Tanchuma, Targum Pseudo-JonathanShemot 24:10-11About Targum Pseudo-Jonathan, RashiShemot 24:10About R. Shelomo Yitzchaki, Chizkuni #1Vayikra 10:1-3About R. Chizkiyah b. Manoach, AbarbanelVayikra 10:1About R. Yitzchak Abarbanel, SefornoVayikra 10:1Vayikra 24:3About R. Ovadyah Seforno, BiurVayikraAbout the Biur (Netivot HaShalom), ShadalVayikra 10:1-3About R. Shemuel David Luzzatto, R. S"R HirschVayikra 10:1-3About R. Samson Raphael Hirsch, R. D"Z Hoffmann, Hoil Moshe

What boundaries were breached? These sources maintain that the brothers erred in bringing an incense offering that they were not authorized to bring, and/or that they came too close to God.

•  Unauthorized Offering – The sources differ regarding the problem:
• Extra incense – Many of these sources¹⁶ explains that the brothers voluntarily brought their own individual incense offering.¹⁷ Since the verse states that "לֹא תַעֲלוּ עָלָיו קְטֹרֶת זָרָה ", any extra incense offering was considered problematic.¹⁸
• Took Aharon's job -– Abarbanel, instead, explains hat the brothers were unauthorized because on the eighth day, Aharon alone was supposed to do all aspects of the service,¹⁹ similar to the service of the Day of Atonement which is done by the high priest alone.²⁰  Seforno goes further to suggest that throughout the period of Wanderings in the Wilderness, only the high priest was allowed to bring incense (or perform any other services in the sanctuary) due to Hashem's constant presence on the Tabernacle.²¹ 

• Coming too close – Commentators offer two possibilities:

• Entered Holy of Holies – One opinion in the Sifra, Bar Kappara in Vayikra Rabbah, and Abarbanel all fault Nadav and Avihu for bringing their offering into the Inner Sanctum which was forbidden to all but the high priest on the Day of Atonement.  As this is where Hashem's presence is most strongly felt, unauthorized entry was not only prohibited but dangerous. 
• Saw God – One opinion in Vayikra Rabbah, Tanchuma, Targum Pseudo-Jonathon and Rashi assert that Nadav and Avihu were punished not (only)²² for their actions on the eighth day, but for having seen God at Mount Sinai, as described in Shemot 24.²³  One might similarly explain that the problem was seeing God on the eighth day itself; as God's presence had descended on the Tabernacle it is possible that the brothers encountered it upon entry into the Sanctuary.²⁴

"אֵשׁ זָרָה" – According to these sources, this phrase is equivalent to "קטורת זרה", meaning an unauthorized incense offering.  The Biur explains that the term "אֵשׁ" is really just a variation of the term "אִשֶּׁה לַי"י'‏", another name for sacrifices.²⁵

לִפְנֵי י"י – According to many of these sources,²⁶ the phrase refers to the Holy of Holies, the forbidden Inner Sanctum.

"אֲשֶׁר לֹא צִוָּה אֹתָם"

• Not commanded – According to most of these sources the fact that the incense offering was not commanded is what made it foreign, and therefore problematic. R. Hirsch emphasizes how there is no such thing as subjectivity in sacrificial service; a person cannot act on their own individual desires, but only on the commands of Hashem.²⁷
• Prohibited  – Chizkuni instead reads the verse to mean "which Hashem commanded not [to bring]", pointing to the prohibition in Shemot 30:9 against bringing a "foreign incense offering".  The brothers were violating an explicit command, and therefore punished.

What motivated the brothers?

• Zeal for Hashem – According to the Biur, R. Hirsch and R. D"Z Hoffmann the brothers' motivations were pure. They brought the sacrifice out of a desire for closeness to Hashem.²⁸
• Mistaken – Seforno suggests that Nadav and Avihu mistakenly assumed that just like an incense is burned after the Daily Offering due to its bringing of Hashem's presence, so too on the eighth day after Hashem's fire descended and His glory was revealed, an incense offering was called for.²⁹
• Honor their father – Hoil Moshe suggests that the brothers were worried about their father's honor.  Seeing that Hashem's glory descended only after Moshe came to the Tabernacle to pray, they thought that others would think that their father was unworthy to brings God's presence.³⁰  As such, they thought to bring an incense to prove that their immediate family, too, was desired by God.
• Arrogance – Shadal, in contrast, attributes the brothers' actions to excessive haughtiness and a desire not to be overshadowed by their father.³¹ Since they had not been given any individual service to perform they took upon themselves one of the most precious rituals.

"בִּקְרֹבַי אֶקָּדֵשׁ "

• Nadav and Avihu were holy – According to the Biur, R. Hirsch and R. D"Z Hoffman, Moshe comforted Aharon in these words, telling him that his sons were among Hashem's most holy. Their actions, though wrong, were motivated by a closeness to God, and not sinful thoughts.  As such, their punishment would bring about more fear of God, sanctifying His name.
• Even the elite punished – Shadal, who views the brothers more negatively, might explain instead that Hashem referred to the brothers as "קְרֹבַי" only because their position as priests had elevated them closer to Hashem.  This, though, made their fall all the greater.  In punishing them Hashem sanctified himself, showing all that no one is immune to punishment.

Severity of the Punishment

• Those who assert that the brothers actually saw Hashem's presence can easily explain the brothers' death. This is the consequence of getting too close; as Hashem says, "לֹא יִרְאַנִי הָאָדָם וָחָי".  It is possible that even just entering sacred space is a serious breach and deserves punishment, regardless of a person's motives.³²
• Those who view the sin as relating only to an unauthorized incense might also view it as a serious sin, especially since a "קְטֹרֶת זָרָה" is explicitly prohibited. The Biur, R. Hirsch and Hoil Moshe, nonetheless, assert that the brothers were only punished so severely due to their high stature.  The Biur compares their punishment to that of Moshe and Aharon by the rock, whose sin merited disproportionately severe consequences. He notes that there too the verse states "וַיִּקָּדֵשׁ בָּם".‎³³ 

Biblical Parallels – Several stories in Tanakh show similar punishments for breach of boundaries:

• Sinai – In Shemot 19, Hashem repeatedly warns the nation not to get too close to the mountain, telling them "כׇּל הַנֹּגֵעַ בָּהָר מוֹת יוּמָת."
• Korach – In the story of Korach, like here, unauthorized incense offerings result in death.
• Uza – In Shemuel II 6, Uza touches the Ark to ensure that it did not fall.  Despite his good intentions, his breaching of boundaries resulted in death.³⁴

The Yom HaKippurim Service – The verses that describe the service of the Day of Atonement  clearly connect it to the deaths of Nadav and Avihu.  Hoil Moshe asserts that the entire service was necessary to cleanse the Inner Sanctum from the impurity caused by the deaths of Nadav and Avihu.  Alternatively, the directives might be coming as a corrective to the sin, teaching Aharon the proper protocol to safely enter the Inner Sanctuary.

Punished for Another's Sin

Nadav and Avihu were killed as a punishment to Aharon for his participation in the Sin of the Golden Calf.

Sources:perhaps Vayikra Rabbah7:1About Vayikra Rabbah and RashiDevarim 9:20About R. Shelomo Yitzchaki³⁵

Vicarious punishment – This approach maintains that sometimes Hashem punishes children for their parent's sins.  For a full discussion of the issue and how to explain the phenomenon, see Are Children Punished for Parents' Sins?

Why now? It is possible that before Aharon could fully serve in the Mishkan his previous sins needed to be atoned and punished.

Work Accident

Nadav and Avihu's actions alone would not have warranted their death, but because they were in the wrong place at the wrong time, they were consumed by Hashem's fire.

Sources:RashbamVayikra 9:23-24Vayikra 10:1-3About R. Shemuel b. Meir³⁶ R. Granot³⁷

Chronology of the verses – Rashbam posits that the story of Nadav and Avihu is written achronologically, and really occurred before Hashem's fire consumed Aharon's offerings as described in Vayikra 9:24.  It is on this backdrop that he explains the rest of the story. .

The incense offering – According to Rashbam, Nadav and Avihu were not bringing an unauthorized incense, but the regular offering brought every morning.

"אֵשׁ זָרָה" – The brothers' only mistake was in bringing "foreign fire" rather than waiting for Godly fire to consume the incense.  Rashbam explains that although a priest is normally allowed to bring fire of his own (אש מן ההדיוט),‎ during the Mishkan's consecration, Hashem had wanted to glorify His name by having all sacrifices be consumed via Hashem's fire.  T. Granot suggests, instead, that the brothers were impatient for Hashem's revelation and tried to "hurry the end".

"אֲשֶׁר לֹא צִוָּה אֹתָם" – Rashbam explains that although normally the brothers' actions would have been permitted, on this day, Hashem did not command them to do so.  As such, Nadav and Avihu had no way of knowing that their actions were not desired.

"וַתֵּצֵא אֵשׁ מִלִּפְנֵי י"י" – Rashbam identifies this fire with that described in Vayikra 9:24,³⁸ claiming that there were not two distinct fires, one that consumed Aharon's offerings on the Outer Altar and another that killed the brothers, but only one.  This fire emanated from "before God", from the Inner Sanctum, where Hashem's presence dwells.  In contrast to most exegetes, Rashbam explains that the godly fire did not come vertically down from the heavens, but horizontally from the Holy of Holes to the Outer Sanctum (where it met the brothers) to the Outer Altar.

Severity of the Punishment – According to this approach, the fire that killed Nadav and Avihu was not intended to punish them but simply to consume Aharon's sacrifices.  They, unfortunately, happened to be in the way and suffered the natural consequences.  In T. Granot's words, "their death was not a punishment but a tragic accident."

Why not bring the fire later? This approach must contend with the question of why Hashem allowed such an accident, rather than waiting to bring the fire when no one was in the way.  It could answer that since the brothers had sinned, albeit erroneously, they were not worthy of a miracle to save them. Alternatively, since the entire nation was outside waiting for Hashem's glory to appear there would be a desecration of His name if there were a delay.

"בִּקְרֹבַי אֶקָּדֵשׁ" – According to this approach it is understandable that the brothers are referred to as "close to Hashem" since they died without major sin.³⁹

Biblical parallels – Other catastrophes in Tanakh have similarly been viewed as natural consequences rather than punishments. For example, see Mystery at the Malon for Ibn Kaspi and Abarbanel's reading of Moshe's near death.

Sanctified to God

Nadav and Avihu's death was not a punishment but a sanctifying of their souls to Hashem.

Sources:PhiloOn Dreams 2:67On Flight and Finding, 59About Philo, HaKetav VeHaKabbalah

Problematic Worship

Nadav and Avihu were punished because of an error in cultic practice.  This position subdivides based on the specific aspect of service that is considered problematic:

Unauthorized Fire

Nadav and Avihu brought the wrong fire for the incense offering.

Sources:R. Akiva in Sifra Vayikra10:1About the Sifra Vayikra, BavliEiruvin 63aYoma 53aAbout the Bavli, Bar Kapparah in Vayikra Rabbah20:8-10About Vayikra Rabbah and Pesikta DeRav Kahana, R. Saadia GaonVayikra 10:1About R. Saadia Gaon, Lekach TovVayikra 10:1About R. Toviah b. Eliezer, RashbamVayikra 9:23-24Vayikra 10:1-3About R. Shemuel b. Meir, Ibn EzraVayikra 10:1-3About R. Avraham ibn Ezra, R. Yosef Bekhor ShorVayikra 10:1-3About R. Yosef Bekhor Shor, R. BachyaVayikra 10:1About R. Bachya b. Asher, RalbagVayikra 10:1-3About R. Levi b. Gershom

"אֵשׁ זָרָה" – All these sources maintain that it was this "fire from a foreign source" that was problematic, explaining that Nadav and Avihu erroneously used fire of their own (מן ההדיוט), from a regular oven.  However, it is not explicit what is wrong with this:

• Not from Hashem's fire – Rashbam and R. Yosef Bekhor Shor explain that although a priest is normally allowed to bring fire "מן ההדיוט",‎⁴⁰ on this special day of the Mishkan's consecration Hashem had wanted the sacrifices to be consumed only via Hashem's fire⁴¹ so as to glorify His name through the miracle.⁴²
• Not from the Copper Altar - The others might suggest, as does the Raavad,⁴³ that although the priest is commanded to light of his own fire for the Copper Altar, this is not true regarding the incense offering.  Its fire needs to be taken from the Outer Altar (as per Vayikra 16:12) while Nadav and Avihu took it from a regular oven.
• From the wrong place on the altar – Ralbag goes further to suggest that the brothers might have even taken fire from the Outside Altar, but from the wrong place on it.

"אֲשֶׁר לֹא צִוָּה אֹתָם" – These sources disagree regarding the meaning of this phrase and what it says about the brothers' actions:

• That was not commanded – Rashbam explains that although normally the brothers' actions would have been permitted, on this day, Hashem did not command them to do so.  Ibn Ezra similarly writes that the phrase means that the brothers acted according to their own understanding, not Hashem's command. Sometimes, acting on the absence of a command is itself problematic, even if unintentional.
• That was prohibited – R. Yosef Bekhor Shor explains in contrast, that the verse should be read as if written "אשר צוה אותם לא",‎⁴⁴ that the brothers acted against an explicit prohibition, "לֹא תַעֲלוּ עָלָיו קְטֹרֶת זָרָה". It is not clear if he thinks that this is a second wrong-doing of the brothers (that the offering itself was unauthorized) or if he thinks that the fact that the fire was unauthorized is enough to make the entire offering a "קְטֹרֶת זָרָה".

"לִפְנֵי י"י " – Though all these sources might agree that from a literal standpoint, the phrase simply means "before Hashem", they disagree regarding its specific connotation in its various appearances in the unit:

• All are geographical markers – According to Rashbam, in each of its appearances the phrase refers to a geographical location, but not to the same one. When the verses states that Nadav and Avihu brought their offering "לִפְנֵי י"י", it refers to the Outer Sanctum, but when it speaks of the fire that came "מִלִּפְנֵי י"י" to consume them, it refers to the Inner Sanctum.  According to him, the fire which killed the brothers is the same godly fire mentioned in Vayikra 9:24 that consumed Aharon's offerings on the Outer Altar.  It did not come vertically down from the heavens, but horizontally from the Holy of Holes to the Outer Sanctum (where it met the brothers) to the Outer Altar.⁴⁵
• Action emanating from Hashem – The other sources might suggest that while the phrase "לִפְנֵי י"י" refers to the Inner Sanctum where the brothers offered the incense, the term "מִלִּפְנֵי י"י" that is mentioned in 9:24 and 10:2 more simply means "from God", and connotes a supernatural fire.
• Spiritual evaluation – Ibn Ezra uniquely understands the phrase "וַיָּמֻתוּ לִפְנֵי י"י" to refer not to a geographical location, but a spiritual one.  The brothers acted and died "before God", thinking that they were doing something pleasing to Him.

What motivated the brothers?

• Mistake – According to some of these sources,⁴⁶ Nadav and Avihu simply made a mistake, erroneously assuming that the law regarding "אש מן ההדיוט" that was true on other days would apply to the eighth day as well. The Bavli and Lekach Tov criticize the brothers for making their own assumptions and not verifying with Moshe. 
• Lack of Faith – One opinion in the Sifra and R. Bachya, instead, explain that the brothers actions stemmed from a lack of faith.  They feared either that no fire would come down, or that there was not enough fire on the Altar to consume everything and thus they brought their own.

"בִּקְרֹבַי אֶקָּדֵשׁ "

• According to Rashbam, the word "קְרֹבַי " (my close ones) refers not to Nadav and Avihu but to Aharon, who was to sanctify Hashem's name by continuing with Hashem's service and not mourning.⁴⁷
• Ibn Ezra and R. Yosef Bekhor Shor,⁴⁸ in contrast, assert that the term refers to Nadav and Avihu , who despite their error were still considered close to Hashem.

Severity of punishment

• Lesson to others – Ralbag maintains that the punishment needed to be severe to teach the nation the importance of being exacting in observing the laws of sacrifices.
• Natural consequence – Drawing on Rashbam's understanding that Nadav and Avihu erred unintentionally and that the fire which killed them was the fire intended to consume Aharon's sacrifices which emanated from the Holy of Holies,⁴⁹ T. Granot suggests that Nadav and Avihu's deaths be viewed not as a punishment but a "work accident".  Though they mistakenly brought the wrong fire, this in and of itself would not have warranted death.  However, since they were in the wrong place at the wrong time, they were naturally burnt when the fire made its way from the Holy of Holies.⁵⁰

Context - prohibition to drink wine – According to this approach, the prohibition to drink wine might follow this story not because the brothers sinned in this regard but as another warning of the need to be exacting and careful when serving in the Mikdash.

Yom Kippur Service

Unauthorized Offering

Nadav and Avihu brought a an incense offering that was not commanded.

Sources:Vayikra Rabbah20:8-10About Vayikra Rabbah, Chizkuni #1Vayikra 10:1-3About R. Chizkiyah b. Manoach, AbarbanelVayikra 10:1About R. Yitzchak Abarbanel,⁵¹ SefornoVayikra 10:1Vayikra 24:3About R. Ovadyah Seforno, BiurVayikraAbout the Biur (Netivot HaShalom), ShadalVayikra 10:1-3About R. Shemuel David Luzzatto, R. S"R HirschVayikra 10:1-3About R. Samson Raphael Hirsch, RDZH

"אֵשׁ זָרָה" – According to these sources, this phrase is equivalent to "קטורת זרה", meaning an unauthorized (and therefore foreign) incense offering.  The Biur explains that the term "אֵשׁ" is really just a variation of  to the term "אִשֶּׁה לַי"י'‏", another name for sacrifices.⁵²  R. D"Z Hoffmann adds that it was not called a "ketoret" since it was not brought on the incense altar.⁵³

Why was the Ketoret unauthorized?

• Additional service – Most of these sources view this as an additional incense offering (not that brought every morning)⁵⁴ that the brothers brought on their own, as individuals and not as representatives of the nation.  Since the verse states that "לֹא תַעֲלוּ עָלָיו קְטֹרֶת זָרָה ", any extra incense offering was considered problematic.

• Aharon's Job -– Abarbanel asserts that on the eighth day, Aharon alone was supposed to do all aspects of the service,⁵⁵ similar to the service of the Day of Atonement which is done by the high priest alone.⁵⁶ According to Seforno, not only on the eighth day but throughout the period of Wanderings in the Wilderness, only the high priest was allowed to bring incense (or perform any other services in the sanctuary).  This was due to Hashem's constant presence on the Tabernacle.

"אֲשֶׁר לֹא צִוָּה אֹתָם"

• According to most of these sources the fact that the offering was not commanded is what made it foreign, and therefore problematic. R. Hirsch emphasizes how there is no such thing as subjectivity in sacrificial service; a person cannot create their own sacrifice nor act on their own individual desires, but only on the commands of Hashem.⁵⁷
• "אֲשֶׁר לֹא צִוָּה אֹתָם""אֲשֶׁר לֹא צִוָּה אֹתָם"

What motivated the brothers? Positive motivation – According to the Biur, R. Hirsch and R. D"Z Hoffmann, the brothers' motivations were pure.  They brought the sacrifice out of a desire for closeness to Hashem.
Mistaken – Seforno suggests that Nadav and Avihu mistakenly assumed that just like an incense is brought after the Daily Offering due to its bringing of Hashem's presence, so too on the eighth day after Hashem's fire descended and His glory was revealed, an incense offering was called for.⁵⁸Negative motivation– Shadal, in contrast, attributes the brothers' actions to excessive haughtiness and a desire not to be overshadowed by their father.⁵⁹ Since they had not been given any individual service to perform they took upon themselves one of the most precious.

"לִפְנֵי י"י" – While Seforno assumes that the brothers brought the incense on the Incense Altar in the Outer Sanctum, Abarbanel, the Biur, and R. Hoffmann assume that "לִפְנֵי י"י" refers to the Holy of Holies.  Abarbanel views this as an additional sin, but the Biur explains that this was not yet prohibited⁶⁰ and as such was not the problem.

"בִּקְרֹבַי אֶקָּדֵשׁ "

• According to the Biur, R. Hirsch and R. D"Z Hoffman, Moshe comforted Aharon in these words, telling him that his sons were amongst Hashem's most holy.  Their actions were motivated by a closeness to God, and not sinful thoughts. 
• Shadal, who views the brothers more negatively, could suggest, as does Rashbam, that the term refers not to Nadav and Avihu, but to Aharon, who was to sanctify Hashem's name by continuing with Hashem's service and not mourning.

Severity of punishment – The Biur explains that the brothers were only punished so severely due to their high stature. He compares their punishment to that of Moshe and Aharon by the rock, whose sin also merited a disproportionately severe punishment. He note that there too the verse states "וַיִּקָּדֵשׁ בָּם".

¹ Most of these commentators point to this as the sin.

² The last three possibilities are raised in Vayikra Rabbah 20 by R. Mani, R. Yehoshua and R. Yochanan in the name of R. Levi.  Regarding intoxication, see also see also R. Yishmael in Vayikra Rabbah 12, Rashi and Targum Pseudo-Jonathon.

³ See the BavliYoma 21bAbout the Bavli which learns from Vayikra 1:7, "וְנָתְנוּ בְּנֵי אַהֲרֹן הַכֹּהֵן אֵשׁ עַל הַמִּזְבֵּחַ", that the priests themselves are normally commanded to bring the fire, even though there is already fire on the altar from Hashem.

⁴ R. Yosef Bekhor Shor asserts that thestory of Nadav and Avihu is not recorded in its chronological place and that they really brought their incense before the fire mentioned in Vayikra 9:24 came down to consume Aharon's offerings.  As such, it was very possible that the nation would conclude that it was their fire, and not Hashem's, that consumed the other offerings, thereby lessening God's glory. [Even if one disagrees, and maintains the chronology of the verses, one might still say that on this first day Hashem wanted all offerings to be consumed by His miraculous fire.]

⁵ The Lekach Tov disagrees with Rashbam, asserting that even on this day it would have been allowed to bring fire from a "הדיוט", but the brothers should not have deduced this from themselves and should have instead asked Moshe. It was the fact that they did not ask permission first which was really problematic. This is presumably what R. Eliezer in the Bavli means as well when he faults Nadav and Avihu "שהורו הלכה בפני משה רבן" (for teaching law before their master, Moshe). However, it is possible that R. Eliezer blames the brothers not only for deciding the law on their own, but because they did

⁶ See the Raavad (as quoted by the RitvaYoma 53aAbout R. Yom Tov b. Ashbel) who suggests that the brothers erroneously assumed that what was true regarding the Outer Altar (where a priest is supposed to bring of his own fire) was also true of the Altar of Incense.

⁷ Ralbag also raises the possibility that the brothers might have even taken fire from the Outside Altar, but from the wrong place on it.

⁸ See R"Y Bekhor Shor who raises this possibility.  As support for rearranging the words of the verse in such a manner, he points to the Yimiyahu 7:31, where the similar phrase "אֲשֶׁר לֹא צִוִּיתִי", also means "אשר צויתי לא" (that I prohibited) and not simply "that I did not command."

⁹ Regarding clothing requirements see Shemot 28:43.  Regarding washing, see Shemot 30:21 and regarding drunkenness, see Vayikra 10:9.  As the first two of these prohibitions precede our story, Nadav and Avihu would have been aware of them.  The command not drink wine, however, follows the story and would seem not to have been commanded as of yet.  These sources might posit that although it was previously commanded, the prohibition is written achronologically, perhaps so as to connect it to this story.

¹⁰ Ibn Ezra uniquely understands the phrase "וַיָּמֻתוּ לִפְנֵי י"י" to refer not to a geographical location, but a spiritual one. The brothers acted and died "before God", thinking that they were doing something pleasing to Him.

¹¹ R. Bachya explains similarly, that they feared that Hashem's fire on the Altar was not sufficient to consume everything and decided to contribute their own fire.

¹² This can be compared to Moshe's sin in hitting the rock. Moshe, fearing that no water was to come from speech alone, decided to hit the rock to bring forth water.  See Moshe's Misstep and Mei Merivah.

¹³ Those who view the brothers as intoxicated might also assume that nonetheless their motives were positive, thinking that it was best to serve Hashem when uninhibited or that drink would raise them to higher levels of zeal.  This, however, is not how Hashem wants to be worshiped.

¹⁴ Since on other days this would have been allowed, and Hashem had never told them otherwise, it would have been an easy mistake to make.  The Bavli and Lekach Tov nonetheless criticize the brothers for making their own assumptions and not verifying with Moshe.

¹⁵ See the descriptions of the nation by the Sin of the Golden Calf, " וַיֵּשֶׁב הָעָם לֶאֱכֹל וְשָׁתוֹ וַיָּקֻמוּ לְצַחֵק".

¹⁶ See Chizkuni, Biur, Shadal, R. S"R Hirsch, R. D"Z Hoffmann, and Hoil Moshe.

¹⁷ In other words, the offering described in the verses was not the regular morning incense offering, but a separate offering of their own.  Cf. Rashbam who disagrees and views it as the daily offering.

¹⁸ It should be noted, however, that not all agree that this verse refers to an unauthorized offering.  See Onkelos and Ibn Ezra  who assert that it refers to a offering which is made of the wrong spices.

¹⁹ He also raises the possibility that Moshe alone was supposed to serve as high priest that day and bring the incense. Either way, it was not Nadav and Avihu's task.

²⁰ See also R. Shpiegelman, "פרשת שמיני - חטאם של בני אהרן", who suggests that Nadav and Avihu mistakenly viewed themselves as high priests since they too were anointed, and thus thought that they were allowed to participate in the service of the eighth day.

²¹ According to this, even entry into the Outer Sanctum was a breach of boundaries.

²² Both Targum Pseudo Jonathon and Rashi attribute other sins to them as well.

²³ Rashi explains that Hashem waited to kill them because He did not want to turn the happiness of the day of receiving the Torah into a tragedy.  It is not clear, however, why He would instead choose to kill them on the day of the Consecration of the Mishkan, a similarly happy occasion.

²⁴ See Shemot 40:35, that when Hashem's glory filled the Tabernacle, even Moshe himself could not enter.

²⁵ Cf. Chizkuni who claims that it is referred to as fire since all such offerings must be accompanied by fire. R. D"Z Hoffmann adds that it was not called a "קטורת זרה" since it was not brought on the incense altar.

²⁶ See opinion in the Sifra, Bar Kappara in Vayikra Rabbah, Abarbanel, the Biur, R. D"Z Hoffmann and Hoil Moshe.  However, not all of these view the action as a sin.  The Biur points out that the prohibition against entering was not commanded until after the brothers' death in Vayikra 16:12.  As such, they were not culpable for unathorized entry, but only for unauthorized offerings.

²⁷ See the Netziv similalrly, "ואמרה תורה דאע"ג דאהבת ה' יקרה היא בעיני ה' אבל לא בזה הדרך אשר לא צוה ". It is probable that both are reacting to the Reform movement, hinting that worship of God is not about getting close to Hashem in whatever way speaks to each individual but about following God's commands.

²⁸ R. Hirsch, nonetheless criticizes the brothers for forgetting their role as priests, whose job is to serve the nation and be their representatives before Hashem.  In such a role there is no room for individual self-expression.

²⁹ R"Y Grossman, in his article, "פרשת שמיני - היום השמיני וחטא נדב ואביהו" moves in a similar direction suggesting that Nadav and Avihu worried that the nation was not worthy of having direct contact with Hashem.  Thus, as soon as He revealed Himself through the fire, they quickly brought an incense offering to mask the revelation. [So, too, on the Day of Atonement, the high priest must bring a cloud of incense, "כִּי בֶּעָנָן אֵרָאֶה עַל הַכַּפֹּרֶת."]

³⁰ Hoil Moshe explains that in fact, it was due to Aharon's sin with eth Godlen Calf, that Hashem did not bring the miracle on his behalf alone.

³¹ Cf. the opinion in the Sifra which states, "מה תלמוד לומר בני אהרן? שלא חלקו כבוד לאהרן" and Bavli Sanhedrin which presents Nadav and Avihu as waiting for their father and Moshe to die so they could lead the nation.

³² See also Shemot 19 and Hashem's repeated warnings not to get too close to the mountain, "כׇּל הַנֹּגֵעַ בָּהָר מוֹת יוּמָת."

³³ R. Hirsch also notes the necessity of teaching the nation of the dangers of subjective worship; if even people of the stature of Nadav and Avihu are punished for such actions all the more so regular people.

³⁴ This chapter was likely chosen as the haftarah for Parashat Shemini due to the similarities between the stories.  In both cases there is a celebration for a consecration of the Tabernacle/ark in which an undefined sin relating to improper worship is punished by death.  It is interesting to note that Uza's father is Avinadav, a combination of the names Nadav and Avihu.

³⁵ Neither of these sources say explicitly that Nadav and Avihu were killed solely for Aharon's sin, but both explain that their death was a punishment to Aharon for the Calf.  See also Hoil Moshe who asserts that Aharon's sin indirectly caused that of his sons, and that Aharon felt that he had caused their deaths.

³⁶ Rashbam is not explicit, but this is the general direction of his comments. 

³⁷ See his article, "פרשת שמיני - גילוי כבוד ה' על המזבח ומות נדב ואביהוא" where he expands on Rashbam's commentary to the story.

³⁸ To support his claim, Rashbam points to other examples where two verses describe an action which originally appear to be distinct but in reality refer to one and the same event.  See the repeated mention of Moshe relaying the nation's words to Hashem in Shemot 19:8-10 and Micha's interactions with his mother in Shofetim 17:1-3.

³⁹ Rashbam himself does not actually think the verse refers to the brothers but to Aharon who sanctified Hashem's name when he continued with Hashem's service rather than mourning.

⁴⁰ From Vayikra 1:1, "וְנָתְנוּ בְּנֵי אַהֲרֹן הַכֹּהֵן אֵשׁ עַל הַמִּזְבֵּחַ", the Bavli Yoma 21bAbout the Bavlilearns that the priests themselves normally bring the fire, even though there is already the original fire from Hashem.

⁴¹ The Lekach Tov disagrees with Rashbam, asserting that even on this day it would have been allowed to bring fire from a "הדיוט", but the brothers should not have deduced this from themselves and should have instead asked Moshe.  It was the fact that they did not ask permission first which was really problematic.  This is presumably what R. Eliezer in the Bavli means as well when he faults Nadav and Avihu "שהורו הלכה בפני משה רבן" (for teaching law before their master, Moshe).  However, it is possible that R. Eliezer blames the brothers not only for deciding the law on their own, but because they did so erroneously, and were mistaken in its application to the eighth day.

⁴² According to both Rashbam and R. Yosef Bekhor Shor the verses are achronological and Nadav and Avihu brought their incense before the fire mentioned in Vayikra 9:24 came down to consume Aharon's offerings.  As such, it was very possible that the nation would conclude that it was their fire, and not Hashem's, that consumed the other offerings, thereby lessening God's glory. [Even if one disagrees, and maintains the chronology of the verses, one might still say that on this first day Hashem wanted all offerings to be consumed by His miraculous fire.]

⁴³ R. Akiva and Bar Kapparah explain that the fire was problematic since it was from a regular oven, suggesting that they also think that it should have been from the Altar.

⁴⁴ As support for such a reading he points to the Yimiyahu 7:31, where the similar phrase "אֲשֶׁר לֹא צִוִּיתִי", also means "that I prohibited" and not simply "that I did not command."

⁴⁵ Cf. R. Yosef Bekhor Shor who agrees that there was only one fire but assumes that this emanated from the heavens. As such, he would probably explain the phrase "מִלִּפְנֵי י"י" to simply mean "from Hashem."

⁴⁶ See the Bavli, Lekach Tov, Rashbam, and R"Y Bekhor Shor.

⁴⁷ He points to Vayikra 21:10-12 which speak of teh high priests' special laws of mourning.  The verse there states, "וּמִן הַמִּקְדָּשׁ לֹא יֵצֵא וְלֹא יְחַלֵּל אֵת מִקְדַּשׁ", teaching that if the priest does continue his service despite the death of a loved one, he will sanctify Hashem.

⁴⁸ R"Y Bekhor Shor brings this as a second possibility, but also raises the suggestion of Rashbam that the verse refers to Aharon.

⁴⁹ See note above that Rashbam identifies the fires of Vayikra 9:24 and 10:2, saying that it came not vertically down from the heavens, but horizontally from the Inner Sanctum.

⁵⁰ He supports the idea by pointing to the fact that even after their actions, they are referred to as "close to Hashem".

⁵¹ This is but one of several sins that Abarbanel attributes to Nadav and Avihu.  He also asserts that they brought unauthorized fire, came into the Holy of Holies and wrongly brought the incense as a pair.

⁵² Cf. Chizkuni who claims that it is referred to as fire since all such offerings must be accompanied by fire.

⁵³ He follows Bar Kapparah that they brought it into the Holy of Holies.

⁵⁴ Cf. Rashbam above who claims that this was the regular morning incense offering.

⁵⁵ He also raises the possibility that Moshe alone was supposed to serve as high priest that day and bring the incense. Either way, it was not Nadav and Avihu's task.

⁵⁶ See also R. Shpiegelman, "פרשת שמיני - חטאם של בני אהרן", who suggests that Nadav and Avihu mistakenly viewed themselves as high priests since they too were anointed, an dthus thought that they were allowed to participate in the service of the eighth day.

⁵⁷ See the Netziv similalrly, "ואמרה תורה דאע"ג דאהבת ה' יקרה היא בעיני ה' אבל לא בזה הדרך אשר לא צוה ".  It is probable that both are reacting to the Reform movement, hinting that worship of God is not about getting close to Hashem in whatever way speaks to each individual but about following God's commands.

⁵⁸ R"Y Grossman, in his article, "פרשת שמיני - היום השמיני וחטא נדב ואביהו" moves in a similar direction suggesting that Nadav and Avihu worried about the nation having direct contact with Hashem.  Thus, as soon as He revealed Himself through the fire, they quickly brought an incense offering to mask the revelation. [So, too, on the Day of Atonement, the high priest must bring a cloud of incense, "כִּי בֶּעָנָן אֵרָאֶה עַל הַכַּפֹּרֶת."]

⁵⁹ Cf. the opinion in the Sifra which states, "מה תלמוד לומר בני אהרן? שלא חלקו כבוד לאהרן" and Bavli Sanhedrin which presents Nadav and Avihu as waiting for their father and Moshe to die so they could lead the nation.

⁶⁰ It is first prohibited in Vayikra 16:1-2, "וְאַל יָבֹא בְכׇל עֵת אֶל הַקֹּדֶשׁ מִבֵּית לַפָּרֹכֶת", after the brothers' deaths.