Avraham's Guests – Angels or Men/2

Avraham's Guests – Angels or Men?

Exegetical Approaches

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Overview

Commentators disagree regarding both the identity of the three guests, and in how they understand the relationship between the three parts of the chapter (Hashem's opening revelation, the guests' visit, and Avraham's negotiations with Hashem over Sedom).  The majority of commentators assume that the guests were celestial angels and that their visit was unconnected to the chapter's opening.  Rashi, thus, relates Hashem's initial appearance to the events of the previous chapter, while R. Saadia connects it to Hashem's subsequent announcement regarding the destruction of Sedom.  In contrast to these sources, Rashbam upholds the unity of the chapter, identifying the revelation of Hashem with the appearance of the angels.

Rationalists, however, shy away from the possibility that the guests were supernatural beings. Ralbag, thus, asserts that they were three human prophets who visited Avraham en route to destroying Sedom, and that their visit was distinct from and preceded Hashem's discussion of the city's fate. A final approach, adopted by Rambam and others, prefers to read the story as taking place in a prophetic dream, with neither the guests' visit nor Hashem's discussion with Avraham about the fate of Sedom taking place in the physical realm.

Humans

The three guests were human, even though they were Divinely dispatched and possessed prophetic capabilities.  Their discussion with Avraham was distinct from and chronologically preceded Hashem's revelation in 18:1.

Sources: Opinion cited by Ibn EzraBereshit 18:1,13,33Bereshit 19:2,12,18About R. Avraham ibn Ezra, R. Yosef Bekhor ShorBereshit 18:1-3,9,17-19Bereshit 19:1,18-19About R. Yosef Bekhor Shor, RalbagBeiur HaMilot Bereshit 18:2,3,13Beiur HaMilot Bereshit 19:13Beiur Divrei HaParashah Bereshit 18:1,2-8,9-10,13-14,16,17-19,20-21,22,33Beiur Divrei HaParashah Bereshit 19:27-28,37-38About R. Levi b. Gershom

Hashem's revelation – "'וַיֵּרָא אֵלָיו ה" – According to R"Y Bekhor Shor and Ralbag, the description of Hashem's revelation to Avraham in 18:1 refers to their dialogue in the second half of the chapter regarding the destruction of Sedom (18:17 and 20ff.).  They, thus, contend that the verse is out of order¹ and, in reality, the story of the angels in 18:2-16 preceded the revelation.  Ralbag suggests that the story of the visit is simply a parenthetical aside, placed here because the guests were en route to destroy Sedom, which was the very matter which Hashem wanted to discuss with Avraham.²

Three visitors and two missions – Only one of the guests came to tell Sarah about the birth of Yitzchak, while the two others were sent to destroy Sedom.  Nonetheless, according to Ralbag, all three came to partake of Avraham's hospitality.  He posits that Avraham's words, "סַעֲדוּ לִבְּכֶם... כִּי עַל כֵּן עֲבַרְתֶּם עַל עַבְדְּכֶם", suggest that two of the visitors had actually detoured from their path just so that they could eat with Avraham even though they had no special message for him.³

The disappearance of the third guest – Ralbag asserts that the prophet who announced the birth of Yitzchak did not continue to Sedom, proving how lowly a prophet he was, as he was not privy to that issue.

Why are the guests referred to as both "אֲנָשִׁים" and "‎מַלְאָכִים"? Since the guests were human, it is readily understandable why the guests are referred to as "men" in the majority of the verses.  Regarding the verses which employ the term "‎מַלְאָכִים", R"Y Bekhor Shor asserts that the word  does not necessarily refer to celestial beings but simply means messengers.⁴  Ralbag attempts to explain why they are called "‎מַלְאָכִים" only when interacting with Lot and not with Avraham by suggesting that prophets are called "‎מַלְאָכִים" only when they are speaking to someone with inferior prophetic powers.⁵

Angelic or human actions – R"Y Bekhor Shor asserts that the fact that the guests ate and slept proves that they cannot be angels.⁶  Their seemingly supernatural actions (foreknowledge that Sarah was to give birth, blinding the people of Sedom etc.) can be explained by their prophetic status.⁷

Prophet visiting a prophet? Abarbanel questions this whole approach, asserting that the visitors could not have been prophets since Avraham was the sole or most important prophet of the time.  Even if there were other prophets,⁸ they were definitely not greater than Avraham, so what would be the point of their sharing news with him?⁹  He further questions how they could attribute the destruction of Sedom to themselves, or decide to save Lot on their own, as life and death are in the hands of Hashem alone.¹⁰

The name "Hashem" – According to this approach, throughout the chapter, the name Hashem refers to Hashem Himself and not the guests.  Ralbag posits one possible exception, suggesting that "וַיֹּאמֶר ה' אֶל אַבְרָהָם לָמָּה זֶּה צָחֲקָה שָׂרָה" in 18:13 might be one of the guests speaking via prophecy.¹¹  He is referred to as Hashem after the One who sent him.¹²

"אֲדֹנָי אִם נָא מָצָאתִי חֵן בְּעֵינֶיךָ" – The exegetes disagree regarding to whom Avraham was speaking:

• Hashem – According to R"Y Bekhor Shor, the term "אֲדֹנָי" here refers to Hashem.  Upon seeing the guests, Avraham offered a prayer to Hashem that the group¹³ would not pass him by without stopping.  This reading easily explains the switch to plural in the following verse ("יֻקַּח נָא מְעַט מַיִם וְרַחֲצוּ רַגְלֵיכֶם"), since only then does Avraham turn to the threesome.
• Guests – Ralbag, in contrast, asserts that the word "אֲדֹנָי" refers to the guests, and means "my masters".  He follows R. Chiyya in Bereshit Rabbah48:10About Bereshit Rabbah in explaining that Avraham initially spoke to the leader specifically (thus the singular "תַעֲבֹר") and only afterwards to the group (thus the plural in verse 4).¹⁴

"וַיֹּאמֶר לוֹט אֲלֵהֶם אַל נָא אֲדֹנָי" – Both Ralbag and R"Y Bekhor Shor maintain that the word "אֲדֹנָי" in this verse refers to the guests.  This works with the beginning of the verse which states that Lot "said to them" ("אֲלֵהֶם"), referring to the guests.  R"Y Bekhor Shor, though, assumes that the next verse ("הִנֵּה נָא מָצָא עַבְדְּךָ חֵן בְּעֵינֶיךָ") is a prayer directed to Hashem.  Presumably he is motivated by the fact that Lot is speaking of killing and saving lives, something which is only in the hands of Hashem.¹⁵

"'וְאַבְרָהָם עוֹדֶנּוּ עֹמֵד לִפְנֵי ה" – This verse is difficult for this approach since it maintains that Hashem did not even appear to Avraham until after the guests left.  Thus it is hard to say that "Avraham was still standing before Hashem".

Why is Avraham not mentioned by name in v.1? This approach does not explain why Avraham is not referred to by name until 18:6.

Polemical motivations – R"Y Bekhor Shor shies away from the alternative approach below that the guests were angels, because he wishes to refute Christian claims that this story buttresses the doctrine of the Trinity.  If the guests are three corporeal people who eat and drink, it is much harder to identify them as three parts of God.  He also points to the fact that only two guests arrive by Lot, to show that these are not a "three-in-one", as one part left.

Philosophical motivations – Ralbag's motivations are more philosophical in nature.  As a staunch rationalist, he explains away all Biblical mentions of angels as being either visions in a dream or as referring to prophets.¹⁶

Angels

The guests who came to Avraham were angels. This position subdivides regarding the relationship between their visit and Hashem's revelation to Avraham in 18:1:

Distinct Events

Hashem's revelation to Avraham in 18:1 was distinct from (and interrupted by) the visit of the three angels.

Sources: R. Chama in Bavli Bava MetziaBava Metzia 86bAbout the Bavli,¹⁷ R. Saadia GaonCommentary Bereshit 18:2,8,17-33Tafsir Bereshit 18:33Tafsir Bereshit 19:18HaNivchar BaEmunot UvaDeiot 2:6About R. Saadia Gaon, RashiBereshit 18:1,2,3,8,16,22,33Bereshit 19:1,18Shevuot 35bAbout R. Shelomo Yitzchaki, RambanBereshit 18:1,3,6,15,20Bereshit 19:24About R. Moshe Nachmanides, Akeidat YitzchakBereshit #19About R. Yitzchak Arama, AbarbanelBereshit 18:1,2,4,9,16,22About R. Yitzchak Abarbanel, Seforno
Bereshit 18:1,2,3,9,12,14,20,22,33Bereshit 19:27About R. Ovadyah Seforno

Hashem's revelation – "'וַיֵּרָא אֵלָיו ה" – According to all of these sources, Hashem's appearance to Avraham was separate from the visit of the three angels.  They differ, though, regarding its purpose and in how to explain why the text does not share the content of Hashem's speech:

• Connected to Chapter 17 – Rashi, Ramban, and Seforno all suggest that the revelation is related to Avraham's circumcision in Chapter 17.¹⁸  Rashi¹⁹ maintains that Hashem appeared to Avraham to visit him as he recuperated,²⁰ while Ramban asserts that the revelation was simply a sign of honor,²¹ a reward to Avraham for having fulfilled Hashem's commandment.  Finally, Seforno posits that Hashem appeared to participate in the covenant of circumcision.²²  According to all these opinions, there was no need for speech as the revelation was the goal itself.
• Connected to news of Sedom – Both R. Saadia and Abarbanel assert that Hashem's appearance here is connected to His later announcement to Avraham regarding the destruction of Sedom; the content of the revelation is, thus, first transmitted to Avraham in verse 20 when Hashem says "זַעֲקַת סְדֹם וַעֲמֹרָה כִּי רָבָּה"‎.²³ R. Saadia suggests that Hashem appeared before the arrival of the angels, even though he was only to speak later, so that Avraham would feel Hashem's presence as the angels arrived and thereby recognize them as celestial beings.²⁴

Why is Avraham not mentioned by name in v.1? Rashi, Ramban, and Seforno all posit that verse 1 is a continuation of the events of Chapter 17.  Thus referring to Avraham simply by the pronoun "אֵלָיו" is understandable since he was the subject of the previous verses.²⁵  They, do however, need to explain why the text provides a setting (time and location) for the event which would seem to imply that it is a new story.²⁶

Did Hashem stay?

• Yes – According to R. Saadia and Abarbanel, Hashem's presence stayed with Avraham throughout the visit of the angels.²⁷  Abarbanel asserts that this explains both how Hashem continuously speaks to Avraham while he interacts with his guests (verses 13 and 20) and how the verse later states that "Avraham was still standing before Hashem".²⁸ 
• No – According to Rashi, Ramban, and Seforno, it would seem that Hashem left after His visit and that there is no connection at all between His initial revelation and the rest of the chapter.²⁹

Calling the angels by the name of Hashem – שם הוייה – According to this approach, which distinguishes between Hashem's revelation and the angels' visit, the name Hashem throughout the chapter refers to Hashem and not the angels.  Thus, it is Hashem who is speaking or referred to in 18:1,13-14,17, 20, 22, 26ff.

Calling the angels by the name of Hashem – שם אדנות – This approach offers two understandings regarding to whom Avraham was speaking when he said, "אֲדֹנָי אִם נָא מָצָאתִי חֵן בְּעֵינֶיךָ":

• Angels – According to most of these sources, in these words Avraham was addressing the angels.³⁰  Ramban and Abarbanel explain that Avraham referred to them by the sacred term "אֲדֹנָי" because he recognized that they were angels.³¹  Alternatively, R. Saadia contends that Avraham assumed that the angels were prophets and meant, "‎איש האלהים"‎³² but spoke in short, skipping the word "‎איש".‎³³  This position must explain the switch from plural (אֲדֹנָי), to singular (אַל נָא תַעֲבֹר) and then back to plural in verse 4 (רַחֲצוּ רַגְלֵיכֶם).  Rashi and Seforno³⁴ suggest that originally, Avraham was only speaking to the leader, while Ramban³⁵ posits that Avraham addressed all in the plural, but then asked each one individually to stay.³⁶  Afterwards he offered hospitality to all as a group.³⁷
• Hashem – Both Rashi and Abarbanel bring a second opinion, following R. Elazar in Bavli ShabbatShabbat 127aAbout Bavli Shabbat, that Avraham was addressing Hashem,³⁸ asking Him not to leave despite the guests' appearance.³⁹  This reading easily explains the switch between singular and plural language, since there is a change in addressee from Hashem to the angels.

Purpose of the angel's visit – According to this approach, the angels' visit is distinct from Hashem's desire to share the fate of Sedom with Avraham, and was instead aimed at telling Sarah⁴⁰ about the impending birth of Yitzchak.  Rashi further suggests that Hashem only sent the angels because he knew that Avraham desired to host guests, while Ramban views their visit as part of Avraham's reward for his circumcision.

The disappearance of the third guest – According to Rashi, each of the angels had a different task, one to announce the birth of Yitzchak, one to destroy Sedom, and one to cure Avraham and save Lot.  After the first angel completed his task, he departed, leaving only two to continue to Sedom.⁴¹

Why are the guests referred to as both "אֲנָשִׁים" and "‎מַלְאָכִים"? The commentators offer several possibilities:

• Interchangeable terms – R. Saadia asserts that the terms are used interchangeably in many places in Tanakh, and one need not question the usage here.⁴²
• Differing perspective – According to Rashi, since Avraham was used to visiting angels, they were not particularly unique and are called simply "men". However, by Lot, who was not accustomed to them, they are called angels.⁴³
• Presence of Hashem – Rashi raises a second possibility, that when Hashem accompanies the angels they are called people (in comparison to Him), but when His presence is lacking they are called angels. This, though, begs the question of why Hashem was with the angels in certain parts of the story and not in others.
• Action-based – According to Abarbanel,⁴⁴ the angels are called men when they behave like humans, but they are referred to as angels when they do godly acts.⁴⁵

Angelic or human actions – The supernatural abilities of the guests is easily explained by their being angels.  These sources differ, though in how they explain their eating:

• Pretense – Rashi and Ramban, following Bereshit Rabbah48:14About Bereshit Rabbah, suggest that the angels simply pretended to eat.
• Consumption by fire – R. Saadia suggests that the root "אכל" is not limited in meaning to eating with one's mouth, but can also connote other forms of consumption, such as eating by fire or sword.⁴⁶  Thus, here, the angels might have burned their food.
• Others ate – R. Saadia also suggests that the verb "וַיֹּאכֵלוּ" refers to Avraham and his servants, but not to the angels.⁴⁷

Did Avraham recognize them as angels?

• Yes – According to Ramban and Abarbanel, Avraham knew that they were angels.
• No – According to R. Saadia, despite Hashem's hints, Avraham mistook the angels for prophets.⁴⁸

Sarah's laughter – Ramban⁴⁹ asserts that Sarah was unaware that the men were angels and thus laughed at their announcement.  She did not hear Hashem's rebuke (since Hashem spoke only to Avraham) but Avraham himself chastised her, leading to her denial.  As such, Sarah was not trying to cover up her actions before Hashem, only before her husband.⁵⁰

"'וְאַבְרָהָם עוֹדֶנּוּ עֹמֵד לִפְנֵי ה" – This verse is not problematic for R. Saadia and Abarbanel who suggest that Hashem's presence had never left Avraham after the initial revelation.  According to the others, though, Avraham was not standing before Hashem at this point of the story:

• תיקון סופרים – Rashi asserts that the verse should really read, "וה' עודנו עומד לפני אברהם" since Hashem had just come to speak to Avraham about Sedom (in verse 20) as he accompanied the guests.  The text was reversed, though, so as not to dishonor Hashem.
• Until the angel's arrival in Sedom – According to Ramban, the phrase is related to the immediately preceding term, "וַיֵּלְכוּ סְדֹמָה", and comes to explain that Avraham stood before Hashem to plead for Sedom during the entire time that it took the angels to travel there.

One Event

Hashem appeared to Avraham via the three angels.

Sources: JubileesChapter 16:1-11,20-23About Jubilees, PhiloOn Abraham XXII-XXIIIAbout Philo, Kirkisani the Karaite, RashbamBereshit 18:1,13,14,16,20,26Bereshit 19:24About R. Shemuel b. Meir, ShadalBereshit 18:1,3,9,13,17,20,22Bereshit 19:17,18About R. S.D. Luzzatto, Hoil Moshe, R. D"Z HoffmannBereshit 18:1-19:38,18:1-2,3-8,6-8,13-14,20-21Bereshit 19:1-3,18-20About R. D"Z Hoffmann

Hashem's revelation – "'וַיֵּרָא אֵלָיו ה" – According to this position, the first verse of the chapter is a general introduction to the story, and the rest of the chapter provides the details (‎‎כלל ופרט).‎⁵¹  Thus, the unit opens by sharing that Hashem revealed Himself, and then explains how this revelation transpired via the three angels visiting Avraham.  As such, there is no missing speech of Hashem; the entire chapter constitutes the revelation.

Why is Avraham not mentioned by name in v.1? Since this position views verse 1 as beginning a new unit,⁵² it is difficult to understand why Avraham is referred to by a pronoun (implying a continuation) and not by his proper name.  R. D"Z Hoffmann suggests that this teaches that the story is integrally related to the preceding one regarding Avraham's circumcision.  Due to the covenant, Avraham achieved a new level of closeness to Hashem, meriting a visit by angels who could behave as his guests and share with him Hashem's plans.

Calling the angels "Hashem" – According to this approach, the Torah often refers to angels by the name of Hashem, since they are His messengers doing His bidding (‎שלוחו של אדם כמותו).‎⁵³  Thus, these sources posit that throughout the chapters, in many of the places where Hashem's name appears, it refers not to Hashem, but to one (or all) of the angels.⁵⁴  See the following points for elaboration.

שם הויה – Verses 18:1, 13, 17, 20, 22, 26 ff – Rashbam⁵⁵ is consistent in reading all occurrences of "Hashem" in the chapters as referring to the angels.  Only in instances where the angels themselves refer back to Hashem in their own speech (in 18:14 and the second occurrence in 19:24), does he say that the word refers to Hashem Himself.⁵⁶  This reading has several advantages:

• It easily explains how Sarah heard the rebuke regarding her laughter and why she dared deny laughing.
• The language of 18:14 is extremely similar to 18:10 since the same person is saying both statements, and simply reinforcing his earlier words.
• According to this reading, Hashem does not constantly interrupt Avraham's interaction with the angels; it is only they who speak throughout.
• Even though Avraham had been accompanying the angels, the verse can still say "וְאַבְרָהָם עוֹדֶנּוּ עֹמֵד לִפְנֵי ה'‏" since this implies only that he continued to talk to the third angel after the others left.
• Only two angels arrive by Lot, because the third remained with Avraham while he prayed for Sedom.
• There is no contradiction between the angels saying they themselves will destroy Sedom and 19:24 which has Hashem destroy it, since Hashem of that verse can be understood to refer to an angel.

שם אדנות – Verses 18:3 and 19:18

• "אֲדֹנָי אִם נָא מָצָאתִי חֵן בְּעֵינֶיךָ" – According to Philo, Shadal, and R. D"Z Hoffmann, the term "אֲדֹנָי" refers to the angels.⁵⁷  To explain the switch between this plural form and the singular form used in the rest of the verse, R. D"Z Hoffmann suggests that Avraham was really speaking only to the most important of the guests, but out of honor, he originally addressed him using the majestic plural.⁵⁸  Kirkisani the Karaite suggests that it is "the way of the text" to use either the singular or the plural when speaking of a group.⁵⁹
• "אַל נָא אֲדֹנָי" – Shadal assumes that, in this verse too, Lot is addressing the angels.  R. D"Z Hoffmann brings this as an option, but appears to prefer the possibility that Lot is praying to Hashem.⁶⁰

Purpose of the vision/visit – According to Shadal and the Hoil Moshe, the main goal of the visit was to tell Avraham about the upcoming destruction of Sedom rather than about the birth of Yitzchak.⁶¹ They point out that there was no reason to repeat the previously delivered (in Chapter 17) news of the impending birth,⁶² and the angels only mentioned it tangentially in response to the fact that Sarah was sitting alone in her tent, presumably lamenting her barrenness.

Why are the guests referred to as both "אֲנָשִׁים" and "‎מַלְאָכִים"? This approach works well with the verses which call the guests "‎מַלְאָכִים", but needs to explain those which call them "אֲנָשִׁים".  Philo suggests that they were so called because they took the form of people,⁶³ but he does not account for the switch in titles.

Angelic or human actions – This approach easily explains how the guests knew that Sarah was to give birth⁶⁴ and how they could blind the people of Sedom or destroy the city, but it has difficulty explaining the angels' seemingly corporeal actions.  Philo explains that the angels simply pretended to eat and drink.⁶⁵  Hoil Moshe, though, asserts that despite being angels, while taking on human form, they were able to eat.⁶⁶

Did Avraham recognize them as angels?

• Immediately – Hoil Moshe explains the term "נִצָּבִים עָלָיו" to mean that the angels suddenly materialized before Avraham, leading Avraham to realize immediately with whom he was dealing.  He suggests that it is for this reason that Avraham treated them with such respect.⁶⁷
• Midway – R. D"Z Hoffmann argues that at first Avraham must not have realized that the guests were angels or he would not have offered them food.⁶⁸  He suggests that it was only after the angels chastised Sarah for her doubt that Avraham began to realize that the beings before him were not human visitors.⁶⁹ 

The disappearance of the third guest – As Shadal and Hoil Moshe assume that the main job of the angels was to tell Avraham about Sedom, it would seem that one angel would have sufficed.  The Hoil Moshe suggests that there was in fact one central angel, but he was accompanied by two lesser servants.  Most of these sources explain that only two of these arrived by Lot, since the main one was detained while Avraham spoke with him about saving the city.

Divine Prophecy

All of Chapter 18 is merely a description of what Avraham saw in his prophetic vision.  Thus, the coming of the "guests" was merely part of Hashem's revelation and not an event that actually transpired in the physical realm.

Sources: RambamMoreh Nevukhim 2:42Moreh Nevukhim 2:45About R. Moshe Maimonides, RadakBereshit 18:1,2,3,4,10,12,13,17,22,33Bereshit 19:1,2,3,11,15,16,18,24About R. David Kimchi, R. Yosef ibn KaspiTirat Kesef 2:3Bereshit 18:3,11Bereshit 19:1About R. Yosef ibn Kaspi, AbarbanelCommentary on Moreh Nevukhim 2:42About Abarbanel⁷⁰

Hashem's revelation – "'וַיֵּרָא אֵלָיו ה" – According to this approach, 18:1 introduces the story, while the following verses provide the details (כלל ופרט).‎⁷¹  Hashem revealed himself to Avraham in a prophetic dream and the visit of the angels occurred as part of that vision.⁷²  As such, the content of the revelation is not missing at all; the entire chapter (and perhaps part of Chapter 19) constitutes the prophecy.

Why is Avraham not mentioned by name in v.1? As this position asserts that the chapter starts a new unit and is not connected to what came before, it is not clear why Avraham is referred to only by a pronoun and not by his name.

"כְּחֹם הַיּוֹם" – Both Radak and Ibn Kaspi assert that this detail is included because it was due to the heat that Avraham fell asleep and dreamed of the guests in his prophecy.

Where does the prophecy end? These commentators differ regarding how much of the story occurred only as part of the prophecy and did not happen in real life:

• Only Chapter 18 included – According to Radak, all of Chapter 18 took place in the vision, but the events of Chapter 19 transpired in reality.⁷³  As evidence, he points to 18:33 ("וַיֵּלֶךְ ה' כַּאֲשֶׁר כִּלָּה לְדַבֵּר אֶל אַבְרָהָם") which appears to signify the end of the prophecy.  Radak is probably also motivated by the desire to show Sedom being destroyed and Lot being saved, for, as Ramban argues, if Chapter 19 was also part of the vision when did this happen?⁷⁴  Radak's position, though, does not explain the origin of Lot's guests, if they had previously been only part of Avraham's dream.

• Both Chapters 18 and 19 included – In contrast to Radak, Abarbanel maintains that Hashem's "leaving" Avraham in 18:33 was also part of Avraham's vision, and that the prophecy ended only at 19:28.⁷⁵  He further asserts that the physical destruction of the city and salvation of Lot are not missing, but are rather described in verse 19:29 (immediately after the conclusion of the prophecy).⁷⁶  This occurred differently than described in the vision, with Hashem rather than the angels acting, and Lot, on his own, deciding to leave the city. 
•  Chapter 18 is Avraham's dream while Chapter 19 is Lot's – Ibn Kaspi asserts that 18:33 marks the end of Avraham's prophecy,⁷⁷ but that 19:1 introduces a similar vision, which Lot received.⁷⁸  According to this position, there are two distinct sets of angels, one group which appeared to Avraham and a different twosome who were part of Lot's dream.⁷⁹  The actual destruction of Sedom does not appear in the verses, but did occur.

Was Sarah's laughter part of the vision? These commentators differ regarding whether Sarah laughed as part of Avraham's dream or not:

• Reality – Radak assumes that Sarah laughed in reality and not as part of the dream.  He asserts that sometimes someone who is standing near a prophet can overhear a portion of the prophecy.⁸⁰  Thus, Sarah heard the news and laughed in disbelief.
• Prophecy – Ibn Kaspi and Abarbanel, in contrast, maintain that Sarah's laughter was part of the vision seen by Avraham.  Ramban questions the point of including this if it did not really happen (especially as it makes Sarah appear negative).  Abarbanel explains that this was Hashem's way of rebuking the couple for their earlier laughter (in 17:17).⁸¹

Purpose of vision/visit – This position must explain the need to repeat to Avraham the news of the upcoming birth of Yitzchak, if he had just received such a prophecy a few verses beforehand.⁸²  This leads Radak to suggest that the goal was to have Sarah overhear the news,⁸³ while Abarbanel suggests that the vision revealed that it was Avraham's hospitality and generosity that merited him to have children.  According to both, it would seem that the main focus of the prophecy was not the birth announcement, but the news regarding the destruction of Sedom.

Purpose of vision's details – Ramban questions the Torah's need to report all the details of Sarah and Avraham's hospitality (baking of cakes, cooking of meat etc.) if it was all just a vision.  Ibn Kaspi and Abarbanel respond that prophetic visions, like dreams, reflect one's actions while awake and thus this prophecy, too, showed what Avraham would have done in reality.  Radak, in contrast, concludes that the details were included to teach the reader the appropriate way to show hospitality.⁸⁴

Why are the guests referred to as both "אֲנָשִׁים" and "‎מַלְאָכִים"? Radak maintains that the guests are called people when they behave like humans, but angels when they act more supernaturally.  Thus, by Avraham, when they appear to eat and wash, and in 19:10 and 16, when they grab Lot (a physical action) they are called men, but when they act to save Lot in 19:15, they are called angels.⁸⁵

Angelic or human actions – According to these sources, all the actions of the guests in Chapter 18 occurred merely in a vision, so there is no issue of angels eating etc.  According to Radak's position that Chapter 19 happened in reality, the supernatural actions of the characters are explained by their being angels.

The disappearance of the third guest – Ibn Kaspi says that one should not question the difference in number of guests since the two chapters represent distinct visions and there is no reason that they should be the same number.

Calling the angels by the name of Hashem

• שם אדנות – According to all these sources, the word "אֲדֹנָי" in 18:3 refers to the angels.⁸⁶  Ibn Kaspi asserts that one should not be troubled by the switch from plural to singular and then back again, because it is natural for people who are speaking to a group to at times turn to on individual and at other times to address the group as a whole.
• שם הויה – Radak says that the name Hashem in 18:10,13, and the first appearance in 19:24 refers to the angels, who are called after the One who sent them, while in 18:1 and 17, the name refer to Hashem Himself.

"'וְאַבְרָהָם עוֹדֶנּוּ עֹמֵד לִפְנֵי ה" – Radak and Abarbanel explain that this phrase comes to share that, though the guests left, the vision did not end and Avraham continued to prophesy.

Philosophical motivations – Rambam here is consistent with his general rationalist approach regarding angels.  He posits that all "מַלְאָכִים" in Tanakh are either part of a prophetic vision or human prophets.⁸⁷  Radak is apparently not motivated by the same issues, as he has no problem saying that the guests of Chapter 19 are celestial angels.⁸⁸

¹ See the opinion brought by Ibn EzraBereshit 18:1,13,33About R. Avraham ibn Ezra who also posits achronology: וי"א שהוא מוקדם ומאוחר, וכן הוא וישא – וכבר נשא עיניו ועשה כך וכך, ואח"כ נראה אליו השם.

² Though this accounts for the juxtaposition, it does not adequately explain why verse 1 could not have been written in its proper place, after the angels left in 18:16.

³ This would explain why the two angels who were heading to destroy Sedom and had no news to share with Avraham nonetheless stopped by.

⁴ Often the Torah uses the term "מַּלְאָכִים" to describe people who are sent by others on some mission. As an example, R"Y Bekhor Shor points to Bereshit 32:4, where Yaakov sends human messengers to his brother and the text calls them "מַלְאָכִים".  Ibn Ezra points to Chaggai 1:13 where the prophet Chagai is called "מַלְאַךְ ה'‏".

⁵ Since Avraham received more prophecies than the guests, they are referred to as "אֲנָשִׁים" when speaking to him. Since Lot was not a prophet, they can be called either "מַּלְאָכִים" or "אֲנָשִׁים" when interacting with him.  Ralbag points to Bereshit 16 (the story of Hagar and the "מלאך") as another example where a prophet is called a "מלאך" because he is talking to someone on a lesser level.

⁶ For proof that angels do not eat, he points to Shofetim 13:16.

⁷ See Melakhim II 6:18 where Elisha the prophet also blinds his enemies. A Karaite commentary attributed to Daniel AlkumsiJQR 15:3, p. 383-384About Daniel AlKumisi the Karaite (see also Abarbanel) questions this parallel, arguing that in Melakhim it is explicit that Elisha prayed to Hashem and that it was Hashem who blinded the enemies.  One might answer that here, too, the prophets prayed, but this fact is simply not mentioned in the text.

⁸ He further asserts that if they were prophets of Hashem, they would have also needed to be circumcised, a fact that would have been mentioned by the Torah.

⁹ Ibn Ezra asks this question as well and responds that the prophets were coming to announce the birth to Sarah, not to Avraham.

¹⁰ This question is also raised in the commentary attributed to Daniel AlKumisi the KaraiteJQR 15:3, p. 383-384About Daniel AlKumisi the Karaite.  Ibn Ezra dismisses the question by pointing to Shemot 11:10, which attributes all the wonders in Egypt to Moshe and Aharon, despite the fact that they were Hashem's doing. Alkumsi responds that Moshe consistently prayed to Hashem before acting and that the text repeatedly says that he was acting "according to the word of Hashem".

¹¹ One advantage of this possibility is that having the prophet speak enables one to understand how Sarah could have heard what was said, and explains how she denied her laughter (something she would not dare to do in front of Hashem.)  Moreover, Ralbag might be hesitant to read this as if Hashem Himself was speaking, because that would require one to assert that Avraham received prophecy while awake, in the midst of dealing with the guests. Ralbag, nonetheless, suggests that it is possible that due to Avraham's great prophetic status, he was able to do so.  In this he disagrees with Rambam (see note below) who maintains that only Moshe was at such a level.

¹² He points to Bereshit 25:23 as another example where a prophet is called "Hashem".  Cf. Rambam Moreh Nevukhim 2:41.

¹³ According to him, the word "תַעֲבֹר" is not a second person masculine, but rather a third person feminine, and it refers to the "חבורה" of prophets.  In this, he differs from R. Elazar in Bavli ShabbatShabbat 127aAbout Bavli Shabbat who claims that Avraham requested that Hashem stay while he dealt with the guests.  R"Y Bekhor Shor rejects that possibility because, according to him, Hashem had not yet revealed Himself to Avraham and was not in the midst of conversing with him.  In fact, he posits that it is specifically because he was not busy with Hashem that Avraham had no problem inviting the guests to stay and eat.

¹⁴ He does not address the problematic vocalization of "אֲדֹנָי" with a kamatz, but interestingly, Ibn Ezra writes that in some manuscripts the word appears with a patach.

¹⁵ Cf. Rashi below.

¹⁶ For other examples, see Ralbag.

¹⁷ The various opinions in Rabbinic literature all appear to adopt the positions that the visitors were angels, and that their visit was distinct from Hashem's personal revelation to Avraham.  However, most of the Rabbinic opinions tend to focus on only one of the issues, and they do not present an explicit position on both questions together.

¹⁸ N. Leibowitz, Iyyunim Besefer Bereshit (Jerusalem, 1992): 116-117, asserts that according to them, 18:1 concludes the story of Chapter 17, rather than introducing the events of Chapter 18. As such, the story of the angels is totally unconnected to the initial revelation of verse 1. 
R"E Samet argues that if this is true, the story of the angels would seem to start in the middle.  It opens with a series of pronouns (...וַיִּשָּׂא עֵינָיו), the subject of whom would be unknown if this is the beginning of  a story.  In addition, he suggests that from Ramban's own words, he seems to view the entire two chapters as part of Avraham's reward.  This, too, though is difficult since there is no hint in the text that the events are connected to the circumcision.  In addition, there would seem to be disproportionate discussion of the reward (two chapters) compared to the good deed (several verses).

¹⁹ In this, he follows  Bavli SotahSotah 14aAbout the Bavli, Bavli Bava Metzia, Tanchuma Vayera 2, and  Tanchuma Ki Tisa 15.  Cf. Bereshit Rabbah47:10About Bereshit Rabbah as well.

²⁰ This approach anthropomorphizes Hashem, having Him act as humans.  Cf. Bavli SotahSotah 14aAbout Bavli Sotah which asserts that one should learn from these deeds of Hashem to act similarly.

²¹ Ramban points to Bereshit 32:2 and Vayikra 9:23 as parallel cases where Hashem similarly appears to people without speaking, simply as a show of honor, to reward them for keeping a commandment. R"E Samet questions Ramban's prooftexts, suggesting that cases where there is something tangible to see (such as "מַלְאֲכֵי אֱלֹהִים" and "כְבוֹד ה'‏") are different than our case in which Hashem appears prophetically.  In the former, there is no need for an accompanying speech since a physical form appears as a sign, yet the language of "וַיֵּרָא ה'‏" is almost always followed by a speech. See, for instance, Bereshit 12:7, 17:1, 26:2,24, and 35:9-10.

²² As evidence that people stand before another when making a covenant, he points to Devarim 29:9 and Melakhim II 23:2.  He also points to the phrase "וַיִּפְגְּשֵׁהוּ ה'‏" in Shemot 4:24 as another example of Hashem "attending" a circumcision, without any accompanying speech.  This example, though, is difficult, as the following phrase,"וַיְבַקֵּשׁ הֲמִיתוֹ" suggests a different purpose to the meeting.  Seforno raises the possibility that our story is the reason behind the custom to prepare a chair (for Eliyahu or the Divine presence) during circumcisions.

²³ Cf. R"Y Bekhor Shor and Ralbag below.  They, too, connect the revelation to the news regarding Sedom but, in contrast to this position which assumes that Hashem revealed himself and then waited until after the guest's visit to relay the content of the revelation, they assert that 18:1 is achronological and Hashem did not even appear until after the visit. [They also differ in viewing the guests as humans.]

²⁴ According to R. Saadia, Hashem generally makes His presence known to prophets through some type of light, so that they recognize that the voice they hear is that of Hashem.

²⁵ See Ramban who makes this point and further asserts that one should not be bothered by the fact that there is a parashah break in the middle since the topic is all one.

²⁶ Rashi attempts to answer that Mamre is specifically mentioned since he is the one who advised Avraham regarding circumcision. The text includes that it was at the heat of the day to show Hashem had purposefully made it hot so as not to bother Avraham with guests.  Ramban and Seforno more simply say that the location is included since that is where Avraham was circumcised.

²⁷ According to a second opinion in Rashi, as well, Hashem stayed, but at the request of Avraham.

²⁸ All of these are difficult for Rashi, Ramban, and Seforno.

²⁹ See the discussion in the note above regarding how these commentators apparently view verse 1 as the conclusion to the events of Chapter 17 and R"E Samet's objections to such a reading.

³⁰ See also the discussion in Bavli ShevuotShevuot 35bAbout the Bavli.

³¹ This explains the vocalization of "נָ"rather than "נַ", as would be expected if the word simply meant "my masters".

³² Cf. Ibn EzraBereshit 18:1,13,33About R. Avraham ibn Ezra who similarly suggests that the word might mean "נביא ה'‏".  This explanation also solves the problem of the problematic vocalization "נָ" rather than "נַ", as it reads the word "אֲדֹנָי" to mean Hashem and not "my masters".
R. Saadia is consistent in reading the term this way throughout the chapters, assuming that in 19:18, too, Lot is addressing the angels as "men of God".

³³ He suggests that this occurs often in the Hebrew language.  As support he points to the phrase "לַי"י וּלְגִדְעוֹן" in Shofetim 7:18 which is short for "חֶרֶב לַי"י וּלְגִדְעוֹן" and Shofetim 16:2 which reads לַעַזָּתִים לֵאמֹר rather than "לַעַזָּתִים הוגד לֵאמֹר".

³⁴ See Bereshit Rabbah48:10About Bereshit Rabbah.

³⁵ Abarbanel agrees with his reading.

³⁶ According to him he said, "אַל נָא תַעֲבֹר מֵעַל עַבְדֶּךָ" three times.

³⁷ Ramban also suggests that throughout Torah we see similar switches in language.  Often, when Hashem addresses the nation, but means to speak to each individual therein, He begins with plural language and then switches to the singular. For examples, see Vayikra 18:5,7, Vayikra 19:9 and Devarim 4:29.

³⁸ On 19:18, as well, Rashi brings the opinion of Bavli ShevuotShevuot 35bAbout the Bavli that Lot's speech "אַל נָא אֲדֹנָי" is directed at Hashem, not the angels.  To explain why, if so, the verse states that "וַיֹּאמֶר לוֹט אֲלֵהֶם", as if Lot were speaking to the angels, Rashi suggests that the first two words of Lot "אַל נָא" were in fact addressed to them.  The word "אֲדֹנָי", though, is attached to the following verse and begins the prayer mentioned there.

³⁹ The Karaite exegete, Yaakov Kirkisani, questions this reading, pointing out that one would have expected Avraham to speak these words to Hashem before he ran to greet the guests in verse 2.

⁴⁰ Ramban suggests that although Avraham was already aware of this, he had not yet told Sarah.

⁴¹ Cf. TryphoJustin Martyr, Dialogue with Trypho 56-57 who asserts that two angels came to destroy Sedom and one to announce the birth.  The one who had finished his task did not continue to Sedom.  R. Saadia and Abarbanel do not elaborate on the specific mission of each angel but explain the missing third in the same way.

⁴² He points to Chagai who is called both prophet and "מלאך ה'‏" (Chagai 1:3,13). See also Bereshit 32:25, Yechezkel 9:2, and Daniel 12:7 which all mention a man (or men) who appear to be angels.  In none of these cases, though, are they referred to as such, and one could argue that, in fact, the verses all speak of human agents and not heavenly ones.

⁴³ Abarbanel points out that this logic does not account for all the cases where they are also called "men" by Lot.

⁴⁴ See Radak below as well.

⁴⁵ He suggests that they traveled from Avraham to Sedom at supernatural speed (or they would not have been able to arrive by dusk, after eating and spending the day with Avraham) and are thus called "angels" upon arrival.
According to this reading though, it is unclear why the messengers are not called "‎מַלְאָכִים" when they blind the people of Sedom, nor why in one verse that describes their saving of Lot they are called "‎מַלְאָכִים", while in the next they are called "אֲנָשִׁים" again.

⁴⁶ For such usages see Bemidbar 13:32, Devarim 7:16, and Yeshayahu 1:20.

⁴⁷ R. Saadia brings other examples where the Torah has a verb refer to a list of objects when really it only refers to those capable of doing the action.See, for example, Bereshit 47:19, Yehoshua 7:25, Yeshayahu 5:12, and Ezra 8:35.

⁴⁸ He claims that Hashem did not correct him, so that he could continue his hosting and hear the news while peacefully seated at a feast.

⁴⁹ Abarbanel explains similarly.

⁵⁰ According to Ramban, it is Avraham (rather  than Hashem) who responds, "No, you laughed."

⁵¹ Rashbam uses this exegetical principle in other places as well. See, for instance, his comments to Bereshit 1:27 and 26:25.

⁵² In support of this idea is the fact that the text provides the setting for the story, including Avraham's location and time of day of the revelation.

⁵³ As evidence Rashbam points to Shemot 3:2-4, where one verse speaks of an angel appearing out of the burning bush and the next verse speaks of Hashem calling from it.  R. D"Z Hoffmann points to similar examples in Bereshit 31:11-13, Bereshit 48:15-16, and Shofetim 6:11-14.

⁵⁴ The sources do not explain, though, why some verses refer to them as "people" and some as "Hashem".  They might suggest that this is simply customary Biblical literary variation.  E. Samet suggests that maybe the different titles represent the perspective of Avraham.  They are called people when he viewed them as such, but in verse 13, when Avraham began to realize that they were angels, the text switches to refer to them as "Hashem". [It is possible that in the opening verse they are called Hashem as well, even though Avraham still thought of them as guests, to hint to the reader that they were, in fact, angels.]

⁵⁵ See also R. D"Z Hoffmann.  Shadal and the Hoil Moshe also adopt this approach in general, but they make an exception regarding verses 18:17-19, which they assumes represent the earlier thoughts of Hashem and not a current speech.  They are presumably picking up on the past perfect language of "וַה' אָמָר".  In addition, Shadal claims that though angels can act and speak on Hashem's orders, these verses speak of thoughts and decision making, which is only in the hands of Hashem (הדבור והמעשה נעשים על ידי שליח, אבל המחשבה והרצון אינם על ידי שליח).

⁵⁶ N. Leibowitz, Iyyunim BeSefer Bereshit, (Jerusalem, 1992):114-115,  sees in these exceptions an inconsistency in Rashbam's approach which leads her to dismiss it. E. Samet, though, points out that this is actually one of the strengths of Rashbam's reading.  Had the speaker of these statements been Hashem Himself, it would not be clear why Hashem refers to Himself in the third person, using His name and not the word "me".  According to Rashbam, though, the speaker is the angel who logically refers to Hashem in third person, using His proper name.

⁵⁷ According to these sources, the word "אֲדֹנָי" is a form of polite address meaning "my masters".  If so, though, one would expect the vocalization under the letter נ to be a patach (נַ) rather than a kamatz (נָ).  Shadal, thus, explains that in reality Avraham actually spoke to just the lead angel, and said "my master".  The Torah, though, changed his language to use the name of Hashem so as to reveal to everyone that the guest was a messenger of Hashem. [See Bavli Shevuot 35b.]
R. Hoffmann explains more simply that the cantillation mark on the nun sometimes takes a pausal from, elongating the patach to a kamatz.

⁵⁸ He would presumably suggest that, in the next verse, when Avraham reverts back to the plural, it is because he is offering all of the angels to wash and eat.

⁵⁹ Thus, it is normal usage for Avraham to first address the angels in plural in the beginning of verse 3, revert to the singular, and then switch back to the plural in verse 4.  For an example of Torah switching between plural and singular verbs when speaking of a group, see Shemot 19:2: "וַיִּסְעוּ מֵרְפִידִים וַיָּבֹאוּ מִדְבַּר סִינַי וַיַּחֲנוּ בַּמִּדְבָּר וַיִּחַן שָׁם יִשְׂרָאֵל נֶגֶד הָהָר".

⁶⁰ One might challenge this from the fact that the verse says, "וַיֹּאמֶר לוֹט אֲלֵהֶם", which would suggest that Lot is talking to the angels.  R. D"Z Hoffmann brings the opinion of the Ritva who asserts that the word "אֲלֵהֶם" should not be understood as "to them" but rather as "before them."  Lot's words were addressed to Hashem but were said in the presence of the angels.

⁶¹ The other commentators agree that the angels were supposed to speak to Avraham about Sedom, but it is unclear if they view the news of Yitzchak's birth as of equal import or if they also think this was just tangential.

⁶² Hashem had just told Avraham that Yitzchak was to be born at the end of Chapter 17.

⁶³ If so, one would have expected them to be called angels in 18:22 after Avraham realized in verse 17 they are not people according to him.

⁶⁴ In fact, since it is so expected that angels know what is going on, Rashbam is bothered by the fact they would need to ask Avraham "Where is Sarah", and he thus suggests that this was really just a way of opening the conversation.

⁶⁵ See also Josephus.

⁶⁶ See also R. D"Z Hoffmann who brings the opinion of Seder EliyahuSeder Eliyahu Rabbah 13About Seder Eliyahu that the angels ate in deference to Avraham.

⁶⁷ He notes that Avraham probably did not bow before every passerby; his actions here were exceptional due to the level of his guests.

⁶⁸ Hoil Moshe responds that since they had assumed the form of men, Avraham treated them as such, and they, in turn, ate.

⁶⁹ See also Philo.

⁷⁰ In his commentary to Moreh Nevuchim, Abarbanel attempts to defend the Rambam against the arguments of Ramban. In the end, though, he concludes that he does not agree with this reading.  See his alternative above.

⁷¹ In this aspect the approach above of "Angels: One Event" is similar to this one.  In other aspects, though, they are almost opposites, as that approach suggests that Hashem revealed Himself in a concrete form, while this one assumes He did so only in a vision.

⁷² Abarbanel attempts to prove that the vision mentioned in 18:1 continues throughout the chapter since later verses (such as 18:13, 20 and 22) mention Hashem speaking. See, though, Rashbam above who explains that in these verses the name "Hashem" refers to the angel.

⁷³ He brings a second option as well, that the prophecy continued to Chapter 19. See below.

⁷⁴ From other places in Tanakh (Devarim 29:22, Yeshayahu 1:9 and 13:19), it is abundantly clear that Sedom was destroyed, so one can not say that the events in the vision never happened.

⁷⁵ He points out that 19:27 ("וַיַּשְׁכֵּם אַבְרָהָם בַּבֹּקֶר אֶל הַמָּקוֹם אֲשֶׁר עָמַד שָׁם אֶת פְּנֵי ה'‏") provides closure to the unit.

⁷⁶ This reading also solves the ostensible repetition between 19:27-28 and 29.  The former verses were part of Avraham's dream, while the latter was a description of reality.

⁷⁷ He notes that the words "וְאַבְרָהָם שָׁב לִמְקֹמוֹ" would seem to be problematic for this position, as Avraham did not really go anywhere.  He suggests that they are written from the perspective of Avraham who felt as if he had left his tent while dreaming, and now found himself back there after awakening.  He points to Yehoshua 2:7 as a parallel case, where the text presents something from the perspective of the characters, although it is not totally accurate.

⁷⁸ Ramban and Ralbag both question how someone on Lot's lower level could have possibly prophesied. Ralbag points out that 19:29 suggests that Lot was saved from Sedom not due to his own righteousness but by the merits of Avraham, so it is unlikely that he was at a high enough spiritual level to receive prophecy. However, both this evaluation of Lot and the assumption that a high spiritual level is required for prophecy can be debated.

⁷⁹ Ramban and Ralbag question how both Sarah and the people of Sedom could talk and act if the angels were not visible and were only parts of someone else's vision.  Ibn Kaspi responds that neither Sarah nor the men of Sedom actually spoke; their roles were also part of what Avraham/Lot saw.  He does point out, though, that the people of Sedom actually committed crimes like those described.

⁸⁰ As another example, he points to Daniel 11:7, where Daniel points out that despite the fact that he alone saw the vision, the other people nearby were filled with trembling.

⁸¹ Abarbanel does not say this explicitly, but this appears to be his intent.  According to this possibility, Sarah had been told of the original prophecy, and like Avraham, had laughed upon hearing it. Such a reading suplies an answer to all those who wonder why Sarah was rebuked for her laughter, while Avraham was not chastised; according to Abarbanel, Hashem does not distinguish and rebukes both.

⁸² Even though the other positions must also grapple with the repetition, it is even more troubling for this approach, since according to it, both announcements were given in the same manner (prophecy) just to Avraham.

⁸³ See above that, according to Radak, Sarah heard part of the prophecy that Avraham envisioned.  Even if one grants that this could be true, it is still perplexing why Hashem would not have simply given Sarah her own prophecy, or allowed her to overhear the first one in Chapter 17.

⁸⁴ Radak often speaks of the reasons why certain stories are included in Tanakh, pointing to the lessons that readers cam learn.  For example, see Bereshit 9:20, 16:6 and 24:64.  For elaboration, see R. David Kimchi (Radak).

⁸⁵ This distinction, though, is somewhat arbitrary, since in 19:10 the guests also blind the people of Sedom, an angelic action, and yet are called people. Similarly, in 19:1 there is nothing particularly supernatural about the guests' arrival in Sedom and yet there they are called angels.  See, though, AbarbanelBereshit 19:1About R. Yitzchak Abarbanel, who suggests that they arrived with supernatural speed.

⁸⁶ Radak says the same about 19:18, while the others do not address that verse.

⁸⁷ In our story, Rambam adopted the first of these options, that the guests were part of a prophetic vision.  Rambam, here, likely did not want to take the alternative approach that the guests were human prophets who interacted with Avraham while he was awake, because Hashem Himself speaks to Avraham (18:13,20-21) while the guests were still present, and according to Rambam only Moshe reached the level of being able to prophesy while awake.  [Cf. Ralbag above who grapples with the same issue, and thus allows for the possibility that Moshe was not unique, and that Avraham, too, achieved the level of being able to prophesy while awake.  See Moshe's Epitaph – Signs and Wonders regarding how each of Rambam and Ralbag understands the description, "וְלֹא קָם נָבִיא עוֹד בְּיִשְׂרָאֵל כְּמֹשֶׁה אֲשֶׁר יְדָעוֹ ה' פָּנִים אֶל פָּנִים", and their similar disagreement regarding whether the Mashiach might surpass Moshe's level of prophecy.]
Had Rambam adopted the alternative approach that the guests were human prophets, he perhaps could have suggested that Hashem's communication with Avraham in verses 13 and 20-21 was transmitted via one of the prophets who had come to visit him (cf. Ralbag above regarding verse 13 only, and Rambam himself in Moreh Nevukhim 2:41 regarding Bereshit 25:22-23).  Such a reading would be very similar to Rashbam's position above, with its concomitant advantages and disadvantages.  However, it would also face the additional difficulty that Avraham, being a prophet himself, should not have needed another prophet to serve as his intermediary in his negotiations with Hashem (cf. Abarbanel above who raises this issue regarding the more limited suggestion of Ralbag).

⁸⁸ Radak, in contrast, may be motivated by a desire to avoid the difficulty of angels manifesting human behavior, such as the eating of the guests in Bereshit 18.  Thus, according to Radak, only Chapter 18 was part of the prophetic vision.