One of Rambam's arguments for the existence of only one god is that the existence of multiple gods by definition implies some form of corporeality.

Hilchos Yesodei HaTorah 1:7

אלוה זה אחד הוא ואינו שנים ולא יתר על שנים אלא אחד שאין כיחודו אחד מן האחדים הנמצאים בעולם לא אחד כמין שהוא כולל אחדים הרבה ולא אחד כגוף שהוא נחלק למחלקות ולקצוות אלא יחוד שאין יחוד אחר כמותו בעולם אילו היו אלוהות הרבה היו גופין וגויות מפני שאין הנמנים השוין במציאותן נפרדין זה מזה אלא במאורעין שיארעו בגופות והגויות ואילו היה היוצר גוף וגוייה היה לו קץ ותכלית שאי אפשר להיות גוף שאין לו קץ וכל שיש לגופו קץ ותכלית יש לכחו קץ וסוף ואלהינו ברוך שמו הואיל וכחו אין לו קץ ואינו פוסק שהרי הגלגל סובב תמיד אין כחו כח גוף והואיל ואינו גוף לא יארעו לו מאורעות הגופות כדי שיהא נחלק ונפרד מאחר לפיכך אי אפשר שיהיה אלא אחד וידיעת דבר זה מצות עשה שנאמר ה' אלהינו ה' אחד

This God is one. He is not two or more, but one, unified in a manner which [surpasses] any unity that is found in the world; i.e., He is not one in the manner of a general category which includes many individual entities, nor one in the way that the body is divided into different portions and dimensions. Rather, He is unified, and there exists no unity similar to His in this world.

If there were many gods, they would have body and form, because like entities are separated from each other only through the circumstances associated with body and form.

Were the Creator to have body and form, He would have limitation and definition, because it is impossible for a body not to be limited. And any entity which itself is limited and defined [possesses] only limited and defined power. Since our God, blessed be His name, possesses unlimited power, as evidenced by the continuous revolution of the sphere, we see that His power is not the power of a body. Since He is not a body, the circumstances associated with bodies that produce division and separation are not relevant to Him. Therefore, it is impossible for Him to be anything other than one.

The knowledge of this concept fulfills a positive commandment, as [implied by Deuteronomy 6:4]: "[Hear, Israel,] God is our Lord, God is one." (Chabad.org)

However, when he discusses angels he asserts that they are also incorporeal, yet he states that there are many different angels.

Hilchos Yesodei HaTorah 2:2-5

כל מה שברא הקב"ה בעולמו נחלק לשלשה חלקים מהן ברואים שהן מחוברים מגולם וצורה והם הווים ונפסדים תמיד כמו גופות האדם והבהמה והצמחים והמתכות ומהן ברואים שהן מחוברים מגולם וצורה אבל אינן משתנין מגוף לגוף ומצורה לצורה כמו הראשונים אלא צורתן קבועה לעולם בגולמם ואינן משתנין כמו אלו והם הגלגלים והכוכבים שבהן ואין גולמם כשאר גולמים ולא צורתם כשאר צורות ומהן ברואים צורה בלא גולם כלל והם המלאכים שהמלאכים אינם גוף וגויה אלא צורות נפרדות זו מזו

ומהו זה שהנביאים אומרים שראו המלאך אש ובעל כנפים הכל במראה הנבואה ודרך חידה לומר שאינו גוף ואינו כבד כגופות הכבדים כמו שנאמר כי ה' אלהיך אש אוכלה הוא ואינו אש אלא משל וכמו שנאמר עושה מלאכיו רוחות

ובמה יפרדו הצורות זו מזו והרי אינן גופין לפי שאינן שוין במציאותן אלא כל אחד מהן למטה ממעלתו של חבירו והוא מצוי מכחו זה למעלה מזה והכל נמצאים מכחו של הקדוש ברוך הוא וטובו וזהו שרמז שלמה בחכמתו ואמר כי גבוה מעל גבוה שומר

Everything which the Holy One, blessed be He, created within His world is divided into three categories. They include:

a) Creations which are a combination of matter and form. They are constantly coming into existence and ceasing to exist; for example, the bodies of man and beasts, plants, and metals.

b) Creations which are [also] a combination of matter and form, but do not change from body to body and from form to form as those in the first category. Rather, their form is permanently fixed in their matter, and they do not change as the others do; for example, the spheres and the stars [which revolve] in them. The matter [from which] they [are composed] differs from [a simple conception of] matter, and their form differs from [a simple conception of] form.

c) Creations which have form, but no matter at all; for example, the angels, for the angels do not possess bodies or corporeal being, but rather are forms which are separate from each other.

What is meant by the prophets' statements that they saw an angel of fire or with wings? All these are prophetic visions and parables, as [Deuteronomy 4:24] states: "God, your Lord, is consuming fire," though He is not fire and [the description of Him in this manner] is only metaphoric. Similarly, [Psalms 104:4] states: "He makes His angels as winds...."

Since they possess no body, what separates the form [of the angels] from each other? Their existence is not alike. Rather each one is below the level of the other and exists by virtue of its influence, [in a progression of levels,] one above the other.

Everything exists by virtue of the influence of the Holy One, blessed be He, and His goodness. Solomon alluded to this [concept] in his wisdom, saying (Ecclesiastes 5:7): "Because above the one who is high there is a watcher [and there are others higher than them]." (Chabad.org)

Why is it that angels can be distinguished from each other without a physical manifestation, yet gods cannot be distinguished from each other without a physical manifestation?

Even if one were to argue, as does R. Elyahu Touger in his footnote to 1:7, that Rambam is even referring to "a spiritual sense of these concepts", it does not explain why gods cannot be differentiated while angels can.

If one were to point out that the very method of differentiation of angels is based on their hierarchy of levels which, if existing for gods would by definition render them non-gods (if there is a god on a higher level, the lower god by definition is lacking a quality of godliness) then Rambam's argument is really a different argument – that the existence of multiple gods is impossible because the definition of god entails absolute power and it is impossible for two separate entities to both have absolute power (as discussed by Saadia Gaon in Emunos V'Deios 2:2).

See also Guide for the Perplexed 2:1 where Rambam writes:

The hypothesis that there exist two Gods is inadmissible, because absolutely incorporeal beings cannot be counted (Prop. XVI.), except as cause and effect; the relation of time is not applicable to God (Prop. XV.), because motion cannot be predicated of Him. (Friedlander translation.)

Once again it appears that this argument must necessarily be predicated on the argument of impossibility of two absolute powers. Thus, the argument from the impossibility of distinguishing incorporeal entities should either be insufficient or unnecessary to prove that there is only one god.

Any answers, or flaws/incorrect assumptions in the question?

[I think the Peirush sort of addresses this, but he makes the proof dependent on a different earlier premise, namely, that there can only be one First Cause. If that is the case then once again this specific proof should be either insufficient or unnecessary.]

  • Corporeal has a narrow sense and a broad sense. The notion of boundaries and corporeality are equivalent at the broad sense. Concept in this point of view has corporeality. Not sure 100% – kouty Feb 8 at 19:38
  • I think that the Rambam misspoke in 1:7, and meant to speak about tzuros, Forms, not gufim ugevios. Which is exactly how the Rambam says the various angels -- who have tzuros beli chomer, Form without Substance -- differ and are distinct entities. But I wouldn't write that in an answer, as there are people who would stone me for saying the Yad contains a misspeech. – Micha Berger Feb 9 at 14:52
  • By the way, there is something similar to what I wrote about forms in the Moreh Nevuchim (sec. 2), but in the reverse. He proves there can only be One G-d, and from there that G-d has no Form -- as Form means divisibility, and thus only a wording difference from positing a cooperating pantheon of multiple gods. Just as the Cause has to be One, the Cause can't have parts, or it too would have a Cause. But again, that's tzurah, not guf. – Micha Berger Feb 9 at 14:54

(As far as I understand)

There are two separate discussions. One discussion is how many gods there are. In that discussion, your points as to the incompleteness of the Rambam's argument, as well as the relevance of Rav Saadia's argument, would apply. That discussion is the topic of the previous halacha in the Rambam, halacha 1:6:

וכל המעלה על דעתו שיש שם אלוה אחר, חוץ מזה--עובר בלא תעשה

Anyone who considers that there is another god other than This One violates a negative commandment ...

Our halacha is now discussing the G-d, which was already established that He is the only one. Now Rambam ise discussing whether this G-d is one or consists of multiplicity, or parts. Thus Rambam starts this halacha with

אלוה זה אחד הוא--אינו לא שניים ולא יתר על שניים, אלא אחד

This G-d is one. He is not two nor three, rather one

In which the Rambam is discussing the "number," so to speak, of this one G-d.

Rambam continues:

אילו היו (ה)אלוהות הרבה--היו גופין וגווייות

If Godliness was many...

The Rambam does not say אילו היו אלוהים הרבה, if there were many gods, but if the concept of G-d were many. In this discussion, differentiating between something which is one unified concept could only be done by the arbitrary distinction of a boundary, or physical distinction. Thus the Rambam negates that possibility.

  • This is a nice chiluk, but it hinges on the word being "האלוהות" not "אלוהות". However, the edition I cited from has the text as "אלהות", as do several others. The Frankel edition notes the divergent manuscript evidence, so it's probably inconclusive. However, in the parallel that I cited from The Guide, the only translation that can be read according to your way is the Ibn Tibbon translation. The Qafih and Schwartz translations are pretty clearly referring to multiple gods and not multiple parts of one god, and the Pines and Friedlander translations are absolutely referring to multiple gods. – Alex Feb 8 at 23:29
  • @Alex I was actually thinking after I wrote this (before I saw this comment) that the inference from האלהות was completely gratuitous and unnecessary for the point. אלהות with a shuruk anyways means "Godliness." אלהים would be the plural for gods. || I think the rest of my points stand independent of that diyuk anyways || I don't follow your point from the Moreh - he is referring there to multiple absolute beings, not to multiplicity of god. – Y     e     z Feb 9 at 4:00
  • As an aside, R' Yaakov Weinberg (who understood this Rambam the same way) said that the Rambam's comment of "and not more than two" (or "and not three" according to some texts) was specifically coming to respond to the Trinity, which (somehow) believes in one god which is three. – Y     e     z Feb 9 at 4:40
  • I'm not entirely convinced about "אלוהות", especially as R. Touger translates it as "gods" both here, and in 2:10. Also, I'm not entirely convinced that "many gods" vs "many parts of god" is much more than a semantic difference. Most importantly, my point from the Guide is that Rambam there uses the same proof, and there it is clear from most of the translations that he is using it to prove the impossibility of multiple gods. – Alex Feb 9 at 20:59
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    The word היו is plural, so אלוהות must also be plural. There is no way to read the words as you do without changing the text – b a Sep 7 at 12:11

Your question:

Why is it that angels can be distinguished from each other without a physical manifestation, yet gods cannot be distinguished from each other without a physical manifestation?

is, in general, based upon a false assumption.

You list all these details that Rambam uses to define G-d's uniqueness. Then you look at Rambam using similar language in the context of angels and make the assumption that because of that similar language it can be applied uniformly to either subject, meaning to G-d and to angels. That assumption, that the two subjects are equal, is incorrect.

G-d is not a 'נברא', a created thing or being. G-d always is, was and will be. All of creation, including all categories of angels are נבראים, creations. They have a beginning (and possibly an end). This distinction is the essence of Mishnah Torah, Hilchot Yesodei HaTorah, 1:1-4.

By definition, you cannot place the limitations of the creations upon that which transcends creation altogether. This is the meaning of what is found in Yalkut Shimoni on the Torah 117:2 which says:

למה מכנין שמו של הקב"ה וקורין אותו מקום מפני שהוא מקומו של עולם ואין העולם מקומו.

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    Can you clarify how this addresses the question? The question was, if plurality implies corporeality then how can angels be both plural and corporeal? Or expressed reversely, if plurality does not imply corporeality then why can't there be multiple gods? – Alex Dec 6 at 18:19
  • @Alex Per your request... – Yaacov Deane Dec 6 at 20:11
  • @Alex It seems he is saying that plurality only implies corporeality for things without beginnings. I don't understand how he knows that though, or why the Rambam didn't state that explicitly – Double AA Dec 6 at 20:15
  • @DoubleAA Agreed. My point was not to say whether the distinction is true or not, only that it doesn't seem to be part of the Rambam's argument. – Alex Dec 6 at 20:19
  • @DoubleAA No, that is not what I said. Rambam states there are creations that are not, in and of themselves corporeal. Yet, they are still in the domain of creations. They are not G-d, who transcends all that and is not a creation. To use the vernacular, you are comparing apples to oranges. It doesn't work. And just to clarify for Alex, angels not being corporeal does not mean they do not interact with the corporeal. This is accomplished by way of the angel dressing in "Garments" which are a mixture of both the corporeal and the non-corporeal. – Yaacov Deane Dec 6 at 20:25

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