The Third Maimonidean Principle is that G-d does not have a body. G-d's corporeality, or lack thereof, has been a debate between Christians and Jews for centuries. The fact that Jesus, the man, is also divine is an essential tenet of Pauline Christianity. The belief of G-d's incorporeality has been a part of Jewish belief for quite some time. But the Jewish belief in G-d's incorporeality does not come without any issues. Just to name three:
1) The primary issue is that Hebrew Scriptures (Tanach) are replete with describing G-d in anthropomorphic terms. To assert G-d's incorporeality is to defy the simplistic, literal meaning (פְּשָׁט) of the text.
2) G-d's incorporeality is not explicitly stated in the Tanach. There are two verses that Maimonides uses as text proofs to this concept.
"'To whom will you liken Me? To what am I equal?' says the Holy One." -Isaiah 40:25
"You have not seen any image." -Deuteronomy 4:15
The issue is that both of these verse have ambiguities. Isaiah 40:18 can allude to a corporeal being that has unique attributes, and Deuteronomy 4:15 does not presumably negate the possibility of there being a corporeal G-d.
3) Earlier rabbis had a corporeal concept of G-d. In Brachos 6a of the Talmud, there is a passage of G-d having His own pair of tefillin He puts on. In Vayikra Rabah, Hillel says that going to the bathhouse is a mitzvah. Why? Because he needs to be clean and proper because he needs to maintain the status of being "in His image."
I have two main counter-arguments to the issues:
A) Many like to presume that the only way to read Scripture is to do so with its plain and literal meaning. It comes with the nice gift-wrapping that because it's "the Divine Word," it should be neatly presented without ambiguity. But a narrow literalism comes with its own issues. Here are but two examples of how problematic literalism can be. Do we literally follow the imperative to stone the disobedient, rebellious child in Deuteronomy 21? Of course not! If we did, there would be no future generations because every child will be disobedient at some point. What do you do about the notion of an eye for an eye, tooth for a tooth (Exodus 21:23-25)? Forget the argument about whether the whole world would end up blind and toothless. What do you do if a blind man takes out your eye or a toothless man takes out your tooth? The verse was meant to teach us about proportionate justice, not a literal "take out his eye, take out his tooth." Plus, what if someone cuts off your ear? The Tanach mentions nothing about someone cutting off your ear. Are you not going to punish the culprit for mutilation? That is why the verse has always been interpreted as monetary compensation.
I can find many more examples of the shortcomings of literalism, but I hope my point has been made.
Simply because we are finite creatures and G-d is infinite, there will always be a gap between the two. That is why the Talmud recognizes that the Torah was written in the language of man (Brachot 31b). Since being finite means that we are limited, an interpretation of a text, even a divine one, is inevitable. That is why we need to use our brains, as well as our tools of observation and [literary] analysis to figure out which interpretations work and which don't.
B) This leads me to my second point, which is we need to use what we already know about G-d. The First Principle states that an infinite being, which we call G-d, must have, by logical necessity, created the universe. Being infinite, G-d, by definition, translates into His Oneness since G-d cannot be defined--G-d just is. G-d's incorporeality is merely a logical extension of Maimonides' first two principles. Corporeality means existing within time and space. Since G-d exists within neither, we know that any language that is used to describe G-d's characters or actions must be figurative.
Plus, it's nice when Joshua said that G-d "is within the heavens and the earth below" (Joshua 2:11), which is a nice way to reaffirm G-d's incorporeality since a corporeal being cannot simultaneously occupy two spaces within a given moment.
If G-d truly is not corporeal, then why have these anthropomorphisms? Because it's much simpler to view G-d as corporeal and to read a text with a narrow literalism. Corporeality is tangible. Corporeality brings G-d closer to us, which means if He resembles us, we can better relate to Him. Since infinity does not exist in time or space, we cannot understand what G-d is, only what He is not. It makes it harder to relate to something that does not exist within time or space. However, recognizing the true nature of Infinite Oneness is a step in the right direction.
You'd think it'd be easier for G-d to automatically create us with this sophisticated understanding of Him, but the gift of intellectual pursuit was a much better gift than a spiritual hand-out.