Within the paradigm of rational theology (in my jargon, God-as-Lord or Īśvara), can God have a form and a body?… Do They need one?

Possible arguments in favour of Their having a body: 

—Yes! They need it to exercise Their will on matter (and, as Kumārila explained, matter does not obey abstract will)

—Yes! They need it so that we can revere Them.

The second argument does not count (it’s part of the God-as-Thou level), but the first seems powerful enough. If God did not have a body, They would have no influence on the world. Do They need a body in order to be omnipresent? And which kind of body? Surely not a limited one (as a deity could have it), since this would limit Their action (They could act only where the body is). Instead, They need to be omnipresent.

Which kind of body could be omnipresent? What would this entail?

In fact, most rational theologians I am aware of speak of God as being omnipresent, in a non-material way, but still as being able to interact with matter at will (so Udayana). Thus, as typical of the God-as-Lord, God is more-than-human, but very close to humans.

However, time and again theologians came to a different solution to God’s body, one which brings them close to the third concept of God, the impersonal Absolute. These theologians think of God’s body as omnipresent and yet material, because it is all that exists.

This all brings me to a more general question: Can there be omnipresence without a (limited) body?

This seems to demand from us a category jump. Because we need to put together presence in space (usually connected with extended bodies) and absence of a body (if conceived as extended in a limited space). 

I can think of at least three solutions:

1. space does not exist for God and is just a category conscious beings superimpose on the word (e.g., Kant, I am not aware of this solution prior to Kant)

2. pantheist version (God is the world) (e.g., Spinoza, Bruno, Rāmānuja)

3. God has something akin to a subtle body, which is omni-pervasive (vibhū) (Nyāya) 

The third case is often said to be a characteristic shared by God and souls (Augustine, Nyāya).

Yet, the souls’ omnipresence seems to be very different from God’s one (possibly because of some additional limitations due to their embodiment, the original sin etc.) 

What else can we say about Their omnipresence? It needs to be complete in each instance. God cannot be present for, e.g., 1/1.000.000.000.000 in the tree in front of my window, since this would entail the risk of Them exercising only a small amount of power on the tree. Moreover, They would be “more” present in bigger objects and less present in small ones! Thus, God needs to be completely present in each atom though being at the same time distributively present in the whole sum of all atoms. This again, calls for a category jump and not just a more-than-human body, since even a subtle matter extending all over the space will not be at the same time completely present in each atom. 

Thoughts and comments are welcome. Please bear with me if I am late in reading comments after the term starts again, on Monday.