Are Leibniz's monads immaterial?

Leibniz says that "souls, like all other Unities of substances, are immaterial, indivisible and imperishable" (Leibniz's letter to Churfuerstin Sophie). These "Unities" are, of course, the monads as Leibniz explicitly notes earlier in the sentence. So Leibniz is claiming that monads are immaterial. I think Leibniz may be making a mistake in exposition of his own view here. It is essential to Leibniz's view that monads are spiritual. But there is a reasonable story to be told on which they are also material.

A plausible story is that to be material is just to have a place in space. But space on Leibniz's picture is just an abstraction from the interrelations of things in space. These interrelations are constituted by the harmoniously ordered interplay of the monads' representations of the universe. But these representations have--Leibniz is explicit about this--have a point of view. We can thus reasonably identify the location of a monad with the location of its point of view. Monads, then, have a place in space. If they have a place in space, then it seems we should say that they are material.

This was a bit too quick, though. First, it might be that some monads--God, for instance (though I don't know that Leibniz ever calls God a monad)--might have a point of view that is non-spatial in nature. Those monads won't be material.

Second, one might think that having a location is insufficient for spatiality. Two examples. First, God is a paradigm of an immaterial being, and yet the tradition holds that God is present everywhere. Second, on dualism, the soul is immaterial, and yet the soul might be said to be located wherever the body is.

The case of God is, I think, easily handled. Maybe materiality involves not just having location, but being locationally limited. Omnipresent beings aren't locationally limited. But those monads that have a single point of view that fits into the spatial order are locationally limited.

The case of the soul is, I think, a bit more difficult. One option is to say that the soul has its location derivatively from the location of something else--viz., the body. So our account of materiality now is: x is material provided that it has a limited location that does not derive from the location of something else.

Leibniz's monads qualify--or at least those that embody a spatially limited point of view. While the monads' location derives from their representations, it does not derive from the location of their representations--it derives from the interrelation of the representations. (Objection: The monad's location derives from the location of its point of view. Response: Leibniz's ontology does not include points of view as entities.)

Perhaps, though, there is something more to materiality than spatiality. Leibniz probably thought that extension is needed. Extension seems to be the occupation of multiple locations. In that case, Leibniz should have said that while individual monads are not material, in aggregate they are material. But I think requiring non-zero extension is a mistake. We might find out that all fundamental particles are unextended, and that shouldn't lead us to hold that they are immaterial.

Here's another move that Leibniz could take, though. He could say that if we try to spell out the definition of materiality, yes the monads do qualify. But it is unhelpful to put the ingredients of Leibniz's quite unique ontology into the straitjacket of other ontologies. Yet if for the sake of exposition we draw analogues, then we can say that Leibniz's monads are more like the immaterial elements of other ontologies than like the material ones.