I’m against taking the division into dualism or monism as metaphysically basic. I therefore do not take it as an adequate division of fundamental alternatives.
The dualist/monist division concerns sorts of things. No one is a dualist because he believes there is more than one individual, but only when he believes there is more than one sort of thing, or more than one sort of thing “at the ground level”. But the word “thing” refers both to sorts and to individuals, so what now?
To make the monist/dualist account work we need the additional premise that every individual is a sort of thing. Even if this were true, it would not give us a twofold division since we cannot give a single division between wholes and parts. An individual nose is not the same thing as the individual with the nose; and seeing the nose as an individual thing neither gives us two individuals nor two sorts of things. The very sorts we speak of are themselves made up of simpler and therefore individual components: a triangle is made up, for example, of different individual lines and an animal of its individual organs and systems. Here’s the problem: If we have only one account of “individual” and “sort” that includes both wholes and their parts, than both of these will be, at the same time and in the same respect, both one and many. It was this odd nature of parts that made Aristotle explicitly set them to the side when he developed his theory of secondary and primary substance, that is, his account of individual things and sorts of things. To say that all wholes are either one thing or many is different from saying all parts are one sort of thing or many. Neither individual nor sort can include both.
Thus, whenever the difference between wholes and parts is relevant to the discussion, the monist/dualist split becomes untenable and inadequate. But this is exactly the situation we are in when we are considering the problem in philosophy of mind since consciousness (or mind, or soul) is either part of a person, or identified with the person; but if the first, then we are not dualists because about the person for the reason just given, if the second we are not dualists about the person because we do not see the person as two. Ex hypothesi, the person just is the one thing.
A similar problem kicks in when we speak about dualism or monism with respect to the world. Either “the world” contains God and spirits as one of its parts, or it doesn’t. If it does, then the dualist/monist split does not apply; if not, then we can mean either that there is no God or spirits at all, or that the world is only an incomplete whole, or that it is somehow comparable to being a part of God and spirit. But even if the first option counts as a sort of monism, the theism that is opposed to it need not count as a dualism, since it could be anything from pantheism to Platonism (of which there is more than one sort) to transcendentalism to any of the many Hegalianisms. Any way we try to account for the split, it cannot be fundamental.
Parts not only are individuals, they are even capable of becoming individuals as much as the individuals they came from, the way parts of carrots or potatoes become themselves carrots and potatoes; the way a person becomes identical twins; or the way anything reproduces itself. This account of soul is a fascinating one: the idea being that, at least for persons, it is that part which, in dividing, reproduces the individual as one not only in species but in person. Fechner saw it this way, and it would help to solve some of the riddles of the Thomistic account of immortality.