We already face a problem: what is meant by “immaterial” and what is meant by “substance”? I will bypass all this to raise a clearer question: is there a significant analogy between the structure of material objects (meaning middle-sized dry goods) and the structure of minds? By “structure” I mean primarily a distinction between primary and secondary qualities (but corpuscular structure can also be considered): does anything like that distinction apply to minds? On the face of it no, because minds don’t have shape and color (etc.), but maybe there is a subtler form of the distinction we can make. One fact about color is generally accepted: colors play no role in the causal powers of objects (though the underlying properties of light do). Let’s say they are epiphenomenal. Is anything like this true of properties of mind? What about color qualia? Aren’t they epiphenomenal? Isn’t the experience of seeming to see something red, construed as a phenomenal property, epiphenomenal? To be sure, the neural basis of it is not, but the phenomenal property itself plays no causal role; it is causally redundant. Just as the color is epiphenomenal, so the subjective impression of a color is epiphenomenal; the causality is carried by underlying primary qualities. Here we have a structural parallel.
But aren’t these properties just brain properties and hence “material”? That is not a good question, given the vagaries of the word “material”, but we can rephrase it into something meaningful. We know that electricity is vital to mental functioning, so that all sensation has electrical correlates: let’s then agree that the causal powers of sensations are based in those electrical correlates. These are the equivalent of primary qualities in objects. Moreover, electricity (electromagnetism) is immaterial on some understandings of the term: it doesn’t fit the mechanistic Cartesian conception of matter. So we can say that mind divides into a phenomenal non-causal set of properties and a causal immaterial set of properties—just as material objects have both non-causal sensible qualities and causal material properties (in the sense of mechanism). It may be said that ordinary objects are not material either—and I have a lot of sympathy for that position—but still we have found a sense in which mind is immaterial (by the standards of mechanism): for mind is electrical, and electricity is not material in the old sense. Now if we extend the concept of substance to include stuff broadly considered (including electrical fields), then we can announce that the mind is an immaterial substance (a non-mechanistic stuff). Moreover, it is an immaterial substance that admits of something like a primary quality/secondary quality distinction.
This electrical substance (stuff) might also have computational properties that play a causal role in mental functioning. That might be the best theory of its structure, analogous to the molecular theory of matter. It isn’t that the phenomenal properties are reducible to electrical and computational properties—as colors are not reducible to wavelengths of light—but we can truly say that the mind is in its nature partly constituted by such properties, because the mind is both causal and phenomenal. Would Descartes disagree with this? Not on the basis of his conception of matter, since electromagnetism counts as immaterial by his criterion of the material. This is a type of dualism we can live with, given that we already have to accept field-based physics before we get to the mind. Moreover, we can accept a corpuscular conception of the mind on the assumption that electricity has a quantum nature (is not a continuous magnitude). So the analogy between mind and matter is quite close except for the question of materiality, and even that might collapse if matter turns out to be less “material” than was imagined. First we discovered electricity, regarding it as spookily non-physical; then we discovered that mental activity depends on electrical activity: didn’t we thereby discover that mind is an immaterial substance (stuff)? The brain is an electrical generator and this electricity is what powers the mind: so the mind has a nature distinct from the world of matter as envisaged by mechanism– it is “immaterial” in one clear sense of the word (and is there any other clear sense?). 
 Prescientific Cartesian dualism conceives of immaterial substance by comparison with supernatural substance such as composes fairies and deities (whatever that may be), but scientific Cartesian dualism conceives of immaterial substance by comparison with electricity and magnetism—perfectly natural phenomena (if not totally devoid of mystery). It isn’t that phenomenal properties are electrical properties (at least under our current conception of electricity), but the causal powers of the mind are provided by brain-based electrical power. Thus we have what might be called “scientific immaterialism”.
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