By definition, a Cartesian soul or spirit is an immaterial substance with mental properties but without physical properties. Immaterial substances are
simple in the sense that they are spatially unextended, i.e.
zero-dimensional, and thus lack proper parts. This means that they are like mathematical points except for having mental properties and hence being concrete objects rather than abstract ones. The basic problem with such "soul-points" is that even though points qua (ideal) 0D objects make logical and mathematical sense, they make little ontological sense as members of concrete reality. It seems that soul-points are much too insubstantial to be substances (and substrates of attributes).
(I know that physicists have postulated 0D point-particles and space(time)-points as ingredients of concrete, physical reality; but in my view they are nothing but mathematical idealizations or fictions.)
"[T]o take away all extension is to reduce a thing only to a mathematical point, which is nothing else but pure negation or non-entity[.]"
(More, Henry.
The Immortality of the Soul. 1659. Pref., §3)
Moreover, like materialist or spiritualist substance monism, substance dualism [SD] is based on
substance-attribute ontology, according to which a substance is different from (the complex of) its attributes, being the possessor or instantiator, the substratum or fundamentum (ground or cause) of the latter. So SD implies the rejection of the reductionistic (Humean) view that substances are nothing but/more than/over and above a complex (bundle/cluster) of attributes.
It follows that immaterial substances are irreducibly different from their mental properties; but in order for that to be the case, they must have some
non-mental properties, some
non-mental nature or essence in addition to their mental properties, since otherwise they would be nothing over and above their (conscious) mind. And since immaterial substances lack physical properties by definition, the required non-mental properties cannot be physical ones; but what other kind of properties could they be? One might say that they are "neutral properties", properties of concrete objects which are
neither mental nor physical; but to postulate such properties is to postulate a mystery, because nobody has any idea what such obscure properties are. And their postulation seems quite
ad hoc, because the only reason for postulating them is to protect SD from collapsing into
pure-event/-process dualism [PD], according to which mental events/processes involve mental attributes but no mental substances.
This view is in effect identical to the Humean bundle theory:
"So we have no idea of substance other than the idea of a collection of particular qualities, and such collections are all we can meaningfully refer to when we talk or think about ‘substance’."
(Hume, David.
A Treatise of Human Nature. 1739/40. Bk. I, pt. I, sec. VI)
"I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement."
(Hume, David.
Treatise of Human Nature. 1739. Bk. 1, pt. IV, sec. VI)
Now, given that there is no plausible reason to accept that the additional non-mental attributes of immaterial substances are
neutral ones, they must be
material/physical ones; but then SD collapses into
materialist substance monism (substance materialism [SM]). So it turns out that SD is no ontologically coherent and stable alternative to SM and PD.
(And PD is no ontologically coherent and stable alternative to SM, because the concept of an absolute or "free-floating" process or event that doesn't involve and depend on any propertied objects or substances is ontologically incoherent too. I know of course that the defenders of
process ontology disagree with me; but I disagree with their disagreement.)
Another anti-SD argument is that, as far as we know from science,
mentality requires complexity, which is to say that having a complex mind such as the one we have is incompatible with its substratum being a simple substance, let alone an immaterial one. The simplicity of immaterial substances—their lack of any (non-mental) structural and functional complexity—prevents them from being an ontological realizer and sustainer of a complex mind.
What is more, even the most primitive sensation or emotion seems to require and to depend on an enormous complexity as we find it in the neurological structure and functioning of brains. The human brain is the most complex material object/substance in the known universe; and there are strong scientific reasons to believe that all possible realizers and subjects of mentality must be extremely complex. (By the way, this constitutes an argument not only against SD but also against panpsychism, which ascribes mental properties to single physical particles.)
But, absurdly, the substance dualists tell us that simple substances (soul-points) can have highly complex minds, with the simple divine substance, God, even having the most complex mind possible. This just doesn't make any coherent ontological sense!
Material point-particles possessing a complex of physical properties make little ontological sense, and immaterial soul-points possessing a complex of mental properties make no ontological sense at all.
"Elementary particles in the ordinary view of things are point particles. A point can’t have many, many properties. A point is too simple to have properties. However, we know that elementary particles have a lot of properties. They have spin, they have electric charge, they have something called isotopic spin, they have a quantum number called color – it’s not got anything to do with ordinary color – they have generations that they belong to, there are whole catalogs of different kinds of quantum numbers, of different kinds of properties that quarks, electrons, netrinos, or photons have. It sounds unreasonable for a point to have that structure. So the feeling most of us have is that, at some level, if you look deeply enough into things, you‘ll discover that particles aren’t points. That they must have all kinds of internal machinery that gives them these properties."
(Leonard Susskind, interview by George Zarkadakis, April 27, 2009.
Feline Quanta Blog. http://felinequanta.blogspot.com/2009/0 ... skind.html.)