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This may be proved in three ways. The first…
Some mop-up proofs about intellects being immaterial. The arguments are plain and there is really only one note of substance.
Chapter 50 That Intellectual Substances Are Immaterial (alternate translation)
1 IT follows from this that intellectual substances are immaterial. For everything composed of matter and form is a body: since matter cannot receive various forms except in respect of its various parts. And this diversity of parts cannot be in matter except inasmuch as common matter is divided into several by the dimensions existing in matter: for without quantity substance is indivisible. Now it has been proved that an intelligent substance is a body. It follows therefore that it is not composed of matter and form.
2 Moreover. Just as man does not exist apart from this man, so matter exists not apart from this matter. Accordingly, whatever subsistent thing is composed of matter and form, is composed of individual form and matter. Now the intellect cannot be composed of individual matter and form. For the species of things understood become actually intelligible through being abstracted from individual matter. And according as they are actually intelligible, they become one with the intellect. Therefore the intellect also must be without individual matter. Therefore the intelligent substance is not composed of matter and form.
Notes When you think of a stampeding herd of elephants (which you’re doing right now), a heard of stampeding elephants is not present materially in your intellect. This intelligible herd was abstracted from individual matter. This same example applies to the next paragraphs. When you think of fire, you do not produce fire. And it’s not just Empedocles who makes this error! All strict materialists are committed to the mistake. For if our intellects are strictly material, e.g. our brains, then a bit of fire must appear when we think of it.
3 Further. The action of anything composed of matter and form, belongs not to the form alone, nor to the matter alone, but to the composite: because to act belongs to that which has being, and being belongs to the composite through its form: wherefore the composite also acts through its form. Accordingly, if the intelligent substance be composed of matter and form, to understand will be the act of the composite. But action terminates in a thing like the agent, wherefore the composite in generating, produces not a form but a composite. If, therefore, to understand be an action of the composite, it would understand neither form nor matter, but only the composite. Therefore the intelligent substance is not composed of matter and form.
4 Again. The forms of sensible things have a more perfect being in the intellect than in sensible things; since they are more simple and extend to more objects: for by the one intelligible form of man, the intellect knows all men. Now a form existing perfectly in matter makes a thing to be actually such, for instance to be fire or to be coloured: and if it does not make a thing to be actually such, it is in that thing imperfectly, for instance the form of heat in the air that carries it, and the power of the first agent in its instrument. Consequently were the intellect composed of matter and form, the forms of the things understood would make the intellect to be actually of the same nature as that which is understood. And this leads to the error of Empedocles, who said that the soul knows fire by fire, and earth by earth, and so on. But this is clearly unreasonable. Therefore the intelligent substance is not composed of matter and form.
5 Further. Whatever is in something is therein according to the mode of the recipient. Wherefore if the intellect be composed of matter and form, the forms of things would be in the intellect materially, just as they are outside the mind. Consequently, just as outside the mind they are not actually intelligible, neither would they be when they are in the intellect.
6 Again. Forms of contraries, according to the being which they have in matter, are contrary: hence they exclude one another. But according as they are in the intellect they are not contrary: in fact one contrary is the intelligible ratio of the other, since one is understood through the other. Consequently they have not a material being in the intellect. Therefore the intellect is not composed of matter and form.
7 Further. Matter does not receive a fresh form except by movement or change. But the intellect is not moved through receiving forms; rather is it perfected, and is at rest, while understanding, whereas its understanding is hindered by movement. Consequently forms are not received by the intellect as by matter or a material thing. Wherefore it is clear that intelligent substances are immaterial as well as incorporeal.
Notes It is cheering, and obvious, to note that your intellect is perfected the more you learn of forms.
8 Hence Dionysius says (Div. Nom. iv.): On account of the rays of the divine goodness all intellectual substances are subsistent, and are known to be both incorporeal and immaterial.