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A quote from Edward Feser’s book “Aquinas”.
.Page 154…suppose that the intellect were a material thing (some kind of brain activity, say). Then for the forms of material things to exist in the intellect would be for them to exist in a certain material thing. But for a form to exist in a material thing is just for that material thing to be the kind of thing the form is a form of. For example, for the form of triangularity to exist in a certain parcel of matter is just for that parcel of matter to be a triangle; the form of “catness” to exist in a certain parcel of matter is just for that parcel of matter to be a cat; and so on. Thus, if your intellect were realy a material thing, it would follow that that material thing - that part of your brain, say - would become a triangle whenever you thought about triangles, or a cat whenever you thought about cats. But of course, that’s absurd. Hence, since the assumption that the intellect is material leads to absurdity, we must conclude the intellect is not material.
.Page 154…suppose that the intellect were a material thing (some kind of brain activity, say). Then for the forms of material things to exist in the intellect would be for them to exist in a certain material thing. But for a form to exist in a material thing is just for that material thing to be the kind of thing the form is a form of. For example, for the form of triangularity to exist in a certain parcel of matter is just for that parcel of matter to be a triangle; the form of “catness” to exist in a certain parcel of matter is just for that parcel of matter to be a cat; and so on. Thus, if your intellect were realy a material thing, it would follow that that material thing - that part of your brain, say - would become a triangle whenever you thought about triangles, or a cat whenever you thought about cats. But of course, that’s absurd. Hence, since the assumption that the intellect is material leads to absurdity, we must conclude the intellect is not material.