  There are two important concepts deployed in this notion. One is that of substance, the other is the dualism of these substances. A substance is characterized by its properties, but, according to those who believe in substances, it is more than the collection of the properties it possesses, it is the thing which possesses them. So the mind is not just a collection of thoughts, but is that which thinks, an immaterial substance over and above its immaterial states. Properties are the properties of objects. If one is a property dualist, one may wonder what kinds of objects possess the irreducible or immaterial properties in which one believes. One can use a neutral expression and attribute them to persons, but, until one has an account of person, this is not explanatory. One might attribute them to human beings qua animals, or to the brains of these animals. Then one will be holding that these immaterial properties are possessed by what is otherwise a purely material thing. But one may also think that not only mental states are immaterial, but that the subject that possesses them must also be immaterial. Then one will be a dualist about that to which mental states and properties belong as well about the properties themselves. Now one might try to think of these subjects as just bundles of the immaterial states. This is Hume’s view. But if one thinks that the owner of these states is something quite over and above the states themselves, and is immaterial, as they are, one will be a substance dualist.