The Soul is the Substance as the Form
“The substance (οὐσία) is the cause of existing, and here, in living things, to exist is to live, and the soul (ψυχή) is the cause and starting-point” (On the Soul II.4.415b).
All natural bodies have natures. The nature is the “starting-point of change and staying unchanged.” It is the organization of the material so that there exists a body of the kind. These natures are forms, and these forms are in matter and separate in account.
In the case of living natural bodies, Aristotle says that the form is a “soul” (ψυχή).
By conceiving of human beings as natural living bodies, and by conceiving of natural bodies as forms in matter, Aristotle tries to correct what he understands as Plato’s mistakes.
Plato thought the soul has an existence that is separate from the existence of the body. Aristotle thinks that this is a mistake. As the form of a natural body, the soul is in matter. It can not exist apart from the body. It is the organization of material so that there is a living natural body. This organization cannot exist without existing as the organization of some material.
Plato thought that the soul can change and that, for example, it can become wise. Aristotle thinks this is a mistake too. Because the soul is the organization of the material so that there is a living natural body, it is not something that can change in this way. A human being can change. A human being can become wiser. It is the human being, however, not the soul, that changes. The soul makes this change possible. It is the starting-point for the ways the living natural bodies can change, but the soul does not change when a body changes in these ways.
So Aristotle’s understanding of the existence of the soul is very different from Plato’s. There are places in the corpus where Aristotle can seem to have the Platonic conception, but his mature view seems to be that the soul is neither the person nor something that can exist after death.