Objection 1. It would seem that the soul is man. For it is written (2 Corinthians 4:16): "Though our outward man is corrupted, yet the inward man is renewed day by day." But that which is within man is the soul. Therefore the soul is the inward man.
Objection 2. Further, the human soul is a substance. But it is not a universal substance. Therefore it is a particular substance. Therefore it is a "hypostasis" or a person; and it can only be a human person. Therefore the soul is man; for a human person is a man.
On the contrary, Augustine (De Civ. Dei xix, 3) commends Varro as holding "that man is not a mere soul, nor a mere body; but both soul and body."
I answer that, The assertion "the soul is man," can be taken in two senses.
First, that man is a soul; though this particular man, Socrates, for instance, is not a soul, but composed of soul and body. I say this, forasmuch as some held that the form alone belongs to the species; while matter is part of the individual, and not the species. This cannot be true; for to the nature of the species belongs what the definition signifies; and in natural things the definition does not signify the form only, but the form and the matter. Hence in natural things the matter is part of the species; not, indeed, signate matter, which is the principle of individuality; but the common matter. For as it belongs to the notion of this particular man to be composed of this soul, of this flesh, and of these bones; so it belongs to the notion of man to be composed of soul, flesh, and bones; for whatever belongs in common to the substance of all the individuals contained under a given species, must belong to the substance of the species.
It may also be understood in this sense, that this soul is this man; and this could be held if it were supposed that the operation of the sensitive soul were proper to it, apart from the body; because in that case all the operations which are attributed to man would belong to the soul only; and whatever performs the operations proper to a thing, is that thing; wherefore that which performs the operations of a man is man. But it has been shown above (Article 3) that sensation is not the operation of the soul only. Since, then, sensation is an operation of man, but not proper to him, it is clear that man is not a soul only, but something composed of soul and body. Plato, through supposing that sensation was proper to the soul, could maintain man to be a soul making use of the body.
Reply to Objection 1. According to the Philosopher (Ethic. ix, 8), a thing seems to be chiefly what is principle in it; thus what the governor of a state does, the state is said to do. In this way sometimes what is principle in man is said to be man; sometimes, indeed, the intellectual part which, in accordance with truth, is called the "inward" man; and sometimes the sensitive part with the body is called man in the opinion of those whose observation does not go beyond the senses. And this is called the "outward" man.
Reply to Objection 2. Not every particular substance is a hypostasis or a person, but that which has the complete nature of its species. Hence a hand, or a foot, is not called a hypostasis, or a person; nor, likewise, is the soul alone so called, since it is a part of the human species.
Source: Summa Theologica (New Advent)