Objection 1. It would seem that the human soul is not something subsistent. For that which subsists is said to be "this particular thing." Now "this particular thing" is said not of the soul, but of that which is composed of soul and body. Therefore the soul is not something subsistent.
Objection 2. Further, everything subsistent operates. But the soul does not operate; for, as the Philosopher says (De Anima i, 4), "to say that the soul feels or understands is like saying that the soul weaves or builds." Therefore the soul is not subsistent.
Objection 3. Further, if the soul were subsistent, it would have some operation apart from the body. But it has no operation apart from the body, not even that of understanding: for the act of understanding does not take place without a phantasm, which cannot exist apart from the body. Therefore the human soul is not something subsistent.
On the contrary, Augustine says (De Trin. x, 7): "Who understands that the nature of the soul is that of a substance and not that of a body, will see that those who maintain the corporeal nature of the soul, are led astray through associating with the soul those things without which they are unable to think of any nature--i.e. imaginary pictures of corporeal things." Therefore the nature of the human intellect is not only incorporeal, but it is also a substance, that is, something subsistent.
I answer that, It must necessarily be allowed that the principle of intellectual operation which we call the soul, is a principle both incorporeal and subsistent. For it is clear that by means of the intellect man can have knowledge of all corporeal things. Now whatever knows certain things cannot have any of them in its own nature; because that which is in it naturally would impede the knowledge of anything else. Thus we observe that a sick man's tongue being vitiated by a feverish and bitter humor, is insensible to anything sweet, and everything seems bitter to it. Therefore, if the intellectual principle contained the nature of a body it would be unable to know all bodies. Now every body has its own determinate nature. Therefore it is impossible for the intellectual principle to be a body. It is likewise impossible for it to understand by means of a bodily organ; since the determinate nature of that organ would impede knowledge of all bodies; as when a certain determinate color is not only in the pupil of the eye, but also in a glass vase, the liquid in the vase seems to be of that same color.
Therefore the intellectual principle which we call the mind or the intellect has an operation "per se" apart from the body. Now only that which subsists can have an operation "per se." For nothing can operate but what is actual: for which reason we do not say that heat imparts heat, but that what is hot gives heat. We must conclude, therefore, that the human soul, which is called the intellect or the mind, is something incorporeal and subsistent.
Reply to Objection 1. "This particular thing" can be taken in two senses.
Firstly, for anything subsistent; secondly, for that which subsists, and is complete in a specific nature. The former sense excludes the inherence of an accident or of a material form; the latter excludes also the imperfection of the part, so that a hand can be called "this particular thing" in the first sense, but not in the second. Therefore, as the human soul is a part of human nature, it can indeed be called "this particular thing," in the first sense, as being something subsistent; but not in the second, for in this sense, what is composed of body and soul is said to be "this particular thing."
Reply to Objection 2. Aristotle wrote those words as expressing not his own opinion, but the opinion of those who said that to understand is to be moved, as is clear from the context. Or we may reply that to operate "per se" belongs to what exists "per se." But for a thing to exist "per se," it suffices sometimes that it be not inherent, as an accident or a material form; even though it be part of something. Nevertheless, that is rightly said to subsist "per se," which is neither inherent in the above sense, nor part of anything else. In this sense, the eye or the hand cannot be said to subsist "per se"; nor can it for that reason be said to operate "per se." Hence the operation of the parts is through each part attributed to the whole. For we say that man sees with the eye, and feels with the hand, and not in the same sense as when we say that what is hot gives heat by its heat; for heat, strictly speaking, does not give heat. We may therefore say that the soul understands, as the eye sees; but it is more correct to say that man understands through the soul.
Reply to Objection 3. The body is necessary for the action of the intellect, not as its origin of action, but on the part of the object; for the phantasm is to the intellect what color is to the sight. Neither does such a dependence on the body prove the intellect to be non-subsistent; otherwise it would follow that an animal is non-subsistent, since it requires external objects of the senses in order to perform its act of perception.
Source: Summa Theologica (New Advent)