Objection 1. It would seem that the soul is composed of matter and form. For potentiality is opposed to actuality. Now, whatsoever things are in actuality participate of the First Act, which is God; by participation of Whom, all things are good, are beings, and are living things, as is clear from the teaching of Dionysius (Div. Nom. v). Therefore whatsoever things are in potentiality participate of the first potentiality. But the first potentiality is primary matter. Therefore, since the human soul is, after a manner, in potentiality; which appears from the fact that sometimes a man is potentially understanding; it seems that the human soul must participate of primary matter, as part of itself.
Objection 2. Further, wherever the properties of matter are found, there matter is. But the properties of matter are found in the soul--namely, to be a subject, and to be changed, for it is a subject to science, and virtue; and it changes from ignorance to knowledge and from vice to virtue. Therefore matter is in the soul.
Objection 3. Further, things which have no matter, have no cause of their existence, as the Philosopher says Metaph. viii (Did. vii, 6). But the soul has a cause of its existence, since it is created by God. Therefore the soul has matter.
Objection 4. Further, what has no matter, and is a form only, is a pure act, and is infinite. But this belongs to God alone. Therefore the soul has matter.
On the contrary, Augustine (Gen. ad lit. vii, 7,8,9) proves that the soul was made neither of corporeal matter, nor of spiritual matter.
I answer that, The soul has no matter. We may consider this question in two ways.
First, from the notion of a soul in general; for it belongs to the notion of a soul to be the form of a body. Now, either it is a form by virtue of itself, in its entirety, or by virtue of some part of itself. If by virtue of itself in its entirety, then it is impossible that any part of it should be matter, if by matter we understand something purely potential: for a form, as such, is an act; and that which is purely potentiality cannot be part of an act, since potentiality is repugnant to actuality as being opposite thereto. If, however, it be a form by virtue of a part of itself, then we call that part the soul: and that matter, which it actualizes first, we call the "primary animate."
Secondly, we may proceed from the specific notion of the human soul inasmuch as it is intellectual. For it is clear that whatever is received into something is received according to the condition of the recipient. Now a thing is known in as far as its form is in the knower. But the intellectual soul knows a thing in its nature absolutely: for instance, it knows a stone absolutely as a stone; and therefore the form of a stone absolutely, as to its proper formal idea, is in the intellectual soul. Therefore the intellectual soul itself is an absolute form, and not something composed of matter and form. For if the intellectual soul were composed of matter and form, the forms of things would be received into it as individuals, and so it would only know the individual: just as it happens with the sensitive powers which receive forms in a corporeal organ; since matter is the principle by which forms are individualized. It follows, therefore, that the intellectual soul, and every intellectual substance which has knowledge of forms absolutely, is exempt from composition of matter and form.
Reply to Objection 1. The First Act is the universal principle of all acts; because It is infinite, virtually "precontaining all things," as Dionysius says (Div. Nom. v). Wherefore things participate of It not as a part of themselves, but by diffusion of Its processions. Now as potentiality is receptive of act, it must be proportionate to act. But the acts received which proceed from the First Infinite Act, and are participations thereof, are diverse, so that there cannot be one potentiality which receives all acts, as there is one act, from which all participated acts are derived; for then the receptive potentiality would equal the active potentiality of the First Act. Now the receptive potentiality in the intellectual soul is other than the receptive potentiality of first matter, as appears from the diversity of the things received by each. For primary matter receives individual forms; whereas the intelligence receives absolute forms. Hence the existence of such a potentiality in the intellectual soul does not prove that the soul is composed of matter and form.
Reply to Objection 2. To be a subject and to be changed belong to matter by reason of its being in potentiality. As, therefore, the potentiality of the intelligence is one thing and the potentiality of primary matter another, so in each is there a different reason of subjection and change. For the intelligence is subject to knowledge, and is changed from ignorance to knowledge, by reason of its being in potentiality with regard to the intelligible species.
Reply to Objection 3. The form causes matter to be, and so does the agent; wherefore the agent causes matter to be, so far as it actualizes it by transmuting it to the act of a form. A subsistent form, however, does not owe its existence to some formal principle, nor has it a cause transmuting it from potentiality to act. So after the words quoted above, the Philosopher concludes, that in things composed of matter and form "there is no other cause but that which moves from potentiality to act; while whatsoever things have no matter are simply beings at once." [The Leonine edition has, "simpliciter sunt quod vere entia aliquid." The Parma edition of St. Thomas's Commentary on Aristotle has, "statim per se unum quiddam est... et ens quiddam."]
Reply to Objection 4. Everything participated is compared to the participator as its act. But whatever created form be supposed to subsist "per se," must have existence by participation; for "even life," or anything of that sort, "is a participator of existence," as Dionysius says (Div. Nom. v). Now participated existence is limited by the capacity of the participator; so that God alone, Who is His own existence, is pure act and infinite. But in intellectual substances there is composition of actuality and potentiality, not, indeed, of matter and form, but of form and participated existence. Wherefore some say that they are composed of that "whereby they are" and that "which they are"; for existence itself is that by which a thing is.
Source: Summa Theologica (New Advent)