Objection 1. It would seem that it is not proper to the Father to be unbegotten. For every property supposes something in that of which it is the property. But "unbegotten" supposes nothing in the Father; it only removes something. Therefore it does not signify a property of the Father.
Objection 2. Further, Unbegotten is taken either in a privative, or in a negative sense. If in a negative sense, then whatever is not begotten can be called unbegotten. But the Holy Ghost is not begotten; neither is the divine essence. Therefore to be unbegotten belongs also to the essence; thus it is not proper to the Father. But if it be taken in a privative sense, as every privation signifies imperfection in the thing which is the subject of privation, it follows that the Person of the Father is imperfect; which cannot be.
Objection 3. Further, in God, "unbegotten" does not signify relation, for it is not used relatively. Therefore it signifies substance; therefore unbegotten and begotten differ in substance. But the Son, Who is begotten, does not differ from the Father in substance. Therefore the Father ought not to be called unbegotten.
Objection 4. Further, property means what belongs to one alone. Since, then, there are more than one in God proceeding from another, there is nothing to prevent several not receiving their being from another. Therefore the Father is not alone unbegotten.
Objection 5. Further, as the Father is the principle of the person begotten, so is He of the person proceeding. So if by reason of his opposition to the person begotten, it is proper to the Father to be unbegotten it follows that it is proper to Him also to be unproceeding.
On the contrary, Hilary says (De Trin. iv): "One is from one --that is, the Begotten is from the Unbegotten--namely, by the property in each one respectively of innascibility and origin."
I answer that, As in creatures there exist a first and a secondary principle, so also in the divine Persons, in Whom there is no before or after, is formed the principle not from a principle, Who is the Father; and the principle from a principle, Who is the Son.
Now in things created a first principle is known in two ways; in one way as the first "principle," by reason of its having a relation to what proceeds from itself; in another way, inasmuch as it is a "first" principle by reason of its not being from another. Thus therefore the Father is known both by paternity and by common spiration, as regards the persons proceeding from Himself. But as the principle, not from a principle He is known by the fact that He is not from another; and this belongs to the property of innascibility, signified by this word "unbegotten."
Reply to Objection 1. Some there are who say that innascibility, signified by the word "unbegotten," as a property of the Father, is not a negative term only, but either that it means both these things together--namely, that the Father is from no one, and that He is the principle of others; or that it imports universal authority, or also His plenitude as the source of all. This, however, does not seem true, because thus innascibility would not be a property distinct from paternity and spiration; but would include them as the proper is included in the common. For source and authority signify in God nothing but the principle of origin. We must therefore say with Augustine (De Trin. v, 7) that "unbegotten" imports the negation of passive generation. For he says that "unbegotten" has the same meaning as "not a son." Nor does it follow that "unbegotten" is not the proper notion of the Father; for primary and simple things are notified by negations; as, for instance, a point is defined as what has no part.
Reply to Objection 2. "Unbegotten" is taken sometimes in a negative sense only, and in that sense Jerome says that "the Holy Ghost is unbegotten," that is, He is not begotten. Otherwise "unbegotten" may be taken in a kind of privation sense, but not as implying any imperfection. For privation can be taken in many ways; in one way when a thing has not what is naturally belongs to another, even though it is not of its own nature to have it; as, for instance, if a stone be called a dead thing, as wanting life, which naturally belongs to some other things. In another sense, privation is so called when something has not what naturally belongs to some members of its genus; as for instance when a mole is called blind. In a third sense privation means the absence of what something ought to have; in which sense, privation imports an imperfection. In this sense, "unbegotten" is not attributed to the Father as a privation, but it may be so attributed in the second sense, meaning that a certain person of the divine nature is not begotten, while some person of the same nature is begotten. In this sense the term "unbegotten" can be applied also to the Holy Ghost. Hence to consider it as a term proper to the Father alone, it must be further understood that the name "unbegotten" belongs to a divine person as the principle of another person; so that it be understood to imply negation in the genus of principle taken personally in God. Or that there be understood in the term "unbegotten" that He is not in any way derived from another; and not only that He is not from another by way only of generation. In this sense the term "unbegotten" does not belong at all to the Holy Ghost, Who is from another by procession, as a subsisting person; nor does it belong to the divine essence, of which it may be said that it is in the Son or in the Holy Ghost from another--namely, from the Father.
Reply to Objection 3. According to Damascene (De Fide Orth. ii, 9), "unbegotten" in one sense signifies the same as "uncreated"; and thus it applies to the substance, for thereby does the created substance differ from the uncreated. In another sense it signifies what is not begotten, and in this sense it is a relative term; just as negation is reduced to the genus of affirmation, as "not man" is reduced to the genus of substance, and "not white" to the genus of quality. Hence, since "begotten" implies relation in God, "unbegotten" belongs also to relation. Thus it does not follow that the Father unbegotten is substantially distinguished from the Son begotten; but only by relation; that is, as the relation of Son is denied of the Father.
Reply to Objection 4. In every genus there must be something first; so in the divine nature there must be some one principle which is not from another, and which we call "unbegotten." To admit two innascibles is to suppose the existence of two Gods, and two divine natures. Hence Hilary says (De Synod.): "As there is one God, so there cannot be two innascibles." And this especially because, did two innascibles exist, one would not be from the other, and they would not be distinguished by relative opposition: therefore they would be distinguished from each other by diversity of nature.
Reply to Objection 5. The property of the Father, whereby He is not from another, is more clearly signified by the removal of the nativity of the Son, than by the removal of the procession of the Holy Ghost; both because the procession of the Holy Ghost has no special name, as stated above (27, 4, ad 3), and because also in the order of nature it presupposes the generation of the Son. Hence, it being denied of the Father that He is begotten, although He is the principle of generation, it follows, as a consequence, that He does not proceed by the procession of the Holy Ghost, because the Holy Ghost is not the principle of generation, but proceeds from the person begotten.
Source: Summa Theologica (New Advent)