Objection 1. It would seem that there are not five notions. For the notions proper to the persons are the relations whereby they are distinguished from each other. But the relations in God are only four (28, 4). Therefore the notions are only four in number.
Objection 2. Further, as there is only one essence in God, He is called one God, and because in Him there are three persons, He is called the Trine God. Therefore, if in God there are five notions, He may be called quinary; which cannot be allowed.
Objection 3. Further, if there are five notions for the three persons in God, there must be in some one person two or more notions, as in the person of the Father there is innascibility and paternity, and common spiration. Either these three notions really differ, or not. If they really differ, it follows that the person of the Father is composed of several things. But if they differ only logically, it follows that one of them can be predicated of another, so that we can say that as the divine goodness is the same as the divine wisdom by reason of the common reality, so common spiration is paternity; which is not to be admitted. Therefore there are not five notions.
Objection 4.On the contrary, It seems that there are more; because as the Father is from no one, and therefrom is derived the notion of innascibility; so from the Holy Ghost no other person proceeds. And in this respect there ought to be a sixth notion.
Objection 5. Further, as the Father and the Son are the common origin of the Holy Ghost, so it is common to the Son and the Holy Ghost to proceed from the Father. Therefore, as one notion is common to the Father and the Son, so there ought to be one notion common to the Son and to the Holy Ghost.
I answer that, A notion is the proper idea whereby we know a divine Person. Now the divine persons are multiplied by reason of their origin: and origin includes the idea of someone from whom another comes, and of someone that comes from another, and by these two modes a person can be known. Therefore the Person of the Father cannot be known by the fact that He is from another; but by the fact that He is from no one; and thus the notion that belongs to Him is called "innascibility." As the source of another, He can be known in two ways, because as the Son is from Him, the Father is known by the notion of "paternity"; and as the Holy Ghost is from Him, He is known by the notion of "common spiration." The Son can be known as begotten by another, and thus He is known by "filiation"; and also by another person proceeding from Him, the Holy Ghost, and thus He is known in the same way as the Father is known, by "common spiration." The Holy Ghost can be known by the fact that He is from another, or from others; thus He is known by "procession"; but not by the fact that another is from Him, as no divine person proceeds from Him.
Therefore, there are Five notions in God: "innascibility," "paternity," "filiation," "common spiration" and "procession." Of these only four are relations, for "innascibility" is not a relation, except by reduction, as will appear later (33, 4, ad 3). Four only are properties. For "common spiration" is not a property; because it belongs to two persons. Three are personal notions--i.e. constituting persons, "paternity," "filiation," and "procession." "Common spiration" and "innascibility" are called notions of Persons, but not personal notions, as we shall explain further on (40, 1, ad 1).
Reply to Objection 1. Besides the four relations, another notion must be admitted, as above explained.
Reply to Objection 2. The divine essence is signified as a reality; and likewise the persons are signified as realities; whereas the notions are signified as ideas notifying the persons. Therefore, although God is one by unity of essence, and trine by trinity of persons, nevertheless He is not quinary by the five notions.
Reply to Objection 3. Since the real plurality in God is founded only on relative opposition, the several properties of one Person, as they are not relatively opposed to each other, do not really differ. Nor again are they predicated of each other, because they are different ideas of the persons; as we do not say that the attribute of power is the attribute of knowledge, although we do say that knowledge is power.
Reply to Objection 4. Since Person implies dignity, as stated above (Question 19, Article 3) we cannot derive a notion of the Holy Spirit from the fact that no person is from Him. For this does not belong to His dignity, as it belongs to the authority of the Father that He is from no one.
Reply to Objection 5. The Son and the Holy Ghost do not agree in one special mode of existence derived from the Father; as the Father and the Son agree in one special mode of producing the Holy Ghost. But the principle on which a notion is based must be something special; thus no parity of reasoning exists.
Source: Summa Theologica (New Advent)