Objection 1. It would seem that the Father and the Son do not love each other by the Holy Ghost. For Augustine (De Trin. vii, 1) proves that the Father is not wise by the Wisdom begotten. But as the Son is Wisdom begotten, so the Holy Ghost is the Love proceeding, as explained above (Question 27, Article 3). Therefore the Father and the Son do not love Themselves by the Love proceeding, which is the Holy Ghost.
Objection 2. Further, the proposition, "The Father and the Son love each other by the Holy Ghost," this word "love" is to be taken either essentially or notionally. But it cannot be true if taken essentially, because in the same way we might say that "the Father understands by the Son"; nor, again, if it is taken notionally, for then, in like manner, it might be said that "the Father and the Son spirate by the Holy Ghost," or that "the Father generates by the Son." Therefore in no way is this proposition true: "'The Father and the Son love each other by the Holy Ghost."
Objection 3. Further, by the same love the Father loves the Son, and Himself, and us. But the Father does not love Himself by the Holy Ghost; for no notional act is reflected back on the principle of the act; since it cannot be said that the "Father begets Himself," or that "He spirates Himself." Therefore, neither can it be said that "He loves Himself by the Holy Ghost," if "to love" is taken in a notional sense. Again, the love wherewith He loves us is not the Holy Ghost; because it imports a relation to creatures, and this belongs to the essence. Therefore this also is false: "The Father loves the Son by the Holy Ghost."
On the contrary, Augustine says (De Trin. vi, 5): "The Holy Ghost is He whereby the Begotten is loved by the one begetting and loves His Begetter."
I answer that, A difficulty about this question is objected to the effect that when we say, "the Father loves the Son by the Holy Ghost," since the ablative is construed as denoting a cause, it seems to mean that the Holy Ghost is the principle of love to the Father and the Son; which cannot be admitted.
In view of this difficulty some have held that it is false, that "the Father and the Son love each other by the Holy Ghost"; and they add that it was retracted by Augustine when he retracted its equivalent to the effect that "the Father is wise by the Wisdom begotten." Others say that the proposition is inaccurate and ought to be expounded, as that "the Father loves the Son by the Holy Ghost"--that is, "by His essential Love," which is appropriated to the Holy Ghost. Others further say that this ablative should be construed as importing a sign, so that it means, "the Holy Ghost is the sign that the Father loves the Son"; inasmuch as the Holy Ghost proceeds from them both, as Love. Others, again, say that this ablative must be construed as importing the relation of formal cause, because the Holy Ghost is the love whereby the Father and the Son formally love each other. Others, again, say that it should be construed as importing the relation of a formal effect; and these approach nearer to the truth.
To make the matter clear, we must consider that since a thing is commonly denominated from its forms, as "white" from whiteness, and "man" from humanity; everything whence anything is denominated, in this particular respect stands to that thing in the relation of form. So when I say, "this man is clothed with a garment," the ablative is to be construed as having relation to the formal cause, although the garment is not the form. Now it may happen that a thing may be denominated from that which proceeds from it, not only as an agent is from its action, but also as from the term itself of the action--that is, the effect, when the effect itself is included in the idea of the action. For we say that fire warms by heating, although heating is not the heat which is the form of the fire, but is an action proceeding from the fire; and we say that a tree flowers with the flower, although the flower is not the tree's form, but is the effect proceeding from the form. In this way, therefore, we must say that since in God "to love" is taken in two ways, essentially and notionally, when it is taken essentially, it means that the Father and the Son love each other not by the Holy Ghost, but by their essence. Hence Augustine says (De Trin. xv, 7): "Who dares to say that the Father loves neither Himself, nor the Son, nor the Holy Ghost, except by the Holy Ghost?" The opinions first quoted are to be taken in this sense. But when the term Love is taken in a notional sense it means nothing else than "to spirate love"; just as to speak is to produce a word, and to flower is to produce flowers. As therefore we say that a tree flowers by its flower, so do we say that the Father, by the Word or the Son, speaks Himself, and His creatures; and that the Father and the Son love each other and us, by the Holy Ghost, or by Love proceeding.
Reply to Objection 1. To be wise or intelligent is taken only essentially in God; therefore we cannot say that "the Father is wise or intelligent by the Son." But to love is taken not only essentially, but also in a notional sense; and in this way, we can say that the Father and the Son love each other by the Holy Ghost, as was above explained.
Reply to Objection 2. When the idea of an action includes a determined effect, the principle of the action may be denominated both from the action, and from the effect; so we can say, for instance, that a tree flowers by its flowering and by its flower. When, however, the idea of an action does not include a determined effect, then in that case, the principle of the action cannot be denominated from the effect, but only from the action. For we do not say that the tree produces the flower by the flower, but by the production of the flower. So when we say, "spirates" or "begets," this imports only a notional act. Hence we cannot say that the Father spirates by the Holy Ghost, or begets by the Son. But we can say that the Father speaks by the Word, as by the Person proceeding, "and speaks by the speaking," as by a notional act; forasmuch as "to speak" imports a determinate person proceeding; since "to speak" means to produce a word. Likewise to love, taken in a notional sense, means to produce love; and so it can be said that the Father loves the Son by the Holy Ghost, as by the person proceeding, and by Love itself as a notional act.
Reply to Objection 3. The Father loves not only the Son, but also Himself and us, by the Holy Ghost; because, as above explained, to love, taken in a notional sense, not only imports the production of a divine person, but also the person produced, by way of love, which has relation to the object loved. Hence, as the Father speaks Himself and every creature by His begotten Word, inasmuch as the Word "begotten" adequately represents the Father and every creature; so He loves Himself and every creature by the Holy Ghost, inasmuch as the Holy Ghost proceeds as the love of the primal goodness whereby the Father loves Himself and every creature. Thus it is evident that relation to the creature is implied both in the Word and in the proceeding Love, as it were in a secondary way, inasmuch as the divine truth and goodness are a principle of understanding and loving all creatures.
Source: Summa Theologica (New Advent)