The Holy Ghost, at least to me, is the most confusing aspect of the Trinity. There follows a few lessons on what He is.
1 Taught by holy Scripture, therefore, we maintain this firmly about the Holy Spirit: that He is true God, subsistent, personally distinct from the Father and the Son. But one ought to consider how a truth of this kind must be grasped somehow, in order to defend it from the attacks of unbelievers.
2 To get at the evidence one must first premise that in every intellectual nature a will must be discovered. For an intellect is made to be in act by an intelligible form so far as it is understanding, as a natural thing is made to be in act in its natural being by its proper form. But a natural thing, through the form by which it is perfected in its species, has an inclination to its proper operations and to its proper end, which it achieves by operations, “for as everything is so does it operate,” and it tends to what is fitting for itself.
Hence, also, from an intelligible form there must follow in one who understands an inclination to his proper operations and his proper end. Of course, this inclination in an intellectual nature is the will, which is the principle of operations in us, those by which he who understands operates for an end. For end and the good are the will’s object. One must, therefore, discover a will in everyone who understands.
Notes A mini-proof of free will, if you like.
3 Although several acts seem to belong to the will, to desire, to delight in, to hate, and others of this kind, nevertheless for all of these love is found to be the one principle and the common root. This can be gathered from the following points. The will, as was said, is related to intellectual things as natural inclination to natural things (this is also called natural appetite). But natural inclination arises thus: The natural thing has an affinity and correspondence from its form (which we have called the principle of the inclination) with that to which it is moved. The heavy has such a relation with the lower place.
Hence, also, every inclination of the will arises from this: by an intelligible form a thing is apprehended as suitable or affective. To be affected toward something—so far as it is of this kind—is to love that thing. Therefore, every inclination of will and even of sensible appetite has its origin from love. For from the fact that we love something we desire that thing if it be absent; we rejoice, of course, if it be present; and we are sad when we are kept from it; and we hate those things which keep us from the beloved, and grow angry against them.
4 Thus, then, what is loved is not only in the intellect of the lover, but in his will as well; but in one way and another. It is in the intellect by reason of the likeness of its species; it is in the will of the lover, however, as the term of a movement is in its proportioned motive principle by reason of the suitability and proportion which the term has for that principle. just so, in a certain way, there is in fire the upper place by reason of that lightness which gives it proportion and suitability to such a place, but the fire which is generated is in the fire which generates by reason of the likeness of its form.
5 Since, then, it has now been shown that in every intellectual nature there is will, and that God, of course, is intelligent was shown in Book I, there must, then, be will in Him; the will of God, to be sure, is not something which accrues to His essence, just as His intellect is not, as was shown above, but the will of God is His very substance. And since the intellect of God, as well, is His very substance, it follows that the one thing in God is intellect and will. However, the manner in which what in other things are many things in God are one thing can be manifest from the points made in Book I.
6 And because it was shown in Book I that the operation of God is His very essence, and that the essence of God is His will, it follows that will is not in God by way of potency, or of habit, but by way of act. It was shown, of course, that every act of will is rooted in love. Hence, in God there must be love.
7 And because, as was shown in Book I, the proper object of the divine will is His goodness, necessarily it is first and principally His goodness and Himself that God loves. But, since it has been shown that the beloved must somehow be in the will of the lover, and that God Himself loves Himself, it needs must be that God Himself is in His will as the beloved in the lover. But the beloved is in the lover so far as it is loved—an act of love, of course, is a kind of act of will—but the act of will of God is His being, just as His will is His being. Therefore, the being of God in His will by way of love is not an accidental one—as it is in us—but is essential being. And so it must be that God, when He is considered existing in His own will, is truly and substantially God.
8 But a thing’s being in the will as a beloved in a lover bears a certain order to the conception by which the intellect conceives the thing, and to the thing itself whose intellectual conception is called a word. For it would not be loved unless it were somehow known; neither is the beloved’s knowledge alone loved, but the beloved as good in itself. Necessarily, therefore, does the love by which God is in the divine will as a beloved in a lover proceed both from the Word of God and from the God whose Word He is.
9 Now, since it has been shown that the beloved is not in the lover by a likeness of species, as the thing understood is present in the one understanding, whereas whatever proceeds from another as one generated does proceed by a likeness of species from the generator, this follows: A thing’s proceeding in order to be in the will as the beloved is in the lover is not a proceeding by way of generation, just as a thing’s proceeding in order to be in the intellect does have the essentials of generation, as was shown above. Therefore, God proceeding by way of love does not proceed as begotten. And He, therefore, cannot be called Son.
Notes Maybe you have the same sticking points as do, which is the difficulty of applying ordinary labels (father, son) to extraordinary things, and therefore believing they have the precise same definitions. Aquinas is trying to show how these labels—Father, Son, Spirit—are metaphorical (where that word is use in it grammatical sense).
10 But, because the beloved in the will exists as inclining, and somehow inwardly impelling the lover toward the very thing beloved, and an impulse of a living thing from within belongs to a spirit, this is suitable: that God proceeding by way of love be called His spirit; as it were a kind of existing spiration.
11 Hence it is that the Apostle attributes to the Spirit and to Love a kind of impulse; for he says in Romans (8:14): “Whoever are led by the Spirit of God, they are the sons of God,” and: “The charity of Christ presses us” (2 Cor. 5:14).
12 However, since every intellectual motion is named from its term, and the love aforesaid is that by which God Himself is loved, quite fittingly is God proceeding by way of love called “Holy Spirit”; for the things assigned to God have customarily been called “holy.”