Objection 1. It would seem that the Father and the Son are not one principle of the Holy Ghost. For the Holy Ghost does not proceed from the Father and the Son as they are one; not as they are one in nature, for the Holy Ghost would in that way proceed from Himself, as He is one in nature with Them; nor again inasmuch as they are united in any one property, for it is clear that one property cannot belong to two subjects. Therefore the Holy Ghost proceeds from the Father and the Son as distinct from one another. Therefore the Father and the Son are not one principle of the Holy Ghost.
Objection 2. Further, in this proposition "the Father and the Son are one principle of the Holy Ghost," we do not designate personal unity, because in that case the Father and the Son would be one person; nor again do we designate the unity of property, because if one property were the reason of the Father and the Son being one principle of the Holy Ghost, similarly, on account of His two properties, the Father would be two principles of the Son and of the Holy Ghost, which cannot be admitted. Therefore the Father and the Son are not one principle of the Holy Ghost.
Objection 3. Further, the Son is not one with the Father more than is the Holy Ghost. But the Holy Ghost and the Father are not one principle as regards any other divine person. Therefore neither are the Father and the Son.
Objection 4. Further, if the Father and the Son are one principle of the Holy Ghost, this one is either the Father or it is not the Father. But we cannot assert either of these positions because if the one is the Father, it follows that the Son is the Father; and if the one is not the Father, it follows that the Father is not the Father. Therefore we cannot say that the Father and the Son are one principle of the Holy Ghost.
Objection 5. Further, if the Father and the Son are one principle of the Holy Ghost, it seems necessary to say, conversely, that the one principle of the Holy Ghost is the Father and the Son. But this seems to be false; for this word "principle" stands either for the person of the Father, or for the person of the Son; and in either sense it is false. Therefore this proposition also is false, that the Father and the Son are one principle of the Holy Ghost.
Objection 6. Further, unity in substance makes identity. So if the Father and the Son are the one principle of the Holy Ghost, it follows that they are the same principle; which is denied by many. Therefore we cannot grant that the Father and the Son are one principle of the Holy Ghost.
Objection 7. Further, the Father, Son and Holy Ghost are called one Creator, because they are the one principle of the creature. But the Father and the Son are not one, but two Spirators, as many assert; and this agrees also with what Hilary says (De Trin. ii) that "the Holy Ghost is to be confessed as proceeding from Father and Son as authors." Therefore the Father and the Son are not one principle of the Holy Ghost.
On the contrary, Augustine says (De Trin. v, 14) that the Father and the Son are not two principles, but one principle of the Holy Ghost.
I answer that, The Father and the Son are in everything one, wherever there is no distinction between them of opposite relation. Hence since there is no relative opposition between them as the principle of the Holy Ghost it follows that the Father and the Son are one principle of the Holy Ghost.
Some, however, assert that this proposition is incorrect: "The Father and the Son are one principle of the Holy Ghost," because, they declare, since the word "principle" in the singular number does not signify "person," but "property," it must be taken as an adjective; and forasmuch as an adjective cannot be modified by another adjective, it cannot properly be said that the Father and the Son are one principle of the Holy Ghost unless one be taken as an adverb, so that the meaning should be: They are one principle--that is, in one and the same way. But then it might be equally right to say that the Father is two principles of the Son and of the Holy Ghost--namely, in two ways. Therefore, we must say that, although this word "principle" signifies a property, it does so after the manner of a substantive, as do the words "father" and "son" even in things created. Hence it takes its number from the form it signifies, like other substantives. Therefore, as the Father and the Son are one God, by reason of the unity of the form that is signified by this word "God"; so they are one principle of the Holy Ghost by reason of the unity of the property that is signified in this word "principle."
Reply to Objection 1. If we consider the spirative power, the Holy Ghost proceeds from the Father and the Son as they are one in the spirative power, which in a certain way signifies the nature with the property, as we shall see later (ad 7). Nor is there any reason against one property being in two "supposita" that possess one common nature. But if we consider the "supposita" of the spiration, then we may say that the Holy Ghost proceeds from the Father and the Son, as distinct; for He proceeds from them as the unitive love of both.
Reply to Objection 2. In the proposition "the Father and the Son are one principle of the Holy Ghost," one property is designated which is the form signified by the term. It does not thence follow that by reason of the several properties the Father can be called several principles, for this would imply in Him a plurality of subjects.
Reply to Objection 3. It is not by reason of relative properties that we speak of similitude or dissimilitude in God, but by reason of the essence. Hence, as the Father is not more like to Himself than He is to the Son; so likewise neither is the Son more like to the Father than is the Holy Ghost.
Reply to Objection 4. These two propositions, "The Father and the Son are one principle which is the Father," or, "one principle which is not the Father," are not mutually contradictory; and hence it is not necessary to assert one or other of them. For when we say the Father and the Son are one principle, this word "principle" has not determinate supposition but rather it stands indeterminately for two persons together. Hence there is a fallacy of "figure of speech" as the argument concludes from the indeterminate to the determinate.
Reply to Objection 5. This proposition is also true:--The one principle of the Holy Ghost is the Father and the Son; because the word "principle" does not stand for one person only, but indistinctly for the two persons as above explained.
Reply to Objection 6. There is no reason against saying that the Father and the Son are the same principle, because the word "principle" stands confusedly and indistinctly for the two Persons together.
Reply to Objection 7. Some say that although the Father and the Son are one principle of the Holy Ghost, there are two spirators, by reason of the distinction of "supposita," as also there are two spirating, because acts refer to subjects. Yet this does not hold good as to the name "Creator"; because the Holy Ghost proceeds from the Father and the Son as from two distinct persons, as above explained; whereas the creature proceeds from the three persons not as distinct persons, but as united in essence. It seems, however, better to say that because spirating is an adjective, and spirator a substantive, we can say that the Father and the Son are two spirating, by reason of the plurality of the "supposita" but not two spirators by reason of the one spiration. For adjectival words derive their number from the "supposita" but substantives from themselves, according to the form signified. As to what Hilary says, that "the Holy ghost is from the Father and the Son as His authors," this is to be explained in the sense that the substantive here stands for the adjective.
Source: Summa Theologica (New Advent)