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cf., Sent.I.D11.Q1.A1, SCG4.C24-25, QDePot.Q10.A4-5, Graecorum.Part2.C27-32, CT.BookI.C49, DeRatio.C4, Ioan.C15.L5, Ioan.C16.L4
After he discusses the name "Holy Spirit" in general, he moves onto discussing the origination of the Holy Spirit in particular. First, he treats the question of the procession of the Spirit from the Son. Second, he discusses the relationship of the Father and Son in this procession.
In this article, the infamous question of the Filioque is treated. This is a question St. Thomas treated throughout his entire life and thus there are a number of different arguments that he brings forward. Here, he gives his famous argument from relative opposition yet, in the texts quoted above, he gives other arguments.
To begin, we must establish that there are two ways of properly predicating things of God. First, we can say that it is absolute. Second, we can say that it is relative. For example, when we say that "God is just" or "God is wise," we are predicating something to God that is absolute. On the other hand, when we say that terms like "Father" or "Son" or "Spirit," we are speaking relatively. The Father is the Father "of" the Son, the Son is the Son "of" the Father, etc.
Obviously, we are not going to distinguish on the basis of what is absolute since the absolute designates what is essential and the persons of the Godhead are of one essence, so we must distinguish on the basis of what is by relation.