Yes, from the love the Father and the Son have for each other proceeds the Holy Spirit. That is, the love the Father and the Son have for each other is fruitful, it produces another divine person, namely, the Holy Spirit who is also called Love and Gift. Analogously, the love of husband and wife for each other which they show towards each other in the sex act is also fruitful, producing a whole other human person, a child who is a gift of their love for each other.
God has no gender but the characteristics of the male and female genders or paternity and maternity God created humans with do have their likenesses in God, in the Trinity, in some manner or other. In the Old Testament, the prophets likened the love of God for the chosen people to both a father and mother’s love towards their children. Jesus himself said “Jerusalem, Jerusalem, you who kill the prophets and stone those sent to you, how often I have longed to gather your children together, as a hen gathers her chicks under her wings, and you were not willing” (Matt. 23:37). Love in the Holy Trinity has both paternal and maternal characteristics which have their reflection in one way or another in the male and female genders in human beings and in the respective roles that humans play as fathers and mothers. In God the Father is paternity for he is the only Father of his only begotten Son and the eternal Son proceeded from the Father without a mother. St Thomas Aquinas says that the Father alone produced the Son as being both the father and mother of the Son in some sense. Although the Holy Spirit proceeds from the Father and the Son, the Holy Spirit is not called the offspring or ‘child’ or son or daughter of the Father and the Son. As divine revelation has revealed to us, in the Trinity there is paternity, filiation, and procession; procession refers to the Holy Spirit.
St Maximilian Kolbe had some deep insights into the interior life of the Trinity. He saw the Holy Spirit as a divine maternity of love in the Trinity. The Holy Spirit is called Love and what better exemplifies this amongst human relations but a mother? The mother of a family we generally tend to see as the ‘heart’ of the family, the bond between child and father. Indeed, the Holy Spirit is called the bond of love between the Father and the Son. St Maximilian Kolbe saw Mary, the mother of Christ and our mother, as the quasi-embodiment or quasi-incarnation of the Holy Spirit. When we look at Mary, the mother of fair love, we can get some idea of the person of the Holy Spirit in the Trinity for the Holy Spirit has taken such a possession of Mary and united her to himself in an inexpressible union that it is as if after a manner of speaking that he has become incarnated in her. Of course, St Maximilian Kolbe is not saying that Mary is the incarnation of the Holy Spirit (this would be heresy) as Jesus is the incarnation of the second person of the Trinity. He is just saying that the union between our Blessed Lady and the Holy Spirit is so close that whatever our Blessed Lady stands for, her person and divine maternity of love, is a reflection of the Holy Spirit, a divine maternity of love in the Trinity. The Holy Spirit as the divine maternity of love in the Trinity should also not be taken as if the Holy Spirit is the mother of the Son of God. The Son proceeds from the Father alone and the Holy Spirit proceeds from the Father and the Son. I think essentially what St Maximilian is saying is that a mother’s or maternal love is a reflection of the love or person of the Holy Spirit in the bosom of the Trinity and our Blessed Lady is the perfect created reflection of this.
Recommended reading: Immaculate Conception and the Holy Spirit - The Marian Teachings of Father Kolbe, by Fr. H. M. Manteau-Bonamy, O.P.
