The Catechism of the Catholic Church states the Blessed Trinity is "the central mystery of the Christian faith and of Christian life” (CCC 261). As such, we cannot arrive at knowledge of the Trinity by the natural light of human reason. It is something we can only know through God’s revelation. Therefore, we believe there are three persons that equally possess the divine nature because God says so.
However, we can apply reason and see that it’s reasonable that there are only three persons in the Godhead. Throughout the history of the Church, the Son is seen as proceeding from the Father by way of the infinite intellect. The Holy Spirit has been taught to proceed from the Father and the Son by way of the infinite will. Since there are only two faculties in the Godhead from which processions can occur, intellect and will, there are only three persons.
