The Spirit, further, is called “Holy” because, on the one hand, of “his unsullied purity and glorious majesty”—not, however, as if he were holier than the Father and the Son, for all are holy and “the divine holiness, being infinite, does not admit of degrees.” Holiness, after all, is expressly attributed both to the Father (John 17:11) and to the Son (Luke 1:35; Acts 4:27), and is a divine attribute that belongs indivisibly to the Godhead: the Father, Son, and Spirit, considered as God are “holy by one and the same holiness.” Holiness, as an essential attribute of the Godhead, is equally attributed to each of the divine persons—and, inasmuch as the divine holiness is infinite, it does not admit of “degrees of comparison”—so that the Holy Spirit is not called “holy” “by way of eminence” in the Godhead itself.

Rather, the specific attribution of holiness to the Spirit arises because it is his special operation to make us holy: “in the order of the divine operations, the sanctification of believers is usually attributed to him, as election is to the Father, and redemption to the Son.” Still, as in the case of all divine operations or works ad extra, sanctification is the work of the entire Godhead: it is not as if the sanctification of believers were a separate work of the Spirit, apart from the will and the work of the Father and the Son—“but such is the order of the operations of God, that although they are effected by the common counsel of the same will, and by the same energy of the same power, yet some of them are appropriated to each person respectively.” Thus, the Holy Spirit is the person of the Godhead “who immediately sanctifies and makes holy the people of God,” while the Father and the Son participate in this work “through the Holy Ghost,” acting “mediately.”

—Richard A. Muller, Post-Reformation Reformed Dogmatics: The Rise and Development of Reformed Orthodoxy; Volume 4: The Triunity of God (Grand Rapids, MI: Baker Academic, 2003), 342–343.