Objection 1. It would seem that it is not proper to Christ to be the Mediator of God and man. For a priest and a prophet seem to be mediators between God and man, according to Deuteronomy 5:5: "I was the mediator and stood between God [Vulgate: 'the Lord'] and you at that time." But it is not proper to Christ to be a priest and a prophet. Neither, therefore, is it proper to Him to be Mediator.
Objection 2. Further, that which is fitting to angels, both good and bad, cannot be said to be proper to Christ. But to be between God and man is fitting to the good angels, as Dionysius says (Div. Nom. iv). It is also fitting to the bad angels--that is, the demons: for they have something in common with God--namely, "immortality"; and something they have in common with men--namely, "passibility of soul" and consequently unhappiness; as appears from what Augustine says (De Civ. Dei ix, 13,15). Therefore it is not proper to Christ to be a Mediator of God and man.
Objection 3. Further, it belongs to the office of Mediator to beseech one of those, between whom he mediates, for the other. But the Holy Ghost, as it is written (Romans 8:26), "asketh" God "for us with unspeakable groanings." Therefore the Holy Ghost is a Mediator between God and man. Therefore this is not proper to Christ.
On the contrary, It is written (1 Timothy 2:5): "There is... one Mediator of God and man, the man Christ Jesus."
I answer that, Properly speaking, the office of a mediator is to join together and unite those between whom he mediates: for extremes are united in the mean [medio]. Now to unite men to God perfectively belongs to Christ, through Whom men are reconciled to God, according to 2 Corinthians 5:19: "God was in Christ reconciling the world to Himself." And, consequently, Christ alone is the perfect Mediator of God and men, inasmuch as, by His death, He reconciled the human race to God. Hence the Apostle, after saying, "Mediator of God and man, the man Christ Jesus," added: "Who gave Himself a redemption for all."
However, nothing hinders certain others from being called mediators, in some respect, between God and man, forasmuch as they cooperate in uniting men to God, dispositively or ministerially.
Reply to Objection 1. The prophets and priests of the Old Law were called mediators between God and man, dispositively and ministerially: inasmuch as they foretold and foreshadowed the true and perfect Mediator of God and men. As to the priests of the New Law, they may be called mediators of God and men, inasmuch as they are the ministers of the true Mediator by administering, in His stead, the saving sacraments to men.
Reply to Objection 2. The good angels, as Augustine says (De Civ. Dei ix, 13), cannot rightly be called mediators between God and men. "For since, in common with God, they have both beatitude and immortality, and none of these things in common with unhappy and mortal man, how much rather are they not aloof from men and akin to God, than established between them?" Dionysius, however, says that they do occupy a middle place, because, in the order of nature, they are established below God and above man. Moreover, they fulfill the office of mediator, not indeed principally and perfectively, but ministerially and dispositively: whence (Matthew 4:11) it is said that "angels came and ministered unto Him"--namely, Christ. As to the demons, it is true that they have immortality in common with God, and unhappiness in common with men. "Hence for this purpose does the immortal and unhappy demon intervene, in order that he may hinder men from passing to a happy immortality," and may allure them to an unhappy immortality. Whence he is like "an evil mediator, who separates friends" [Augustine, De Civ. Dei xv].
But Christ had beatitude in common with God, mortality in common with men. Hence "for this purpose did He intervene, that having fulfilled the span of His mortality, He might from dead men make immortal--which He showed in Himself by rising again; and that He might confer beatitude on those who were deprived of it--for which reason He never forsook us." Wherefore He is "the good Mediator, Who reconciles enemies" (De Civ. Dei xv).
Reply to Objection 3. Since the Holy Ghost is in everything equal to God, He cannot be said to be between, or a Mediator of, God and men: but Christ alone, Who, though equal to the Father in His Godhead, yet is less than the Father in His human nature, as stated above (Question 20, Article 1). Hence on Galatians 3:20, "Christ is a Mediator [Vulgate: 'Now a mediator is not of one, but God is one'," the gloss says: "Not the Father nor the Holy Ghost." The Holy Ghost, however, is said "to ask for us," because He makes us ask.
Source: Summa Theologica (New Advent)