Objection 1. It would seem that the Holy Ghost is not fittingly sent in a visible manner. For the Son as visibly sent to the world is said to be less than the Father. But the Holy Ghost is never said to be less than the Father. Therefore the Holy Ghost is not fittingly sent in a visible manner.
Objection 2. Further, the visible mission takes place by way of union to a visible creature, as the Son's mission according to the flesh. But the Holy Ghost did not assume any visible creature; and hence it cannot be said that He exists otherwise in some creatures than in others, unless perhaps as in a sign, as He is also present in the sacraments, and in all the figures of the law. Thus the Holy Ghost is either not sent visibly at all, or His visible mission takes place in all these things.
Objection 3. Further, every visible creature is an effect showing forth the whole Trinity. Therefore the Holy Ghost is not sent by reason of those visible creatures more than any other person.
Objection 4. Further, the Son was visibly sent by reason of the noblest kind of creature--namely, the human nature. Therefore if the Holy Ghost is sent visibly, He ought to be sent by reason of rational creatures.
Objection 5. Further, whatever is done visibly by God is dispensed by the ministry of the angels; as Augustine says (De Trin. iii, 4,5,9). So visible appearances, if there have been any, came by means of the angels. Thus the angels are sent, and not the Holy Ghost.
Objection 6. Further, the Holy Ghost being sent in a visible manner is only for the purpose of manifesting the invisible mission; as invisible things are made known by the visible. So those to whom the invisible mission was not sent, ought not to receive the visible mission; and to all who received the invisible mission, whether in the New or in the Old Testament, the visible mission ought likewise to be sent; and this is clearly false. Therefore the Holy Ghost is not sent visibly.
On the contrary, It is said (Matthew 3:16) that, when our Lord was baptized, the Holy Ghost descended upon Him in the shape of a dove.
I answer that, God provides for all things according to the nature of each thing. Now the nature of man requires that he be led to the invisible by visible things, as explained above (Question 12, Article 12). Wherefore the invisible things of God must be made manifest to man by the things that are visible. As God, therefore, in a certain way has demonstrated Himself and His eternal processions to men by visible creatures, according to certain signs; so was it fitting that the invisible missions also of the divine persons should be made manifest by some visible creatures.
This mode of manifestation applies in different ways to the Son and to the Holy Ghost. For it belongs to the Holy Ghost, Who proceeds as Love, to be the gift of sanctification; to the Son as the principle of the Holy Ghost, it belongs to the author of this sanctification. Thus the Son has been sent visibly as the author of sanctification; the Holy Ghost as the sign of sanctification.
Reply to Objection 1. The Son assumed the visible creature, wherein He appeared, into the unity of His person, so that whatever can be said of that creature can be said of the Son of God; and so, by reason of the nature assumed, the Son is called less than the Father. But the Holy Ghost did not assume the visible creature, in which He appeared, into the unity of His person; so that what is said of it cannot be predicated of Him. Hence He cannot be called less than the Father by reason of any visible creature.
Reply to Objection 2. The visible mission of the Holy Ghost does not apply to the imaginary vision which is that of prophecy; because as Augustine says (De Trin. ii, 6): "The prophetic vision is not displayed to corporeal eyes by corporeal shapes, but is shown in the spirit by the spiritual images of bodies. But whoever saw the dove and the fire, saw them by their eyes. Nor, again, has the Holy Ghost the same relation to these images that the Son has to the rock, because it is said, "The rock was Christ" (1 Corinthians 10:4). For that rock was already created, and after the manner of an action was named Christ, Whom it typified; whereas the dove and the fire suddenly appeared to signify only what was happening. They seem, however, to be like to the flame of the burning bush seen by Moses and to the column which the people followed in the desert, and to the lightning and thunder issuing forth when the law was given on the mountain. For the purpose of the bodily appearances of those things was that they might signify, and then pass away." Thus the visible mission is neither displayed by prophetic vision, which belongs to the imagination, and not to the body, nor by the sacramental signs of the Old and New Testament, wherein certain pre-existing things are employed to signify something. But the Holy Ghost is said to be sent visibly, inasmuch as He showed Himself in certain creatures as in signs especially made for that purpose.
Reply to Objection 3. Although the whole Trinity makes those creatures, still they are made in order to show forth in some special way this or that person. For as the Father, Son and Holy Ghost are signified by diverse names, so also can They each one be signified by different things; although neither separation nor diversity exists amongst Them.
Reply to Objection 4. It was necessary for the Son to be declared as the author of sanctification, as explained above. Thus the visible mission of the Son was necessarily made according to the rational nature to which it belongs to act, and which is capable of sanctification; whereas any other creature could be the sign of sanctification. Nor was such a visible creature, formed for such a purpose, necessarily assumed by the Holy Ghost into the unity of His person, since it was not assumed or used for the purpose of action, but only for the purpose of a sign; and so likewise it was not required to last beyond what its use required.
Reply to Objection 5. Those visible creatures were formed by the ministry of the angels, not to signify the person of an angel, but to signify the Person of the Holy Ghost. Thus, as the Holy Ghost resided in those visible creatures as the one signified in the sign, on that account the Holy Ghost is said to be sent visibly, and not as an angel.
Reply to Objection 6. It is not necessary that the invisible mission should always be made manifest by some visible external sign; but, as is said (1 Corinthians 12:7)--"the manifestation of the Spirit is given to every man unto profit"--that is, of the Church. This utility consists in the confirmation and propagation of the faith by such visible signs. This has been done chiefly by Christ and by the apostles, according to Hebrews 2:3, "which having begun to be declared by the Lord, was confirmed unto us by them that heard."
Thus in a special sense, a mission of the Holy Ghost was directed to Christ, to the apostles, and to some of the early saints on whom the Church was in a way founded; in such a manner, however, that the visible mission made to Christ should show forth the invisible mission made to Him, not at that particular time, but at the first moment of His conception. The visible mission was directed to Christ at the time of His baptism by the figure of a dove, a fruitful animal, to show forth in Christ the authority of the giver of grace by spiritual regeneration; hence the Father's voice spoke, "This is My beloved Son" (Matthew 3:17), that others might be regenerated to the likeness of the only Begotten. The Transfiguration showed it forth in the appearance of a bright cloud, to show the exuberance of doctrine; and hence it was said, "Hear ye Him" (Matthew 17:5). To the apostles the mission was directed in the form of breathing to show forth the power of their ministry in the dispensation of the sacraments; and hence it was said, "Whose sins you shall forgive, they are forgiven" (John 20:23): and again under the sign of fiery tongues to show forth the office of teaching; whence it is said that, "they began to speak with divers tongues" (Acts 2:4). The visible mission of the Holy Ghost was fittingly not sent to the fathers of the Old Testament, because the visible mission of the Son was to be accomplished before that of the Holy Ghost; since the Holy Ghost manifests the Son, as the Son manifests the Father. Visible apparitions of the divine persons were, however, given to the Fathers of the Old Testament which, indeed, cannot be called visible missions; because, according to Augustine (De Trin. ii, 17), they were not sent to designate the indwelling of the divine person by grace, but for the manifestation of something else.
Source: Summa Theologica (New Advent)