What does it mean that the Holy Spirit is the third person of the Trinity?
The expression "third person of the Trinity" carries two truths that Scripture is careful to establish: first, that the Holy Spirit is a person — not merely an influence or a force — and second, that He is God, co-equal with the Father and the Son.
The Holy Spirit is a Person, not an influence
A common error is to reduce the Holy Spirit to an impersonal power. Samuel Ridout confronts this directly:
Samuel RidoutStrange as it may seem, we are met at the very outset by a question which we must answer before we can take up what is properly before us tonight. Men have asked, "Is there such a person as the Holy Ghost?" Is not all reference to a person in Scripture simply a striking way of referring to the attributes of God? Is not the Spirit simply an all pervading, divine influence?
Now we need not be long detained upon this matter, but we must speak in no uncertain way. This question involves a denial of the very being of God, and therefore must be treated as all other unbelieving questions. God has been pleased to reveal something of the infinite depths of the mystery of His Holy Person to us. He is — in Christianity — revealed as Father, Son and Holy Spirit. We must tread softly here, for we are on holy ground. There are depths which we cannot fathom, but we can at least look and wonder, confess and worship. A denial of either of these divine Persons is a denial of God.
J. T. Mawson reinforces this in equally plain terms:
J. T. MawsonWe often hear Him spoken of as an influence, or a power, but this is certainly not the teaching of Scripture. It is true that He exercises an influence, and is the power by which God operates in the souls of men, but He is a Person, and not only a Person, but the third Person in the Godhead — the Holy Ghost.
F. B. Hole adds that this personal character has practical consequences — the Spirit is not a tool at our disposal but a sovereign Person who acts according to His own will:
F. B. HoleThe Spirit of God is a Person. He wields an incalculable influence. Yet it is as a Person He indwells. ... He is not given to us as a power or influence at our disposal, but rather that we may be at His disposal.
The Holy Spirit is God — co-equal with Father and Son
Scripture ascribes to the Holy Spirit every attribute that belongs to God alone. Samuel Ridout traces these carefully:
Samuel Ridout"Whither shall I go from Thy Spirit? or whither shall I flee from Thy presence?" (Ps. 139:7-8). Here one of the attributes of God — His omnipresence — is ascribed to the Holy Spirit.
"Christ, who through the eternal Spirit, offered Himself without spot to God" (Heb. 9:14). Here we have another attribute — that of eternity. The Spirit of God is ever existent.
"The Spirit searcheth all things, yea, the deep things of God ... the things of God knoweth no man, but the Spirit of God" (1 Cor. 2:10-11). Omniscience, another attribute of Deity alone, is before us here as belonging to the Spirit.
"The Spirit of God hath made me, and the breath of the Almighty hath given me life" (Job 33:4). God the Creator is almighty, omnipotent. None but Him can call into being. When therefore creation is ascribed to the Holy Spirit, it in the strongest way teaches both His personality and His Deity.
Thus the Spirit is omnipresent, eternal, omniscient and omnipotent. He is God.
"Third" does not mean lesser
The word "third" refers only to the customary order in which the Persons are named — drawn largely from the baptismal formula of Matthew 28:19. It implies no rank or inferiority. A. J. Pollock is emphatic on this point:
A. J. PollockWe are accustomed to speak of the first, second and third Persons of the Holy Trinity, the Father, Son, and Holy Spirit. Doubtless the formula for baptism has led to this order, and the wisdom of it can be easily seen. But we must be very careful not to place the Persons in our minds as in order of importance. ... The Father is God; the Son is God; the Spirit is God — the Spirit equal in nature and substance to the Father and the Son. If the three Persons of the Godhead are each of them God, it does not follow that there are three Gods. That were impossible. There can be only one God, supreme and unique. Orthodox Christendom believes in three Persons in the Godhead, yet one God, indivisible and unique — the three Persons in the Godhead with one will, one purpose, each sharing to the full every thought and desire and purpose in the minds of the others.
The distinct role of the Spirit within the Trinity
Though equal in nature, each Person acts in a distinct way toward mankind. J. T. Mawson captures this beautifully with three prepositions:
J. T. MawsonTHE FATHER is the source of love and life, the spring of all good and blessing for men.
THE SON is the perfect expression of the Father, the Revealer of all this good and blessing to men.
THE HOLY GHOST is the One who, by His power and wisdom, interprets that which has been revealed, and makes the revelation a reality in men.
The three Persons in the Ever-blessed Godhead work together for the salvation of men, and if we keep in mind the three prepositions "for," "to," and "in" in this connection, they will help us to understand the relative position of Father, Son, and Holy Ghost in the carrying out of this gracious purpose.
F. B. Hole draws out the same distinction in slightly different terms:
F. B. HoleTo God the Father belongs initiative. All purpose, counsel, direction, are His. To God the Son belongs administration — the execution of the Divine purpose whether in creation, redemption, or judgment. To God the Holy Ghost belongs the energy all-pervading that, acting always in perfect harmony with the Father's counsels and the Son's administration, produces the desired effects whether upon matter in creation, or upon the souls and ultimately the bodies of saints in connection with redemption.
Synthesis
To say that the Holy Spirit is "the third person of the Trinity" is to affirm two things at once. First, He is a divine Person — not an impersonal force or abstract influence, but One who speaks, teaches, guides, can be grieved, and acts with sovereign will. Second, He is fully God — possessing every attribute of Deity (omnipresence, eternity, omniscience, omnipotence) and co-equal in nature with the Father and the Son. The word "third" indicates nothing about rank; it is simply the order Scripture uses when naming the three Persons together. Within the Godhead, the Spirit's distinctive work is to make real in us what the Father purposes for us and the Son has accomplished toward us — taking the things of Christ and bringing them home to the heart and conscience of the believer.