All the members of the Trinity are coexistent, co-eternal, and co-equal. God eternally exists in three Persons who are in complete unity. One God but three Persons. God has revealed Himself to us as Father, Son, and Holy Spirit.
In Matthew 28:19, as part of the Great Commission, Jesus said, “Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.” The Holy Spirit is often called the third Person of the Trinity because, in this “Trinitarian formula,” He is listed third.
The Spirit is also the third Person of the Trinity because, in the progress of revelation, He was the third to be revealed as an individual Person. In Genesis 1:2 the Spirit of God is hovering over the waters at creation. Later, the Spirit of the Lord would come upon a person (Samson, for instance, in Judges 13—16) to accomplish a specific task. However, these references would have been understood as “the power of God” rather than a specific personality who is God.
It is not until Jesus is on earth that we begin to understand the Trinity. The Father (the first Person) sent the Son (the second Person). However, the Son said that, when He left the world, He would send a third Person who was God—the Holy Spirit (John 14:16–17; 16:12–15). From Jesus’ words, it is clear that the Holy Spirit is not just the impersonal power of God but God Himself—a third Person who was not previously revealed. The Spirit is God, but He is neither the Father nor the Son. He is a third individual—a third Person.
When Christians use the terms first, second, and third in relation to the Persons of the Trinity, they are not suggesting that different Persons of the Trinity are more importance than others. Each Person is equally significant. In the words of the Athanasian Creed, written, as we think, by Athanasius, an archbishop of Alexandria in the fourth century AD, “We worship one God in trinity and the Trinity in unity, neither confusing the persons nor dividing the divine being. For the Father is one person, the Son is another, and the Spirit is still another. But the deity of the Father, Son, and Holy Spirit is one, equal in glory, coeternal in majesty. . . . And in this Trinity, no one is before or after, greater or less than the other; but all three persons are in themselves, coeternal and coequal; and so we must worship the Trinity in unity and the one God in three persons.”
As God exists, all three Persons are co-equal. However, as God has revealed Himself to us and as He interacts with us, each Person of the Trinity has taken on certain roles. The Spirit directs attention to the Son (John 16:14), and the Son directs attention to the Father (John 14:13). In this sense, also, the Holy Spirit is third.