Most Bible students realize that most of the New Testament books are letters—epistolé in Greek and our "epistle," which is a written communication between parties. Paul's epistles, as well as those of James, Peter, John, and Jude, are written primarily to church congregations, although a few, such as those to Timothy, Titus, Philemon, and Gaius (III John), are written to individuals. Many consider the book of Hebrews to be an epistle, but it is technically a treatise (a systematic argument about a subject) with a letter-like conclusion.
A typical letter during New Testament times followed a fairly strict format. It began with the writer's name, followed by the recipient(s) and a greeting to him/her/them. The body of the letter ensued, and at the end, the writer closed with additional greetings and perhaps a date. Occasionally, other material is attached to the full salutation, either within or after it, but such material may not technically be part of the formal greeting (see, for example, II Peter 1:3-4). In many cases, the writer makes parenthetic remarks about the recipients (see, for example, I Peter 1:2).
Thumbing through the salutations of the epistles brings out a curious fact: The greetings are all essentially the same. Time after time, the authors write something akin to this from Romans 1:7: "Grace to you and peace from God our Father and the Lord Jesus Christ." Almost all of Paul's epistles follow this wording—perhaps with the word "mercy" thrown into the mix—and some of the other writers' greetings follow suit. This shows how standardized this part of the letter format was during the first century.
Of the four other epistle writers, James pens a workmanlike, "James, a bondservant of God and of the Lord Jesus Christ, to the twelve tribes which are scattered abroad: Greetings" (James 1:1). Peter's first epistle simply states, "Grace to you and peace be multiplied" (I Peter 1:2), to which he appends in his second letter, "in the knowledge of God and of Jesus our Lord" (II Peter 1:2). John dispenses with the standard greeting altogether in his first epistle (which may suggest that, like Hebrews, it is not technically an epistle), while in the second he writes one of the longest: "Grace, mercy, and peace will be with you from God the Father and from the Lord Jesus Christ, the Son of the Father, in truth and love" (II John 1:3). In his third letter, his greeting to Gaius is terse but kind: "To the beloved Gaius, whom I love in truth" (III John 1:1). Finally, like II John, Jude includes a longer greeting: "To those who are called, sanctified by God the Father, and preserved in Jesus Christ: Mercy, peace, and love be multiplied to you."
The most curious—and theologically significant—facet of these epistolary salutations is the wholesale absence of greetings from the Holy Spirit. In nearly every greeting, the writer sends greetings from God the Father and God the Son, Jesus Christ. A Bible reader brought up in traditional Christianity would expect that the so-called Third Person of the Trinity would get equal billing with the Father and the Son from the apostles, but the biblical text omits all mention of the Holy Spirit in terms of personal greetings to the churches. Is this just a mistake? An embarrassing omission? A slight?
If greetings from the Holy Spirit were absent in some but not all the salutations, we might make a case for any of these explanations, but because they are entirely absent among the greetings of twenty epistles (not counting Hebrews) from five apostles, they make an implicit theological point: The Holy Spirit sends no greetings because there is no Third Person in the Godhead to send them! Put simply, the Father and His Son are the only divine Persons, and in grace, mercy, and peace they send their personal greetings to the church. Not being an additional, distinctive entity, the Holy Spirit does not send any greetings.
The clearest biblical explanation of this truth appears in John 14, where Jesus Himself provides the correct understanding:
. . . I will pray the Father, and He will give you another Helper, that He may abide with you forever—the Spirit of truth, whom the world cannot receive, because it neither sees Him nor knows Him; but you know Him, for He dwells with you and will be in you. I will not leave you orphans; I will come to you. . . . If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him and make Our home with him. (John 14:16-18, 23)
Jesus teaches here that the Holy Spirit is not another personality but the divine essence of both the Father and the Son that comes to and resides in each of God's chosen sons and daughters.
Since Jesus Christ is the One who most often interacts with humans, the apostles single Him out most frequently as "the Spirit." In II Corinthians 3:17, Paul states this plainly, "Now the Lord is the Spirit. . . ." It does not get much clearer than that! The apostle also equates "the Spirit Himself mak[ing] intercession for us" (Romans 8:26) with "Christ who died, and furthermore is also risen, who is even at the right hand of God, who also makes intercession for us" (verse 34). The "Christ in you" statements (see Romans 8:10; Galatians 2:20; Ephesians 3:17; Colossians 1:27; etc.) also have this sense: The Spirit of the Son lives, abides, or continues with us.
Broadly, the Holy Spirit is the personality, mind, and power of God to do His will throughout His creation. But for those of us who believe and love Him, it is also the means by which the Father and the Son live in us, interact with us, empower us, and enable us throughout our developing relationship with them. In a way that we as humans cannot fully fathom, the Spirit is both of them in us, uniting us with them, as Jesus explains in His prayer in John 17:20-23:
I do not pray for these [disciples] alone, but also for those who will believe in Me through their word; that they all may be one, as You, Father, are in Me, and I in You; that they may be one in Us, that the world may believe that You sent Me. And the glory which You gave Me I have given them, that they may be one just as We are one: I in them, and You in Me; that they may be made perfect in one, and that the world may know that You have sent Me, and have loved them as You have loved Me.
Because the Father and the Son are fully united in all things, when Christ is in us, the Father is in us also, and we are thus united with both of them in spirit and growing to become united with them in character. There is no need for a Third Person of a Trinity. It is truly amazing what can be learned from realizing that we must live by every word of God—even what the salutations of the epistles do not say is instructive!