(3) And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent.
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The term "know" implies intimate, experiential knowledge, not merely bookish or theoretical knowledge. Jesus Christ suggests that having an intimate relationship with the Father and Son causes us to become one with them. The only way we can do that is by living the way God does by faith. He walks—lives life—with those who agree with Him. The One who already had this unique relationship with God reveals to us the knowledge of how to do that.
Originally given to a spiritually faltering people, Amos 5:4 adds a vital command: "For thus says the LORD to the house of Israel: 'Seek Me and live.'" The word "seek" is not being used in the sense of "search" because God had already revealed Himself to them. Instead, it conveys the sense of "turn to Me," "seek to live as I do," "turn to My way of life," "seek to know Me in intimate detail."
In John 17:3, "eternal" is translated from the Greek aionis. Here, it deals not so much with duration of life, since by itself living forever would not necessarily be good. Rather, it implies "quality." Eternal life is the life of God, the way He lives life. To possess it is to experience a small measure of its splendor now.
Four times in this chapter (verses 6, 11, 12, and 26), Jesus uses the word "name" in reference to God. "Name" represents, identifies, signifies, and encompasses what He is revealing to us about God. It includes what He is in His Person, His attributes, and His purpose. God's name keeps, guards, and sustains us, both by our trusting what it signifies and then, through obedience, expressing what it means.
Psalm 9:2, 10 declares, "I will be glad and rejoice in You; I will sing praise to Your name, O Most High. . . . And those who know Your name will put their trust in You; for You, LORD, have not forsaken those who seek You." "Name" does not refer to what He is called or the sound of that name, but to what He is like in His nature and character. We can trust what He is. This has marvelous implications for us. Matthew 28:19-20 says:
Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age.
The word "in" in verse 19 can just as correctly be translated as "into," meaning that we are immersed into the name of the Father and Son. We now bear that name! They are God, and we are children of God. Baptism and the receipt of the Holy Spirit are the entrance into that name and all it implies! We have entered into the Family of God! Just as a son bears his father's name, God's name is our spiritual family name.
— John W. Ritenbaugh