John's statement of purpose is directly linked with Jesus' blessing upon those who have not seen and yet have believed (v. 29). John says, "therefore" (oun, left out of the NIV), while (men) Jesus did many other signs, these (tauta de) are written that you may believe. John refers to the Gospel as a whole, this book, and this entire sentence (vv. 30-31 are one sentence in the Greek) is appropriate for the whole Gospel, not just for the present chapter. The reference to the presence of his disciples is probably due to the crucial role their witness plays in the faith of those who come later. They had been with him from the beginning (15:27) and thus had received the full revelation. While many of Jesus' signs were done in the presence of others, the presence of his disciples is the crucial fact, for it is they who have believed and been enabled to, by the Spirit, understand their significance and bear witness to Jesus and Jesus' witness to the Father.
John's purpose is precisely to enable others to experience the blessedness that Jesus has just spoken of, which comes through faith. The two central titles for Jesus are Christ and Son of God, representing in this Gospel both the fulfillment of Jewish expectation and much more--the personal presence of God himself in our midst. The purpose (or result; hina can mean either) of this believing is to have life in his name. This life "belongs to the Father (5:26; 6:57) and the Son (11:25; 14:6), and is offered to men through Jesus' words (6:63; 10:10) and death (3:16; 7:39) on the basis of faith (3:16; 5:24; 20:31)" (Osborne 1984:176). Thus, it is the very life of God himself made available in the Son. It is in his name because it is in fellowship with him as he has made himself known (see comment on 1:12). He has brought life, but this life is not a gift separate from himself. Rather, it is a life in himself who, like the Father, is life itself (1:4; 5:26; 11:25; cf. Chrysostom In John 87.2). To live in his name is to live his own life, with its source in the Father, and therefore to live his pattern of life. This means to love as he loved (13:34; 1 Jn 2:6), obedient to God, totally trusting him and interpreting all the events in our own lives in the light of his divine presence. John expresses this same call--to share in God's life--at the beginning of his first letter. "The life appeared; we have seen it and testify to it, and we proclaim to you the eternal life, which was with the Father and has appeared to us. We proclaim to you what we have seen and heard, so that you also may have fellowship with us. And our fellowship is with the Father and with his Son, Jesus Christ" (1 Jn 1:2-3).
There has been much discussion about whether John is writing for non-Christians, that they might come to faith, or for Christians, that they might continue and grow in the faith. This difference is perhaps reflected in the two main readings in the manuscripts for the word believe. Some texts have an aorist tense (pisteusete) and some a present (pisteuete), only one letter distinguishing them from one another. The aorist could be rendered "begin to believe," and the present, "continue to believe." The manuscript support is fairly evenly divided between the two. The Gospel as it now stands contains elements that clearly have in mind someone who has not heard the story before (1:38) as well as other elements that assume readers (or hearers) do know the story (11:2; cf. 12:3). Furthermore, given John's dynamic view of faith (20:29), there is a sense in which every believer is to continue to grow in his or her faith. While it appears John's primary purpose was to encourage believers, there was probably also an evangelistic concern. Certainly the Gospel has proved quite valuable for both purposes!