We have established that the aorist tense form is probably the most origina reading herel. So does that prove that John’s Gospel is meant to be evangelistic rather than (though not mutually exclusive to) building up readers in the faith? Let me put it blutnly- no! The tense of the verb alone will not tell you if the type of belief is initial or continual. The tense-form, either aorist or present, does not give us any grounds for supposing that John is talking about belief caused by evangelism (i.e., conversion) or belief reinforced through teaching (i.e., discipleship). The Evangelist can use either tense-form of pisteuo to signify coming to faith or continuing in the faith. Furthermore, the difference between the aorist and present tense-forms is not temporal, but aspectival. The aorist is perfective and views an action from an exterior point of view, while the present is imperfective and provides an interiorized perspective. Concerning the aspect of subjunctive verbs, Constantine Campbell notes: ‘Whereas the present subjunctive may be found giving expression to proverbial and general statements, due to its imperfective aspect, the aorist subjunctive typically portrays events that are particular.’ The present tense-form highlights the general state of believing not the persistence of belief. That said, the aorist tense-form is arguably ingressive (i.e., it depicts the entrance or beginning of a new action) when the perfective aspect is combined with a stative lexeme (i.e., pisteuo means the state of believing), so that pisteusete in this case is more likely to mean ‘coming to belief’.
The fact remains that whether John was written to evoke faith or reinforce faith must be determined by other contextual factors relating to the Fourth Gospel. On the one hand the Gospel of John seems to assume a certain degree of familiarity with the life story of Jesus by readers/auditors that one would expect among a Christian audience (see esp. 1:32 [= Mark 1:9-10]; 3:24 [= Mark 6:17]; 6:70 [= Mark 3:13-15]). It is difficult to imagine the rancorous polemic against ‘the Jews’ in 8:31-59 as inviting Jews to join a movement that denounces them as demonic. Then again one cannot help but notice that John is really pressing his case, through signs and witnesses, with apologetic ardor and evangelical ethos, that Jesus is the Messiah, the Son of God. People like Andrew, Nathanael, the Samaritan woman, and Martha are paradigmatic examples of people who come to faith in Jesus as the Messiah and the implied audience is urged to emulate them. In addition, the goal of believing in 20:31 is ‘life’ (zoe) and life in the Fourth Gospel is what is received through believing in and coming to Jesus which speaks to an evangelical purpose (3:15-16, 36; 4:14; 5:24, 39-40; 6:40, 47; 17:3). Ultimately it is difficult to restrict the Gospel to a single purpose for either evangelism or discipleship. If the Gospel of John was written amidst a loose network of fellow Christ-believers who were still in contact with Jewish circles (though not necessarily an isolated and introspective ‘Johannine community’), then there is a high probability that at some level the Gospel was composed for an evangelical utility among the Jews and to also encourage believers in their faith despite Jewish objections to their beliefs. Similarly, the Evangelist might have intended his account of Jesus to circulate widely among believers in other places and perhaps even among non-believers too. In which case, we do not have to choose between a believing or unbelieving audience. We can say more confidently that the Gospel of John can certainly function to both strengthen disciples in their faith and to invite people to faith in Jesus.
 Note the similar caution by G.R. Beasley-Murray, John (WBC; Waco, TX: Word, 1987), 387.  Dodd, Interpretation of the Fourth Gospel, 9; Carson, Gospel according to John, 662.
 Constantine R. Campbell, Verbal Aspect and Non-Indicative Verbs (New York: Peter Lang, 2008), 56.
 Constantine R. Campbell, Basics of Verbal Aspect in Biblical Greek (Grand Rapids, MI: Zondervan, 2008), 87-88.
 Richard Bauckham, ‘John for Readers of Mark,’ in The Gospels for All Christians, ed. R. Bauckham (Grand Rapids, MI: Eerdmans, 1998), 147-71.
 But note Ben Witherington’s (John’s Wisdom: A Commentary on the Fourth Gospel [Louisville, KY: Westminster John Knox, 1995], 226) remark: ‘Despite all the polemics, there is no indication that the community had given up its witness or some hopes of its success even in the synagogue, despite rejection, ejection, and persecution. Jesus and his followers still longed for all sorts of people to be drawn to the Christ and so become children of light.’
 F.F. Bruce (The Gospel & Epistles of John [Grand Rapids, MI: Eerdmans, 1983], 395) stated: ‘Probably we are not shut up to two mutually exclusive alternatives, regardless of the reading adopted: John’s record has the power to awaken new faith and to revive faith already awakened.’ Carson (Gospel according to John, 663) comments: ‘Even if John’s purpose is primarily evangelistic, it must be admitted that throughout the history of the church this Gospel has served not only as a means for reaching unbelievers but as a means for instructing, edifying and comforting believers. Still, one must not confuse purpose with result. A modern evangelist aiming at the conversion of hearers may still find that Christians who attend his ministry are greatly edified. John’s purpose in writing was to evangelize; the impact of his Gospel, i.e. the result of his writing, has far exceeded any hope he could have entertained.’ For Painter (Quest, 104): ‘Jn is a church book, written for those who believe, to enable faith to grow so that the Johannine community might, not only survive, but fulfil God’s purpose for it in the world. Thus Jn is a missionary document in the sense that it gives expression to a theology of mission for the believing community. The Johannine community is commissioned to perpetuate the mission of Jesus to the world. In order to do this it was necessary to bind the believers to the revelation of God in Jesus and it was to fulfil this purpose that Jn was written.’
 Cf. Edward M. Klink, ‘The Gospel Community Debate: The State of the Question,’ CBR 3 (2004): 60-85; idem, The Sheep of the Fold: The Audience and Origin of the Gospel of John (SNTSMS 141; Cambridge: CUP, 2007); Michael F. Bird, ‘Bauckham’s The Gospels for All Christians Revisited,’ EJT 15 (2006): 5-13.