If I testify about myself, my testimony is not true. There is another who testifies in my favor, and I know that his testimony about me is true. You have sent to John and he has testified to the truth. Not that I accept human testimony; but I mention it that you may be saved. (John 5:31-34, NIV)
In this pericope, Jesus is appealing to the witness of him by his cousin, John the Baptist, as a tool to bring about the salvation of his Jewish listeners. Further, in this text, v. 34 uses a subjunctive “that you may be saved” (ἵνα ὑμεῖς σωθῆτε). Ινα is a “purpose clause” in Greek and the verb σωζω here appears in second person plural subjunctive passive form σωθητε. This cannot be a jussive subjunctive (grammatical mood of verbs for issuing orders/commands) within the context; instead, it is connotative. This being the case, it serves to refute TULIP, as it presents the Jews Jesus is addressing as having the ability to accept or reject the gospel, that grace can be resisted, and that salvation is conditional, not unconditional and strictly predestined.
Commenting on this text, Marianne Meye Thompson wrote the following:
Jesus turns first to invoke the witness of the Baptist (vv. 33-35). From the beginning of the Gospel, John “has born witness” (memartyrēken) and “bears witness” (martyrei, 1:15; cf. 5:32) to Jesus as the Son of God, the Lamb of God, the one on whom the Spirit has descended, the one sent by God (5:36-37; cf. 3:26-27). Ironically, while people “were willing” (ēthelēsate, 5:35) to rejoice in John’s light, they are not willing (ou thelete, 5:40) to come to Jesus, even though John was a lamp that was lit and went on shining precisely so that people would see the “true Light” (cf. 1:7-8). Because John’s human testimony (5:34) might seem inadequate to confirm that Jesus speaks on behalf of God, Jesus turns to a witness “greater than John’s” (v. 36). Even so, John’s human testimony about Jesus was intended to lead people to have and see the true light of life and “be saved” (v. 34). (Marianne Meye Thompson, John: A Commentary [Louisville, Ky.: Westminster John Knox Press, 2015], 133)
D.A. Carson, himself a Calvinist, offered the following comment on John 5:33-34:
Jesus’ hearers clearly need corroborative testimony, and to this Jesus now turns. The first witness he mentions is John the Baptist, who came into the world to bear witness to the true light (1:7). Not only had he borne witness to the delegation sent by the religious leaders in Jerusalem (1:19-28), but he had also publicly identified Jesus as the Lamb of God, the Spirit-anointed Son of God (1:29-34). The perfect tenses (‘You have sent . . . he has testified’) ‘present his testimony as an established datum’ (Barret, p. 264).
Although everything John the Baptist said about Jesus was true (cf. 10:40-41), Jesus himself did not, could not, accept human testimony – i.e., he himself did not depend on it to establish who he was in his own mind. The preceding verses (5:19-30) have emphasized Jesus’ intimate knowledge of the Father: he is able to say everything the Father gives him to say, he is able to do all that the Father does. As far as Jesus’ self-consciousness is concerned, the ‘another’ (v.32) who testifies in his favour is God himself. How could the witness of John the Baptist add to that? Jesus mentions the Baptist’s witness, not for his own sake, but for the sake of his hearers, that they may be saved. People are saved by believing in Jesus; John the Baptist’s witness may help them believe: that was its purpose (cf. 1:7), and hence Jesus’ appeal to such witness is justified. (D.A. Carson, The Gospel of John [The Pillar New Testament Commentary; Grand Rapids, Mich.: Eerdmans, 1990], 260, italics in original)
For an article presenting just some of the many problems of Calvinism, see An Examination and Critique of the Theological Presuppositions Underlying Reformed Theology