Some have 'solved' this seeming discrepancy by arguing that Matthew's account of the Commission represents a later development, i.e. it represents the practice of the church at a subsequent period in time. According to this approach there was no reference to a Trinitarian baptism by Jesus before his ascension. The Trinitarian 'formula' came to be used increasingly as the church developed its theology. If, as some have argued (e.g. Lewis An ), Jesus commissioned his disciples to baptise in his name and not in the name of the Trinity, the change represents a later departure by the church from Jesus' express instruction, a departure so radical that it not only requires but demands a satisfactory explanation. In fact there is no evidence either that the initial commission required baptism in the nameof Jesus, or that the initial commission was not in the name of the Trinity. It is simply supposition.
It is significant that those who see a discrepancy frequently speak of 'the Trinitarian formula' and contrast it with the 'formula' as we have it on the lips of Peter at Pentecost and in connection with other references to baptism in the Book of Acts. But the word 'formula' seems to be particularly inappropriate to describe either words used by Jesus or words used by the Apostles in those very early days of the church. It is a loaded word the very use of which has the effect of pre-empting discussion. It predetermines the outcome. Carson comments, "The term 'formula' is tripping us up. There is no evidence… that the church regarded Jesus' command as a baptismal formula, a liturgical form the ignoring of which was a breach of canon law. The problem has too often been cast in anachronistic terms. E Riggenbach (Der Trinitarische Taufbefehl Matt 28.19 [Gütersloh:C Bertelsmann, 1901]) points out that as late as the Didache, baptism in the name of Jesus and baptism in the name of the Trinity coexisted side by side: the church was not bound by precise 'formulas' and felt no embarrassment at a multiplicity of them…" The Expositor's Bible Commentary
Whereas Carson is commenting on the Trinitarian 'formula' Calvin makes a similar point commenting on the 'formula' in Acts. He asks the question, "was Peter entitled to change the form prescribed by Christ?" In answer he says, "In the first place we must hold that Christ did not give the apostles magic words to be used for incantation… Then again I maintain that Peter is not speaking in this passage of the form of baptism but simply declaring that the whole efficacy of baptism is contained in Christ; although Christ cannot be grasped by faith without the Father by whom He was given to us and the Spirit by whom he renews and sanctifies us… The answer consists simply in this ,that it is not a fixed formula that is being dealt with here, but the recalling of the faithful to Christ, in whom alone we obtain all that baptism prefigures to us." The Acts of the Apostles 1-13 Expositor's Bible Commentary Expositor's Bible
It is an assumption that either Jesus or Peter or Paul were giving precise words to be used at baptism. We cannot be sure. But it is just as likely that they were indicating the significance of baptism. Christian baptism signifies, on the one hand, the redemption which is the work of all three Persons of the Trinity and, on the other hand, that Jesus Christ is the door through which the believer passes to enter into that redemption. Father, Son and Spirit have decreed that it is through the name of Jesus that salvation is bestowed upon men and women.
Presumably the same can be said of theLord's Supper. We are told, for example that Jesus "took the cup, gave thanks and offered it to them, saying, 'Drink from it all of you. This is my blood of the covenant, which is poured out for many for the forgiveness of sins '"(Matt 26.27f). Are Jesus' words here a 'formula' which must be used prior to the distribution of wine at the Lord's Supper? If when distributing the wine we do not use the phrase "blood of the covenant" – a crucial explanatory element of the meal – is there a conflict? The word 'formula' is inappropriate.