John 20:31 is the thesis and purpose statement of the Gospel of John: ταῦτα δὲ γέγραπται ἵνα πιστεύ[ς]ητε ὅτι Ἰησοῦς ἐστιν ὁ Χριστὸς ὁ υἱὸς τοῦ
θεοῦ, καὶ ἵνα πιστεύοντες ζωὴν ἔχητε ἐν τῷ ὀνόματι αὐτοῦ. My translation agrees with D.A. Carson’s understanding of this verse. I translate it this way: “These things have been written so that you might believe that the Christ is Jesus, and so that when you believe, you will have life in His name.” Most translations of this verse reverse the subject and predicate in this way: “These things have been written so that you will believe that Jesus is the Christ,” etc. The problem with the latter translation is that the definite article goes with “Christ” and not with “Jesus.” Typically, when you have a copula (a verb form of “is”) connecting two nouns in Greek, the one with the article is the subject, and the one without is the predicate, regardless of word order. That is Carson’s argument, and I agree with him. The difference may seem small, but the implications are fairly large for the understanding of John as a whole.
The translation “that Jesus is the Christ” implies that you could say many things about Jesus, and one of them is that He is the Christ. The translation I favor implies that you could claim many people to be the Christ, but that Jesus is the only one Who can be proven to be the Messiah. In other words, is John primarily written to Gentiles (which the translation “that Jesus is the Christ” favors), or primarily to Jews (which the translation “that the Christ is Jesus” favors)? On either supposition, of course, John does not ignore the other people group.
The theological implications run this way: believing that the Christ is Jesus (knowing what we know about the Old Testament expectations concerning the nature of the Christ) brings with it life in His name. I can’t think of a more important thing to believe in life and in death.