Readers interested in this topic will enjoy this summary by Andrew Wilson of a recent lecture by Simon Gathercole on this issue (Gathercole is a NT scholar always worth reading).

Gathercole argues that the inclusion of the four gospels we have in the canon is far from arbitrary. Wilson writes in one place:

His argument is effectively threefold: (1) the apostolic preaching about Jesus, from the beginning, involved four key elements; (2) all four of the canonical gospels have these four elements in common; and (3) the extracanonical gospels do not, and in most cases do not clearly have any of them. These four key elements, identified by Paul in the mid fifties and clearly representing an even earlier tradition, are summarised in 1 Cor. 15:3-4 – (i) the identity of Jesus as the Christ, anointed by the creator God of Israel, (ii) his fulfilment of the Jewish Scriptures, (iii) his effective atoning death on behalf of others, and (iv) his bodily resurrection from death. These four elements, Gathercole argues, are the key constituent parts of the apostolic preaching from the start of the Christian movement, and therefore form the regula fidei against which subsequent accounts of “the gospel” are judged.