There are several of ways to demonstrate that 1 Corinthians 4:6 can't rescue sola scriptura from the realm of myth. First, note that none of the Reformers attempted to use this verse to vindicate sola scriptura. In fact, John Calvin says Paul's use of the phrase "what is written" is probably either a reference to the Old Testament verses he quotes within his epistle or to the epistle itself (Commentary on 1 Corinthians 4:6). Not only did Calvin not see in 1 Corinthians any support for sola scriptura, a theory he vociferously promoted, he regarded the verse as obscure at best and of negligible value in the effort to vindicate Protestantism.
Some commentators see in 1 Corinthians 4:6 an allusion to "what is written" in the Book of Life (Ex. 32:32-33, Rev. 20:12). This is quite possibly what Paul had in mind, since the context of 1 Corinthians 4:1-5 is divine judgment (when the Book of Life will be opened and scrutinized). He admonishes the Corinthians against speculating about how people will be judged, leaving it up to "what has been written" in the Book of Life. Although that interpretation of the text is a possibility, being consistent with the rest of Scripture, it is by no means certain.
What is certain is that Paul, in saying, "do not go beyond what is written," was not teaching sola scriptura. If he had, he would have been advocating one of four principles, which are inconsistent with the rest of his theology: (1) Accept as authoritative only the Old Testament writings; (2) accept as authoritative only the Old Testament writings and the New Testament writings penned as of the date Paul wrote 1 Corinthians (circa A.D. 56); (3) accept as authoritative orally transmitted doctrine only until it has been reduced to writing (scripture) and only while the apostles are alive, then disregard all oral tradition and adhere only to what is written; or (4) the most extreme position, accept as authoritative only doctrine that has been reduced to writing.
The difficulties with these options are immediately clear. No Protestant would agree with option one, that the Old Testament is a sufficient authority in matters of doctrine. Nor would he accept option two, for this would mean all New Testament books written after the year 56 would not qualify under the 1 Corinthians 4:6 guideline. Hence, John's Gospel, Acts, Romans, 2 Corinthians, Galatians, Ephesians, Philippians, Colossians, Philemon, Titus, 1 & 2 Timothy, Hebrews, James, 1 & 2 Peter, 1, 2, & 3 John, Jude, and Revelation would all have to be jettisoned as non-authoritative.
Option three fails because in order for sola scriptura to be a "biblical" doctrine there must be, by definition, at least one Bible verse which says Scripture is sufficient, or that oral Tradition is to be disregarded once Scripture has supplanted it, or that Scripture is superior to oral Tradition. But there are no such verses; and as we'll see, 1 Corinthians 4:6 is no exception.
Option four is likewise untenable because it contradicts Paul's express command in to "Stand fast and hold firm to the traditions that you were taught, either by an oral statement or by a letter of ours" (2 Thess. 2:15). Thus, for 1 Corinthians 4:6 to support the theory of sola scriptura, Paul would have been talking out of both sides of his mouth, on one side demanding adherence to the written word only, and on the other urging fastidious adherence to both written and oral tradition.
And then there's that small matter of the unity of doctrine among the apostles. If Paul had been promulgating sola scriptura in 1 Corinthians 4 he would have been in conflict with the practice of the rest of the apostles. Most of the apostles never wrote a single line of Scripture; instead they transmitted the deposit of faith orally. Did their oral teachings carry any less weight of authority than the written teachings of Paul or Peter or John?
None of the other apostles taught sola scriptura. In fact, John said, "I have much to write to you, but I do not wish to write with pen and ink. Instead, I hope to see you soon when we can talk face to face" (3 John 13). Why would the apostle emphasize his preference for oral Tradition over written Tradition (a preference he reiterates in 2 John 12) if, as proponents of sola scriptura assert, Scripture is superior to oral Tradition?
The already flimsy case for sola scriptura is further weakened by Paul's comments in 1 Corinthians 11:2 where he praises the Christians in Corinth for holding fast to the traditions just as he had handed them on to them. It's clear from the context that he was referring to oral Tradition because the Corinthians had as yet no New Testament Scriptures, 1 Corinthians being the very first letter Paul had sent them. Prior to this letter all his teaching had been oral.
The same is true in the case of the Ephesians to whom Paul said, "I did not shrink from proclaiming to you the entire plan of God" (Acts 20:27). This statement undercuts sola scriptura. Paul remained in Ephesus for over two years teaching the faith so diligently that "all the inhabitants of the province of Asia heard the word of the Lord" (Acts 19:10), yet his epistle to the Ephesians is a scant four or five pages and could not even begin to touch upon all the doctrines he taught them orally."