You hear it said that 1 Corinthians 4:6 teaches that Christian doctrine must be restricted to what it written in the Bible.
I have applied all this to Apollos and myself for your benefit, brothers and sisters, so that you may learn through us the meaning of the saying, “Nothing beyond what is written,” so that none of you will be puffed up in favor of one against another.
I think these Catholic commentaries are right when they argue that the context suggests a narrower application than the question of how Christian doctrine is determined (which actually has nothing to do with the context):
you might learn that one be not puffed up against the other, and above that which is written, against the admonitions given in the holy Scriptures of being humble: or against what I have now written to you, that we must strive for nothing, but to be the faithful ministers of God, and not seek the esteem of men.
Haydock, G. L. (1859). Haydock’s Catholic Bible Commentary (1 Co 4:6). New York: Edward Dunigan and Brother.
not to go beyond what is written: Paul cautions believers to stay within the limits of personal humility defined by the Scriptures. He is referring specifically to the string of OT warnings about boasting quoted earlier in the letter (1:19, 31; 3:19–20). Paul’s purpose here is to halt the damaging effects of arrogance in Corinth, as indicated by the clarification that follows. Interpretations of this verse that suggest Paul is restricting the basis for Christian doctrine and morals to what is explicitly set forth in the books of the Bible (sola Scriptura) are misleading and untenable. Nothing in the context points to such a broad concern, and in any case Paul insists elsewhere that even the inspired preaching of the apostles is on a par with the written word of God (1 Thess 2:13; 2 Thess 2:15; 3:6).
The Ignatius Catholic Study Bible: The New Testament. (2010). (p. 289). San Francisco: Ignatius Press.
That last reference, 2 Thess. 3:6 provides an important contrast. If we apply the same hermeneutic approach to this verse as the one applied to 1 Cor. 4:6 to legitimize “the Bible alone,” then 2 Thess. 3:6 similarly legitimizes “tradition alone” and we have a contradiction. But if we don’t bring to our reading of either verse considerations about formal principles and allow the respective contexts to point us to a narrower scope of intended meaning, then the contradiction disappears. St. Paul wasn’t saying “Bible alone” in the one verse or “tradition alone” in the other.
Also, 2 Thess. 2:15 deserves notice here.
So then, brothers and sisters, stand firm and hold fast to the traditions that you were taught by us, either by word of mouth or by our letter.
The immediate context of this passage, in which St. Paul discusses the gospel, salvation and “belief in the truth,” suggests a wider, more general applicability than the aforementioned verses, and is more directly tied to what in later times would be called a formal principle. And here we have direct instruction from an apostle to “hold fast to the traditions” he taught them regardless of whether he did so in written or oral form. This, then, was the formal principle of the early Church: apostolic authority. As witnesses by St. Irenaeus a century afterward, this principle was still operative in the bishops who held this authority by succession. And this was the understanding of all orthodox Christians until 1517.