In dialoguing with Catholics about sola Scriptura, I am often challenged to “prove” that Scripture truly is the supreme authority in the church independent of any interpretation (or misinterpretation) to which it might be subject. I understand why Catholics would demand this; on their view — in which the Bible owes its existence and efficacy to the living tradition and teaching magisterium of the church (through which, of course, the Spirit guides into all truth) — such proof would logically be required since Scripture, for them, never stands sola.
However, the problem with this, as I have come to see, is that the demand to prove Scripture’s unique authority is, from a Protestant standpoint, a non-starter. That is to say, if sola Scriptura (which, by the way, does not mean that Scripture is the only authority in the church but rather the highest authority) is true, then by definition it is impossible to prove. In saying this, it might seem as though I am conceding that sola Scriptura is either untenable or false (or maybe even both). Such a conclusion would be mistaken, however, for in reality, recognizing the impossibility of proving sola Scriptura is the only possibility left to those who realize that when they read the Bible, they are being personally confronted by the living voice of God who speaks through its pages with undeniable majesty and power.
Karl Barth explains this well when he writes:
If we were to presume to attempt such a proof [of the supreme authority of Scripture] we should as it were confound ourselves; we should ourselves prove [by that very act], not its impossibility, but in the closest accord with the adversary whom we are supposed to refute, its possibility. To prove that the juxtaposition of the Word of God and Church tradition is not just a relative one as maintained, that it is not a distinction within the Church of the present itself, that the Word of God in the Bible encounters and continually confronts Church proclamation as a judicial authority, that the Bible as this supreme authority which addresses the Church is not at all the Bible that is already dogmatically and historically interpreted by the pope or the professor but the Bible that is not yet interpreted, the free Bible, the Bible that remains free in face of all interpretation—to prove that we should obviously have to put ourselves in a place above proclamation and the Bible, we should have to share the opinion that it is for us to make this relation clear, to order it one way or the other, and that we can establish the supremacy of the Word of God in this relation.
But then the Bible whose supremacy we could establish would obviously not be the free Bible which constitutes an effective court. It would obviously have become a Bible interpreted already in a particular way, a Bible made over to us and thus put as an instrument in our hands. To that degree, even though we could perhaps prove its supremacy, it would still be only an element in the Church of the present which we ourselves constitute. We shall thus be on our guard against attempting this kind of proof. It could only prove the opposite of what it is supposed to prove. At this point we can only point to a fact, and in view of this fact, with no more proof than before, lodge an objection. The fact is again the significance that the Bible actually has in the Church irrespective of all theories about its significance.
What Barth does here is retrieve the basic logic that the Reformers, particularly John Calvin, used when defending their commitment to Scripture as the supreme authority in the church. For Calvin, Scripture’s supreme authority — based on the conviction that Scripture is not simply “just a book” vulnerable to human manipulation but the living and active Word of God that will infallibly accomplish its divine purpose — is ultimately self-authenticating, and it must necessarily be so if it is, in truth, the Word of God. Argues Calvin:
Let this point therefore stand: that those whom the Holy Spirit has inwardly taught truly rest upon Scripture, and that Scripture indeed is self-authenticated; hence, it is not right to subject it to proof and reasoning. And the certainty it deserves with us, it attains by the testimony of the Spirit. For even if it wins reverence for itself by its own majesty, it seriously affects us only when it is sealed upon our hearts through the Spirit. Therefore, illumined by his power, we believe neither by our own nor by anyone else’s judgment that Scripture is from God; but above human judgment we affirm with utter certainty (just as if we were gazing upon the majesty of God himself) that it has flowed to us from the very mouth of God by the ministry of men. We seek no proofs, no marks of genuineness upon which our judgment may lean; but we subject our judgment and wit to it as to a thing far beyond any guesswork!
If, as sola Scriptura asserts, it is true that the Bible is the inspired means by which God addresses his church, and if that inspiration is unique to the Bible alone (as opposed to including within that realm of inspiration the living tradition and teaching magisterium of the church), then sola Scriptura cannot be proved without falsifying the very thing for which it stands.
To sacrifice a bit of nuance for the sake of clarity, let me put it this way. If biblical authority equals God’s own authority, then an attempt to “prove” the supremacy of biblical authority equals an attempt to “prove” the supremacy of God’s authority. But if we could “prove” the supremacy of God’s authority, then we would effectively be undermining it in the very act of doing so, for an authority that is supreme does not derive its supremacy from anything other than itself. If we could “prove” that God possesses supreme authority, then it would actually be our proof that possesses supreme authority rather than God! The same logic, then, applies to Scripture through which, from a Protestant perspective, God uniquely exercises his supreme authority. This is why Barth states that proof of God’s, and thus Scripture’s, supreme authority “could only prove the opposite of what it is supposed to prove”. This is the “impossible possibility” (to borrow a Barthian phrase from another context) of proving sola Scriptura: if it were possible to do so, then sola Scriptura would be false. On the other hand, if sola Scriptura is true, then it is impossible to prove.
Thus, for Barth, the Protestant “can only point to a fact” which is “the significance that the Bible actually has in the Church irrespective of all theories about its significance”. Does this mean that the Protestant system fails on account of its formal principle? In responding to a critic who considered the impossibility of demonstrating the supremacy of biblical authority “the Achilles’ heel of the Protestant system”, Barth offered this simple statement:
…the Protestant Church and Protestant doctrine has necessarily and gladly to leave his question unanswered, because there at its weakest point, where it can only acknowledge and confess, it has all its indestructible strength.
 Karl Barth, Church dogmatics I/1 (London; New York: T&T Clark, 2004), 259-260.
 John Calvin, Institutes of the Christian Religion, J. T. McNeill, ed. (Louisville, KY: Westminster John Knox Press, 2011), I.vii.5.
 Karl Barth, Church dogmatics I/2 (London; New York: T&T Clark, 2004), 537.