His first question is whether a prolegomena is indeed necessary. Barth answers in the affirmative, but only after a lengthy argument.
First, Barth deals with the issue of prolegomena taking the form of apologetics. Should a theologian seek to argue for the faith on the basis of human reason, as a way to confound unbelievers and thus lay a rock solid foundation for dogmatics. Barth answers in the negative. For, to do so takes one away from the task of dogmatics itself, and takes unbelief far too seriously.
On the contrary, only other faith, or other belief ought to be taken seriously, that is that only heresy in which one can discern a true faith in the "other" should serious debate take place. And for heresy, Barth finds that only with the reformation does a true heresy become a real possibility for the church. Barth writes:
"That only since the reformation has heresy become a generally and fundamentally experienced problem. If there was nothing new formally, it was something quite new materially that the Evangelical Church of a Luther or Calvin should see heresy in the Papacy and Roman Catholicism of the 16th and 17th centuries and vice versa. It was then for the first time that the Church learned what is meant by divergent faith." (CD I.1 p. 35)That is, only with the divergence of Roman Catholicism and Protestant theology were there two divergent faiths that must deal seriously with one another. It is for this reason that Barth believes that only after the reformation is there a real need for a prolegomena to dogmatics.
Barth then moves to his second question, and that is of the possibility of a prolegomena to dogmatics. To illustrate this possibility, Barth plays his Evangelical way of thinking off of the Evangelical Faith's two sparring partners, the theology of modernists and the theology of Roman Catholics. These are the two "heresies" in which the Evangelical recognizes faith, a heretical faith, but nevertheless one which must be taken seriously.
On the one hand, Barth finds a problem with modernist (By which I take him to mean protestant liberalism, embodied most fully in Schleiermacher) prolegomena to dogmatics in that they find their foundation for the way of knowledge in dogmatics in an "anthropological prius." By this "anthropological prius" Barth is referring to a dogmatics based on a way of knowledge found in the fact of the existence of humans. The existence of humans becomes the basis for knowledge of the divine. That is, in fallen humanity, there is some "point of contact" with the divine. From this point of contact, one can then construct a dogmatics or true talk about God. Barth utterly rejects this notion of an "anthropological prius."
On the other hand, Barth finds a problem with Roman Catholic prolegomena to dogmatics in that they find their foundation for a way of knowledge in scripture, church tradition, and living Catholic teaching through the infallibility of the Pope. Barth takes issue with this foundation for true talk about God, in that he sees the free act of God and the reality of the Church bound up in the human institution of the Roman Catholic Church as a limitation of the true God. God is no longer free to act after being institutionalized and subjected to the Roman Catholic Church.
Therefore, Barth finds only one foundation for a way of knowledge of true talk about God, and that foundation is the Word of God itself. Now, the next section in CD will be an elucidation of Barth's doctrine of the Word of God, so I cannot speak fully on this doctrine at this moment. Yet, it is clear that for Barth, the Word of God is not merely equal to holy scripture, just as it is not bound up in Roman Catholic Church tradition or teaching. The Word of God is the free revelation of God to humans, it is an event. For, as Barth himself summarizes his thoughts on a prolegomena to dogmatics:
"The place from which the way of dogmatic knowledge is to be seen and understood can be neither a prior anthropological possibility [contra modernists] nor a subsequent ecclesiastical reality [contra Roman Catholics], but only in the present moment of the speaking and hearing of Jesus Christ Himself, the divine creation of light in our hearts." (CD I.1. p. 41).