I'm currently working through the Gifford Lectures of James Barr, who is looking at the notion of Natural Theology and asking the question of whether or not the Bible approves of Natural Theology. Prior to reading Barr's Gifford Lectures, I read the Gifford Lectures of Karl Barth. I am happy to say that the conclusions that I came to as I read through Karl Barth are the same conclusions that James Barr comes to in his book.
At the beginning of his career as an Old Testament Scholar he was sympathetic with the Barthian rejection of Natural Theology, however, in examining the arguments advanced by Barth and Barthian theologians he came to the conclusion that "His exegesis, however we may evaluate it in general, was thus selectively and tendentiously applied, magnifying the elements which fitted with the needs of his theology, and minimizing those which his theology opposed. (Barr, Biblical Faith and Natural Theology, p. 136)". A couple of pages earlier he notes that "Barth's apparent biblical emphasis and rejection of natural theology was in part a matter of appearance rather than of reality. His theology was at bottom a dogmatic-philosophical system, in which the biblical exegetical foundation, however many pages it occupied was logically incidental. (Ibid., p. 131)"
On the same page he notes a problem with Barth, which is also a problem for Van Til, and presuppositionalism in general. "Revelation was central and must be accepted, but there were no real arguments to be offered why any particular claims to revelation should be believed. (Ibid., p. 131-32)" In other words, we are obligated to simply believe revelation. However, it seems that we are permitted to ask, "which revelation claim?" (i.e. - the Koran, the Jewish interpretation of the Old Testament, The Book of Mormon).
A further problem, which Barr notes a little bit later in the book is, how does Barth, and, consequently, how do we, know that HIS interpretation of the Bible is the RIGHT interpretation of the Bible? Especially when he claims to be simply espousing the reformed view of theology, and yet, his claims about Natural Theology clash with the claims of John Calvin, and other Calvinists such as Charles Hodge. Who holds the true interpretation of scripture? This same problem seems to apply equally to Van Til and presuppositionalism in general. On the question of Interpretation Barr notes that "the more we stress the importance of interpretation, the more we render probable the influence of something like natural theology. Influenced by the dialectical theology, people have been inclined to think of interpretation as something that followed and expounded the contours of revelation without going in any way outside this narrow channel of thought. Interpretation, seen in this way, not only interprets revelation but interprets it solely by the use of categories which themselves derive from revelation and are internal to it. Some of the peculiar contortions of modern interpretative theory are probably half-conscious attempts to demonstrate this. But it would really be very strange if there was interpretation which used no categories whatever that were external to the material being interpreted. (Ibid., 150)" Barr goes on to show that, as he has already clearly demonstrated in previous chapters, that the Old Testament is chock full of Natural Theology of some sort.
So far I have been thoroughly enjoying Barr's cautious approach to the question of Divine written revelation, and the notion of Natural Theology.