This work brings the critically realistic interpretation of Barth's dialectical theology into conversation with the modern dialogue between science and theology. Philosophy of science, philosophy of mathematics and logic, and considerations of the problem of rationality raised in the science and theology dialogue are brought to bear upon Barth's theology in an attempt to explicate the rationality of his dialectical method. Its deep and abiding radical nature and character are lifted up, emphasized, and explored. The results of this study are then used to answer some long-standing criticisms of Barth. What emerges are an understanding of how Barth uses philosophy and why he declines to do philosophy. La Montagne opens the way for Barth scholars to enter into the dialogue between theology and science.