A number of sections of Eberhard Busch’s The Great Passion: An Introduction to Karl Barth’s Theology deal with Barth’s criticisms of natural theology.  In one section, Busch helpfully puts this in the context of Barth’s reaction to Nazism and his effort to trace the roots of violence and tyranny to the early modern period.  Busch summarizes:

“first the interpretation of the covenant of grace in terms of the creation, and then creation without reference to this covenant, and ultimately without any reference at all to God; the understanding of ‘nature’ as humanity’s mass of manageable things and then its negatability by humans; the understand of the human person without reference to the fellow person and then in terms of the animal - this entire pathway began, for Barth, in a theology that thought God without the human and the world, saw him in relation to creation as one not essentially connected to it.”

This produced a “double bookkeeping” theology:

“Certainly this theology spoke about God’s covenant of grace with humanity n Christ with regard to the complex of sin and forgiveness.  Nevertheless, in broad areas - in the doctrines of the state and of creation - this theology could not say much at all.  For these themes, it opened up other books, and its discourse, even when speaking about God, ignored the God who relates himself to us in grace.”  No man can serve two masters, and in this theology Barth saw divided service to a double master.

In short, “Natural theology thinks of God and his revelation and grace in terms of the ‘world,’ and the outcome is that natural theology does not really think of God and his revelation of grace, but of a godless, graceless, and inhuman world.”  Theology must instead, in Barth’s works, insist that “in faith in God’s particular revelation man sees God before he sees the general history of creation . . . the history of nature.”  This is Barth’s version of Calvin’s “spectacles.”