This paper broaches ‘natural theology’ in terms of the conceptual systems through which revelation is understood, as opposed to questions regarding the sources of revelation. I do so by analysing Barth’s rejection of natural theology in terms of what it can mean to treat a logic of prior possibility as determining what revelation’s conditions of possibility must be. I begin by reading Emil Brunner’s ‘Nature and Grace’ alongside Ludwig Wittgenstein’s reflections on mathematical necessity in order to show that Brunner’s thinking of possibility subordinates the necessities of revelation to what Wittgenstein calls ‘the logical machine’. I then argue that Barth’s rejection of natural theology involves rejecting the workings of this machine and so rejecting the axiomatic force of prior possibility for theology. I conclude by tracing two consequences of this rejection, one related to creativity, the other to political crisis.