Infinity and the Sublime

In this paper we intend to connect two different strands of research concerning the origin of what I shall loosely call "formal" ideas: firstly, the relation between logic and rhetoric - the theme of the 2006 Cambridge conference to which this paper was a contribution -, and secondly, the impact of religious convictions on the formation of certain twentieth century mathematical concepts, as brought to the attention recently by the work of L. Graham and J.-M. Kantor. In fact, we shall show that the latter question is a special case of the former, and that investigation of the larger question adds to our understanding of the smaller one. Our approach will be primarily historical.