Infinity and the Sublime

In their recent work, L. Graham and J.-M. Kantor discuss a remarkable connection between diverging conceptions of the mathematical infinite in Russia and France at the beginning of the twentieth century and the religious convictions of their respective authors. They expand much more on the Russian side of the cultural equation they propose; I do believe, however, that the French (or rather ‘West European’) side is more complex than it seems, and that digging deeper into it is worthwhile. In this paper I shall therefore broaden the path laid out in Graham and Kantor’s work, by connecting two different strands of research concerning the origin of what I loosely call ‘formal’ ideas: firstly, the rich but complex relation between logic and rhetoric throughout European cultural history, and secondly, the impact of religious convictions on the formation of certain mathematical and scientific ideas during Renaissance and Early Modernity, especially but not exclusively in France.