Infinity and the Sublime

TL;DR

This paper explores the historical connections between logic, rhetoric, and religious influences on mathematical ideas, revealing how religious convictions shaped formal concepts in mathematics and their relation to rhetorical strategies.

Contribution

It demonstrates that the influence of religious beliefs on mathematical concepts is a specific instance of the broader relationship between logic and rhetoric, using a historical approach.

Findings

Religious convictions impacted the development of mathematical ideas.

The relationship between logic and rhetoric is foundational to understanding formal concepts.

Historical analysis clarifies the influence of religious and rhetorical factors on mathematics.

Abstract

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.