Hermann Broch: Briefe: Dokumente und Kommentare zu Leben und Werk

Modernism, Fiction and Mathematics

“…Rather, the 'unquestionable fruitfulness of the ideal elements' enhances the discipline. 73 With the notion of useful yet empirically non-existent ideal formations, Cassirer reflects Nietzsche's view of mathematics as a necessary fiction. However, he also proposes that since the concept of number expresses the rational method in general, the mathematical crisis impacts on the very foundations of knowledge: as modern maths limits itself to working inside its self-created structures, it is '[f]or the purposes of knowledge of nature, in the positivistic sense of the word, [.…”

“…a constant danger'. 74 Turning away from physical reality and 'let[ting] the empirical determinateness of being disappear into the freedom and caprice of thought', the discipline at the foundation of knowledge is at the core of a general epistemological crisis. 75 Hans Vaihinger, one of the first academic philosophers to engage with Nietzsche's work, further examines the relation between mathematical ideals and fiction in The Philosophy of 'As If', published in 1911. Claiming that 'all ideals, logically considered, are fictions', Vaihinger argues that the ideal elements of mathematics, such as 'negative numbers, fractions, and irrational INTRODUCTION 17 and imaginary numbers', are paradoxical fictions and that mathematics as a whole is 'based upon an entirely imaginary foundation, indeed upon contradictions'.…”

“…72 Given what he calls the self-restriction of the scientific sphere, Broch claims that it is the role of literature to cover the areas no longer encompassed by science, namely the irrational aspects of life. 73 Literature can achieve this since, so he argues, it does not rely on language as the sciences do, but exists in the Not for distribution or resale. For personal use only.…”

“…When modern literature has to account for the irrational but also for the spirit of scientific thinking, it unities these opposed aspects and can satisfy human beings' 'desire for the totality of the worldview'. 74 In Broch's fictional and non-fictional writings on language, literature and science that he develops over several decades and that include modifications and contradictions, it can be challenging to locate mathematics -a structural science that is part of many scientific endeavours but in its abstractness can also be close to the creative possibilities of literary fiction. That it takes an unstable position among the two cultures and moreover veers between formalist and intuitionist conceptions indicates that Broch uses maths not as a fixed model but as a field in which controversies crystallise and that therefore lends itself to exploring change in the early twentieth century.…”