On Blumenberg’s Mathematical Caves, or: How Did Blumenberg Read Wittgenstein’s Remarks on the Philosophy of Mathematics?

In the chapter “Im Fliegenglas” from his book Höhlenausgänge, Blumenberg refers to Wittgenstein’s views on mathematics, logic, and mathematical proof on several occasions. One of Blumenberg’s key points concerning Wittgenstein’s famous statement that philosophy’s aim is to show the fly the way out of the fly-bottle is discussed with a rather surprising example: a geometrical puzzle that involves decomposing a rectangle. Although Blumenberg is not known for developing a comprehensive theory of the philosophy of mathematics or mathematical practices, this chapter analyzes Blumenberg’s reflections on mathematics and mathematical concepts, which were prompted by his reading of Wittgenstein. I argue that this distinctive approach allows for the identification of an original position held by Blumenberg with regard to mathematics and its practices. This position emerges not only from an analysis of how Blumenberg interprets Wittgenstein’s views, but also from an examination of Blumenberg’s conception of mathematical proofs.