“What Line Can’t Be Measured With a Ruler?”: Riddles and Concept-Formation in Mathematics and Aesthetics

Abstract

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.