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

Author:

Wheeler Samuel,Brenner William

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.

Publisher

University of Bergen Library

Reference21 articles.

1. Baker, G. and Hacker, P.M.S., 1985. An Analytical Commentary on The Philosophical Investigations, Vol. 2. Oxford, UK: Blackwell Publishers Ltd.

2. Bold, P., 2022. “Three Essays on Later Wittgenstein’s Philosophy of Mathematics: Reality, Determination, & Infinity.” PhD diss. University of North Carolina at Chapel Hill.

3. Diamond, C., 1991. The Realistic Spirit. Cambridge, MA: MIT Press.

4. Mounce. H.O., 1981. Wittgenstein’s Tractatus An Introduction. Chicago, IL: The University of Chicago Press.

5. Floyd, J. and Mühlhölzer, F., 2020. Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics: An Investigation of Wittgenstein’s Non-Extensionalist Understanding of the Real Numbers. Switzerland: Springer Publishing.

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