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


  • Samuel Wheeler The University of Chicago
  • William Brenner Old Dominion University




Later Wittgenstein, Mathematics, Ludwig Wittgenstein


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 twofold: first, to bring out and elucidate the essentially riddle-like character of these problems; second, to show that the comparison with riddles does not reduce their solution to an exercise in bare subjectivity.

Author Biographies

Samuel Wheeler, The University of Chicago

Samuel J. Wheeler received his B.A. in Philosophy at Old Dominion University and is a PhD student in Philosophy at the University of Chicago. He is the author of "Defending Wittgenstein's Remarks on Cantor from Putnam" and "Wittgenstein on Miscalculation and the Foundations of Mathematics" published in Philosophical Investigations

William Brenner, Old Dominion University

William H. Brenner is Professor Emeritus at Old Dominion University and is author of Logic and Philosophy: An Integrated Introduction and Wittgenstein's Philosophical Investigations


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