Witigenstein and the Regular Heptagon

Abstract

The later Wittgenstein holds that the sole function of mathematical propositions is to determine the concepts they invoke. In the paper this view is discussed by means of a single example: Wittgenstein's investigation of the concept of a regular heptagon as used in Euclidean geometry (i.e., the Euclidean construction game with ruler and compass) and in Cartesian analytic geometry. Going on from some well-known passages in Wittgenstein’s Lectures on the Foundations of Mathematics, and completing these passages, it is shown that Wittgenstein’s view makes perfectly good sense and can be very well defended.