Proofs versus experiments

wittgensteinian themes surrounding the four-color theorem

Gisèle Dalva Secco

Luiz C. Pereira

pp. 289-307

in: Marcos Silva (ed), How colours matter to philosophy, Berlin, Springer, 2017

Abstract

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970s, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken's procedure for the proof and a reconstruction of Thomas Tymoczko's argument for the novelty of 4CT's proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the "characteristic Wittgensteinian invention" (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem.

Cited authors

Wittgenstein Ludwig