Brouwer’s Equivalence Between Virtual and Inextensible Order

Abstract

Brouwer’s theorem of 1927 on the equivalence between virtual and inextensible order is discussed. Several commentators considered the theorem at issue as problematic in various ways. Brouwer himself, at a certain time, believed to have found a very simple counterexample to his theorem. In some later publications, however, he stated the theorem in the original form again. It is argued that the source of all criticisms is Brouwer’s overly elliptical formulation of the definition of inextensible order , as well as a certain ambiguity in his terminology. Once these drawbacks are removed, his proof goes through.