 I am grateful to Dirk van Dalen and Göran Sundholm for discussions of some of the issues involved. Helpful comments by the editors and Rosalie Iemhoff led to various improved formulations, corrections, and clarifications. Van Dalen kindly granted permission to quote from materials in the Brouwer Archive (at Utrecht at the time, now at the Noord-Hollands Archief in Haarlem). Thanks also to van Dalen and Eckhart Menzler-Trott for their search for Bernays’ letter to Brouwer, and to Sundholm and Michael Hegarty for a copy of de Iongh 1949. In  section 3.6  I have drawn on van Atten 2004a; I thank the Association for Symbolic Logic for granting permission to do so.