Brouwer and cardinalities

This note is a somewhat personal account of a paper that L.E.J. Brouwer published in 1908 and that dealt with the possible cardinalities of subsets of the continuum. That paper is of interest because it represents the first time that Brouwer presented his ideas on foundations in an international forum.I found Brouwer’s notions and arguments at times hard to grasp if not occasionally perplexing. I hope that this note contributes to a further discussion of the definitions and reasonings as presented in Brouwer’s paper.