 A positive by-product of Richard’s paradox in Brouwer’s work (1907, p. 149) is the notion of denumerably unfinished set, i.e., a set in which we can determine only denumerable subsets of elements, but where these denumerable subsets do not exhaust the given set, so that one can immediately produce new elements of the set from any given denumerable such subset. Typical examples of denumerably unfinished sets are the totality of countable ordinals, the points of the continuum, and in particular, as could be shown using Richard’s paradox, the set of all definable points of the continuum (1907, p. 150). Brouwer considers Burali-Forti’s contradiction not as a mathematical paradox, since it concerns a logical structure (the collection of all ordinals), which is not a well-defined mathematical object and has no proper mathematical content. Mathematically speaking, the contradiction can be avoided by denying that the largest well-ordered type has a successor order type (p. 153; this is analogous to Bernstein 1905b).