 The need for a specification of infinite sets is crucial in the discussion of the related well-ordering problem. It also affects the related issue of the classification of discontinuous functions and analytically representable functions of real variables, tackled by the French semi-intuitionists Borel, Baire and Lebesgue. At the same time, they held the view that a mathematical entity (like an infinite set or a function) exists only insofar as it is “nameable by a finite number of words”, against the platonistic views of Hadamard and Zermelo (see Borel et al. 1905).