 Poincaré is often invoked in the philosophy of mathematics because of his discussions of the paradoxes and his diagnosis, which became the vicious circle principle. According to Poincaré’s pragmatic and anti-Platonist standpoint, mathematical definitions and proof-procedures should be limited to predicative ones. Herman Weyl (1918) was the first to propose a predicative continuum, while later Lorenzen (1955, 1965) and, especially, Kreisel (1960) and Feferman (1964) each tried to find predicatively definable sets following Poincaré’s rough sketch. Hintikka (2012) argues that logicians and mathematicians did not know how to implement Poincaré’s insight because they did not pay enough attention to the quantifier dependence and independence and proposes a solution with IF-logic. Poincaré’s critical remarks about the logicist project and about the new logic in general have been evaluated many times and continue to be discussed in the literature and to inspire those with sympathy towards intuitionistic or Kantian points of view (Cassirer 1910; Dingler 1931; Folina 1992; Goldfarb 1988; Heinzmann 1995). Although the influences on Wittgenstein’s work are notoriously difficult to interpret, there are clearly evident similarities to Poincaré’s fundamental views (Rodych 2011).