 Poincaré was strongly influenced by and attuned to the French philosophical scene, which refers to the Kantian tradition to show the limits of methodological positivism. Members of the so-called Critique de la science movement (Benrubi 1928), which includes members of the “Boutroux Circle” (Nye 1979) advocate a mixture of positivism and Neo-Kantianism. They criticize both Comte’s determinism and Kant’s static view of the mind’s structure. According to Poincaré, mathematics requires intuition not only in the context of discovery but also in the context of justification, especially in arithmetic and logic. So it is not surprising that Poincaré was discussed in German philosophical circles in the Kantian tradition, for example by Ernst Cassirer (1910), Ilse Rosenthal-Schneider (1914), who is a disciple of Alois Rhiel, and Moritz Schlick (1918). Thus, Poincaré was taken to be one of the Neo-Kantian precursors of logical positivism. However, unlike Kant, the arithmetical “pure intuition” Poincaré introduces is intellectual in character and Poincaré does not in the least solve the problem of the unity of spontaneity and receptivity by the introduction of a pure sensibility. Rather, he changes the terms of the Kantian contrast, emphasizing the balance between exactness, that which is common to many minds and is transmissible by discourse, and subjective acquaintance, which is intransmissible sensation. He expresses this difficult balance in a formula well known due to its popularization by Einstein: