 While it has been stressed by all commentators that Poincaré’s concerns with the foundations of mathematics are very different from those of the logicians, there is no unanimity on the focus of the dispute. Emile Boutroux and Warren Goldfarb claim that Poincaré is condemning the “logical” point of view for not providing psychological conviction (Boutroux 1914; Goldfarb 1985), while Detlefsen and Heinzmann argue for a difference at the epistemological level rather than a psychological one (Detlefsen 1992, 1993; Heinzmann 1995). In a famous response to Russell, Poincaré refuses to consider logic or epistemology independently from psychology (Poincaré 1909: 482). It would be false, however, to believe that he thus conflates logic and psychology. Indeed, Poincaré does not use the term psychology in the modern sense, but rather in all situations where he wants to emphasize the dimension of understanding, in particular its historical elements, which he contrasts with the mere correct logical exposition of the result. It is therefore not surprising that, according to Poincaré, mathematics requires intuition, interpreted as an element of understanding, not only in the context of discovery, but equally in the context of justification. As we have already seen, in arithmetic pure intuition is necessary to justify the complete (or mathematical) induction principle. It should also be noted that the term “intuition” is quite ambiguous, a fact that is well known and explicitly discussed by Poincaré himself. In The Value of Science, he distinguished three kinds of intuition: an appeal to sense and to imagination, generalization by induction, and intuition of pure number—whence comes the axiom of induction in mathematics. The first two kinds cannot give us certainty, but, he says, “who would seriously doubt the third, who would doubt arithmetic?” (Poincaré 1905b: 33; 1913b: 216).