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|A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967
Peano, unlike Poincaré, explicitly states the principle of induction as one of his postulates, with the aid of which he defines the integers. He is therefore in a position to prove the consistency of his postulate system.
Poincaré agrees with Peano that a group of postulates must be proved as consistent before the system is given a real meaning. He claims, however, that Peano's attempt to prove the contradiction has failed because it is circular.
Peano actually uses the induction principle in two ways: as a postulate and then as a rule.