|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._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Selected works of Giuseppe Peano Toronto 1973