Dictionary of Arguments

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A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967

46
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.
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47
Peano actually uses the induction principle in two ways: as a postulate and then as a rule.


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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.

Peano I
Giuseppe Peano
Selected works of Giuseppe Peano Toronto 1973


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Ed. Martin Schulz, access date 2018-11-15
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