Philosophy Dictionary of ArgumentsHome
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| Induction: Induction in logic is a type of reasoning in which we draw general conclusions from specific observations. It is the opposite of deductive reasoning, where we draw specific conclusions from general premises. See also Deduction, Grue, Generalization, Generality, Conclusions._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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G. Peano on Induction - Dictionary of Arguments
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. >Consistency, >Proofs, >Provability, >Postulates, 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. >Circular reasoning, >H. Poincaré. 47 Peano actually uses the induction principle in two ways: as a postulate and then as a rule. >Rules, >Rule system._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" 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 2024-04-19