Philosophy Dictionary of ArgumentsHome
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| Expansion, philosophy: when expanding theories it comes to the question whether a consistent theory remains consistent when it is expanded. Maximum consistent theories are not expandable. See also axioms, maximum consistent, theories, consistency, maximum._____________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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F. Waismann on Expansion - Dictionary of Arguments
I 21 Extension/Waismann: e.g. the law am x an = am + n would lose its validity for n = 0. Through the convention a° = 1 the existing laws not only remain in force, they are also extended to a larger area. The maintenance of the laws thus regulates conceptual formation. I 44 Caution: rational numbers are not an extension of the integers. The system of the integers can be mapped to a part of the rational numbers such that the four types of arithmetic are preserved: one-to-one, similar, isomorphic._____________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. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
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Ed. Martin Schulz, access date 2024-04-18