|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. |
Extension/Waismann: e.g. the law a m times a n = a m + 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.
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.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976