Philosophy Dictionary of ArgumentsHome
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| Postulates: Postulates are fundamental assumptions or principles in a specific field, accepted without proof. They serve as starting points for reasoning and deriving further conclusions within that domain. See also Theories, Axioms, Method, Proofs, Provability._____________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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A. d’Abro on Postulates - Dictionary of Arguments
A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967 42 Postulates are not the only elements that need to be examined; we must also consider the laws to which they are subject to. >Laws, >Review, >Verification, >Confirmation. 43/44 Existence/consistency/d'Abro: E.g. the famous Dirichlet problem is an existential theorem. It is about whether or not there is always a solution for the Laplace equation satisfying certain boundary conditions. An inconsistent model has just as little claim to mathematical existence as a round square. >Contradictions, >Round square. 44 The compatibility of a postulate system can only be checked if it has only a finite number of consequences. Hilbert's postulates, however, allow infinitely many conclusions. 44/45 Hilbert circumvents this difficulty by saying that the system is proved to be consistent, if it succeeds to prove the existence of a model which confirms the system. So existence equals the lack of an internal inconsistency. >Models, >Model theory. Hilbert then asserts that the numerical model satisfies this requirement. He thus accepts the consistency of the arithmetic continuum. The only problem is that we are not sure about it. >D. Hilbert. Brouwer and Weyl are seriously questioning them, with the result that we can only believe the 5th Hilbertian postulate and all the models which are to be confirmed. Logic alone does not help. >L. Brouwer, >Formalism, >Intuitionism. Is it true that we get the Euclidean geometry only if we apply the logical rules to Hilbert's postulates? Poincaré denies this question. >H. Poincaré._____________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. |
d’ Abro I A. d’ Abro The Rise of the New Physics Mineola, NY 1951 |
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> Counter arguments against d’Abro
> Counter arguments in relation to Postulates
Ed. Martin Schulz, access date 2024-04-20