Philosophy Dictionary of ArgumentsHome
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| Impredicativeness: Impredicatives are concepts which are defined only by means of the propositional sets to which they themselves belong. Problems arise in connection with possible circular conclusions. To avoid paradoxes, the demand is sometimes made to avoid impredicative concepts. See also Paradoxes, Russellian Paradoxy, Poincaré._____________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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Henri Poincaré on Impredicativeness - Dictionary of Arguments
Thiel I 324 Impredicativeness/Paradoxes/Poincaré: Poincaré believed with this that the decisive criterion had been found: illegitimate, "non-predicative" conditions are those that contain such a circle. >impredicative/Russell. At first, it seemed sufficient to require expressions for the relation between element and set that in "x ε y" the second relation term y should belong to exactly one step higher than x (>type theory), thus the requirement that each permissible expression should be formed not only "predicatively" itself (i.e. not impredicatively) but also all arguments occurring in it must meet this condition, to form a >"ramified type theory"._____________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. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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> Counter arguments against Poincaré
> Counter arguments in relation to Impredicativeness
Ed. Martin Schulz, access date 2024-04-20