Psychology Dictionary of ArgumentsHome
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| Russell's Paradox: The set of all sets that do not contain themselves as an element. The problem is that the condition for being included in this set is also the condition for not being included in the same set. See also paradoxes, sets, set theory,_____________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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Friedrich Waismann on Russell’s Paradox - Dictionary of Arguments
I 52 Russell's antinomy/Waismann: The set of all humans is not a human, but the set of all concepts is a concept. It therefore contains itself, not normally. The set of all humans does not contain itself, normal. "N". Let us ask whether "N" is normal or not; i.e. whether it contains itself or not! Suppose, initially, N contains itself as an element, then the set N occurs among its elements. Thus, N contains a non-normal set, which is N, whereas, by definition, it should contain only normal sets. The assumption was therefore wrong. Thus only the opposite can be true, but this also leads to a contradiction: If N does not contain itself as an element, then N is a normal set. However, since N should contain all normal sets, it must also contain the normal set N, i.e. containing itself - but this is again a contradiction. It follows from the concept of the set itself. >Contradictions, >Concepts, >Self-reference, >Circular reaoning, >Paradox._____________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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> Counter arguments against Waismann
> Counter arguments in relation to Russell’s Paradox
