@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Waismann,Friedrich}, subject = {Russell’s Paradox}, note = {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.}, note = { Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=538169} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=538169} }