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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Peter Geach on Russell’s Paradox - Dictionary of Arguments
I 83 Russell's Paradox/Geach: the predicate "containing itself as an element" and "not containing itself as an element" will never have the same meaning, even if one accepts such an object that both conditions correspond to at the same time. I 225 Russell's Paradox/Solution/Quine: two predicates can have the same class as the extension, although they do not apply to the same objects: For example, the predicates "__is a class that does not belong to itself" and "__ is a class belonging to a class, but not to itself" have the same class as their extension. But there is a class - obviously this common extension itself - which only suffices for the first predicate, not the second. So they do not stand for the same property! Geach: simpler example "Booth shot Lincoln" and "Booth shot Booth": contain the common predicate "Booth shot___" - i.e. not that the last expression occurs twice in both sentences! For both sentences contain no strokes, but the two sentences have the common property of being related to "Booth shot___" in the same way. And this common property is the common predicate. ((s) Intension instead of extension). >Intension, >Extension, >Predicate, >Properties._____________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. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
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> Counter arguments against Geach
> Counter arguments in relation to Russell’s Paradox
