|Geach, Peter T.
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|Russell’s Paradox||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.
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).
Logic Matters Oxford 1972