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2 ideas
17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
Full Idea: Various authors have argued that identity statements arising in the context of the 'Julius Caesar' problem in philosophy of mathematics constitute category mistakes. | |
From: Ofra Magidor (Category Mistakes [2013], 1.1 n1) | |
A reaction: [She cites Benacerraf 1965 and Shapiro 1997:79] |
6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
Full Idea: I think that no one will dispute that from certain ideas and axioms of formal logic, but with the help of the logic of relations, all pure mathematics can be deduced. | |
From: Bertrand Russell (Logical Atomism [1924], p.145) | |
A reaction: It has been said for a long time that Gödel's Incompleteness Theorems of 1930 disproved this claim, though recently there have been defenders of logicism. Beginning with 'certain ideas' sounds like begging the question. |