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2 ideas
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
From: Georg Kreisel (Hilbert's Programme [1958], 05) |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |