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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.
Gist of Idea
The study of mathematical foundations needs new non-mathematical concepts
Source
Georg Kreisel (Hilbert's Programme [1958], 06)
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.213
A Reaction
Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job.
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |