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 Reference
'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.