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Ideas of Georg Kreisel, by Text

[Austrian, b.1923, Refugee who taught at Reading and then Stanford]

1958 Hilbert's Programme
05 p.212 Gödel showed that the syntactic approach to the infinite is of limited value
     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)
06 p.213 The study of mathematical foundations needs new non-mathematical concepts
     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.
13 p.220 The natural conception of points ducks the problem of naming or constructing each point
     Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points.
     From: Georg Kreisel (Hilbert's Programme [1958], 13)
     A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one.