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.
Gist of Idea
Gödel showed that the syntactic approach to the infinite is of limited value
Source
Georg Kreisel (Hilbert's Programme [1958], 05)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.212