 Of the various fields of philosophy, Gödel’s theorems are obviously most immediately relevant for the philosophy of mathematics. To begin with, they pose, at least prima facie, serious problems for Hilbert’s program (this issue is discussed in some detail in the section on the impact of incompleteness in the entry on  Hilbert’s Program).  Then again, they have important consequences for intuitionism (see the entry on  intuitionism in the philosophy of mathematics)  (see also Gödel 1933, 1941; Raatikainen 2005).