Full Idea
Where Gödel's First Theorem sabotages logicist ambitions, the Second Theorem sabotages Hilbert's Programme.
Gist of Idea
Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme
Source
comment on Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 36
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.343
A Reaction
Neo-logicism (Crispin Wright etc.) has a strategy for evading the First Theorem.