Full Idea
Most would cite Russell's paradox, the non-logical character of the axioms which Russell and Whitehead's reconstruction of Frege's enterprise was constrained to employ, and the incompleteness theorems of Gödel, as decisive for logicism's failure.
Gist of Idea
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro)
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.-1
Related Idea
Idea 13895 The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]