Full Idea
It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited.
Gist of Idea
Did logicism fail, when Russell added three nonlogical axioms, to save mathematics?
Source
Bernard Linsky (Russell's Metaphysical Logic [1999], 6)
Book Reference
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.89
A Reaction
Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic.