### Single Idea 21713

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

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.