### Single Idea 21715

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

Full Idea

ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic.

Gist of Idea

For those who abandon logicism, standard set theory is a rival option

Source

Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1)

Book Reference

Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.91

A Reaction

Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be.