Single Idea 13640

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets]

Full Idea

The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets.

Gist of Idea

Russell's paradox shows that there are classes which are not iterative sets

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 1.3)

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.19


A Reaction

In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20.