more from B Russell/AN Whitehead

Single Idea 10044

[catalogued under 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory]

Full Idea

Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements).

Gist of Idea

Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element


report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.459

A Reaction

Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table?