### Single Idea 10094

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory]

Full Idea

The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}.

Gist of Idea

The theory of types seems to rule out harmless sets as well as paradoxical ones.

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.47

A Reaction

Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness.