### Single Idea 10092

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

Full Idea

In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types.

Clarification

'Ramified' means having complex extensions

Gist of Idea

In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc.

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.46

A Reaction

The objects are Type 0, the basic sets Type 1, etc.