more from Stewart Shapiro

Single Idea 13651

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set]

Full Idea

If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members.

Gist of Idea

A set is 'transitive' if contains every member of each of its members

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 4.2)

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.85


A Reaction

The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set.