Single Idea 18836

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I]

Full Idea

There seem strong grounds for rejecting the thesis that a set consists of its members. For one thing, the empty set is a perpetual embarrassment for the thesis.

Gist of Idea

A set may well not consist of its members; the empty set, for example, is a problem

Source

Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4)

Book Reference

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.240


A Reaction

Rumfitt also says that if 'red' has an extension, then membership of that set must be vague. Extensional sets are precise because their objects are decided in advance, but intensional (or logical) sets, decided by a predicate, can be vague.