Single Idea 6407

[catalogued under 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox]

Full Idea

The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox.

Gist of Idea

The class of classes which lack self-membership leads to a contradiction

Source

report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2

Book Reference

Grayling,A.C.: 'Russell' [OUP 1996], p.30


A Reaction

A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory.