Single Idea 21694

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

Full Idea

With Russell's antinomy, ...each tie the trouble comes of taking a membership condition that itself talks in turn of membership and non-membership.

Gist of Idea

Membership conditions which involve membership and non-membership are paradoxical

Source

Willard Quine (The Ways of Paradox [1961], p.13)

Book Reference

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.13


A Reaction

Hence various stipulations to rule out vicious circles or referring to sets of the 'wrong type' are invoked to cure the problem. The big question is how strong to make the restrictions.