Single Idea 13367

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

Full Idea

Mirimanoff: φ(x) is 'x is well founded', so that w is the cumulative hierarchy of sets, V; &delta(x) is just the power set of x, P(x). If x⊆V, then V∈V and V∉V, since δ(V) is just V itself.

Gist of Idea

The next set up in the hierarchy of sets seems to be both a member and not a member of it

Source

Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2)

Book Reference

-: 'Mind' [-], p.27