[DSRP Evidence](https://dsrpevidence.org/)

# A set that contains only itself

Measurement & self-reference · 

## Why it looked like it would break the theory

In non-well-founded set theory, a set may contain itself, A = {A}. This appears to violate the System pattern because the part and the whole are the same identity.

## Why it failed

**The counterexample failed** because the System pattern imposes no inequality constraint on p and w. It requires only the contains–belongs structure: S := p ↔ w. If a whole contains itself and belongs to itself, the System pattern remains fully instantiated. Recursive self-containment is an ordinary system structure, not a new primitive.

Settled by [R7](https://dsrpevidence.org/resolution/7). Not yet published.

[Read it](https://plato.stanford.edu/entries/self-reference/)

[All cases](https://dsrpevidence.org/counterexamples)