Self Reference

A sentence, S, can either describe itself, or not. If it does not, we could replace it with a sentence that does describe S, but this might falsify the new description. Iterating, one of three things could happen:

1. convergence: a sentence eventually describes itself, stop.
2. cycling: s_n describes s_n-1, ..., describes s₁, describes s_n, for n>1.
3. divergence: neither of the above.