# closed loops

**Closed systems: what a loop costs**

If the top level loops back to the bottom, the system effectively vouches for its own consistency, and the second theorem says a consistent system cannot do that. So a closed loop has to give up one of three things.

Consistency: Priest and the dialetheists accept some true contradictions. Total truth: Kripke’s theory lets a system talk about its own truth, but sentences like the liar stay neither true nor false. The ladder itself: Aczel’s non-well-founded sets contain themselves.

Hofstadter’s tangled hierarchy is the intuitive version: you climb levels and end up where you started. The Gödel sentence is already a tiny closed loop, one step long.

Connects to:
- [three views](https://mapideas.org/i/tr_views)
- [which cost?](https://mapideas.org/i/tr_q2)
- [Hofstadter](https://mapideas.org/i/c_hof)

Sources:
- Kripke, S. (1975). Outline of a Theory of Truth. Journal of Philosophy 72(19), 690–716.

Source: https://mapideas.org/i/tr_loops · open on the map: https://mapideas.org/#tr_loops