## 20090920

### psychedelia, contradiction, and theorem proving

Suppose we have a system which generates new facts from a body of axioms, derivation rules, and previously-known facts, i.e. a theorem-proving system. For this to be done tractably, the system much have some heuristic for exploring the space of possible facts. As long as it is functioning properly, the "shape" of the set of known truths within this space will depend both on the formal system itself and on this exploration heuristic.

Now suppose we introduce a logical contradiction into the system's body of known facts. Now all points in our space of facts are reachable. If the system had unbounded computational power, the entire space would "light up" at once. In a finitely-powerful system, we see an expanding shape, now determined solely by the exploration heuristic, i.e. by the properties of the theorem prover and not the thing which it is supposed to be studying.

This is the sense in which psychedelia is "mind-manifesting".