The Gödel sentence for some formal system only limits a machine while it is implementing that formal system. But when the machine is implementing some other formal system, the machine may be able to prove the previous system's Gödel sentence.
Daniel Dennett (1972).
- Dennett presents this argument as a special case in his broader discussion of how a physical object can implement various Turing machines.
- Also see the "Is the brain a computer?" arguments on Map 1, the "Functional states generate consciousness?" argument on Map 6, and sidebar "Formal Systems: An Overview" on this map.