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What exactly is meant by 'use reflection'? How is it something that a computer cannot do? It seems to be just convincing yourself. Gödel's theorum itself doe
by Lerc 2y ago
What exactly is meant by 'use reflection'?
How is it something that a computer cannot do? It seems to be just convincing yourself.
Gödel's theorum itself does not help you here because you are trying to identify a undecidable but true. Gödel only showed that there are undecidable true statements, not what they are.
- enugu 2y agoGodel explicitly constructs the statements (which are essentially encoding a particular self-referential statement into logic). Penrose makes this more concrete where given an accurate, but necessarily partial procedure for detecting when a program halts, one can use diagonalization to show that a program wont halt even though the earlier process couldn't detect it. https://news.ycombinator.com/item?id=43257904 https://news.ycombinator.com/item?id=43257904 This construction is something that a computer can do, but not the original system itself. Once you augment the system, there is now a new statement it cant see and so on. (so on, here involves ordinals).