I’m trying to label the capacity of humans to create proofs like Godel’s incompleteness proofs or the halting problem. Cats and cows cannot create proofs like these, and it doesn’t seem to be a shortfall in intelligence.
What makes those proofs any different from proofs of other mathematical theorems? I imagine that the halting problem, in particular, would not be beyond the capability of some existing automated theorem prover, assuming you could encode the statement; its proof isn’t too involved.
If your argument is that humans understand these proofs because of some magical out-of-the-box-thinking ability, then I am skeptical.
I’m trying to label the capacity of humans to create proofs like Godel’s incompleteness proofs or the halting problem. Cats and cows cannot create proofs like these, and it doesn’t seem to be a shortfall in intelligence.
Is there a better label you would suggest?
What makes those proofs any different from proofs of other mathematical theorems? I imagine that the halting problem, in particular, would not be beyond the capability of some existing automated theorem prover, assuming you could encode the statement; its proof isn’t too involved.
If your argument is that humans understand these proofs because of some magical out-of-the-box-thinking ability, then I am skeptical.