Not much to add, I haven’t spent enough time thinking about structural selection theorems.
I’m a fan of making more assumptions. I’ve had a number of conversations with people who seem to make the mistake of not assuming enough. Sometimes leading them to incorrectly consider various things impossible. E.g. “How could an agent store a utility function over all possible worlds?” or “Rice’s theorem/halting problem/incompleteness/NP-hardness/no-free-lunch theorems means it’s impossible to do xyz”. The answer is always nah, it’s possible, we just need to take advantage of some structure in the problem.
Finding the right assumptions is really hard though, it’s easy to oversimplify the problem and end up with something useless.
I think I ger what you mean, though making more assumptions is perhaps not the best way to think about it. Logic is monotonic (classical logic at least), meaning that a valid proof remains valid even when adding more assumptions. The “taking advantage of some structure” seems to be different.
Thoughts, @Jeremy Gillen?
Not much to add, I haven’t spent enough time thinking about structural selection theorems.
I’m a fan of making more assumptions. I’ve had a number of conversations with people who seem to make the mistake of not assuming enough. Sometimes leading them to incorrectly consider various things impossible. E.g. “How could an agent store a utility function over all possible worlds?” or “Rice’s theorem/halting problem/incompleteness/NP-hardness/no-free-lunch theorems means it’s impossible to do xyz”. The answer is always nah, it’s possible, we just need to take advantage of some structure in the problem.
Finding the right assumptions is really hard though, it’s easy to oversimplify the problem and end up with something useless.
Yes. I would even say that finding the right assumptions is the most important part of proving nontrivial selection theorems.
I think I ger what you mean, though making more assumptions is perhaps not the best way to think about it. Logic is monotonic (classical logic at least), meaning that a valid proof remains valid even when adding more assumptions. The “taking advantage of some structure” seems to be different.