I think you’re misunderstanding me. I’m saying that there are problems where the right action is to mark it “unsolvable, because of X” and then move on. (Here, it’s “unsolvable because of unbounded solution space in the increasing direction,” which is true in both the “pick a big number” and “open boundary at 100″ case.)
But if we view this as an actual (albeit unrealistic/highly theoretical) situation rather than a math problem we are still stuck with the question of which action to take. A perfectly rational agent can realize that the problem has no optimal solution and mark it as unsolvable, but afterwards they still have to pick a number, so which number should they pick?
But if we view this as an actual (albeit unrealistic/highly theoretical) situation
There is no such thing as an actual unrealistic situation.
A perfectly rational agent can realize that the problem has no optimal solution and mark it as unsolvable, but afterwards they still have to pick a number
They do not have to pick a number, because the situation is not real. To say “but suppose it was” is only to repeat the original hypothetical question that the agent has declared unsolved. If we stipulate that the agent is so logically omniscient as to never need to abandon a problem as unsolved, that does not tell us, who are not omniscient, what that hypothetical agent’s hypothetical choice in that hypothetical situation would be.
The whole problem seems to me on a level with “can God make a weight so heavy he can’t lift it?”
But if we view this as an actual (albeit unrealistic/highly theoretical) situation rather than a math problem we are still stuck with the question of which action to take. A perfectly rational agent can realize that the problem has no optimal solution and mark it as unsolvable, but afterwards they still have to pick a number, so which number should they pick?
There is no such thing as an actual unrealistic situation.
They do not have to pick a number, because the situation is not real. To say “but suppose it was” is only to repeat the original hypothetical question that the agent has declared unsolved. If we stipulate that the agent is so logically omniscient as to never need to abandon a problem as unsolved, that does not tell us, who are not omniscient, what that hypothetical agent’s hypothetical choice in that hypothetical situation would be.
The whole problem seems to me on a level with “can God make a weight so heavy he can’t lift it?”