Our notion of narrowness is that we are interested in solving the problem where the question we’re asking is such that a state always resolves a question. E.g. there isn’t any ambiguity around whether a state “really contains a diamond”. (Note that there is ambiguity around whether the human could detect the diamond from any set of observations because there could be a fake diamond or nanobots filtering what the human sees). It might be useful to think of this as an empirical claim about diamonds.
This “there isn’t any ambiguity”+”there is ambiguity” does not seem possible to me: these types of ambiguity are one and the same. But it might depend on what “any set of observations” is allowed to include. “Any set” suggests being very inclusive, but remember that passive observation is impossible. Perhaps the observations I’d want the human to use to figure out if the diamond is really there (presuming there isn’t ambiguity) would include observations you mean to exclude, such as disabling the filter-nanobots first?
I guess a wrinkle here is that observations need to be “implementable” in the world. If we’re thinking of making observations as intervening on the world (e.g., to decide which sensors to query), then some observations may be inaccessible because we can’t make that intervention. Rewriting this all without relying on “possible”/”can” concepts would be instructive.
I don’t think we have any kind of precise definition of “no ambiguity.” That said, I think it’s easy to construct examples where there is no ambiguity about whether the diamond remained in the room, yet there is no sequence of actions a human could take that would let them figure out the answer. For example, we can imagine simple toy universes where we understand exactly what features of the world give rise to human beliefs about diamonds and where we can say unambiguously that the same features are/aren’t present in a given situation.
In general I feel a lot better about our definitions when we are using them to arbitrate a counterexample than if we were trying to give a formal definition. If all the counterexamples involved border cases of the concepts, where there was arguable ambiguity about whether the diamond really stayed in the room, then it would seem important to firm up these concepts but right now it feels like it is easy to just focus on cases where algorithms unambiguously fail.
(That methodological point isn’t obvious though—it may be that precise definitions are very useful for solving the problem even if you don’t need them to judge current solutions as inadequate. Or it may be that actually existing counterexamples are problematic in ways we don’t recognize. Pushback on these fronts is always welcome, but right now I feel pretty comfortable with the situation.)
This “there isn’t any ambiguity”+”there is ambiguity” does not seem possible to me: these types of ambiguity are one and the same. But it might depend on what “any set of observations” is allowed to include. “Any set” suggests being very inclusive, but remember that passive observation is impossible. Perhaps the observations I’d want the human to use to figure out if the diamond is really there (presuming there isn’t ambiguity) would include observations you mean to exclude, such as disabling the filter-nanobots first?
I guess a wrinkle here is that observations need to be “implementable” in the world. If we’re thinking of making observations as intervening on the world (e.g., to decide which sensors to query), then some observations may be inaccessible because we can’t make that intervention. Rewriting this all without relying on “possible”/”can” concepts would be instructive.
I don’t think we have any kind of precise definition of “no ambiguity.” That said, I think it’s easy to construct examples where there is no ambiguity about whether the diamond remained in the room, yet there is no sequence of actions a human could take that would let them figure out the answer. For example, we can imagine simple toy universes where we understand exactly what features of the world give rise to human beliefs about diamonds and where we can say unambiguously that the same features are/aren’t present in a given situation.
In general I feel a lot better about our definitions when we are using them to arbitrate a counterexample than if we were trying to give a formal definition. If all the counterexamples involved border cases of the concepts, where there was arguable ambiguity about whether the diamond really stayed in the room, then it would seem important to firm up these concepts but right now it feels like it is easy to just focus on cases where algorithms unambiguously fail.
(That methodological point isn’t obvious though—it may be that precise definitions are very useful for solving the problem even if you don’t need them to judge current solutions as inadequate. Or it may be that actually existing counterexamples are problematic in ways we don’t recognize. Pushback on these fronts is always welcome, but right now I feel pretty comfortable with the situation.)