This doesn’t feel like it resolves that confusion for me, I think it’s still a problem with the agents he describes in that paper.
The causes Cj are just the direct computation of Φ for small values of x. If they were arguments that only had bearing on small values of x and implied nothing about larger values (e.g. an adversary selected some x to show you, but filtered for x such that Φ(x)), then it makes sense that this evidence has no bearing on∀x:Φ(x). But when there was no selection or other reason that the argument only applies to small x, then to me it feels like the existence of the evidence (even though already proven/computed) should still increase the credence of the forall.
I didn’t intend the causes Cj to equate to direct computation of \phi(x) on the x_i.
They are rather other pieces of evidence that the powerful agent has that make it believe \phi(x_i). I don’t know if that’s what you meant.
I agree seeing x_i such that \phi(x_i) should increase credence in \forall x \phi(x) even in the presence of knowledge of C_j. And the Shapely value proposal will do so.
This doesn’t feel like it resolves that confusion for me, I think it’s still a problem with the agents he describes in that paper.
The causes Cj are just the direct computation of Φ for small values of x. If they were arguments that only had bearing on small values of x and implied nothing about larger values (e.g. an adversary selected some x to show you, but filtered for x such that Φ(x)), then it makes sense that this evidence has no bearing on∀x:Φ(x). But when there was no selection or other reason that the argument only applies to small x, then to me it feels like the existence of the evidence (even though already proven/computed) should still increase the credence of the forall.
I didn’t intend the causes Cj to equate to direct computation of \phi(x) on the x_i. They are rather other pieces of evidence that the powerful agent has that make it believe \phi(x_i). I don’t know if that’s what you meant.
I agree seeing x_i such that \phi(x_i) should increase credence in \forall x \phi(x) even in the presence of knowledge of C_j. And the Shapely value proposal will do so.
(Bad tex. On my phone)