I don’t know, that line of reasoning that U()=10 seems like a pretty clear consequence of PA+Sound(PA)+A()=a, and the lack of a counterfactual for “X is false” doesn’t violate any of my intuitions. It’s just reasoning backwards from “The agent takes action a” to the mathematical state of affairs that must have produced it (there is a short proof of X).
On second thought, the thing that broke the original trolljecture was reasoning backwards from “I take action a” to the mathematical state of affairs that produced it. Making inferences about the mathematical state of affairs in your counterfactuals using knowledge of your own decision procedure does seem to be a failure mode at first glance.
Maybe use the counterfactual of “find-and-replace all instances of X’s source code in the universe program U with action a, and evaluate”? But that wouldn’t work for different algorithms that depend on checking the same math facts. There needs to be some way to go from “X takes action A” to “closely related algorithm Y takes action B”. But that’s just inferring mathematical statements from the combination of actions and knowing X’s decision rule.
I’ll stick with the trolljecture as the current best candidate for “objective” counterfactuals, because reasoning backwards from actions and decision rules a short way into math facts seems needed to handle “logically related” algorithms, and this counterexample looks intuitively correct.
I don’t know, that line of reasoning that U()=10 seems like a pretty clear consequence of PA+Sound(PA)+A()=a, and the lack of a counterfactual for “X is false” doesn’t violate any of my intuitions. It’s just reasoning backwards from “The agent takes action a” to the mathematical state of affairs that must have produced it (there is a short proof of X).
On second thought, the thing that broke the original trolljecture was reasoning backwards from “I take action a” to the mathematical state of affairs that produced it. Making inferences about the mathematical state of affairs in your counterfactuals using knowledge of your own decision procedure does seem to be a failure mode at first glance.
Maybe use the counterfactual of “find-and-replace all instances of X’s source code in the universe program U with action a, and evaluate”? But that wouldn’t work for different algorithms that depend on checking the same math facts. There needs to be some way to go from “X takes action A” to “closely related algorithm Y takes action B”. But that’s just inferring mathematical statements from the combination of actions and knowing X’s decision rule.
I’ll stick with the trolljecture as the current best candidate for “objective” counterfactuals, because reasoning backwards from actions and decision rules a short way into math facts seems needed to handle “logically related” algorithms, and this counterexample looks intuitively correct.