I wonder if we can cash this counterfactual mugging out in terms of ignorance about physical facts. This dodges the difficulty of logical counterfactuals, but maybe not too boringly.
After all, what Omega says to you is “I calculated 22222 and took different actions depending on the result.” When you take the logical counterfactual problem head-on, you are attempting to answer “what if 22222 was different than what it was?” But there is another possible question, which is “why 22222?” Or, “what is my (prior-ish; we’re being updateless) distribution over this parameter that Omega used in deciding what action to take?”
If we knew Omega was just going to use something like a big tower of exponents, the distribution over the first digit follows Benford’s law. But maybe was also think Omega might have chosen a digit of pi, and so we have to add in some uniform contribution, etc.
I wonder if we can cash this counterfactual mugging out in terms of ignorance about physical facts. This dodges the difficulty of logical counterfactuals, but maybe not too boringly.
After all, what Omega says to you is “I calculated 22222 and took different actions depending on the result.” When you take the logical counterfactual problem head-on, you are attempting to answer “what if 22222 was different than what it was?” But there is another possible question, which is “why 22222?” Or, “what is my (prior-ish; we’re being updateless) distribution over this parameter that Omega used in deciding what action to take?”
If we knew Omega was just going to use something like a big tower of exponents, the distribution over the first digit follows Benford’s law. But maybe was also think Omega might have chosen a digit of pi, and so we have to add in some uniform contribution, etc.