Thanks for the explanation, I think I understand this better now.
My response to your second point: I wasn’t sure how the sequence prediction approach to induction (like Solomonoff induction) deals with counterfactuals, so I looked it up, and it looks like we can convert the counterfactual question into a sequence prediction question by appending the counterfactual to all the data we have seen so far. So in the nuclear launch codes example, we would feed the sequence predictor with a video of the launch codes being posted to the internet, and then ask it to predict what sequence it expects to see next. (See the top of page 9 of this PDF and also example 5.2.2 in Li and Vitanyi for more details and further examples.) This doesn’t require a decomposition into laws and conditions; rather it seems to require that the events E be a function that can take in bits and print out more bits (or a probability distribution over bits). But this doesn’t seem like a problem, since in the values case the policy π is also a function. (Maybe my real point is that I don’t understand why you are assuming E has to be a sequence of events?) [ETA: actually, maybe E can be just a sequence of events, but if we’re talking about complexity, there would be some program that generates E, so I am suggesting we use that program instead of L and C for counterfactual reasoning.]
My response to your first point: I am far from an expert here, but my guess is that an Occam’s Razor advocate would bite the bullet and say this is fine, since either (1) the degenerate predictors will have high complexity so will be dominated by simpler predictors, or (2) we are just as likely to be living in a “degenerate” world as we are to be living in the kind of “predictable” world that we think we are living in.
Thanks for the explanation, I think I understand this better now.
My response to your second point: I wasn’t sure how the sequence prediction approach to induction (like Solomonoff induction) deals with counterfactuals, so I looked it up, and it looks like we can convert the counterfactual question into a sequence prediction question by appending the counterfactual to all the data we have seen so far. So in the nuclear launch codes example, we would feed the sequence predictor with a video of the launch codes being posted to the internet, and then ask it to predict what sequence it expects to see next. (See the top of page 9 of this PDF and also example 5.2.2 in Li and Vitanyi for more details and further examples.) This doesn’t require a decomposition into laws and conditions; rather it seems to require that the events E be a function that can take in bits and print out more bits (or a probability distribution over bits). But this doesn’t seem like a problem, since in the values case the policy π is also a function. (Maybe my real point is that I don’t understand why you are assuming E has to be a sequence of events?) [ETA: actually, maybe E can be just a sequence of events, but if we’re talking about complexity, there would be some program that generates E, so I am suggesting we use that program instead of L and C for counterfactual reasoning.]
My response to your first point: I am far from an expert here, but my guess is that an Occam’s Razor advocate would bite the bullet and say this is fine, since either (1) the degenerate predictors will have high complexity so will be dominated by simpler predictors, or (2) we are just as likely to be living in a “degenerate” world as we are to be living in the kind of “predictable” world that we think we are living in.