I am not sure you actually justified your claim, that OR follows from the laws of probability with no empirical input.
Reading your arguments carefully you seem to have snuck in some prior knowledge about the universe (that age does not matter much to the weight of cows after a certain age for example).
There is a big mystery to me as to why the universe is so simple e.g. the laws of physics can be written out (though not explained) in a few pages. Why are they so small, not to mention finite, not to mention not uncountable...
Yes, the thing about the age is totally dependent on the actual state of the universe (or, put more mundanely, dependent on the actual things I know or think I know about cows).
In regard to the short laws of the universe… I am saying that, if you’re already in the framework of probability theory, then you know you can’t gain from random guessing. Like how the optimal strategy for guessing whether the next card will be blue or red, in a deck 70% red, is “always guess red”. A hypothetical non-Occam prior, if it doesn’t tell you anything about cards, won’t change the fact that that this strategy is best. To convince someone who disagrees that this is true, using real examples, or actually drawing actual cards, would help. So again there I’d use empirical information to help justify my claim. I guess what I’m trying to say is: I didn’t mean to argue that everything I said was devoid of empiricism.
I am not sure you actually justified your claim, that OR follows from the laws of probability with no empirical input.
Reading your arguments carefully you seem to have snuck in some prior knowledge about the universe (that age does not matter much to the weight of cows after a certain age for example).
There is a big mystery to me as to why the universe is so simple e.g. the laws of physics can be written out (though not explained) in a few pages. Why are they so small, not to mention finite, not to mention not uncountable...
Marcus Hutter’s AIXI has a prior that makes simple worlds more likely. See also https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference
Yes, the thing about the age is totally dependent on the actual state of the universe (or, put more mundanely, dependent on the actual things I know or think I know about cows).
In regard to the short laws of the universe… I am saying that, if you’re already in the framework of probability theory, then you know you can’t gain from random guessing. Like how the optimal strategy for guessing whether the next card will be blue or red, in a deck 70% red, is “always guess red”. A hypothetical non-Occam prior, if it doesn’t tell you anything about cards, won’t change the fact that that this strategy is best. To convince someone who disagrees that this is true, using real examples, or actually drawing actual cards, would help. So again there I’d use empirical information to help justify my claim. I guess what I’m trying to say is: I didn’t mean to argue that everything I said was devoid of empiricism.