Perhaps I’m being dim, but a prior is a probability distribution, isn’t it? Whereas Occam’s Razor and induction aren’t: they’re rules for how to estimate prior probability.
But we can think about probability that Occam’s razor produces correct answers, this probability is a prior.
Our ‘absolutely universal’ laws can be shown to have predictive power over an infinitesimal speck of the cosmos. Our ability to observe even natural experiments in the rest of the universe is extremely limited. … Experience teaches us that, at any given time, the majority of our beliefs will be wrong, and the only thing that makes even approximate correctness possible is precisely what we cannot apply to the universe as a whole.
Our ability to observe natural experiments even on Earth is extremely limited (e.g. we surely haven’t seen most of elementary particles that can be produced here on Earth if one had sufficient energy). But what’s the problem with that? Experience teaches us that most of our beliefs have limited domain of validity, rather than are wrong. Newtonian physics is not “wrong”, it is still predictive and useful, even when we have got now better theories valid in larger set of situations.
Perhaps it’s better to reformulate Eliezer’s statement about universal laws something like that “all phenomena we encountered could be described by relatively simple set of laws; every newly discovered phenomenon makes the laws more precise, instead of totally dicarding them”. I think this is not completely trivial statement, as I can imagine a world where the laws were as complicated as the phenomena themselves, thus a world where nothing was predictable.
Perhaps I’m being dim, but a prior is a probability distribution, isn’t it? Whereas Occam’s Razor and induction aren’t: they’re rules for how to estimate prior probability.
But we can think about probability that Occam’s razor produces correct answers, this probability is a prior.
Our ‘absolutely universal’ laws can be shown to have predictive power over an infinitesimal speck of the cosmos. Our ability to observe even natural experiments in the rest of the universe is extremely limited. … Experience teaches us that, at any given time, the majority of our beliefs will be wrong, and the only thing that makes even approximate correctness possible is precisely what we cannot apply to the universe as a whole.
Our ability to observe natural experiments even on Earth is extremely limited (e.g. we surely haven’t seen most of elementary particles that can be produced here on Earth if one had sufficient energy). But what’s the problem with that? Experience teaches us that most of our beliefs have limited domain of validity, rather than are wrong. Newtonian physics is not “wrong”, it is still predictive and useful, even when we have got now better theories valid in larger set of situations.
Perhaps it’s better to reformulate Eliezer’s statement about universal laws something like that “all phenomena we encountered could be described by relatively simple set of laws; every newly discovered phenomenon makes the laws more precise, instead of totally dicarding them”. I think this is not completely trivial statement, as I can imagine a world where the laws were as complicated as the phenomena themselves, thus a world where nothing was predictable.