Roland and Ian C. both help me understand where Eliezer is coming from. And PK’s comment that “Reality will only take a single path” makes sense. That said, when I say a die has a 1⁄6 probability of landing on a 3, that means: Over a series of rolls in which no effort is made to systematically control the outcome (e.g. by always starting with 3 facing up before tossing the die), the die will land on a 3 about 1 in 6 times. Obviously, with perfect information, everything can be calculated. That doesn’t mean that we can’t predict the probability of a specific event.
Also, I didn’t get a response to the Gomboc ( http://tinyurl.com/2rffxs ) argument. I would say that it has an inherent 100% probability of righting itself. Even if I knew nothing about the object, the real probability of it righting itself is 100%. Now, I might not bet on those odds, without previous knowledge, but no matter what I know, the object will right itself. How is this incorrect?
It seems to me you’re using “perceived probability” and “probability” interchangeably. That is, you’re “defining” probability as the probability that an observer assigns based on certain pieces of information. Is it not true that when one rolls a fair 1d6, there is an actual 1⁄6 probability of getting any one specific value? Or using your biased coin example: our information may tell us to assume a 50⁄50 chance, but the man may be correct in saying that the coin has a bias—that is, the coin may really come up heads 80% of the time, but we must assume a 50% chance to make the decision, until we can be certain of the 80% chance ourselves. What am I missing? I would say that the Gomboc (http://tinyurl.com/2rffxs) has a 100% chance of righting itself, inherently. I do not understand how this is incorrect.