All of Ty-Guy9's Comments + Replies

If you have an arbitrary proposition -- a random sequence of symbols constrained only by the grammar of whatever language you're using -- then perhaps it's about equally likely to be true or false, since for each proposition p there's a corresponding proposition not p of similar complexity. But the "beliefs" people are mostly interested in are things like these: * There is exactly one god, who created the universe and watches over us; he likes forgiveness, incense-burning, and choral music, and hates murder, atheism and same-sex marriage. * Two nearby large objects, whatever they are, will exert an attractive force on one another proportional to the mass of each and inversely proportional to the square of the distance between them. and the negations of these are much less interesting because they say so much less: * Either there is no god or there are multiple gods, or else there is one god but it either didn't create the universe or doesn't watch over us -- or else there is one god, who created the universe and watches over us, but its preferences are not exactly the ones stated above. * If you have two nearby objects, whatever force there may be between them is not perfectly accurately described by saying it's proportional to their masses, inversely proportional to the square of the distance, and unaffected by exactly what they're made of. So: yeah, sure, there are ways to pick a "random" belief and be pretty sure it's correct (just say "it isn't the case that" followed by something very specific) but if what you're picking are things like scientific theories or religious doctrines or political parties then I think it's reasonable to say that the great majority of possible beliefs are wrong, because the only beliefs we're actually interested in are the quite specific ones.

I don't think "converse" is the word you're looking for here - possibly "complement" or "negation" in the sense that (A || ~A) is true for all A - but I get what you're saying. Converse might even be the right word for that; vocabulary is not my forte. If you take the statement "most beliefs are false" as given, then "the negation of most beliefs is true" is trivially true but adds no new information. You're treating positive and negative beliefs as though they're the same, and that's absolutely not true. In the words of this post, a positive belief provides enough information to anticipate an experience. A negative belief does not (assuming there are more than two possible beliefs). If you define "anything except that one specific experience" as "an experience", then you can define a negative belief as a belief, but at that point I think you're actually falling into exactly the trap expressed here. If you replace "belief" with "statement that is mutually incompatible with all other possible statements that provide the same amount of information about its category" (which is a possibly-too-narrow alternative; unpacking words is hard sometimes) then "true statements that are mutually incompatible with all other possible statements that provide the same amount of information about their category are vastly outnumbered by false statements that are mutually incompatible with all other possible statements that provide the same amount of information about their category" is something the I anticipate you would find true. You and Eliezer do not anticipate a different percentage of possible "statements that are mutually incompatible with all other possible statements that provide the same amount of information about their category" being true. As for universal priors, the existence of many incompatible possible (positive) beliefs in one space (such that only one can be true) gives a strong prior that any given such belief is false. If I have only two possible beliefs and