Finally, on an empirical level, it seems like there are more false n-bit statements than true n-bit statements.
I’m pretty certain this intuition is false. It feels true because it’s much harder to come up with a true statement from N bits if you restrict yourself to positive claims about reality. If you get random statements like “the frooble fuzzes violently” they’re bound to be false, right? But for every nonsensical or false statement you also get the negation of a nonsensical or false statement. “not( the frooble fuzzes violiently)”. It’s hard to arrive at a statement like “Obama is the 44th president” and be correct, but it’s very easy to enumerate a million things that do not orbit Pluto (and be correct).
(FYI: somewhere below there is a different discussion about whether there are more n-bit statements about reality that are false than true)
I’m pretty certain this intuition is false. It feels true because it’s much harder to come up with a true statement from N bits if you restrict yourself to positive claims about reality. If you get random statements like “the frooble fuzzes violently” they’re bound to be false, right? But for every nonsensical or false statement you also get the negation of a nonsensical or false statement. “not( the frooble fuzzes violiently)”. It’s hard to arrive at a statement like “Obama is the 44th president” and be correct, but it’s very easy to enumerate a million things that do not orbit Pluto (and be correct).
(FYI: somewhere below there is a different discussion about whether there are more n-bit statements about reality that are false than true)