I'm kinda surprised that it's only been mentioned once in the comments (I only just discovered this site, really really great, by the way) and one from 2010 at that, but it seems to me that "a magical symbol to stand for "all possibilities I haven't considered" " does exist: the symbol "~" (i.e. not). Even the commenter who does mention it makes things complicated for himself: P(Q or ~Q)=1 is the simplest example of a proposition with probability 1.
The proposition is of course a tautology. I do think (but I'm not sure) that that is the only sort of statement that receives probability 1. This is in sync with Eliezer's "amount... (read more)
I'm kinda surprised that it's only been mentioned once in the comments (I only just discovered this site, really really great, by the way) and one from 2010 at that, but it seems to me that "a magical symbol to stand for "all possibilities I haven't considered" " does exist: the symbol "~" (i.e. not). Even the commenter who does mention it makes things complicated for himself: P(Q or ~Q)=1 is the simplest example of a proposition with probability 1.
The proposition is of course a tautology. I do think (but I'm not sure) that that is the only sort of statement that receives probability 1. This is in sync with Eliezer's "amount... (read more)