“I believe it’s possible that I’ll die in a car accident” is a statement of uncertainty in the event “I’ll die in a car accident”
Nitpick: No, it’s not. Things that are necessary are all also possible. For instance, it is possible that 2+2=4, because it is not impossible that 2+2=4. It’s not as strong a statement as someone who believed that death by car accident was inevitable could make, but it’s not an expression of uncertainty all by itself unless the speaker is doing something with tone of voice (“Sure, I guess I think it’s possible that I could die in a car accident...”)
Actually, it’s just as strong a statement of certainty; but it is expressing certainty that the proposition “it is possible that I will die in a car accident” is true, not that “I will die in a car accident” is true.
That’s not what I was talking about, interpreting “It’s possible that X will happen” as “the event X is non-empty” is as wrong as interpreting “I believe X will happen” as “negation of even X is empty”. Uncertainty is just lack of certainty, “it’s possible” expresses probability lower than that of “it’s probable”, way below “it’s certain”. See also the references from the Possibility article on the wiki.
Nitpick: No, it’s not. Things that are necessary are all also possible. For instance, it is possible that 2+2=4, because it is not impossible that 2+2=4. It’s not as strong a statement as someone who believed that death by car accident was inevitable could make, but it’s not an expression of uncertainty all by itself unless the speaker is doing something with tone of voice (“Sure, I guess I think it’s possible that I could die in a car accident...”)
Actually, it’s just as strong a statement of certainty; but it is expressing certainty that the proposition “it is possible that I will die in a car accident” is true, not that “I will die in a car accident” is true.
That’s not what I was talking about, interpreting “It’s possible that X will happen” as “the event X is non-empty” is as wrong as interpreting “I believe X will happen” as “negation of even X is empty”. Uncertainty is just lack of certainty, “it’s possible” expresses probability lower than that of “it’s probable”, way below “it’s certain”. See also the references from the Possibility article on the wiki.