Those statements aren’t even approximately independent though, if Jupiter turns out to be really small, they’re all true. That’s why mine were so weird, the independence clause.*
*(they still aren’t actually independent, but I’m >99.99% sure you couldn’t make a set of statements that were)
However, it’s possible to make a set of statements that are mutually exclusive, which might actually be a superior task “I am not the 11,043rd sentient entity ever to exist. I am not the 21,043rd sentient entity ever to exist, etc.”
Those statements aren’t even approximately independent though, if Jupiter turns out to be really small, they’re all true. That’s why mine were so weird, the independence clause.*
*(they still aren’t actually independent, but I’m >99.99% sure you couldn’t make a set of statements that were)
However, it’s possible to make a set of statements that are mutually exclusive, which might actually be a superior task “I am not the 11,043rd sentient entity ever to exist. I am not the 21,043rd sentient entity ever to exist, etc.”