Kingreaper comments on Infinite Certainty - Less Wrong
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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."