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It's not mathematically correct: both all statements of ZFC and the provable have the same cardinality: there's no sense to "half of statements" in ZFC.
by chalst 15y ago
It's not mathematically correct: both all statements of ZFC and the provable have the same cardinality: there's no sense to "half of statements" in ZFC.
- omaranto 15y agoAgain it's a joke, so let's not take it too seriously but I think the sense in which it is half is not cardinality (that would be silly, as you point out), but density. Look at the probability that a random statement of length at most n is true. Since for every statement it's negation has practically the same length and the opposite truth value, the probability should tend to 1/2 as n goes to infinity.