So, can we or can’t we write a mathematically meaningful version of the statement, “This statement has less than .5 probability within the system”?
That would lead to a self-containing set, which is infinite. Infinite sets are allowed only if they’re approached by a convergent limiting expression, which is not given here, so Bayesian statistics of the E.T. Jaynes variety would not assign that statement a probability at all.
That would lead to a self-containing set, which is infinite. Infinite sets are allowed only if they’re approached by a convergent limiting expression, which is not given here, so Bayesian statistics of the E.T. Jaynes variety would not assign that statement a probability at all.
Gödel’s sentence doesn’t use a self-containing set. This is supposed to work the same.