> But the “riddle” requires P to be exactly true or false. Your choice of P (whether the continuum hypothesis holds) is still ill-defined! This is because the

> But the “riddle” requires P to be exactly true or false. Your choice of P (whether the continuum hypothesis holds) is still ill-defined! This is because the answer depends on the system of axioms one subscribes to. Or, if you feel like playing God, you may pick an answer (CH holds / does not hold) and find axioms that support it. (Which can be as simple as ZF + CH holds/does not hold.)