The continuum hypothesis being independent just means that it's an additional rule you can add or remove from the game you are trying to play. It doesn't mean we are lacking in knowledge and that if we were to work harder we would solve this problem. We do know which aleph c is: it's aleph_1 with CH and some other aleph without CH. Just take your pick which version you like better.
It's not like we don't know which one is the true model of military combat: chess or checkers. They're just two different games with two different rule sets, and you get to pick which one you like to play more.
It's not like we don't know which one is the true model of military combat: chess or checkers. They're just two different games with two different rule sets, and you get to pick which one you like to play more.