[Question] Is LessWrong dead without Cox’s theorem?

Cox’s theorem seems to be pretty important to you guys but it’s looking kind of weak right now with Halpern’s counter-example so I was wondering: what implications does Cox’s theorem not being true have for LessWrong? There seem to be very few discussions in LessWrong about alternative formulations for fixing probability theory as extended logic in light of Halpern’s paper. I find this quite surprising given how much you all talk about Jaynes-Cox probability theory. I asked a question about it myself, but to no avail: https://​​www.lesswrong.com/​​posts/​​x7NyhgenYe4zAQ4Kc/​​has-van-horn-fixed-cox-s-theorem