 Subjectivists aren’t thereby entirely helpless in the face of the problem of induction, though. According to them, any initial assignment of probabilities is reasonable, including Carnap’s. So if you do happen to start out with a Carnap-esque assignment, you will be an inductive optimist, and reasonably so. It’s just that you don’t have to start out that way. You could instead start out treating each possible sequence of \(\mathsf{H}\)s and \(\mathsf{T}\)s as equally probable, in which case you’ll end up an inductive skeptic. That’s reasonable too. According to subjectivism, induction is perfectly rational, it just isn’t the only rational way to reason.