What is the meaning of a higher-order probability, like a 20% chance of a 30% chance of x happening—especially if x is something like the extinction of humanity, where a frequentist interpretation doesn’t make sense? I asked a question related to this https://www.lesswrong.com/posts/MApwwvQDTNdhx43cJ/how-to-quantify-uncertainty-about-a-probability-estimate
Now that is a big philosophical question.
One answer is that there is no difference between ‘orders’ of random variables in Bayesian statistics. You’ve either observed something or you haven’t. If you haven’t, then you figure out what distribution the variable has.
The relationship between that distribution and the real world is a matter of your assiduousness to scientific method in constructing the model.
Lack of a reported distribution on a probability, e.g. p=0.42, isn’t the same as a lack of one. It could be taken as the assertion that the distribution on the probability is a delta function at 0.42. Which is to say the reporter is claiming to be perfectly certain what the probability is.
There is no end to how meta we could go, but the utility of going one order up here is to see that it can actually flip our preferences.