The limit of [the effect your original prior has on your ultimate posterior] as [the number of updates you’ve done] approaches infinity is zero. In the grand scheme of things, it doesn’t matter what prior your start with. As a convenience, if we have literally no information or evidence, we usually use the uniform prior (equally likely as not, in this case), and then our first update is probably to run it through occam’s razor.
This doesn’t address my objection. You are responding as if I were skeptical of assigning some particular prior, whereas in fact I was objecting to assigning any prior, or indeed any posterior—because one cannot assign a probability to a string of gibberish! Probability (in the Bayesian framework, anyway—not that any other interpretations would save us here) attaches to beliefs, but I am saying that I can’t have a belief in a statement that is incoherent. (What probability do you assign to the statement that “fish the inverted flawlessly on”? That’s nonsense, isn’t it—word salad? Can the uniform prior help you here?)
This doesn’t address my objection. You are responding as if I were skeptical of assigning some particular prior, whereas in fact I was objecting to assigning any prior, or indeed any posterior—because one cannot assign a probability to a string of gibberish! Probability (in the Bayesian framework, anyway—not that any other interpretations would save us here) attaches to beliefs, but I am saying that I can’t have a belief in a statement that is incoherent. (What probability do you assign to the statement that “fish the inverted flawlessly on”? That’s nonsense, isn’t it—word salad? Can the uniform prior help you here?)
Fair enough. I don’t see them as gibberish, so treating them that way is hard. I admit I didn’t actually see what you meant.