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That was one of the objections listed in the post, Scott's response was that you should only be neutral about elementary propositions, not about compound ones ("bloxors are greeblic AND bloxors are grue").
I personally think that this entire kind of objections can be dismissed by pointing out that Bayesian math works correctly and without contradictions, and when looking at actual priors there's not much disagreement about how to choose them either, in practice. Nobody actually has arguments against assigning a symmetric prior to a coin bias, or even can muster a lot of enthusiasm to argue that you should use a gaussian instead of a uniform prior.
People get hot and bothered when they feel that someone tries to hide how much information they have actually updated on and how much is their prior.
How do I know that "bloxor-1 is greeblic" is elementary, if I am totally uncertain about this proposition, and I don't even understand the terms? Additionally, it's arbitrary to say that one should be neutral about the elementary propositions.
What do you mean "correctly"?
Depends. If you interpret the probabilities as subjective degrees of belief and interpret degrees of belief in terms of idealised betting dispositions, then it's not obvious that people can introspect their own odds. Experimental work from about the Allais paradox onwards doesn't suggest that Bayesianism is a good fit with how humans actually reason under uncertainty, and without some evidence of reliability of personal introspection of priors, "My prior is X" is potentially just hot air.
How many of the arguments in probability theory have you read to come to this judgement? Because I can think of large parts of the literature dedicated to exactly this point.
Skill issue.
That I, doing Bayesian math about some bets against you, will leave you poor and destitute in the long run, unless you're using Bayes too. What do you want to use instead of Bayes for the record?
My point is not that the poors are always instinctively right. My point is that they have well-honed instincts for when someone is trying to take advantage of them, and the usual Bayesian reasoning like the above rightfully triggers it, even if they don't have the concepts or the introspection to communicate to us what was that, that triggered them.
My point is that a Bayesian megamind is entirely justified in asking the yudkowsky what fraction of his prediction came from the data, and basing his bet amount on that, and grumbling about the yudkowsky being useless if he refuses to answer.
Huh?
It's possible to set up some types of games where this is true, as well as some types of games when using Bayesian math can lead to disasters. See this paper for a pretty simple example of how setting up the game in a way that Bayesianism looks good is more complex than you seem to think: https://www.jstor.org/stable/40210799
If you're thinking of conditionalization as part of "Bayesian math" and alluding to diachronic Dutch Book Arguments, the problems here are particularly vexing. See here: https://link.springer.com/article/10.1007/s10670-020-00228-1
Richard Pettigrew, who has a background in both mathematics and philosophy, has done a lot of great work on these issues. Here's a brief and relatively simple introduction: http://m-phi.blogspot.com/2018/10/dutch-books-and-conditionalization.html
Basically, the literature thus far has been a long series of failed attempts to squeeze Bayesian epistemological juice out of pragmatic rocks.
The task is underspecified and hence so is your question. Can you explain more?
I agree.
One strand: Bayesians tend to be subjectivists, so symmetric priors are only a personal decision. Another strand: imprecise probabilists (like set-based Bayesians) tend to deny that any additive prior is mandatory (and perhaps not even permissible). Another strand: frequentists are critical of the whole Bayesian enterprise; note that criticisms of frequentists' positive claims are beside the point here.
Of course, all those criticisms of symmetric priors (as mandatory) might be wrong, but it's not true that symmetric priors are controversial, even among people with apparent expertise in the relevant mathematics and logic.
You might say, "Well, obviously if I asked you what the probability of heads is with this perfectly ordinary coin, you'd say 50%." However, we are both far from lacking any evidence with respect to that coin, and "The probability is 50%" can be interpreted in all sorts of different ways, e.g. a frequentist would want to interpret it in terms of hypothetical frequencies in a mathematical model of the coin tossing; some Bayesians would interpret it in terms of degrees of evidential support; other Bayesians would interpret it in terms of degrees of belief; some Bayesians would interpret it in terms of the degrees of belief that a rational person should have given the evidence...
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