Could you sketch the argument?

There is no hope for LessWrong as long as people keep conflating Perfect Bayesian and Subjective Bayesian.

Let's take Subjective Bayesian first. The problem is - Subjective Bayesian breaks basic laws of probability as a routine matter.

Take the simplest possible law of probability P(X) >= P(X and Y).

Now let's X be any mathematical theorem which you're not sure about. 1 > P(X) > 0.

Let Y be some kind of "the following proof of X is correct".

Verifying proofs is usually very simple, so very once you're asked about P(X and Y), you can confidently reply P(X and Y) = 1. Y is not a new information about the world. It is usually conjunction of trivial statements which you already assigned probability 1.

That is - there's infinite number of statements for which Subjective Bayesian will reply P(X) < P(X and Y).

For Subjective Bayesian X doesn't even have to involve any infinities, just ask a simple question about cryptography which is pretty much guaranteed to be unsolvable before heat death of the universe, and you're done.

At this point people far too often try to switch Perfect Bayesian for Subjective Bayesian.

And this is true, Perfect Bayesian wouldn't make this particular mistake, and all probabilities of mathematical theorems he'd give would be 0 or 1, no exceptions. The problem is - Perfect Bayesians are not possible due to uncomputability.

If your version of Perfect Bayesian is computable, straightforward application of Rice Theorem shows he won't be able to answer every question consistently.

If you claim some super-computable oracle version Perfect Bayesian - well, first that's already metaphysics not mathematics, but in the end, this way of working around uncomputability does not work.

At any mention of uncomputability people far too often try to switch Subjective Bayesian for Perfect Bayesian (see Eliezer's comment).