The ‘rationalist’ group being discussed here aren't Cartesian rationalists, who dismissed empiricism; rather, they're Bayesian empiricists. Bayesian probability turns out to be precisely the unique extension of Boolean logic to continuous real probability that Aristotle (nominally an empiricist!) was lacking. (I think they call themselves “rationalists” because of the ideal of a “rational Bayesian agent” in economics.)
However, they have a slogan, “One does not simply reason over the joint conditional probability distribution of the universe.” Which is to say, AIXI is uncomputable, and even AIXI can only reason over computable probability distributions!
Bayesian inference is very, very often used in the types of philosophical/speculative discussions that Rationalists like instead of actual empirical study. It's a very convinient framework for speculating wildly while still maintaining a level of in-principle rationality, since, of course, you [claim that] you will update your priors if someone happens to actually study the phenomenon in question.
The reality is that reasoning breaks down almost immediately if probabilities are not almost perfectly known (to the level that we know them in, say, quantum mechanics, or poker). So applying Bayesian reasoning to something like the number of intelligent species in the galaxy ("Drake's equation"), or the relative intelligence of AI ("the Singularity") or any such subject allows you to draw any conclusion you actually wanted to draw all along, and then find premises you like to reach there.
They can call themselves empiricists all they like, it only takes a few exposures to their number to come away with a firm conviction (or, let's say, updated prior?) that they are not.
First-principles reasoning and the selection of convenient priors are consistently preferenced over the slow, grinding work of iterative empiricism and the humility to commit to observation before making overly broad theoretical claims.
The former let you seem right about something right now. The latter more often than not lead you to discover you are wrong (in interesting ways) much later on.
Who are all the rationalists you guys are reading?
I read the NYT and rat blogs all the time. And the NYT is not the one that's far more likely to deeply engage with the research and studies on the topic.
However, they have a slogan, “One does not simply reason over the joint conditional probability distribution of the universe.” Which is to say, AIXI is uncomputable, and even AIXI can only reason over computable probability distributions!