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!
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!