One possible connection between "postmodern" (i.e. recent Continental) philosophy and Bayesian rationality may be found in the notion of "embodied philosophy" or "embodied cognition" — e.g. the work of George Lakoff in linguistics and Hans Moravec in robotics.

This is on my mind recently because I've been reading Lakoff's Women, Fire, and Dangerous Things.

Take meaning, for instance — the assignment of referents to symbols. The classical view of meaning is that there are objectively true meanings that are discovered, out there in the world. The embodied view of meaning is that meaning is necessarily subjective; there are no "God's-eye view" meanings: meaning only takes place in minds in bodies, which arrive at meanings not by objectively observing an exterior world, but by participating in the world.

(This connects to the Bayesian view of causality, at least so far as I understand it: reasoning about causation involves reasoning about interventions and not merely about observations. Observed correlation can only tell us about statistical, rather than causal, regularities; in order to discover authentic causes, we have to consider intervention.)

That meaning is subjective does not mean that it is arbitrary, or that you get to come up with whatever meanings you like and give them equal validity to meanings assigned through processes such as language acquisition, science, or social construction. Like Bayesian probability, meaning is subjectively objective: it takes place only inside (world-involved) minds, but you can still do it wrong by not paying attention to the world.