Congratulations Eliezer, this subject is very interesting.

Nontheless useful, i.e. Monter Carlo methods with pseudo-random numbers ARE actually deterministic, but we discard the details (very complex and not useful for the application) and only care about some statistical properties. This is a state of subjective partial information, the business of bayesian probability, only this partial information is deliberate! (or better, a pragmatic compromise due to limitations in computational power. Otherwise we'd just use classical numerical integration happily in tens of dimensions.)

This bayesian perspective on ""random"" algorithms is not something usually found. I think frequentist interpretations is still permeating (and dragging) most research. Indeed, more Jaynes is needed.