Just outstanding, Doc -- and so helpful to a non-specialist!
This fourth type of "random" system seems to go straight to the idea of contingency, which is more a philosophical idea than a strictly scientific one. The germ cell here on earth is affected by a discrete event on Sirius -- which probably no observer of the germ cell here on earth could be aware of. And yet the mutation we observe is contingent on the action of that unseen event. From the standpoint of the observer of the germ cell, the mutation may appear to be a "random" happenstance. Yet for a hypothetical observer whose view includes the cosmos in toto, there would be nothing at all "random" about the mutation: That observer would see that it had a cause on Sirius. And because it was "caused," from the point of view of the local observer it becomes fair game for scientific observation, and the natural laws are then found to apply from that point on. But the fact that the cause of the mutation was "hidden from view" means that an important predictive factor remains undisclosed to the scientific method. At least for a while. :^) If I might express it that way.
As you say, nothing in the physics or chemistry of DNA caused the volcano to erupt, or the germ cell to be bombarded by cosmic rays. But we can certainly perceive the effects.... Whereupon we may start speculating on the nature of the cause, and never even come close to actually, correctly identifying it. Which is to say, We usually don't know what we don't know. But we have to carry on any way.
Thanks so much for your excellent post.
PH, I meant to ping you to #318 but somehow neglected to do it....