>"I'd say that the way I conceived of it, I was making a distinction between events that were determined by antecedents (physical or otherwise) on the one hand and events whose outcome was uncaused, or random, on the other."
I don't pretend to understand randomness on any sophisticated level, but it is my understanding that a phenomena being random does not mean that it is uncaused.
It simply means that it cannot be known ex ante.
>"The idea of a system to which causality doesn't apply is interesting. My intuition is that that doesn't make sense, and my secondary intuition is that the first intuition is unjustified."
Materialism is the paradigmatic way of understanding the world today. It is the basic ontological assumption of the scientific revolution over the last several hundred years. So it is natural to think that anything which deviates from it is implausible, or even inconceivable. But given that, from within this paradigm, we lack even the most basic understanding of what the mind is, it is at least possible that it can only be understand from without it. Of course, it could also be that we simply lack sufficient understanding from within materialism. My point is that we simply aren't in a position to know.
I would also point out an area that we already know of where causality seems to break down: the physical constants. For materialists, this is simply were the explanatory buck stops.