John, (it says anonymous, but I assume you've been hit by the time out on login).
This is an interesting discussion which offers some insight into both information/reality and deterministic/non-deterministic. I will concede (and I hope you do as well) that both arguments can be used to fit the empirical evidence. However, the choice between the two is not simply a matter of taste. The choice speaks to the entire nature of physical law.
You argue (I hope I paraphrase correctly):
1) That we are able to determine the actual state of physical things in the present. A sequence of events up to the present may be determined by plotting a trajectory of such states through a state space.
2) Some events or outcomes are fundamentally indeterminate. That is, there are some fundamentally stochastic (= somehow inherently "random" or somehow "uncaused") events. Thus, we are unable to predict future outcomes.
I argue:
1) That all events are entirely predetermined (or fated if you will). This is an assumption about the nature of all physical law - a character of the ontological domain.
2) That we (and "we" emphatically includes God) may never know a physical state. We may only know the result of experiments. Since we cannot know even a single physical state, we cannot know a trajectory in state space, even in the past. Since we can never know a current state or past trajectory, we can never predict with certainty the outcomes of future experiments, even in the context of deterministic evolution. This is a statement about what we can know and what we can predict - a character of the epistemic domain.
Your argument can not be rejected out of hand. Indeed, it is essentially the one which is at the heart of orthodox QM, and which has now had about a century of primacy. However, I think it leads to many of the paradoxes and interpretational difficulties of QM, which have not been resolved in that century.
I propose to resolve many of those issues by assigning probability, wavefunctions, and any other predictive tool, to the epistemic domain, the domain of information, where they rightfully belong, and "purifying" the ontological domain, the domain of reality, so that it is entirely governed by deterministic physical law. I do not think that determinism implies fore-knowledge at all. Knowledge is the epistemic domain, not the ontological. Predetermined and predictable do not mean the same thing. An event may be predetermined (a characterization of events in the ontological domain) but yet be unpredictable (a characterization of events in the epistemic domain).
I could be be wrong, and as I said, both approaches can fit the evidence. I just think that after a 100 years of relative futility in resolving quantum paradoxes, we might try a different approach.
Nice discussion. Thanks for engaging.
Regards, Mark