But they are, in any physical example obedient to physical law.
Being obedient to physical law does not necessarily make it deterministic. If the physical law is one of inherent indeterminism then they are obedient to that inherent indeterminism. And probability is inherently indeterministic.
You appear to be overlooking - still - the essential role of nonlinear feedback in generating our universe.
We assumed a deterministic universe, not ours. Deal with the one we assumed, please.
When one crosses a logical level - such as by establishing a nonlinear feedback loop - one must take that into account in analysis.
Only if you can show that, in a deterministic universe, it offers an actual ability to do otherwise. And none of your examples thus far have shown that.
Your attempted approach here- excluding any sufficiently complex feedback system from the category "deterministic" - is drastic and counterintuitive (it excludes coin flips as "indeterministic", for example), and eliminates any possibility of a deterministic universe.
I am excluding anything that is simply you pointing at something at going “ooh, look, complexity!” If you think a sufficiently complex feedback system within a deterministic universe offers the ability to do otherwise, feel free to actually provide something more than examples that don’t show it, and subsequent appeals to complexity.
I am also not excluding such things from being deterministic. I am simply waiting for you to put, what, an actual argument together?
The example of the coin toss was analogous, not an example, where one starts with the assumption that the result is probabilistic. But you choose to ignore that.
Nor do I eliminate any possibility of a deterministic universe. For Pete’s sake we have assumed that the universe we are discussing is deterministic. Don’t hold me at fault for your woeful misunderstanding of what that entails.
Are we discarding determinism, 48 pages into the fourth or fifth thread of its assumption? That is unnecessary, at best. Nonsupernatural freedom requires no such limiting of analysis.
Of course we’re not discarding it! It is the fundamental premise of this, and the previous, discussions. Your meandering into probabilistic notions, however, can be discarded for being irrelevant to the deterministic universe.
As the coin flip example illustrates, distribution of outcomes according to a probability function has nothing to do with whether or not each individual outcome was produced in alignment with physical law and conditions ( i.e. determined) - let alone the collective shape of them, which is what one describes via mathematical functions and uses for prediction.
Being produced according to physical law does not per se make something deterministic. You need to understand this so that you stop making the same mistake. Peeing produced according to physical law would make the philosophy physicalist, or materialist, but not necessarily deterministic. Probabilistic systems are not deterministic.
In our case - the assumed deterministic universe - the conditions are completely determining the outcome just as they would be in producing any other physical pattern - the probability functions describe the shape or form of the outcomes, playing the same role as other functions used in physical analysis play (such as a function that describes the physical production of a straight line, or a hexagon, or a parabolic curve,
The probability function only gets you as far as the probability of the outcome, but not the actual specific outcome. That is where it stops being deterministic. If the specific outcome that you actually end up with can not be completely determined by the causes then it is not deterministic. With probabilistic systems you can get to the probability function but since two examples of the same cause can lead to two different outcomes, this is simply contradictory to determinism.
or Richard's logistic (which can produce chaos within a deterministic system, another example of the deterministic but individually unpredictable in theory or practice) -
Chaos is not equatable to theoretical unpredictability but to practical unpredictability based on inaccuracy of knowledge of starting conditions. It is about how small changes in initial conditions can have significant impacts on the future state. It is how the practical unpredictability (due to inaccuracy of knowledge of starting conditions) of chaotic systems increases (exponentially) the further foreword you try to predict. But theoretically, in a deterministic system if one knew the starting conditions and knew the process then one would be able to predict the future perfectly.
As soon as you add probability into the mix you change the system from a deterministic one to indeterministic, though, and it becomes irrelevant to the discussion where a deterministic universe has been assumed.
or Mandelbrot's Set - which likewise describes individual event unpredictability, even with perfect knowledge: completely deterministic outcomes that are individually unpredictable in theory or practice.
Nonsense. Every single point on the Mandelbrot set can theoretically be calculated, and is thus theoretically predictable. For any given starting point you can calculate the output. The unpredictability comes when you only have an approximation of the starting conditions, in which case the predictability of the output for chaotic systems worsens exponentially the further forward you try to predict.
You may want to brush up on the these basics, along with your understanding of what a deterministic system is.