But thats also all determinism requires, that it is determined, not that we could determine it.
Well at that point you are getting into semantics. Often, the term "deterministic system" is used to describe a system that changes in ways we are capable (in theory) of predicting if we know the initial conditions. But quantam mechanics limits us to probabilitic predictions, not because of an incomplete knowledge of physics, but because of the observation effect. However, that doesn't mean (as you point out) that in another sense the movement of particles, like everything else, isn't completely governed and determined by physical laws.
Id argue that the self-ordering is a result of the laws of physics rather than something independent of them. I dont really see any reason why large groups of neurons would act independently to the laws of physics purely because of the number involved.
It isn't that such systems are acting completely independently of the laws of physics. Rather, they are constrained instead of determined by these laws. Nor is it a simple manner of complexity. There are deterministic systems which are stochastic and impossible (at least currently) to model very accurately. I'm talking about a system of a qualitatively different type.
Take, for example, the classic example of a swinging pendulum. It's movement is governed by a 2-dimensional nonlinear equation- the second derivative of theta with respect to time added to the acceleration due to gravity over the length of the pendulum multiplied by the sin theta = 0. This is a relatively simple nonlinear equation, but over even a fairly short period of time perturbations make modeling the movement of the pendulum extremely difficult. However, it's movement is still deterministic, it is just our inability to solve the equation adequately enough to do more than approximate its movement under many conditions.
Essentially, (and please correct me if I am wrong) you are arguing that all complex systems are like this. We may not be able to mathematically represent the functions involved or solve the necessary differential equations, but this is simply due to our limits, not because the system isn't completely determined.
However, pendulums, waterwheels, population models of bacteria, etc., while chaotic, behave in complex ways because they are highly sensitive to a number of parameters.
What I'm suggesting (and I'm certainly not taking credit for this type of analysis; there is a lot of literature on the topic), is that the "mind" is more than just an extremely sensitive complex system. It is
not completely governed a vast number of parameters. Unlike the pendulum, the internal and external forces acting on the "mind" (the external environment, chemical/electral signals sent to the brain, other signals sent from parts of the brain which are not usually considered as part of the "mind") do not determine how the packets of information will cause the "mind" to form new patterns and states. This isn't saying that the individual neurons underlying conscious choice/thought disobey physics. Rather, the behavior of individual neurons aren't governed solely by these laws because they are components of a system which organizes itself in a non-reductionist manner. A multi-level heirarchical network capable of recursive processes and downward causation. Of course, the very complexity of such a system makes even qualitative description, let alone quantitative description, extremely difficult. Nor do philosophers, mathematicians, physicists, and others who believe that systems like this exist agree on what their nature may be.
But to simplify things a bit, let's go back to the individual neurons, subject to the laws of physics. If the "mind" is a determinisitc (albeit unpredictable) system, then each neuron is completely governed in some way by the laws of physics. However, if neural networks are only constrained by the laws of physics because they are capable of reorganization according to "laws" the network itself defines, then physics only constrains the system, it doesn't determine it.
Hence why simulators are important in that particular field, I recall reading a couple years ago about an IBM supercomputer they were using to simulate part of a cats brain.
I'll address the above in the moment but I wanted to use your computer example to illustrate (hopefully) what I wrote above in a clearer fashion. A typical computer, from an old, cheap laptop to a massive supercomputer, possesses hardware analogous to the brain. However, (ignoring things like equipment failure) the computer is completely determined by a series of explicit algorithms. What I am suggesting is that the brains "hardware" allows it to rewrite, develop, analyze, and alter its "software." The neurons have to obey physical laws, but beause of the way in which they are organized and the manner in which they exchange information, the patterns which emerge are largely the result of "laws" created by the system. Knowing the state of every neuron isn't enough to predict future states of the "mind" because as a whole the behavior of neurons cannot be reduced to the individual parts. Self-organization/government is subject to the laws of physics, but not determined by them.
Going back to your supercomputer example, it's true that A.I. has come a long way, and it is also true that cognitive models are heavily influenced by computer science. In fact, many cognitive scientists are mainly computer scientists who work on A.I. research. Interestingly enough, the classical approach to cognitive science and A.I. (which we can probably say began with Turing), in which congnitive scientists thought of the brain in terms of algorithms has become increasingly obsolete and replaced by simlulations of neural networks. Also interesting is that while even the most complex of these systems doesn't come remotely near the complexity of even a cat's brain, they do reach levels of complexity such that while the system will return the answer it is designed to (say, facial recognition), it is impossible for the programmers to know how the network reached that decision.