NoDeity: Tenderfoot: All my discussions of randomness have been to support the plausibility of the "non-deterministic" portion of this definition. I think all the other portions are generally accepted.
I think it would be helpful if you could show how wave-particle duality makes self-causal freewill plausible.
The fundamentally unpredictable nature of individual atoms makes it plausible that non-deterministic (i.e. random) events occur in the brain. In fact, it makes it certain, since the brain is constructed of atoms.
Computers are also constructed of atoms, of course, so random events occur within them as well, but the computer's circuits do not pay attention to individual events, only to large numbers of such events. The behaviours of large numbers of objects (e.g. electrons) are statistically predictable. Therefore the random behaviour of each individual electron within a computer chip does not matter.
As computer chips are miniaturized, these random behaviours will become more and more important, eventually reaching a point where they cannot be ignored. At that point, future miniaturization will become impossible. A Cal Tech article on this topic says:
...in the next few decades, our ability to miniaturize circuits in silicon will hit bottom. “Information technologies for the most part treat electrons and photons like they were basketballs,” says Preskill. “You bat electrons around in a circuit, or send photons down a fiber and count them.” But we’re approaching the size where classical physics falters and quantum effects take over."
Brain components (e.g. the cellular components within each neuron) are much smaller than the components within a computer chip. It therefore seems plausible that random quantum effects manifest themselves, at least occasionally, in ways that affect events within the brain.
Extremely tiny events in a complex system can have profound effects on the outcome. The popular illustration of this phenomenon involves a butterfly flapping its wings in China, thereby causing a hurricane to hit Florida. Solid mathematics stand behind this.
If a random, quantum event occurs within a single neuron, causing it to fire a fraction of a millisecond sooner or later than it otherwise would, this can plausibly have a profound effect on brain function. Millions of neurons are always firing simultaneously in chain reactions. It is probably very important whether the impulses from one group of neurons reach a particular brain area slightly sooner or slightly later than impulses from a different group. Random quantum events that affect this timing could therefore be profoundly important.
When a brain needs to come up with a solution to a problem, it searches its storehouse of memories for patterns and recollections that might be relevant and useful. It tries to piece together disparate items of information in order to invent new solutions to its current problem. The choice of the memories it selects during this process would obviously be crucial. The process of accessing memories involves firing neurons in sequence. If the sequential order is disturbed by random quantum events, different memories will be accessed. This means the brain has access to randomly-generated sets of information from which different potential answers can be extrapolated. It allows the brain to engage in stochastic simulations (which require true randomness in order to be useful).
The random, entirely unpredictable quantum events I have described occur entirely within the brain. Nothing outside the brain causes the events to be random, or can prevent them from being random. Therefore, they can only be described as self-causal.
Putting these pieces together, we have a fairly plausible (albeit speculative) description of self-causal, non-deterministic brain activities. This is only one portion of my definition of free will, but it's a crucial one.