Ok, I'm following you thus far...
...and now you've lost me. Are you a computer programmer? Could you explain how, in a computer, randomness can be both not truly random and not deterministic?
Yes, I'm a programmer, and sure, I can explain. I'll use two examples - the first is very different from how humans work but easy to understand while the other is similar to how humans work but slightly trickier.
Imagine a computer that's programmed to play 5 in a row - the game similar to tic-tac-toe but where you have a much larger board and you need five markers in a row to win.
The most rudimentary way to implement such a program is to let the computer check the board for existing rows - 2 in a row, 3 in a row and 4 in a row. At the end of each such row, it will check if there is an empty space. If so, it will set an "importance factor" on that square 2 for 2 in a row, 3 for 3 in a row etc. Then it will look for more rows until all are found.
Then it's time for the computer to place a marker. It will have a number of empty spaces to choose from and each space will have an importance factor. It will always choose the square with the highest importance factor. However, it is very likely that several squares have the same importance factor and that this factor is the highest on the board. How to choose? Well, the easiest way is to choose one of the most important squares at random. Voila - determism and randomness in one process. Obviously, one can balance this differently - the computer might choose between the squares that are most important and those that are almost as important. Then you get more randomness and less determinism.
Another, more sophisticated mechanism is the neural network. I'll describe the simplest artificial neural network we can construct - the perceptron. This is a truly simple single-layered "network" that can't actually achieve much, but the power of neural networks is that you can add as many layers as you want and as you do so, the processing power of the net increases.
The perceptron is a simple beast. It is a data structure with x number of binary inputs and one binary output. Each input has an associated weight, w(x) between 0 and 1 and the perceptron has an internal threshold value T between 0 and 1. Both the weights and the threshold are floating or fixed point numbers. They are also variable.
When input is recieved, it is put through a formula that calculates the sum of all inputs multiplied by their weight - that is, the sum of x*w(x) for every x. If this number is greater than T, the perceptron output is set to 1. Otherwise, output is set to 0.
Now comes the nifty part: since both w(x) and T are variable, one can train this perceptron. If you start by giving all w(x) and T random values, you'll get something that's probably useless. But you may want a perceptron that works as an AND function for 2 inputs. If so, you give it two inputs - x1 and x2 - and run it parallel to a normal AND function. If the perceptron does not give the same output as the AND function, you change w(x1), w(x2) or T - or all of them - or some of them. The change is done automatically according to a simple mathematical formula, usually a semi-random function that represents a sigmoid curve.
Eventually (usually rather quickly since the system is so simple) the perceptron will get closer and closer to a true AND function and eventually mimic one perfectly. The perceptron has then been trained. A typical AND-perceptron will have w(x1) = w(x2) = 0.5 and T = 0.75. If you had trained it for OR instead, it might look like w(x1) = w(x2) = 1, T = 0.5.
I hope this explanation was easy to understand, even if it was a bit long winded.
This currently seems to be the only usable mechanism to describe how the universe works. However, I'm not entirely convinced that free will couldn't be described by such a mechanism. One word in particular seems to stick out: rationality. What is rationality?
Rationality is simply the ability to make appropriate choices. That is, to take a number of circumstances into account and perform an action that according to those circumstances are beneficial to oneself (what is beneficial is, of course, subjective).
I have heard a few claim that free will is indeed a mix between determinism and randomness. I can live with such a definition and I accept that it is possible - even probable - that it accurately describes our selves and our universe. However, it means that the concept of free will is reduced to simple, natural type of system that is really quite unremarkable. I'm fine with that too, but most people seem not to be, particularily those who maintain that free will is somehow supernatural.
