Oh goodie. Another free will discussion.
Ultimately, the realization of whether free will exists or not does not come from arguments that we are machines or God's omnipotence. It comes from the realization that the very concept of free will is incoherent. Free will does not exist for the same reason that four-sided triangles don't - the definition is a contradiction of terms.
Let me demonstrate. There are two types of systems that we know can theoretically exist - random systems and deterministic systems. There may be more - I'll get to that later.
In a completely random system, effects do not depend on any prior cause. This makes things that happen in a random system "free" in the sense that it's impossible to tell what will happen in the future, but all basis for order and rationality are obviously missing in such a system. Obviously, neither our universe or our minds are completely random for this very reason.
In a completely deterministic system, all effects depend fully on prior causes. This means that, given perfect knowledge of the system, one can perfectly predict the behaviour of that system. Given partial knowledge of the system, one can approximate the future behaviour of that system. The approximation will improve with the available information. This fits rather well with both our universe and our selves, although scientists tell us that there are some things that seem to not be deterministic. In any event, we can approximate the behaviour of those around us, and we get better at it the better we know the people around us. Obviously, a deterministic system can be rational, but it is certainly not free.
There is a third option. A system that is partially deterministic and partially random. Computer based decision making systems are typically constructed according to this model (although the randomness is not true randomness, but that has no relevance here). Such a system can be very similar to a deterministic system, but even with perfect knowledge of the system it is not possible to fully predict its behaviour. However, when the system does not behave according to a "perfect" prediction, it does not do so out of rationality but out of chance. The behaviour in that instance will be chaotic. Therefore, these occasions are signs of free actions that do not fit the description of will, because they cancel out the effects of premeditation. This system therefore does not fit the idea of free will.
So my question to free will proponents is this: if none of the 3 types of systems above fit free will, then just what the heck IS free will? I've asked that question many times, and NOONE has been able to give me an answer.
So how can you argue for something that isn't even possible to define? How do you propose that free will can exist when the very concept of free will is so nebulous that noone knows what it is? I've heard people declare that it is none of the three options above (which is why I brought them up). But a definition must include a positive description - saying what free will isn't is not enough. We must know what it IS if you are to assert its existence.
Technically, one could come up with a reasonable definition of free will under the wholly deterministic label.
Let U be the universe and {E, O} be a partition of U, respectively the entity which we want to determine if it has free will or not and the outside world. For instance, I could partition the universe into my brain and everything else.
Now let's look at the following two probability distributions: P(O(t+1)|O(t)) and P(O(t+1)|O(t), E(t)). The former represents what the outside world will be like in a moment, given knowledge of what it is now. The latter represents what the outside world will be in a moment, given knowledge of what it is now, PLUS knowledge about the entity E.
From there, we could simply define free will to be a measure of the difference between those two distributions (could be something like Kullback–Leibler divergence). Indeed, the greater the difference, the more the outside world depends on E. Basically, instead of splitting the universe into a deterministic system and a random system as you did earlier, I split it into an entity (the one we want to know if it has free will or not) and the rest and then I look at the amount of correlation between the two.
Of course, there are drawbacks to this definition. For example, somebody could make a program, erase all source files, commit suicide and then, technically, the free will of the program would be great. Worse yet, a nuclear bomb would have low a priori probability but great impact, hence great free will. Unfortunately I don't think a formal definition of free will can avoid those cases. Well, I guess we could throw in a measure of complexity of E or some sort of normalization, but that's probably putting too much effort into it.
Regardless, the trap pretty much everybody falls in when discussing free will is that they never even bother to think about the entity they're talking about. When I say X has free will, what is X? From what I can see of debates, X is inexplicably taken in such a way that it cannot be anything but the empty set. I know this sounds weird, but when people talk about the free will of X, they are all really talking about the free will of nothing at all, because they never bother to define X and their discourse is inconsistent with X being nonempty.
What happens with you fill X? Obviously, X will contain a certain amount of information. Furthermore, evidently, X cannot "choose" what information it will contain, because if X was anything else, it would not actually be X, it would be something else. It's nonsensical for an entity to choose their own nature. Therefore, knowledge of X should not bear any consequence on its free will, and in fact it is required in order to identify X in the first place. From there, we could directly conclude that free will is nonsense because it's not even logically possible for an entity to have options: there's a bijection between actions and people, you do Y because you are X and you are X because you do Y. On the other hand, we could say that free will should be a measure of how the behavior of X as a physical entity is correlated to its information content. For example, a rock would have lower free will than a human because its behavior is much less dependant on its contents than the behavior of a human is on his or her brain. (Un?)surprisingly, it doesn't actually have anything to do with determinism or randomness.
Now, as I said, the gates are wide open for many things to have free will that "we might not want to", but you know, there is no denying that the concept of free will is much more emotional than it is rational.
So the point I'm raising is that sure you can say that determinism implies that we can trace back our actions to physical causes, but if those causes are actually part of how we are defined in the first place, well... I hope you can see the loophole there.
Another way to view things is to consider that a person is defined by her behavior and that any different behavior would actually correspond to another person. In that situation, people do choose their behavior, because if they did not, that would imply that several behaviors could be attributed to the same person, which is contradictory with the previous hypothesis. Counterintuitive, I know, but we humans are typically pretty bad at inferring in the correct direction
Consider the computer program to be system A. Our universe as a whole is system B. Obviously, system A is part of system B. An agent in system B can look at the random number generator and conclude that it is deterministic. Since A is part of B, this is still true in A from a technical POV.
But philosophically, we can consider system A to be separate from system B. And in such a case, there is no way to determine what the next number in the pseudorandom sequence will be (assuming we've put the RNG in a separate process). Therefore, from a philosophical POV, we can point at the system and say that it is partly deterministic, partly random.
Technically and philosophically, each invokation of the RNG leaks a certain quantity of information from A to B (a bit, for example). Assuming the RNG has a finite description, this means that as time tends to infinity, enough information would leak into B for A to be deterministic from B's perspective.